Contributions to the study

PhD Thesis
CONTRIBUTIONS TO THE STUDY OF POOL BOILING AND
SPRAY EVAPORATION ON HORIZONTAL TUBES
Author
D. Ángel Álvarez Pardiñas
Thesis Director
Prof. Dr. José Fernández Seara
Área de Máquinas e Motores Térmicos
Vigo, 2016
This thesis applies for the degree of “Doutor con Mención Internacional”
Agradecementos
Semella que remata este proceso que foi tan longo e tan cheo de reveses, pero tamén de
moi bos momentos e moi boas persoas que axudaron dunhas ou outras maneiras. Tamén cheo
de aprendizaxe, porque algo debín de aprender neste proceso de converterme en Doutor. É
tamén cheo de cousas que agradecer.
Ao meu director de tese, José Fernández Seara. É certo que ás veces nos pos en
situacións extremas, de traballo contra reloxo e sen descanso, pero consegues que todos e
cada un dos que pasamos polas túas mans saibamos defendernos en calquera situación e que
aprendamos máis do que un doutorado esixe.
Aos meus compañeiros de laboratorio. Aos novos e aos vellos. Rubén, Fran, Diego, Javi,
Iago Novo e Iago Vello, Marta, Alex, Xandre, Alberto, Carolina... Pasamos moitas horas xuntos,
moitas situacións difíciles (incluso perigosas) e algún ata tivo que aturar un berro meu; pero
podo prometer e prometo que unha das razóns polas que quedaría sen dúbida nese laboratorio
é por seguir compartindo momentos convosco.
Ás “vellas glorias” de Industriais e agregados. Prometo seguir encargándome da xestión
deste grupo. Porque nunca nos falte unha xuntanza ao ano onde podamos seguir contándonos
as nosas boas novas e os nosos éxitos.
Aos que considero como os meus mellores amigos e espero que sexa recíproco. Charlos,
Varela, Coru, Lastres, Flisplis, Sandra, Maciu e Cane. Sempre estivestes aí e sei que vos terei
dunha forma ou outra na miña vida. Por moitos anos e moitas vivencias (e visitas a Noruega).
A Raquel, porque non sei que dicir que ti non saibas… Ti fuches un apoio sen o cal non
estaría aquí tan cedo. Fuches o final desta gran etapa e a persoa coa que vou compartir a
vindeira e toda unha vida. Gracias por non dubidar e por demostrar que se fai falla iremos
xuntos ao fin do mundo.
Á familia, que nunca falla. Mamá, papá e Carmela. Sempre apoiándome, sendo igual o
destino escollido. Gracias aos tres (e tamén á abuela) por ser os meus confidentes e axudarme
a tomar decisións difíciles. E gracias, pais, por darme a oportunidade de chegar a este punto
da miña formación, sobre todo persoal. Son o que son por vós e non teño queixa ningunha do
resultado. Non reclamarei nin pedirei a devolución ou o cambio.
Abstract
Refrigeration cannot stay aside from the environmental and energy challenges that
humanity is about to face in the coming years. Montreal’s Protocol and later revisions marked
the beginning of usage restrictions of CFCs and HCFCs, due to environmental issues such as
ozone layer depletion and global warming. R134a and other HFCs will be soon phased out due
to their global warming potential (GWP). Natural refrigerants such as CO2, ammonia or
hydrocarbons appear as interesting alternatives from environmental and performance points of
view. The high pressures of CO2 systems, the toxicity of ammonia or the flammability of
hydrocarbons are important disadvantages of these fluids. Natural refrigerants combined with
more efficient systems should be the investigation line followed in the future.
Falling film evaporators, also known as spray evaporators, have been widely employed in
petrochemical industry, desalination processes and OTEC (Ocean Thermal Energy Conversion)
systems. The experience in other fields such as heat pumps and refrigeration is limited, but
falling film evaporators appear as an interesting alternative to flooded evaporators due to
potential benefits in terms of refrigerant charge reduction and heat transfer improvement. In
addition, the boiling temperature increase caused by hydrostatic head in flooded evaporators is
avoided, the temperature approach between refrigerant and cooled fluid decreases and the
efficiency of the cycle improves and the evaporators can be of smaller size. The main drawback
of falling film evaporators is that the design of the distribution system is critical and, if incorrect,
may cause heat transfer deterioration due to dryout of the falling film.
Falling film evaporators in refrigeration systems are heat exchangers with a shell-and-tube
structure. Spray nozzles or other spreading devices distribute liquid refrigerant over the first
rows of tubes of a tube bundle. Part of the refrigerant boils on the top row, cooling the fluid
flowing inside the tubes, and the rest forms a film that flows to the following row. This boiling
and flowing process occurs from one row to the next one. The exceeding refrigerant is collected
at the bottom of the evaporator and recirculated to the distribution unit (with intermediate
conditioning steps if needed).
A large number of parameters affect the performance of falling film evaporators, but authors
disagree about the effect of each of them. Those with a higher influence are heat flux, film flow
rate, geometry of the tube, refrigerant properties and distribution system. The use of enhanced
tubes enhances heat transfer if compared to plain tubes. In addition, most enhanced tubes
delay film breakdown, maintaining the surface wet. Only those geometries that limit liquid axial
movement, such as low-finned tubes with a high concentration of fins, should be avoided in
these systems.
An experimental setup available in the laboratory was redesigned in order to allow spray
evaporation tests. These tests consist in distributing the liquid refrigerant, in conditions very
close to saturation, on the tested tube/s, simulating the situation that occurs in spray
evaporators.
The main modification developed was to include a liquid distribution system to distribute the
liquid refrigerant. The system was designed to allow testing different types of spreading devices.
Among the different possibilities, full cone nozzles have been selected. The equipment permits
different spacings between the nozzles, as well as choosing between two positions for the tube
that receives the refrigerant from the nozzles. In addition, it allows comparing the heat transfer
coefficients obtained when the tested tube receives the liquid refrigerant directly from the
nozzles and when the liquid refrigerant falls by gravity from a conditioning tube above the tested
one.
The experimental setup does not follow a typical vapour compression cycle. Instead, pool
boiling/spray evaporation and condensation occur at the same pressure and refrigerant flows
from one shell-and-tube heat exchanger to the other due to the differences of density between
liquid and vapour refrigerant. This configuration allows, on the one hand, testing very different
conditions and refrigerants and, on the other hand, discarding the effect of lubricants on the
heat transfer coefficients determined.
The test rig is prepared for tubes of nominal external diameters up to 20 mm, but we tested
tubes of nominal external diameter 3/4” (19.05 mm), which are widely extended in shell-and-
tube heat exchangers. We chose tubes with plain and enhanced external surfaces, and the
material depends on the refrigerant used (compatibility refrigerant – material).
The compatibility with ammonia was the main consideration during the selection of
materials for building the experimental setup. Thus, we used stainless steel (AISI-316L) in
almost every component.
As previously mentioned, due to the working principle of the experimental facility, a wide
range of condensation and evaporation conditions can be tested. We chose liquid temperatures
between 0 and 10 ºC for our pool boiling and spray evaporation tests, common temperatures in
water chillers. This range of temperatures allowed using water as secondary fluid both for
condensing the vapour refrigerant at the condenser tubes and for vaporising the liquid at the
evaporator tubes. The use of water is very convenient since its properties are very accurately
determined using the temperatures measured.
The experimental facility stabilises the refrigerant pool temperature or the liquid distribution
temperature (boiling saturation pressure), for pool boiling and spray evaporation tests,
respectively. The distributed liquid refrigerant flow rate is also controlled accurately, maintaining
the rest of the conditions constant. The temperatures and flow rates of the secondary fluids can
also be regulated and stabilised at the values needed for each test.
The experimental setup allowed measuring the conditions (temperature, pressure and flow
rate) of the refrigerant and secondary fluids. Several sensors were also included to determine
the conditions of the distributed refrigerant.
We designed an experimental methodology to obtain pool boiling and spray evaporation
heat transfer coefficients. The methodology is based on determining the different thermal
resistances of the overall heat transfer process that occurs at the tubes.
The design of experiments has focused on studying the boiling heat transfer coefficients
under temperature conditions close to those found at water chillers, and with the largest range
of heat fluxes possible. We have conceived a specific experimental methodology to analyse the
influence of the impingement effect on the heat transfer coefficients with distribution of the liquid
refrigerant.
Pool boiling tests consisted in registering the values measured by the different sensors of
the test rig, keeping constant the mean heating water temperature and flow rate through the
tube and the refrigerant pool temperature. Except for special sets of experiments, a group of
tests (constant pool temperature) started with the maximum mean heating water temperature
possible. When stationary conditions were achieved, data were registered for a minimum of 15
minutes. After that, the mean heating water temperature was lowered and fixed at the next
testing condition. When finished a group of tests, a new was began at another refrigerant pool
temperature, repeating the procedure explained in the previous lines.
In spray evaporation experiments there are two new parameters to be considered: the
relative position between the tested tube and the distribution tube and the liquid refrigerant
distributed mass flow rate. The relative position of the tested tube and the distribution tube was
introduced as a new experimental variable because other authors observed that the liquid
droplet impingement effect could enhance heat transfer. Thus, we should expect differences in
the heat transfer performance between those tubes that receive refrigerant directly from the
distribution devices and those that are wetted by the excess liquid from the row of tubes placed
above them. Therefore, we have designed two different spray evaporation tests to illustrate
these two possibilities. The first tests, named ST tests, consist in distributing the refrigerant
directly from the nozzles to the tested tube, being the distance from the tip of the nozzle to the
tube axis 59 mm. In the second tests, named SB tests, the refrigerant is distributed on the same
tube, which works as a conditioning tube, forming a film that falls to the tube placed underneath
(distance of 45 mm between tube axes). No heating water circulates through the conditioning
tube to prevent liquid refrigerant from vaporising before falling to the tested tube.
We started with ST tests. The liquid refrigerant distribution temperature was fixed and, for
each group of tests, the mean heating water temperature started at the maximum value
achievable by the experimental test rig. Then, the liquid refrigerant distribution flow rate was set
at the maximum of the experimental set points considered, which was different for each of the
refrigerants tested. When stationary conditions were achieved, data were registered for a
minimum of 15 minutes. After that, the liquid refrigerant distribution flow rate was lowered and
the process repeated. When all the flow rates were tested, the mean heating water temperature
was lowered and fixed at the next testing condition and the sequence of tests was repeated.
Once finished ST tests, we repeated the whole process with SB tests.
Independently of the kind of tests, the heating water flow rate was kept as high as possible
to minimise the inner thermal resistance at the evaporator tubes, reduce the uncertainty of the
heat transfer coefficients and homogenise the boiling process along the tube (similar wall
temperature conditions). The cooling water flow rate was kept as low as possible to increase the
cooling water temperature difference between the inlet and the outlet of the condenser tube/s
and to calculate with more accuracy the heat flow at this heat exchanger.
We explain the calculation method to determine the heat transfer coefficients from the
experimental data from the test rig. The methodology is based on the separation of all the
thermal resistances that are part of the overall heat transfer process occurring in heat
exchangers. Prior to including the refrigerant pump in the refrigerant cycle and taking into
account the working principle of the experimental test rig and the good insulation applied, the
overall thermal resistance was accurately calculated with the heat flow at the condenser. After
its installation, we observed that the heat flow at the evaporator tubes was seen to match the
electric power delivered to the heating water at the electric boiler.
We also detail the method to estimate the fraction of liquid refrigerant reaching the studied
tubes under spray conditions and defined the enhancement factor to compare the heat transfer
coefficients calculated for different tubes and different boiling process, at the same conditions.
The results shown include uncertainties and these uncertainties prove the quality and
reliability of the results. There is an appendix in the document that explains the process followed
to calculate these uncertainties, which is based on the Guide to the Expression of Uncertainty in
Measurements.
We performed validation experiments to check the assumptions considered at the
calculation process. The validation process has been successful and, thus, the heat transfer
coefficients obtained with this experimental facility and procedure result from a convenient
process.
We show the pool boiling heat transfer coefficients obtained experimentally for this thesis.
The refrigerants studied have been R134a and ammonia. With the former we tested copper
tubes of plain and enhanced surfaces (Turbo-B and Turbo-BII+); and with the latter we tested
titanium tubes of plain and enhanced surface (Trufin 32 f.p.i.).
We observed that the vast majority of our experimental results are included in the nucleate
boiling region of Nukiyama’s boiling curve, where the slope is steep and heat flux increases
rapidly with superheating.
Concerning the pool boiling heat transfer coefficients, we observed that they generally
increase with increasing saturation temperatures, being constant the heat flux. We also
observed for all the tubes except for Turbo-B that pool boiling heat transfer coefficients rise as
the heat flux rises, independently of the saturation temperature. This effect was clearer with the
plain tubes.
With ammonia we also tested the influence of hysteresis on the nucleation process. Several
works of the literature show different results when experiments were conducted in increasing
heat flux direction and in decreasing heat flux direction. We confirmed the existence of this
hysteresis effect and that it is more important with the enhanced surface tested (Trufin 32 f.p.i.).
However, our experiments show that increasing heat flux tests are time-dependent, i.e. the heat
transfer coefficients obtained when the experimentation process follows an increasing heat flux
direction rise (even when the test conditions remain constant) until they reach a value very
close to that obtained with the decreasing heat flux tests.
We compared our experimental results with well-known correlations from different works
from the literature. In the case of plain tubes, the best agreement existed with Gorenflo and
Kenning correlation with R134a and with Mostinski correlation with ammonia.
The surface enhancement techniques are more effective with R134a than with ammonia.
With R134a, the surface enhancement factors are as high as 11.8 and 7 with the Turbo-B and
Turbo-BII+, respectively. In contrast, with ammonia the surface enhancement factor is never
greater than 1.3.
We included the photographic reports of the pool boiling of ammonia on the plain tube and
the Trufin 32 f.p.i. tube. The pictures show the increase of density of nucleation sites and of the
bubble diameters as the heat flux increases. The visual differences between tubes are very
slight, confirming the surface enhancement factor results determined.
Concerning spray evaporation, we studied R134a and ammonia with plain tubes. The tubes
used with R134a were made of copper and the tubes used with ammonia were made of
titanium.
We observed that the vast majority of our spray evaporation experimental results are
included in the nucleate boiling region of the boiling curve. The slope of the boiling curve is
steep, i.e. heat flux increases rapidly with superheating.
Spray evaporation heat transfer coefficients with R134a and the copper tube increase,
generally, if the heat flux is higher, independently of the mass flow rate of the film per side and
meter of tube. We also observed that the effect of the mass flow rate on the heat transfer
coefficients is negligible.
The spray evaporation heat transfer coefficients obtained with R134a and the tube placed
directly underneath the refrigerant distribution tube (ST tests) are, on average, 13.2% greater
than those determined with the tube that receives refrigerant from the conditioning tube (SB
tests), if kept the heat flux and distributed mass flow rate constant. The heat transfer
enhancement occurs due to the liquid droplet impingement effect.
We compared spray evaporation and pool boiling under similar conditions and we observed
that spray evaporation enhances heat transfer only if the heat flux is low (lower than 20000
W/m2). Enhancement is never higher than 60%. The results concerning heat transfer
enhancement are in line with others shown in the specialised literature.
An analysis of the photographs taken during the experiments allowed confirming the
existence of dry patches on the tube. Dryout occurred even when the distributed refrigerant was
significantly greater than the amount of refrigerant that vaporised on the tube (overfeed rates
well over 1).
The spray evaporation heat transfer coefficients with ammonia and the titanium tube
depend on both heat flux and mass flow rate of refrigerant per side and meter of tube.
Generally, they increase as the heat flux increases, but this trend is even opposite under
conditions of high heat flux and low mass flow rate.
We observed that the spray evaporation heat transfer coefficients obtained with ammonia
and the tube placed directly underneath the refrigerant distribution tube (ST tests) are, on
average, 38.7% higher than those determined with the tube that receives refrigerant from the
conditioning tube (SB tests). Droplet impingement effect is responsible of this effect.
From the comparison of spray evaporation and pool boiling of ammonia on the plain tube,
we concluded that spray evaporation enhances importantly heat transfer. Spray enhancement
factors are well over 1, particularly when the refrigerant on the tested tube arrived directly from
the nozzles (ST tests). The maximum enhancement factor has been over 6 and the best results
occurred in the low heat flux range (up to 20000 W/m2).
We analysed the snapshots taken when conducting the tests and the most important
conclusion is that we could confirm that dry patches occurred under certain conditions. Dryout
explains some of the tendencies we obtained from our experimental results. However, we
calculated the overfeed ratio for the conditions of the tests shown in the photographs and
realised that dryout occurred even when the overfeed rates greater than 1.
The experimental results obtained make clear the importance of having a proper distribution
of the liquid refrigerant on the tubes of spray evaporators. Thus, developed a computer
programme, based on a geometric study, to optimise the design of liquid distribution systems
with spray nozzles. The programme calculates the percentage of liquid distributed by a given
spray nozzle that reaches a generic tube, defining concepts such as those of the theoretical and
real limit angles from a nozzle to a tube or the dimensionless column factor.
We also developed a parametric analysis with a 1-meter-long tube bundle with 8 rows and 8
tubes per row (7 for even rows in staggered pitch layout), varying parameters such as the
horizontal and vertical pitch, the tube bundle pattern, the spray nozzle angle, etc. We observed
that, in general, 60º nozzles lead to an even distribution and more efficient use of the liquid
distributed. However, they require a larger distance between the spray nozzles and the first row
of the tube bundle to optimise distribution and, thus, there is an important part of the shell that
must be clear of tubes. The performance of systems with 90º nozzles is slightly lower, but the
distance required is also shorter and they are convenient from that point of view.
The parametrical analysis proves that the even distribution of liquid on the different columns
of inline tube bundles is easier than when the pattern is staggered. In fact, staggered tube
bundles seem unsuitable for this kind of distribution systems with nozzles and without
intermediate devices. Only when staggered bundles had a high horizontal pitch between tubes
of the same row was high (2 in this case), we observed a convenient distribution between the
different columns. However, an increase of this horizontal pitch leads to the loss of
compactness of staggered bundles, which is the main advantage of such tube pattern.
Resumo
O sector da refrixeración non pode permanecer alleo aos retos medioambientais e
enerxéticos aos que se enfrontará a humanidade nos vindeiros anos. Os protocolos de
Montreal e posteriores revisións marcaron o comezo das restrición do uso de refrixerantes
clorofluorocarbonados (CFCs) e hidrocloroflorocluorocarbonados (HCFCs) debido á destrución
da capa de ozono. O R134a e outros refrixerantes tipo hidrofluorocarbonados (HFCs) están
eliminándose gradualmente debido ao seu potencial de quecemento global (GWP). Os
refrixerantes naturais, como CO2, o amoníaco ou os hidrocarburos, semellan alternativas
interesantes aos anteriores desde os puntos de vista medioambiental e de eficiencia. Porén, as
elevadas presións dos sistemas de CO2, a toxicidade do amoníaco ou a inflamabilidade dos
hidrocarburos son as súas principais desvantaxes. A combinación de refrixerantes naturais e
sistemas máis eficientes é a liña de investigación a seguir no futuro.
Os evaporadores de caída de película, tamén coñecidos como evaporadores en spray,
teñen sido amplamente utilizados na industria petroquímica, en procesos de desalgado de
augas e en sistemas de conversión de enerxía cas diferencias térmicas do océano (OTEC). A
experiencia con estes equipos noutros campos como as bombas de calor ou a refrixeración é
limitado, pero estes aparecen como unha interesante alternativa aos evaporadores inundados,
debido a que poden implicar unha diminución da carga de refrixerante ou unha mellora da
transmisión de calor. Ademais, evítase o aumento da temperatura de ebulición que aparece
nos evaporadores inundados debido á presión hidrostática; redúcese a diferenza de
temperatura entre o refrixerante e o fluído a arrefriar, co que mellora a eficiencia do ciclo
termodinámico; e redúcese o tamaño dos evaporadores. A maior desvantaxe dos evaporadores
con caída de película é que o deseño do sistema de distribución é crítico e pode implicar un
empeoramento da transmisión de calor debido á aparición de zonas secas na película de
líquido refrixerante.
Os evaporadores de caída de película en sistemas de refrixeración son intercambiadores
de tipo carcasa e tubos. Boquillas de spray ou outros sistemas de distribución reparten o
líquido refrixerante sobre as primeiras filas do banco de tubos. Parte do refrixerante vaporiza
sobre a fila superior, arrefriando o fluído que circula polo interior dos tubos, mentres que o resto
forma unha película que avanza ao seguinte tubo. Este proceso de vaporización e avance
continúa ao longo do banco de tubos. O exceso de refrixerante recóllese na parte inferior do
evaporador e recircúlase á unidade de distribución (con acondicionamentos intermedios se son
necesarios).
A eficiencia dos evaporadores con caída de película vese afectada por un gran número de
parámetros, pero os diferentes autores están en desacordo acerca do efecto de cada un deles.
Os parámetros con maior influencia son a densidade de fluxo de calor, o caudal másico
distribuído, a xeometría dos tubos, as propiedades do refrixerante e o tipo de sistema de
distribución. Os tubos con superficies melloradas fan que a transmisión de calor sexa máis
eficiente, se os comparamos cos tubos lisos. Ademais, estas superficies soen retrasar a
aparición de zonas secas, aínda que hai que evitar aquelas que limitan o movemento axial do
líquido, tales como os tubos con aletas integradas e elevada densidade de aletas.
Redeseñouse un equipo experimental existente no laboratorio para permitir a realización de
ensaios de evaporación en spray. A particularidade destes ensaios é que hai que distribuír un
líquido refrixerante, en condicións moi próximas ás de líquido saturado, sobre o tubo ou tubos
ensaiados, simulando as condicións que ocorren en evaporadores en spray.
A principal modificación realizada foi a inclusión do sistema de distribución de líquido para
o refrixerante. O sistema deseñouse para que fose versátil e permitise o emprego de diferentes
sistemas de distribución. De entre as diferentes posibilidades, escolléronse as boquillas de
spray tipo “full cone”. O equipo permite modificar a distancia entre as boquillas, así como
seleccionar entre dúas posicións para o tubo que recibe o refrixerante das mesmas. No equipo
tamén se poden comparar os coeficientes de transmisión de calor para os tubos que reciben o
líquido refrixerante directamente desde o sistema de distribución co daqueles tubos
alimentados polo fluído restante dun tubo superior (tubo de acondicionamento).
O equipo experimental non segue un ciclo de compresión de vapor típico. En cambio, os
procesos de condensación e vaporización (con caída de película ou inundada) ocorren á
mesma presión e de forma simultánea (en cadanseu intercambiador). O refrixerante flúe dun
intercambiador de calor a outro debido ás diferencias de densidade entre o líquido e o vapor de
refrixerante. Esta configuración permite, por un lado, probar un amplo rango de refrixerantes e
condicións e, por outro lado, evitar a presencia de lubricante durante a determinación dos
coeficientes de transmisión de calor.
O banco de ensaios está preparado para tubos de ata 20 mm de diámetro nominal exterior.
Para estes ensaios seleccionamos tubos de 3/4" (19,05 mm) de diámetro exterior, cuxo uso
está moi estendido en intercambiadores de calor de carcasa e tubos. Escollemos tubos con
superficies exteriores lisa e mellorada, e o material dos mesmos depende do refrixerante
empregado, buscando a compatibilidade entre ambos.
A compatibilidade co amoníaco foi a consideración principal á hora de seleccionar os
materiais para construír o equipo experimental. Por iso, empregouse aceiro inoxidable tipo
AISI-316L na maioría dos compoñentes.
Como se mencionou anteriormente, debido ao principio de funcionamento do equipo
experimental pódese probar un amplo rango de condicións de condensación e
evaporación/ebulición. Escollemos temperaturas de líquido entre 0 ºC e 10 ºC para os ensaios
de ebulición inundada e de evaporación en spray, que son temperaturas típicas en
arrefriadoras de auga. Este rango de temperaturas permite empregar auga como fluído
secundario tanto para condensar o vapor de refrixerante nos tubos do condensador como para
vaporizar el líquido refrixerante en los tubos del evaporador. O emprego de auga é moi
interesante xa que se coñecen as súas propiedades con moita precisión a partir da
temperatura.
O equipo experimental controla a temperatura de piscina de líquido ou a temperatura de
distribución de líquido refrixerante para os ensaios de ebulición inundada e evaporación en
spray, respectivamente. Tamén se pode axustar o caudal másico de líquido refrixerante
distribuído mantendo o resto de condicións constantes. As temperaturas e caudais dos fluídos
secundarios tamén se poden regular e estabilizar con precisión en función do ensaio.
Os diferentes sensores de temperatura, presión e caudal que existen no banco de ensaios
permiten medir as condicións do refrixerante e dos fluídos secundarios. Durante as
modificacións do equipo, houbo que incluír novos sensores para determinar as condicións do
refrixerante distribuído.
Deseñamos unha metodoloxía experimental para obter os coeficientes de transmisión de
calor dos procesos de ebulición inundada e evaporación en spray. Esta metodoloxía baséase
en determinar as diferentes resistencias térmicas do proceso global de transferencia de calor.
O deseño dos experimentos centrouse en estudar os coeficientes de transmisión de calor
baixo condicións de temperatura preto das que existen en arrefriadoras de auga, e co maior
rango de densidades de fluxo de calor posible. Desenvolvemos unhas metodoloxía
experimental específica para analizar o efecto do impacto do líquido nos coeficientes de
transmisión de calor nos evaporadores en spray.
Nos ensaios de ebulición inundada rexistráronse valores dos diferentes sensores da
bancada experimental, mantendo constante a temperatura media e o caudal da auga de
quecemento que pasa polo tubo do evaporador, así como a temperatura da piscina de líquido
refrixerante. Excepto para algún experimento con finalidade específica, cada grupo de ensaios
a temperatura de piscina constante comeza co valor máximo de auga de quecemento (máxima
densidade de fluxo de calor). Cando se alcanza o estado estacionario, rexístranse datos por un
mínimo de 15 minutos. Despois, redúcese o valor da temperatura media da auga de
quecemento e fíxase na seguinte condición de ensaio. Cando finalizan os ensaios a unha
temperatura de piscina de líquido, modifícase esta e comézase un novo grupo de ensaios,
repetindo o procedemento anterior.
Nos experimentos de evaporación en spray hai dous novos parámetros a considerar: a
posición relativa entre o tubo ensaiado e o tubo de distribución e o caudal másico de líquido
refrixerante distribuído. A posición relativa introduciuse xa que hai traballos da literatura
especializada nos que se indica que o impacto do líquido refrixerante sobre o tubo pode
mellorar a transmisión de calor. Por iso, debemos agardar diferenzas nos coeficientes de
transmisión de calor entre os tubos que reciben refrixerante directamente dos equipos de
distribución e os que reciben o refrixerante doutros tubos. Deseñamos dous tipos de
experimentos de evaporación en spray para ilustrar estas dúas posibilidades. No primeiro tipo
de ensaios, denominados ensaios ST, o tubo ensaiado localízase directamente debaixo dos
equipos de distribución, sendo a distancia entre a punta das boquillas e o centro do tubo
ensaiado igual a 59 mm. No segundo tipo de ensaios, denominados ensaios SB, o refrixerante
distribúese sobre o tubo anterior, que neste caso traballa como tubo de acondicionamento.
Sobre el fórmase unha película de líquido que cae no tubo ensaiado, que está 45 mm por
debaixo do de acondicionamento. Polo tubo de acondicionamento non circula auga de
quecemento para evitar a vaporización do líquido refrixerante distribuído.
O proceso comeza cos ensaios ST. A temperatura do líquido refrixerante distribuído fíxase,
e establécese a temperatura media da auga de quecemento máxima que se pode alcanzar co
equipo experimental. Tamén é necesario axustar o caudal de líquido refrixerante distribuído
nun dos valores a ensaiar. Cando se alcanza o estado estacionario, rexístranse datos por un
mínimo de 15 minutos. Despois modifícase o valor do caudal e se repite o proceso. Cando
finaliza o grupo de ensaios a unha mesma temperatura media da auga de quecemento,
redúcese este parámetro ata a seguinte condición de ensaio e repítese a secuencia. Unha vez
rematados os ensaios ST, procédese de igual xeito cos ensaios SB.
Independentemente do tipo de experimentos, mantívose o caudal de auga de quecemento
polos tubos do evaporador nun valor elevado para minimizar a resistencia térmica do proceso
de convección interior, reducir a incertidume dos coeficientes de transmisión de calor
determinados e homoxeneizar o proceso de ebulición ao longo do tubo (temperaturas de
parede semellantes en todo o tubo). O caudal de auga de arrefriamento estableceuse nun valor
baixo para aumentar a diferenza de temperaturas neste fluído entre a entrada e a saída dos
tubos do condensador e calcular con maior precisión os fluxos de calor no intercambiador.
O método de cálculo dos coeficientes de transmisión de calor a partir dos datos rexistrados
polos sensores da bancada está detallado no documento. A metodoloxía baséase na
separación das resistencias térmicas que do proceso global de transmisión de calor. Antes de
incluír a bomba de refrixerante no ciclo e tendo en conta o principio de funcionamento do
equipo experimental e o bo illamento do mesmo, podíase calcular a resistencia térmica global
nos tubos do evaporador co fluxo de calor no condensador. De todos os xeitos, trala instalación
da bomba foi necesario modificar isto. Observouse que o fluxo de calor transferido no
evaporador correspondíase á potencia eléctrica transmitida na caldeira á auga de quecemento
dos tubos do evaporador.
Desenvolveuse un método para o cálculo da fracción de líquido refrixerante do total
distribuído que chega aos tubos ensaiados baixo condicións de evaporación en spray. Tamén
definimos dous parámetros para a determinación dos factores de mellora derivados do
emprego de tubos con superficies melloradas con respecto aos tubos lisos e derivados da
utilización de técnicas de spray con respecto aos evaporadores inundados, ás mesmas
condicións de ensaio.
Os resultados que se mostran na tese levan asociadas as incertidumes para probar a
calidade e fiabilidade dos mesmos. Inclúese un anexo no que se explica o proceso para o
cálculo destas incertidumes, o cal está baseado na Guía para a Expresión da Incertidume nas
Medidas.
Os ensaios de validación permitiron comprobar as hipóteses consideradas para o proceso
de cálculo. A validación realizouse con éxito e, polo tanto, os coeficientes de transmisión de
calor obtidos con este equipo e procedemento experimental son resultado dun proceso
conveniente.
Os coeficientes de transmisión de calor dos procesos de ebulición inundada incluídos nesta
tese de doutoramento corresponden aos refrixerantes R134a e amoníaco. Co primeiro deles
ensaiamos tubos de cobre de superficie lisa e mellorada (Turbo-B e Turbo-BII+) e co segundo
os tubos foron de titanio, con superficie lisa e mellorada (Trufin 32 f.p.i.).
A gran maioría dos nosos resultados experimentais de ebulición inundada están incluídos
dentro da zona de ebulición nucleada da curva de ebulición de Nukiyama, onde a pendente é
pronunciada e a densidade de fluxo de calor medra rapidamente con pequenos aumentos da
diferencia de temperaturas entre a parede e o refrixerante.
En xeral, os coeficientes de transmisión de calor en ebulición inundada aumentan conforme
aumenta a temperatura de saturación (sendo constante a densidade de fluxo de calor). Para
todos os tubos excepto no caso do Turbo-B, ao medrar a densidade de fluxo de calor
increméntanse os coeficientes de transmisión de calor, independentemente da temperatura de
saturación. Este efecto observouse máis claramente para os tubos lisos.
Con amoníaco tamén se fixeron ensaios para analizar a histérese no proceso de
nucleación. Varios traballos da literatura mostran que, para unhas mesmas condicións,
chéganse a diferentes valores dos coeficientes de transmisión de calor segundo os ensaios se
realicen en sentido ascendente ou descendente da densidade de fluxo de calor. Confirmamos a
existencia deste efecto e que é máis importante en superficies melloradas (Trufin 32 f.p.i.). De
todos os xeitos, os nosos experimentos demostran que é un efecto que depende do tempo, xa
que os coeficientes de transmisión de calor obtidos na secuencia de experimentos con
densidade de fluxo ascendente van aumentando pese a que se manteñan as condicións de
ensaio constantes. Ademais, tenden ao valor obtido durante os ensaios realizados en sentido
decrecente da densidade de fluxo de calor.
A comparación dos resultados experimentais obtidos cos tubos lisos con correlacións da
literatura mostrou que as que mellor se axustan son a de Gorenflo e Kenning no caso do
R134a e a de Mostinski no caso do amoníaco.
Os tubos de superficie mellorada demostraron ser máis efectivos co refrixerante R134a que
con amoníaco. Deste xeito, os factores de mellora chegaron a valores de 11,8 e 7 co Turbo-B e
Turbo-BII+, respectivamente. Por el contrario, con amoníaco e o Trufin 32 f.p.i. o factor de
mellora nunca superou 1,3.
As gravacións levadas a cabo para os ensaios de ebulición inundada de amoníaco sobre
os tubos de titanio serviron para complementar os resultados experimentais obtidos. As
capturas dos vídeos mostran que efectivamente existe un aumento do densidade de puntos de
nucleación e dos diámetros das burbullas ao aumentar a densidade de fluxo de calor. As
diferencias visuais entre os tubos, a igualdade de condicións de ensaio, son moi lixeiras. Isto
confirma os valores próximos á unidade do factores de mellora calculados.
En canto á evaporación en spray, estudamos os refrixerante R134a e amoníaco sobre os
mesmos tubos lisos utilizados para os ensaios de ebulición inundada. Observamos que, ao
igual que ocorrera no caso da ebulición inundada, a maioría dos ensaios realizados atópanse
dentro da rexión de ebulición nucleada da curva de ebulición.
Os coeficientes de transmisión de calor no caso da evaporación en spray de R134a sobre o
tubo liso de cobre aumentan, xeralmente, co aumento da densidade de fluxo de calor e
independentemente do caudal másico de refrixerante distribuído polas boquillas. Tamén
observamos que o efecto que ten o caudal másico sobre a transferencia de calor, dentro do
rango ensaiado, é desprezable. Observouse que o incremento dos coeficientes de transmisión
de calor en evaporación en spray debidos ao impacto do líquido sobre o tubo ensaiado é, de
media 13,2%.
Comparáronse os resultados experimentais de evaporación en spray e ebulición inundada,
mantendo unhas condicións experimentais semellantes. Observouse que a evaporación en
spray mellora os coeficientes de transmisión de calor sempre e cando a densidade de fluxo de
calor sexa baixa (inferior a 20000 W/m2). A mellora obtida nunca superou o 60%. As tendencias
e resultados calculados están en liña con outros que se atopan en traballos da literatura
especializada.
Un análise das imaxes gravadas durante estes ensaios permitiu confirmar a existencia de
zonas secas sobre o tubo. A rotura da película ocorreu incluso cando o caudal másico de
refrixerante distribuído era claramente superior ao caudal másico que evapora no tubo (taxa de
sobrealimentado ben por enriba da unidade).
Os coeficientes de transmisión de calor na evaporación en spray de amoníaco e o tubo de
titanio dependen tanto da densidade de fluxo de calor e do caudal másico de refrixerante
distribuído. En xeral, cando aumenta a densidade de fluxo calor increméntanse os coeficientes
de transmisión de calor. Pola outra parte, esta tendencia é a contraria con condicións de
elevada densidade de fluxo de calor e baixo caudal distribuído.
O efecto do impacto do líquido sobre o tubo do evaporador é superior no caso do amoníaco
que no do R134a. Esta diferenza entre o tubo que recibe o refrixerante directamente das
boquillas e o que o recibe da película que se forma no tubo de acondicionamento cuantificouse
nun 38.7% de media.
A comparación de evaporación en spray e ebulición inundada no caso do amoníaco e o
tubo liso serve para afirmar que se mellora a transmisión de calor ca primeira. Os factores de
mellora debido ao spray son ben superiores a 1, en particular nos casos para os que o
refrixerante chega aos tubos directamente das boquillas. Os maiores factores de mellora foron
superiores a 6 e ocorreron con densidades de fluxo de calor inferiores a 20000 W/m2.
Da análise das imaxes tomadas durante os experimentos de evaporación en spray con
amoníaco e tubo liso extráese a conclusión de que existen zonas secas sobre o tubo baixo
certas condicións experimentais. A rotura de película explica moitas das tendencias e
resultados determinados. De todos os xeitos, a taxa de sobrealimentado é superior a 1 nas
condicións nas que aparecen zonas secas.
Os resultados experimentais obtidos serven para darse de conta da importancia que ten
unha distribución de líquido apropiada e suficiente sobre os tubos dos evaporadores en spray.
É por iso que desenvolvemos un programa informático, baseado nun estudo xeométrico, para
optimizar os deseño dos sistemas de distribución de líquido con boquillas de spray. O
programa calcula a porcentaxe do total do líquido distribuído por un sistema de sprays dado
que chega a un tubo calquera do intercambiador. Para iso definíronse conceptos como o dos
ángulos límite teóricos e reais entre boquilla e tubo ou o do factor de columna adimensional.
Para probar o programa desenvolvido, levamos a cabo unha análise paramétrica para 1
banco de tubos de 1 m de longo, con 8 filas de tubos con 8 tubos por fila (7 tubos nas filas
pares dos bancos de tubos triangulares). Variamos parámetros tales como o “pitch” horizontal e
vertical entre tubos, a disposición do banco de tubos, o ángulo de cono do spray, etc.
Observamos que, en xeral, as boquillas de 60º levan a unha distribución moi ben repartida e
eficiente do líquido distribuído. De todas formas, requiren unha distancia entre a boquilla e a
primeira fila de tubos máis longa que outras boquillas para optimizar a distribución e, polo tanto,
unha parte importante da carcasa quedaría libre de tubos con esta distribución. O
funcionamento dos sistemas de boquillas de 90º é lixeiramente peor, pero a distancia requirida
é menor e polo tanto resulta conveniente para intercambiadores.
A análise paramétrica demostra que a distribución homoxénea do líquido entre as
diferentes columnas nos bancos de tubos cadrados é máis sinxela que en bancos de tubos
triangulares. De feito, os triangulares semellan pouco convenientes para este tipo de sistemas
de boquillas e sen distribuidores intermedios. Soamente cando os bancos triangulares teñen un
“pitch” horizontal entre tubos elevado (2 no noso caso) observamos unha distribución
homoxénea. De todos os xeitos, este incremento do “pitch” fai que os bancos de tubos
triangulares perdan a súa principal bondade, que é a súa compactidade.
Contents
CONTENTS .................................................................................................................................... I
LIST OF FIGURES ........................................................................................................................ V
LIST OF TABLES ........................................................................................................................ XI
NOMENCLATURE ..................................................................................................................... XIII
CHAPTER 1 INTRODUCTION ..................................................................................................... 1
1.1. FALLING FILM EVAPORATION ......................................................................................... 2
1.2. FALLING FILM EVAPORATOR VS. FLOODED EVAPORATOR: ADVANTAGES AND
DISADVANTAGES.............................................................................................................. 3
1.3. FALLING FILM AROUND HORIZONTAL TUBES .............................................................. 4
1.4. HORIZONTAL INTERTUBE FALLING FILM ...................................................................... 5
1.4.1.
Flow patterns ........................................................................................................... 5
1.4.2.
Transition between flow modes ............................................................................... 8
1.4.3.
Entrainment ........................................................................................................... 10
1.5. DRY PATCHES AND FALLING FILM BREAKDOWN ...................................................... 12
1.6. HEAT TRANSFER COEFFICIENTS: THEORETICAL AND ANALYTICAL WORKS ....... 15
1.7. HEAT TRANSFER COEFFICIENTS: EXPERIMENTAL WORKS AND CORRELATIONS ..
.......................................................................................................................................... 17
1.7.1.
Plain tubes (smooth tubes) .................................................................................... 17
1.7.2.
Enhanced tubes ..................................................................................................... 19
1.7.3.
Solutions to dry patches ........................................................................................ 23
1.8. GENERAL CONSIDERATIONS ....................................................................................... 25
1.8.1.
Flow modes and transitions ................................................................................... 25
1.8.2.
Film dryout ............................................................................................................. 25
1.8.3.
Film flow rate ......................................................................................................... 25
1.8.4.
Heat flux ................................................................................................................. 26
1.8.5.
Distribution method ................................................................................................ 26
1.8.6.
Enhanced tubes ..................................................................................................... 26
1.8.7.
Other considerations.............................................................................................. 26
1.9. CONCLUSIONS ................................................................................................................ 27
REFERENCES ............................................................................................................................ 28
CHAPTER 2 EXPERIMENTAL FACILITY ................................................................................. 33
2.1. EXPERIMENTAL SETUP PHILOSOPHY ......................................................................... 34
2.2. EXPERIMENTAL FACITILITY DESCRIPTION................................................................. 36
2.2.1.
Experimental facility ............................................................................................... 36
2.2.2.
Distribution tube calculation ................................................................................... 38
2.3. DATA ACQUISITION SYSTEM ........................................................................................ 42
2.4. ESPECIFICATIONS OF THE TUBES EMPLOYED ......................................................... 44
2.5. CONCLUSIONS ................................................................................................................ 47
REFERENCES ............................................................................................................................ 48
CHAPTER 3 EXPERIMENTAL METHODOLOGY ..................................................................... 49
3.1. CONVECTION HEAT TRANSFER COEFFICIENTS ....................................................... 50
3.2. BOILING EXPERIMENTS ................................................................................................. 53
3.2.1.
Pool boiling experiments ....................................................................................... 53
3.2.2.
Spray evaporation experiments ............................................................................. 53
3.3. DATA REDUCTION .......................................................................................................... 55
3.3.1.
Refrigerant side heat transfer coefficient determination ........................................ 55
3.3.2.
Inner heat transfer coefficients .............................................................................. 56
3.3.3.
Mass flow rate reaching the tubes ......................................................................... 57
3.3.4.
Enhanced surface enhancement factor ................................................................. 59
3.3.5.
Spray evaporation enhancement factor................................................................. 60
3.4. UNCERTAINTY DETERMINATION .................................................................................. 61
I
3.5. EXPERIMENTAL FACILITY VALIDATION ....................................................................... 62
3.6. CONCLUSIONS ................................................................................................................ 71
REFERENCES ............................................................................................................................ 72
CHAPTER 4 POOL BOILING OF PURE REFRIGERANTS: R134A AND AMMONIA ............. 73
4.1. POOL BOILING OF R134A ON PLAIN TUBE .................................................................. 74
4.1.1.
Refrigerant side heat transfer coefficients ............................................................. 74
4.1.2.
Comparison with correlations ................................................................................ 76
4.2. POOL BOILING OF R134A ON ENHANCED SURFACES .............................................. 79
4.2.1.
Refrigerant side heat transfer coefficients on Turbo-B .......................................... 79
4.2.2.
Refrigerant side heat transfer coefficients on Turbo-BII+ ...................................... 80
4.2.3.
Comparison with experimental works from the literature ...................................... 82
4.2.4.
Surface enhancement factors ................................................................................ 83
4.3. POOL BOILING OF AMMONIA ON PLAIN TUBE ............................................................ 85
4.3.1.
Refrigerant side heat transfer coefficients ............................................................. 85
4.3.2.
Comparison with correlations ................................................................................ 86
4.3.3.
Hysteresis .............................................................................................................. 87
4.3.4.
Photographic report ............................................................................................... 89
4.4. POOL BOILING OF AMMONIA ON ENHANCED TUBE .................................................. 91
4.4.1.
Refrigerant side heat transfer coefficients on Trufin 32 f.p.i .................................. 91
4.4.2.
Surface enhancement factors ................................................................................ 92
4.4.3.
Hysteresis .............................................................................................................. 93
4.4.4.
Photographic report ............................................................................................... 96
4.5. CONCLUSIONS ................................................................................................................ 98
REFERENCES ............................................................................................................................ 99
CHAPTER 5 SPRAY EVAPORATION OF PURE REFRIGERANTS: R134A AND AMMONIA
................................................................................................................................................... 101
5.1. SPRAY EVAPORATION OF R134A ON PLAIN TUBE .................................................. 102
5.1.1.
Spray evaporation heat transfer coefficients ....................................................... 102
5.1.2.
Spray enhancement factors ................................................................................. 105
5.1.3.
Photographic report ............................................................................................. 107
5.2. SPRAY EVAPORATION OF AMMONIA ON PLAIN TUBE ............................................ 111
5.2.1.
Spray evaporation heat transfer coefficients ....................................................... 111
5.2.2.
Spray enhancement factors ................................................................................. 115
5.2.3.
Photographic report ............................................................................................. 117
5.3. CONCLUSIONS .............................................................................................................. 121
REFERENCES .......................................................................................................................... 122
CHAPTER 6 OPTIMISATION OF THE NOZZLE DISTRIBUTION SYSTEM IN SHELL-ANDTUBE EVAPORATORS ............................................................................................................ 123
6.1. INTRODUCTION ............................................................................................................. 124
6.2. AIM OF THE STUDY AND PREVIOUS CONSIDERATIONS ........................................ 126
6.3. GEOMETRIC CALCULATIONS ...................................................................................... 127
6.3.1.
Characterisation of the spray produced by a full cone nozzle ............................. 127
6.3.2.
Optimal position of adjacent nozzles and 1 nozzle system ................................. 129
6.3.3.
Optimal position of adjacent nozzles and multiple nozzle systems ..................... 131
6.3.4.
Repositioning of the distribution systems and their nozzles ................................ 134
6.3.5.
Liquid distribution from a nozzle to a generic tube. Limit angles ......................... 135
6.3.6.
Liquid flow rate reaching a generic tube .............................................................. 139
6.4. PROGRAMME FOR THE CALCULATION OF HEAT EXCHANGERS .......................... 142
6.4.1.
Inputs ................................................................................................................... 142
6.4.2.
Calculation process ............................................................................................. 143
6.4.3.
Outputs ................................................................................................................ 143
6.5. PARAMETRIC ANALYSIS .............................................................................................. 146
6.5.1.
Input parameters.................................................................................................. 146
6.5.2.
Results ................................................................................................................. 146
6.6. CONCLUSIONS .............................................................................................................. 155
REFERENCES .......................................................................................................................... 156
II
CHAPTER 7 GENERAL CONCLUSIONS AND FUTURE WORKS ........................................ 157
7.1. GENERAL CONCLUSIONS............................................................................................ 158
7.2. FUTURE WORKS ........................................................................................................... 160
APPENDIX A UNCERTAINTY DETERMINATION .................................................................. 161
A.1. GENERAL FEATURES ................................................................................................... 162
A.2. UNCERTAINTIES OF DIRECTLY MEASURED MEASURANDS .................................. 163
A.2.1.
Uncertainty of temperatures ................................................................................ 163
A.2.2.
Uncertainty of refrigerant pressures .................................................................... 163
A.2.3.
Uncertainty of water volumetric flow rates ........................................................... 163
A.2.4.
Uncertainty of the electric power at the electric boiler ......................................... 163
A.2.5.
Uncertainty of the distributed liquid refrigerant mass flow rate ........................... 163
A.2.6.
Uncertainty of the distributed liquid refrigerant density ....................................... 163
A.2.7.
Uncertainty of lengths and diameters .................................................................. 163
A.3. PROPAGATED UNCERTAINTIES ................................................................................. 164
A.3.1.
Uncertainty of the mean heating water temperature ........................................... 164
A.3.2.
Uncertainty of the heating water temperature difference between inlet and outlet ...
............................................................................................................................. 164
A.3.3.
Uncertainty of the heating water properties ......................................................... 164
A.3.4.
Uncertainty of the heating water mass flow rate ................................................. 165
A.3.5.
Uncertainty of the heating water heat flow .......................................................... 165
A.3.6.
Uncertainty of heat exchange areas .................................................................... 166
A.3.7.
Uncertainty of the heating water heat fluxes ....................................................... 166
A.3.8.
Uncertainty of the cooling water mean temperature............................................ 167
A.3.9.
Uncertainty of the cooling water temperature difference between outlet and inlet ...
............................................................................................................................. 167
A.3.10. Uncertainty of the cooling water properties ......................................................... 167
A.3.11. Uncertainty of the cooling water mass flow rate .................................................. 168
A.3.12. Uncertainty of the cooling water heat flow ........................................................... 168
A.3.13. Uncertainty of the liquid refrigerant mean temperature ....................................... 169
A.3.14. Uncertainty of the temperature difference at each end of the evaporator section ....
............................................................................................................................. 169
A.3.15. Uncertainty of the logarithmic mean temperature difference at the evaporator .. 169
A.3.16. Uncertainty of the overall thermal resistance at the evaporator .......................... 170
A.3.17. Uncertainty of the heating water Reynolds number in the evaporator tube ........ 170
A.3.18. Uncertainty of the heating water Prandtl number ................................................ 171
A.3.19. Uncertainty of the Darcy-Weisbach friction factor ............................................... 172
A.3.20. Uncertainty of the heating water Nusselt number with plain tube ....................... 172
A.3.21. Uncertainty of the heating water Nusselt number with enhanced tubes ............. 173
A.3.22. Uncertainty of the heating water convection HTC in tubes ................................. 174
A.3.23. Uncertainty of the inner thermal resistance ......................................................... 174
A.3.24. Uncertainty of the tube wall thermal resistance ................................................... 175
A.3.25. Uncertainty of the outer thermal resistance ......................................................... 175
A.3.26. Uncertainty of the outer convection HTC on tubes.............................................. 176
A.3.27. Uncertainty of the temperature at the inner tube wall.......................................... 176
A.3.28. Uncertainty of the temperature at the outer tube wall ......................................... 177
A.3.29. Uncertainty of the superheating at the outer tube wall ........................................ 177
A.3.30. Uncertainty of the enhanced surface enhancement factor .................................. 178
A.3.31. Uncertainty of the spray evaporation enhancement factor .................................. 178
A.3.32. Uncertainty of the distance from the tip of the nozzle to the tangents on the tubes .
............................................................................................................................. 179
A.3.33. Uncertainty of the spray cone diameter at the distance z from the tip of the nozzle .
............................................................................................................................. 179
A.3.34. Uncertainty of the angle formed by the tangents to the tube from the nozzle ..... 180
A.3.35. Uncertainty of the projected tube radius at a distance z from the tip of the nozzle ...
............................................................................................................................. 180
A.3.36. Uncertainty of the projected tube lengthwise dimension at a distance z from the tip
of the nozzle ......................................................................................................................... 181
A.3.37. Uncertainty of the projected area of tube reached from the distribution system . 181
A.3.38. Uncertainty of the spray cone area of n nozzles at a distance z ......................... 181
III
A.3.39.
A.3.40.
A.3.41.
A.3.42.
A.3.43.
IV
Uncertainty of the mass flow rate reaching the top of the tube ........................... 182
Uncertainty of the film flow rate at each side per meter of tube .......................... 182
Uncertainty of the liquid refrigerant properties .................................................... 183
Uncertainty of the film flow Reynolds number at the top of the tube ................... 183
Uncertainty of the liquid refrigerant overfeed ratio .............................................. 184
List of Figures
Figure 1.1. Horizontal tube falling film evaporator......................................................................... 2
Figure 1.2. Falling film evaporation, simplified model as described in [4] ..................................... 4
Figure 1.3. Intertube flow patterns in Hu and Jacobi [9]. a) Droplet mode. b) Droplet-column
mode. c) Inline column mode. d) Staggered column mode. e) Column-sheet mode. f) Sheet
mode ........................................................................................................................................ 6
Figure 1.4. Droplet deflection entrainment as described in reference [16] ................................. 10
Figure 1.5. Dry patch formation and film breakdown on a plate, as described in reference [40] 12
Figure 1.6. Thermal regions in a falling film. a) Two regions (reference [47]). b) Three regions
(reference [48]). c) Four regions (reference [49])................................................................... 15
Figure 1.7. Distribution methods used by Fujita and Tsutsui [24]. a) Sintered tube. b) Perforated
tube. c) Perforated plate ......................................................................................................... 18
Figure 1.8. HTCs vs. film Re number in a single array, as described in reference [21], and
bundle effect, as observed in reference [11] .......................................................................... 21
Figure 1.9. Tube bundle with liquid catchers, as described in references [64,65]. ..................... 23
Figure 1.10. Tube bundles with interior spraying tubes. a) Triangular-pitch (reference [69]). b)
Square-pitch (reference [70]) ................................................................................................. 24
Figure 2.1. Experimental test rig for condensation and pool boiling experiments ...................... 34
Figure 2.2. Isometric view of the experimental test rig model ..................................................... 35
Figure 2.3. Photographs of the experimental facility. a) Front. b) Back ...................................... 35
Figure 2.4. Sketch of the experimental test rig............................................................................ 36
Figure 2.5. Viewing and recording process for pool boiling and spray evaporation tests ........... 38
Figure 2.6. a) Circular wide angle full cone nozzles chosen. b) Nozzles connected to the
distribution tube ...................................................................................................................... 39
Figure 2.7. Nozzle-tube system. a) Front view. b) Top view ....................................................... 40
Figure 2.8. Optimal distance between two adjacent nozzles, for the considered tube and
distance .................................................................................................................................. 41
Figure 2.9. Main screen of the programme developed in LabVIEW 8.5 ..................................... 43
Figure 2.10. Plain tubes used. a) Copper tube. b) Titanium tube ............................................... 44
Figure 2.11. Photographs of the Turbo-B tube. a) External surface. b) Cross section ............... 44
Figure 2.12. Photographs of the Turbo-BII+ tube. a) External surface. b) Cross section ........... 45
Figure 2.13. Photographs of the Trufin 32 f.p.i. tube. a) External surface. b) Cross section ...... 46
Figure 3.1. Original Wilson plot ................................................................................................... 51
Figure 3.2. Types of spray evaporation tests. Left, liquid refrigerant on the tube directly from the
nozzle (ST tests). Right, liquid refrigerant from a conditioning tube (SB tests) ..................... 54
Figure 3.3. Nozzle-tube system. a) Front view. b) Top view ....................................................... 58
Figure 3.4. Optimal distance between two adjacent nozzles, for the considered tube and
distance .................................................................................................................................. 59
Figure 3.5. Heat flow at the condenser vs. heat flow at the evaporator of R134a pool boiling
experiments developed with the cooper plain tube at the evaporator ................................... 62
Figure 3.6. Heat flow at the condenser vs. heat flow at the evaporator of R134a pool boiling
experiments developed with the cooper Turbo-B tube at the evaporator .............................. 63
V
Figure 3.7. Heat flow at the condenser vs. heat flow at the evaporator of R134a pool boiling
experiments developed with the cooper Turbo-BII+ tube at the evaporator .......................... 63
Figure 3.8. Electric power at the electric boiler vs. heat flow at the evaporator obtained at the
specific validation experiments under pool boiling of ammonia and with a titanium plain tube
................................................................................................................................................ 64
Figure 3.9. Electric power at the electric boiler vs. heat flow at the evaporator obtained at the
ammonia pool boiling experiments with a titanium plain tube ................................................ 65
Figure 3.10. Electric power at the electric boiler vs. heat flow at the evaporator obtained at the
ammonia pool boiling experiments with a titanium Trufin 32 f.p.i. ......................................... 65
Figure 3.11. Electric power at the electric boiler vs. heat flow at the evaporator obtained at the
R134a spray evaporation experiments with a copper plain tube ........................................... 66
Figure 3.12. Electric power at the electric boiler at the electric boiler vs. heat flow at the
evaporator obtained at the ammonia spray evaporation experiments with a titanium plain
tube ........................................................................................................................................ 66
Figure 3.13. Temperature of the distributed liquid R134a vs. saturation temperature at the
pressure in the refrigerant tank .............................................................................................. 68
Figure 3.14. Temperature of the distributed liquid ammonia vs. saturation temperature at the
pressure in the refrigerant tank .............................................................................................. 68
Figure 3.15. Spray cone angles obtained with R134a and different distributed flow rates. a)
1000 kg/h. b) 1250 kg/h. c) 1500 kg/h.................................................................................... 69
Figure 3.16. Spray cone angles obtained with ammonia and different distributed flow rates. a)
450 kg/h. b) 550 kg/h. c) 650 kg/h. d) 750 kg/h. e) 850 kg/h ................................................. 70
Figure 4.1. Nukiyama boiling curve, Nichrome wire, d = 0.535 mm, water temperature = 100 °C
(reference [4]) ......................................................................................................................... 74
Figure 4.2. Heat flux on the outer surface of the copper plain tube vs. surface superheating,
under R134a pool boiling conditions, with the different saturation temperatures tested ....... 75
Figure 4.3. R134a pool boiling HTCs vs. heat flux on the outer surface of the copper plain tube,
with the different saturation temperatures tested ................................................................... 75
Figure 4.4. Section of the copper tube chosen for the roughness determination ....................... 76
Figure 4.5. R134a pool boiling HTCs obtained with correlations vs. experimental pool boiling
HTCs from this work, with a copper plain tube and under the same conditions .................... 78
Figure 4.6. Heat flux on the outer surface of the copper Turbo-B tube vs. surface superheating,
under R134a pool boiling conditions, with the different saturation temperatures tested ....... 79
Figure 4.7. R134a pool boiling HTCs vs. heat flux on the outer surface of the copper Turbo-B
tube, with R134a and with the different saturation temperatures tested................................ 80
Figure 4.8. Heat flux on the outer surface of the copper Turbo-BII+ tube vs. surface
superheating, under R134a pool boiling conditions, with the different saturation temperatures
tested ...................................................................................................................................... 81
Figure 4.9. R134a pool boiling HTCs vs. heat flux on the outer surface of the copper Turbo-BII+
tube, with the different saturation temperatures tested .......................................................... 81
Figure 4.10. R134a pool boiling HTCs vs. heat flux on the outer surface of the copper enhanced
tubes, both from our experimental results and from other works of the literature ................. 82
Figure 4.11. Surface enhancement factor vs. heat flux on the outer surface of the copper TurboB tube, with R134a and with the different saturation temperatures tested ............................ 84
Figure 4.12. Surface enhancement factor vs. heat flux on the outer surface of the copper TurboBII+ tube, with R134a and with the different saturation temperatures tested ........................ 84
Figure 4.13. Heat flux on the outer surface of the titanium plain tube vs. surface superheating,
under ammonia pool boiling conditions, with the different saturation temperatures tested ... 85
VI
Figure 4.14. Ammonia pool boiling HTCs vs. heat flux on the outer surface of the titanium plain
tube, with the different saturation temperatures tested .......................................................... 86
Figure 4.15. Ammonia pool boiling HTCs obtained with correlations vs. experimental pool
boiling HTCs from this work, with a titanium plain tube and under the same conditions ....... 87
Figure 4.16. Heat flux on the outer surface of the titanium plain tube vs. surface superheating,
under ammonia pool boiling conditions (10 ºC), with both decreasing and increasing heat flux
tests ........................................................................................................................................ 88
Figure 4.17. Ammonia pool boiling HTCs vs. heat flux on the outer surface of the titanium plain
tube, for both decreasing and increasing heat flux tests, at a pool temperature of 10 ºC ..... 88
Figure 4.18. Detail photographs of the ammonia pool boiling process on a titanium plain tube
with different heat fluxes on the outer surface and pool temperature of 10 ºC. a) 3300 W/m2.
b) 11000 W/m2. c) 19200 W/m2. d) 29900 W/m2. e) 42100 W/m2. f) 47900 W/m2 ................ 89
Figure 4.19. Unstable nucleation sites during an experiment at the transition between natural
convection and nucleate boiling (heat flux of 7700 W/m2) ..................................................... 90
Figure 4.20. Heat flux on the outer surface of the titanium Trufin 32 f.p.i. tube vs. surface
superheating, under ammonia pool boiling conditions, with the different saturation
temperatures tested ............................................................................................................... 91
Figure 4.21. Ammonia pool boiling HTCs vs. heat flux on the outer surface of the titanium Trufin
32 f.p.i. tube, with the different saturation temperatures tested ............................................. 92
Figure 4.22. Surface enhancement factor vs. heat flux if compared the titanium Trufin 32 f.p.i.
tube to the plain tube, with ammonia as refrigerant and with the different saturation
temperatures tested ............................................................................................................... 93
Figure 4.23. Heat flux on the outer surface of the titanium Trufin 32 f.p.i. tube vs. surface
superheating, under ammonia pool boiling conditions, with decreasing and increasing heat
flux tests and with the different saturation temperatures ....................................................... 94
Figure 4.24. Ammonia pool boiling HTCs vs. heat flux on the surface of the titanium Trufin 32
f.p.i. tube, for both decreasing and increasing heat flux tests, with the different saturation
temperatures .......................................................................................................................... 94
Figure 4.25. Temperatures of the pool of refrigerant and the heating water vs. time at the
special tests for studying the stability during hysteresis ........................................................ 95
Figure 4.26. Heat flux on the outer surface of the titanium Trufin 32 f.p.i. tube vs. surface
superheating, under ammonia pool boiling conditions (10 ºC), with decreasing and
increasing heat flux and hysteresis stability tests .................................................................. 95
Figure 4.27. Detail photographs of the ammonia pool boiling process on the titanium Trufin 32
f.p.i tube with different heat fluxes on the outer surface and pool temperature of 10 ºC. a)
3700 W/m2. b) 10200 W/m2. c) 17600 W/m2. d) 28400 W/m2. e) 38500 W/m2. f) 50600 W/m2
................................................................................................................................................ 97
Figure 5.1. Heat flux on the outer surface of the copper plain tube vs. surface superheating,
under R134a ST spray evaporation tests, with the different mass flow rates per side and per
meter of tube and with a refrigerant distribution temperature of 10 ºC ................................ 102
Figure 5.2. Spray evaporation HTCs vs. heat flux on the outer surface of the copper plain tube,
under R134a ST spray evaporation tests, with the different mass flow rates per side and per
meter of tube and with a refrigerant distribution temperature of 10 ºC ................................ 103
Figure 5.3. Heat flux on the outer surface of the copper plain tube vs. surface superheating,
under R134a SB spray evaporation test, with the different mass flow rates per side and per
meter of tube and with a refrigerant distribution temperature of 10 ºC ................................ 104
Figure 5.4. Spray evaporation HTCs vs. heat flux on the outer surface of the copper plain tube,
under R134a SB spray evaporation tests, with the different mass flow rates per side and per
meter of tube and with a refrigerant distribution temperature of 10 ºC ................................ 104
VII
Figure 5.5. Spray evaporation HTCs vs. heat flux on the outer surface of the copper plain tube,
under R134a ST and SB spray evaporation tests, with the different mass flow rates per side
and per meter of tube and with a refrigerant distribution temperature of 10 ºC ................... 105
Figure 5.6. Spray enhancement factors vs. heat flux on the outer surface of the copper plain
tube, under R134a ST spray evaporation tests, with the different mass flow rates per side
and per meter of tube and with a refrigerant distribution temperature of 10 ºC ................... 106
Figure 5.7. Spray enhancement factors vs. heat flux on the outer surface of the copper plain
tube, under R134a SB spray evaporation tests, with the different mass flow rates per side
and per meter of tube and with a refrigerant distribution temperature of 10 ºC ................... 106
Figure 5.8. Spray evaporation and pool boiling HTCs vs. heat flux of R134a on the outer surface
of a copper plain tube obtained by Moeykens [5] ................................................................ 107
Figure 5.9. Dripping active sites with R134a and the copper plain tube as a function of the mass
flow rate per side and per meter of tube, Γ, under nearly adiabatic conditions. a) Γ = 0.0093
kg/m·s. b) Γ = 0.0116 kg/m·s. c) Γ = 0.0139 kg/m·s ............................................................ 108
Figure 5.10. Dripping active sites with R134a and the copper plain tube as a function of heat
flux, q̇, with mass flow rate per side and per meter of tube, Γ = 0.0093 kg/m·s. a) q̇ = 4300
W/m2. b) q̇ = 12200 W/m2. c) q̇ = 27400 W/m2.................................................................... 109
Figure 5.11. Dripping active sites with R134a and the copper plain tube as a function of heat
flux, q̇, with mass flow rate per side and per meter of tube, Γ = 0.0139 kg/m·s. a) q̇ = 4400
W/m2. b) q̇ = 12700 W/m2. c) q̇ = 28200 W/m2.................................................................... 109
Figure 5.12. Dry patches on the copper plain tube with R134a. a) Γ = 0.0139 kg/m·s and q̇ =
4400 W/m2. b) Γ = 0.0139 kg/m·s and q̇ = 12700 W/m2. c) Γ = 0.0093 kg/m·s and q̇ = 20400
W/m2. c) Γ = 0.0093 kg/m·s and q̇ = 27400 W/m2................................................................ 110
Figure 5.13. Heat flux on the outer surface of the titanium plain tube vs. surface superheating,
under ammonia ST spray evaporation tests, with the different mass flow rates per side and
per meter of tube and with a refrigerant distribution temperature of 10 ºC .......................... 111
Figure 5.14. Spray evaporation HTCs vs. heat flux on the outer surface of the titanium plain
tube, under ammonia ST spray evaporation tests, with the different mass flow rates per side
and per meter of tube and with a refrigerant distribution temperature of 10 ºC ................... 112
Figure 5.15. Heat flux on the outer surface of the titanium plain tube vs. surface superheating,
under ammonia SB spray evaporation tests, with the different mass flow rates per side and
per meter of tube and with a refrigerant distribution temperature of 10 ºC .......................... 113
Figure 5.16. Spray evaporation HTCs vs. heat flux on the outer surface of the titanium plain
tube, under ammonia SB spray evaporation tests, with the different mass flow rates per side
and per meter of tube and with a refrigerant distribution temperature of 10 ºC ................... 114
Figure 5.17. Spray evaporation HTCs vs. heat flux on the outer surface of the titanium plain
tube, under ammonia ST and SB spray evaporation tests, with the different mass flow rates
per side and per meter of tube and with a refrigerant distribution temperature of 10 ºC ..... 115
Figure 5.18. Spray evaporation HTCs obtained with the correlation of Zeng and Chyu [8] vs. our
experimental spray evaporation HTCs with ammonia and a titanium plain tube ................. 116
Figure 5.19. Spray enhancement factors vs. heat flux on the outer surface of the titanium plain
tube, under ammonia ST spray evaporation tests, with the different mass flow rates per side
and per meter of tube and with a refrigerant distribution temperature of 10 ºC ................... 116
Figure 5.20. Spray enhancement factors vs. heat flux on the outer surface of the titanium plain
tube, under ammonia SB spray evaporation tests, with the different mass flow rates per side
and per meter of tube and with a refrigerant distribution temperature of 10 ºC ................... 117
Figure 5.21. Dripping active sites with ammonia and the titanium plain tube as a function of the
mass flow rate per side and per meter of tube, Γ, under adiabatic conditions. a) Γ = 0.0042
kg/m·s. b) Γ = 0.0061 kg/m·s. c) Γ = 0.0078 kg/m·s ............................................................ 118
Figure 5.22. Dripping active sites with ammonia and the titanium plain tube as a function of heat
flux, q̇, with mass flow rate per side and per meter of tube, Γ = 0.0051 kg/m·s. a) q̇ = 10000
W/m2. b) q̇ = 24800 W/m2. c) q̇ = 38800 W/m2.................................................................... 118
VIII
Figure 5.23. Dripping active sites with ammonia and the titanium plain tube as a function of heat
flux, q̇ with mass flow rate per side and per meter of tube, Γ = 0.0071 kg/m·s. a) q̇ = 10200
W/m2. b) q̇ = 25600 W/m2. c) q̇ = 44400 W/m2.................................................................... 119
Figure 5.24. Dry patches on the titanium plain tube with ammonia. a) Γ = 0.0042 kg/m·s and q̇ =
0 W/m2. b) Γ = 0.0042 kg/m·s and q̇ = 35200 W/m2. c) Γ = 0.0071 kg/m·s and q̇ = 0 W/m2. c)
Γ = 0.0071 kg/m·s and q̇ = 44400 W/m2 .............................................................................. 119
Figure 5.25. Nucleate boiling and bubbles entrained by drops on the titanium plain tube with
ammonia. a) Γ = 0.0051 kg/m·s and q̇ = 31700 W/m2. b) Γ = 0.0061 kg/m·s and q̇ = 33000
W/m2. c) Γ = 0.0071 kg/m·s and q̇ = 34600 W/m2. c) Γ = 0.0078 kg/m·s and q̇ = 44300 W/m2
.............................................................................................................................................. 120
Figure 6.1. Combined liquid distribution system and liquid-vapour separator from reference [1]
.............................................................................................................................................. 124
Figure 6.2. Distribution system proposed in patent US 2014/0366574 A1 [6] .......................... 125
Figure 6.3. Representation of the spray cone produced by a spray nozzle and coordinate
systems used throughout the study ..................................................................................... 127
Figure 6.4. Representation of a nozzle spreading refrigerant on a general tube ...................... 128
Figure 6.5. Position between adjacent nozzles. a) Distance greater than the optimal. b) Distance
lower than the optimal .......................................................................................................... 129
Figure 6.6. Optimal distance between adjacent nozzles ........................................................... 130
Figure 6.7. Position between adjacent nozzles of multi nozzle systems. a) Nozzles in a square
nozzle pattern. b) Squares in a equilateral triangle nozzle pattern ...................................... 132
Figure 6.8. Recalculation of the position between adjacent circular nozzles and their nozzle
systems ................................................................................................................................ 134
Figure 6.9. Theoretical limit angles from a given nozzle to a generic tube ............................... 136
Figure 6.10. Effect of the nozzle angle on the limit angles from a nozzle to a generic tube ..... 137
Figure 6.11. Effect of the interaction between tubes on the limit angles from a nozzle to a
generic tube.......................................................................................................................... 138
Figure 6.12. Definition of the real limit tube angles from the real spray limit angles................. 138
Figure 6.13. Representation of the differential area of a tube accessible from a nozzle .......... 140
Figure 6.14. Position and numbering of the tubes in the bundle. a) Inline tube pattern. b)
Staggered tube pattern ........................................................................................................ 142
Figure 6.15. Flow chart of the calculation process of the programme ...................................... 143
Figure 6.16. 3D-plot of the tube bundle, the shell and the spray cones for each solution ........ 144
Figure 6.17. 2D representation of the real limit angles for each tube of the bundle and for a
representative nozzle of each nozzle system ...................................................................... 144
Figure 6.18. Percentage of the total flow rate distributed that reaches the inline tube bundles
considered, as a function of the number of nozzle systems, the horizontal pitch of the tube
bundle and the cone angle of the spray nozzles.................................................................. 147
Figure 6.19. Percentage of the total flow rate distributed that reaches the staggered tube
bundles considered, as a function of the number of nozzle systems, the horizontal pitch of
the tube bundle and the cone angle of the spray nozzles.................................................... 147
Figure 6.20. Optimal distance between the first row of tubes and the nozzles (spray cone origin)
as a function of the number of nozzle systems, the horizontal pitch of the tube bundle and
the cone angle of the spray nozzles..................................................................................... 148
Figure 6.21. Optimal number of nozzles of the whole distribution system as a function of the
number of nozzle systems, the horizontal pitch of the tube bundle and the cone angle of the
spray nozzles ....................................................................................................................... 149
IX
Figure 6.22. Dimensionless column factor vs. the numbering of the column of tubes, for an inline
pattern bundle with horizontal pitch of 1.25 and vertical pitch of 1.25, and as a function of the
number of nozzle systems and the cone angle of the spray nozzles .................................. 150
Figure 6.23. Dimensionless column factor vs. the numbering of the column of tubes, for an inline
pattern bundle with horizontal pitch of 1.5 and vertical pitch of 1.5, and as a function of the
number of nozzle systems and the cone angle of the spray nozzles .................................. 150
Figure 6.24. Dimensionless column factor vs. the numbering of the column of tubes, for an inline
pattern bundle with horizontal pitch of 2 and vertical pitch of 2, and as a function of the
number of nozzle systems and the cone angle of the spray nozzles .................................. 151
Figure 6.25. Dimensionless column factor vs. the numbering of the column of tubes, for a
staggered pattern bundle with horizontal pitch of 1.25 and vertical pitch of 1.08 (60º angle),
and as a function of the number of nozzle systems and the cone angle of the spray nozzles
.............................................................................................................................................. 151
Figure 6.26. Dimensionless column factor vs. the numbering of the column of tubes, for a
staggered pattern bundle with horizontal pitch of 1.5 and vertical pitch of 1.3 (60º angle), and
as a function of the number of nozzle systems and the cone angle of the spray nozzles ... 152
Figure 6.27. Dimensionless column factor vs. the numbering of the column of tubes, for a
staggered pattern bundle with horizontal pitch of 2 and vertical pitch of 1.73 (60º angle), and
as a function of the number of nozzle systems and the cone angle of the spray nozzles ... 153
Figure 6.28. Dimensionless column factor vs. the numbering of the column of tubes, for a
staggered pattern bundle with horizontal pitch of 2 and vertical pitch of 1 (45º angle), and as
a function of the number of nozzle systems and the cone angle of the spray nozzles ........ 153
X
List of Tables
Table 1.1. Review of experimental works on falling film evaporation intertube flow patterns and
falling film breakdown. .............................................................................................................. 5
Table 1.2. Review of experimental works on falling film evaporation HTCs ............................... 17
Table 2.1. Main characteristics of the chosen spray nozzles ...................................................... 39
Table 2.2. Features and accuracy of the different sensors used ................................................ 42
Table 2.3. Geometrical characteristics of the 3D microfinned tubes........................................... 45
Table 2.4. Geometrical characteristics of the Trufin 32 f.p.i. tube............................................... 46
Table 3.1. Average and maximum deviation between the heat flows determined in the
experiments with the copper tubes and R134a under pool boiling; and average and
maximum uncertainties of these heat flows ........................................................................... 64
Table 3.2. Average and maximum deviation between the electric power and the heating water
heat flow determined in the experiments with the titanium tubes and ammonia under pool
boiling; and average and maximum uncertainties of the electric power and heat flow .......... 67
Table 3.3. Average and maximum deviation between the electric power and the heating water
heat flow determined in the experiments with the cooper and titanium tubes under spray
evaporation; and average and maximum uncertainties of the electric power and heat flow . 67
Table 4.1. Mean roughness height, Ra, per profile and arithmetic mean of Ra for the 10 profiles
................................................................................................................................................ 76
Table 4.2. Comparison of the experimental pool boiling HTCs (R134a and copper plain tube)
with those calculated with correlations ................................................................................... 78
Table 4.3. Comparison of the experimental pool boiling HTCs determined with R134a and the
copper Turbo-B tube with those from studies obtained with boiling enhanced tubes............ 83
Table 4.4. Comparison of the experimental pool boiling HTCs determined with R134a and the
copper Turbo-BII+ tube with those from studies obtained with boiling enhanced tubes ....... 83
Table 4.5. Comparison of the experimental pool boiling HTCs (ammonia and titanium plain tube)
with those calculated with correlations ................................................................................... 87
Table 6.1. RAuseless as a function of the nozzle pattern and the number of nozzle systems ..... 133
Table 6.2. Horizontal and vertical pitches analysed in the parametric analysis ........................ 146
Table 6.3. Maximum dimensionless column factor for each inline tube bundle as a function of
the horizontal and vertical pitch, the number of nozzle systems and the cone angle of the
spray nozzles ....................................................................................................................... 154
Table 6.4. Maximum dimensionless column factor for each staggered tube bundle as a function
of the horizontal and vertical pitch, the number of nozzle systems and the cone angle of the
spray nozzles ....................................................................................................................... 154
XI
XII
Nomenclature
ROMAN SYMBOLS
A
Area (m2)
a
Uncertainty range of a sensor
cp
Specific heat capacity of the liquid (J/kg·K)
d
Diameter (m)
dist
Distance (m)
f
Function
FS
Full scale
G
Total effective acceleration (m/s2)
g
Gravity acceleration (m/s2)
h
Heat transfer coefficient (W/m2·K)
hlv
Latent heat of vaporization (J/kg)
k
Thermal conductivity (W/m·K)
L
Tube length (m)
M
Molar mass (kg/mol)
ṁ
Mass flow rate (kg/s)
m(z)
Projected dimension (m)
n
Number (dimensionless)
O
Origin of a spray cone
P
Tube pitch (m)
PD
Pressure drop (Pa)
p
Pressure (Pa)
q
Heat flow (W)
q̇
Heat flux (W/m2)
q̇idp
Breakdown criterion heat flux (W/m2)
R
Thermal resistance (K/W)
r
Radius (m)
r(z)
Projected dimension (m)
Ra
Average height roughness (µm)
Rp
Peak roughness (µm)
s
Tube spacing, distance from the nozzle to the top of the tube (m)
T
Temperature (ºC, K)
u
Velocity (m/s)
XIII
u(xk)
Uncertainty of a general physical magnitude
v
Volumetric flow rate (m3/s)
w
width (m)
x
Distance along the heating surface (m)
xk
General physical magnitude
z'
Distance from the nozzle to the tangents on the tube (m)
GREEK SYMBOLS
α
Spray angle in the XZ plane (º, rad)
β
Nozzle angle (º, rad), contact angle (º)
γ
Deflection angle (º), thermal diffusion rate (m2/s)
Γ
Film flow rate at each side of the tube per meter (kg/m·s)
δ
Film thickness (m)
ζ
Volumetric film flow rate at one side per meter of tube (m3/m·s)
θ
Deflection critical angle, spray angle in parallel plane to Z=0 (º, rad)
λ
Instability wavelength, distance between adjacent jets/droplets (m)
μ
Dynamic viscosity (Pa·s)
ν
Kinematic viscosity (m2/s)
ξ
Capillary constant (m)
ρ
Density (kg/m3)
σ
Surface tension (N/m)
φ
Spray angles translated to the tube (º, rad)
Φ
Angular position at the tube (º)
FITTING CONSTANTS
a1, a2
Equation (1.19)
b1, b2, b3, b4
Equation (1.21)
C
Equation (3.5)
cw
Equation (4.3)
e1, e2
Equation (1.29)
f1, f2
Equation (1.33)
i1, i2, i3, i4
Equation (1.67)
j1, j2
Equation (1.72)
m1, m2
Equation (1.74)
n
Equation (1.7)
o1, o2
Equation (1.76)
XIV
SUBSCRIPTS AND SUPERSCRIPTS
array
Array of tubes
b
Boiling
bdl
Bundle of tubes
boiler
Boiler
bubble
Bubble
bulk
Bulk
cl
Column
const
Constant
crit
Critical
cw
Cooling water
dist
Distributed
div
Division
dr
Drop
dry
Dry
dryout
Dryout
e
Evaporation
en
Enhanced
end
End
evap
Evaporator
f
Film
fd
Fully developed
ff
Falling film
foul
Fouling
g
Gas
hor
Horizontal
i
Inner
im
Impingement
in
Inlet
j
Jet
l
Liquid
lim
Limit
max
Maximum
n
Reduced velocity exponent
nozzle
Nozzle
XV
o
Outer
opt
Optimal
out
Outlet
ov
Overall
p
Primary drops
pb
Pool boiling
peak
Peak
pl
Plain
proj
Projected
r
Row
real
Real
rec
Recalculated
red
Reduced
s
Saturation
sensor
Sensor
sf
Surface
SH
Superheating
sp
Spray
st
Stagnation
sys
System
t
Tube
td
Thermal developing
th
Theoretical
threshold
Dryout onset
top
Top
total
Total
u
Unstable
useful
Useful
useless
Useless
v
Vapour
ver
Vertical
w
Wall
wet
Wet
x
Distance along the heating surface
*
Dimensionless
XVI
―
Average
DIMENSIONLESS NUMBERS
B
Empirical bundle factor (dimensionless)
c
Primary drop constant (dimensionless)
cd
Drag coefficient (dimensionless)
F
Wet area fraction (dimensionless)
Fcol
Column factor (dimensionless)
Gt-s
Tube specific factor (dimensionless)
Ga*
Modified Galileo number (dimensionless)
K
Transition dimensionless number (dimensionless)
Kff
Falling film multiplier (dimensionless)
Kmidp
Breakdown criterion (dimensionless)
Kp
Liquid film superheat parameter (dimensionless)
Nu
Nusselt number (dimensionless)
OF
Overfeed ratio (dimensionless)
Pr
Prandtl number (dimensionless)
pred
Reduced pressure (dimensionless)
RAuseless
Useless area fraction (dimensionless)
Re
Reynolds number (dimensionless)
RPF
Row performance factor (dimensionless)
STC
Sieder and Tate correlation constant (dimensionless)
Θ
Dimensionless heat flux (dimensionless)
Λ
Dimensionless length scale (dimensionless)
XVII
XVIII
Chapter 1
Introduction
Refrigeration cannot stay aside from the environmental and energy challenges that
humanity is about to face in the coming years. Montreal’s Protocol and later revisions marked
the beginning of usage restrictions of CFCs and HCFCs, due to environmental issues such as
ozone layer depletion. R134a and other HFCs will be soon phased out due to their global
warming potential (GWP). Natural refrigerants such as CO2, ammonia or hydrocarbons appear
as interesting alternatives from environmental and performance points of view. The high
pressures of CO2 systems, the toxicity of ammonia or the flammability of hydrocarbons are
important disadvantages of these fluids [1]. Natural refrigerants combined with more efficient
systems should be the investigation line followed in the future.
Falling film evaporators, also known as spray evaporators, have been widely employed in
petrochemical industry, desalination processes and OTEC (Ocean Thermal Energy Conversion)
systems. The experience in other fields such as heat pumps and refrigeration is limited, but
falling film evaporators should outperform flooded evaporators in terms of refrigerant charge
reduction and heat transfer improvement [2].
The sections included in the introduction to this thesis focus on horizontal-tube falling film
evaporators for its use in refrigeration heat exchangers. It includes a short description of these
evaporators, as well as their advantages and disadvantages compared with flooded
evaporators. It continues explaining the conclusions of works concerning falling film shape on
tubes, intertube flow patterns and breakdown of this falling film. An overview is included of
experimental and theoretical works on shell-side heat transfer coefficients (HTCs) in falling film
evaporators as a function of parameters such as heat flux, distribution system, etc.
Experimental works also compare spray evaporation and pool boiling. This chapter finishes with
some general considerations that could be helpful in the design of falling film evaporators.
1
Chapter 1
1.1.
Introduction
FALLING FILM EVAPORATION
Falling film evaporators in refrigeration systems are heat exchangers with a shell-and-tube
structure, as shown in Figure 1.1. Spray nozzles or other spreading devices distribute liquid
refrigerant over the first rows of tubes of a tube bundle. Part of the refrigerant boils on the top
row, cooling the fluid flowing inside the tubes, and the rest forms a film that flows to the
following row. This boiling and flowing process occurs from one row to the next one. The
exceeding refrigerant is collected at the bottom of the evaporator and recirculated to the
distribution unit (with intermediate conditioning steps if needed).
Figure 1.1. Horizontal tube falling film evaporator
The falling film evaporation process is controlled by two heat transfer mechanisms, which
can co-exist. Conduction and/or convection across the liquid film control the process at low heat
fluxes, being the heat transfer performance a function of the film thickness and regime (laminar
or turbulent). Nucleate boiling, which improves the performance of the process, occurs at heat
fluxes over an onset value. Bubbles form right beside the heat exchange surface and run
through the refrigerant film until they reach the interface.
2
Chapter 1
Introduction
1.2.
FALLING FILM EVAPORATOR VS. FLOODED EVAPORATOR: ADVANTAGES AND
DISADVANTAGES
The main difference between falling film and flooded evaporators lies in how the shell-side
liquid reaches the external surface of tubes. In the former, the refrigerant is distributed on the
tube bundle by spray nozzles or another distribution device, and in the latter, the tubes are
immersed in a liquid refrigerant pool. This difference explains several advantages of falling film
evaporators over flooded evaporators, such as:






Lower refrigerant charge is needed, interesting in operation costs and safety.
Higher HTCs can be achieved.
The boiling temperature increase caused by hydrostatic head in flooded evaporators is
avoided.
The closer temperature approach between refrigerant and cooled fluid improves the
cycle thermodynamic efficiency.
Smaller size evaporators can be designed.
Oil removal is simpler.
Falling film evaporators present as well some disadvantages, which are listed below:




A special liquid distribution system is needed and should guarantee the complete
wetting of the tube bundle with low overfeed degree, to minimize the refrigerant charge
and the pumping power consumption.
The vapour refrigerant flow could affect the distribution and cause dry patches (film
breakdown).
If dry patches occur, HTCs diminish significantly.
The design experience for falling film evaporators is insufficient.
The design of a falling film evaporator in reference [2], for its use in a chemical plant to
replace a flooded evaporator, illustrates these potential advantages. A more compact shell-andtube evaporator was obtained, with less tubes, smaller diameter, half its building cost and
approximately 20 times less charge of ammonia. Freeze-up was also avoided and a closer
temperature approach achieved.
3
Chapter 1
1.3.
Introduction
FALLING FILM AROUND HORIZONTAL TUBES
The refrigerant falling film that forms on the evaporator tubes cools the fluid that flows inside
them by evaporating part of this refrigerant. Figure 1.2 depicts the theoretical physical model of
a falling film (laminar regime) around a horizontal tube. Moalem and Sideman [3] stated that the
thickness of the film is maximum at the stagnation point, decreases with Φ, is minimum at
Φ = 90º and increases again when approaching the bottom of the tube. For the mass transfer in
the film they noted the tendency is the opposite. Sideman et al. [4] defended that mass transfer
is almost independent of the angular position on the tube and assume that an incorrect initial
value of mass transfer at the stagnation point was considered in reference [3].
Figure 1.2. Falling film evaporation, simplified model as described in [4]
The falling film thickness theoretical approach from reference [3] was confirmed by Jafar et
al. [5], where the results of numerical simulations developed with CFD software are shown. The
authors of references [6,7] included two expressions, obtained from a numerical study, to
calculate the mean velocity in the film, (1.1), and the film thickness, (1.2), as a function of the
angular position. Their results agreed with those from the works previously mentioned but were
greater than their own experimental values. Neglecting the effect of heat loss and entrainment
in the numerical study was the reason for this difference, according to the authors.



 

u  g  l -  g sin  4  l rt  sin 


    4  l  rt g  l -  g sin  2
4
(1.1)
(1.2)
Chapter 1
1.4.
Introduction
HORIZONTAL INTERTUBE FALLING FILM
This section explains the most important issues on intertube falling films in horizontal shelland-tube evaporators. Experimental works concerning this topic have been listed in Table 1.1.
Table 1.1. Review of experimental works on falling film evaporation intertube flow patterns and
falling film breakdown.
Author(s)
Fluid(s)
Tube(s)
Notes
Mitrovic [8]
Isopropyl alcohol,
Water
Plain
Three intertube flow modes (droplet, column and
sheet). Transitions between them.
Hu and Jacobi [9,10]
Water, 2 ethylene
glycol solutions,
hydraulic oil, ethyl
alcohol
Plain
Five intertube flow modes (droplet, droplet-column,
column, column-sheet and sheet). Correlations for the
transitions experimentally determined, Ref=a1·Ga*a2.
Active site distance depends on film flow rate, fluid
properties and intertube distance.
Habert [11]
R134a, R236fa
Plain, condensation
(Wieland Gewa-C+LW),
two boiling (Wieland
Gewa-B4, Wolverine
Turbo-EDE2)
Falling film breakdown determination based on heat
transfer results [40].
Correlation for the onset of breakdown. Negligible
effect of refrigerant on breakdown onset. Enhanced
tubes delay falling film breakdown.
Christians [12]
R134a, R236fa
2 boiling (Wolverine
Turbo-B5, Wieland
Gewa-B5)
Negligible effect of saturation temperature, tube or
refrigerant on flow mode transitions. Measured active
sites separation, between λc and λu.
Falling film breakdown determination as [10,40].
Ref,threshold correlation includes a tube geometric factor.
Isopropyl alcohol,
Water
Plain
Active site distance correlation, includes the effect of
tube diameter.
Subcooled distilled
water
Plain
Tube spacing and falling film flow rate affect flow
patterns, but not active site distance. Site distances
smaller than those predicted by Taylor instability.
Breakdown heat flux increases with Ref and tube
spacing.
Highly viscous silicone
oils
Plain
Active site distances for highly viscous fluids greater
than theoretical.
Yung et al. [16]
Water, ethyl alcohol,
ammonia
Plain
Formula to define the most likely wavelength (active
site distance). n=2 thin film, n=3 thick films. Flow mode
transition between droplet and column modes,
depends on the fluid. Study entrainment causes.
Honda et al. [17]
R113, methanol, npropanol
Bundle of low-finned
tubes
Study of transitions between flow modes. Definition of
transition dimensionless number, K.
Water-ethylene glycol
solutions
Plain, three low-finned,
two boiling and three
condensation
Flow maps and transition correlations based on
Ref=a1·Ga*a2.
R134a
Plain, three boiling
(Wolverine TurboBIIHP, Wieland GewaB, UOP High-Flux)
Flow patterns analysis under adiabatic and nonadiabatic conditions. Transitions difficult to identify due
to low viscosity of refrigerant. Transitions affected by
nucleate boiling.
Falling film breakdown varies with heat flux and film
Reynolds number. Visual determination. Correlations
that relate Ref and qf,dryout.
Water, 10% aqueous
ethyl alcohol solution,
FC72
Vertical plate
Falling
film
breakdown
caused
mainly
by
thermocapillary forces. Breakdown dimensionless
number definition, function of Ref.
Water, ethanol
Plain, porous
Porous surface prevents from the formation of dry
patches.
R11
Plain
Falling film breakdown study in a tube bundle. Dry
patches in bottom tubes first (receive less flow rate
due to evaporation). Correlation for the breakdown
heat flux.
R134a
Plain
Developed the criterion to determine falling film
breakdown through heat transfer results. Correlation to
predict Ref,threshold.
Armbruster
Mitrovic [13]
and
Ganic and Roppo [14]
Taghavi-Tafreshi
Dhir [15]
and
Roques et al. [18-20]
Roques [21]
Zaitsev et al. [22]
Ganic and Getachew
[23]
Fujita and Tsutsui [24]
Ribatski
[25]
1.4.1.
and
Thome
Flow patterns
As aforementioned, in horizontal tube falling film evaporators, refrigerant is distributed to the
top row of tubes, forms films around the tubes and falls to the following rows. The flow between
5
Chapter 1
Introduction
a row and the next is called intertube flow and its flow pattern is of great importance since it
affects the falling film HTCs and the appearance of dry patches. Mitrovic [8] classified the
existing flow patterns into three: droplet mode (Figure 1.3a), with intermittent flow of fluid
between tubes; jet mode (Figure 1.3d), with discrete intertube continuous columns of liquid; and
sheet mode (Figure 1.3f), with an unbroken film of liquid between consecutive tubes. He stated
that the existence of one or another flow rate depends on film flow rate, liquid properties and
intertube distance. Hu and Jacobi [9] classified them into five groups: droplet mode (Figure
1.3a), droplet-column mode (Figure 1.3b), column mode (inline type in Figure 1.3c and
staggered type in Figure 1.3d), column-sheet mode (Figure 1.3e) and sheet mode (Figure 1.3f).
The division between inline and staggered column mode was first seen in this work.
Figure 1.3. Intertube flow patterns in Hu and Jacobi [9]. a) Droplet mode. b) Droplet-column mode.
c) Inline column mode. d) Staggered column mode. e) Column-sheet mode. f) Sheet mode
1.4.1.1. Sheet mode
According to references [9,11], the sheet mode is the most convenient for falling film
evaporation, because it involves a lower probability of dry patch formation and higher HTCs. In
the same line, Christians [12] states that the optimum from a flow pattern perspective is to
choose a refrigerant that achieves the sheet mode at the lowest Reynolds number. However,
sheet mode requires more energy to feedback the excess liquid to the distributor. Sideman et
al. [4] determined analytically and experimentally the mass transfer rate of a sheet intertube flow
and saw it depended slightly on the film Reynolds number up to 600. Experimental results
showed an increase of these average mass transfer rates for higher Reynolds numbers.
Sideman and co-workers observed that increasing the intertube spacing changes the sheet to
droplet mode, but the average mass transfer coefficient is multiplied by two.
1.4.1.2. Active site spacing in droplet and jet modes
In droplet and jet modes, the flow occurs at fixed-spaced active sites. The distance between
them affects heat transfer of an evaporator. Even though droplet mode and jet mode are welldifferenced flow patterns, the separation between active sites in both cases has been identically
6
Chapter 1
Introduction
explained by the Taylor instability theory. Taylor instability appears between two fluids of
different densities, when the lighter fluid pushes the heavier. According to reference [26], if the
wavelength of the perturbation is lower than a critical wavelength, surface tension stabilises this
perturbation. Equation (1.3) defines the critical wavelength, λc, for planar geometries. The
fastest growth of a perturbation happens for the most unstable wavelength (also called most
dangerous wavelength), λu, which is related to the λc by a constant ( 3 according to reference
[26]). Hu and Jacobi [9,10] expect that λu is the distance between active sites (λ in Figure 1.3).
Armbruster and Mitrovic [13] proposed a different correlation for λ, (1.4), which predicted the
results they obtained experimentally within ±7.5%, and depended on the film Reynolds and
modified Galileo numbers. Ref and Ga* general definitions are (1.5) and (1.6), respectively.
However, Armbruster and Mitrovic [13] defined their film Reynolds number as half this value.
 

c   G  l -  g 1 2
  u  2 2
(1.3)
g  l -  g   1 Ref

Ga * 0.25 

0.8 
  2 d2
t


(1.4)
Re  4  
(1.5)
Ga *    3   4 g 


(1.6)
Sideman et al. [4] determined experimentally that, with Reynolds numbers under 150, the
average distance between drop-formation sites increased. For greater Ref and complete wetting
of the tube, the distance remained practically constant. This distance also increased with
increasing surface tension, drop frequency and distance between tubes according to reference
[27]. In contrast, Ganic and Roppo [14] stated that tube spacing or falling film flow rate affected
flow patterns but not the separation between active sites. They also observed smaller
separations than those calculated by Taylor instability theory. In contrast, Taghavi-Tafreshi and
Dhir [15] concluded that the wavelength values with high viscosity fluids were greater than those
predicted (calculated for inviscid fluids). Yung et al. [16] proposed a different formula for λ with
inviscid fluids, (1.7), where n is 2 for thin liquid films and 3 for thick liquid films. Equations (1.8)
and (1.9), included in reference [28], are two formulae for λc and λu, respectively, that neglect the
effect of vapour density and define new parameters such as the dimensionless tube radius rt*
(1.10) and the dimensionless wavelength λ* (1.11). ξ stands for the capillary constant (1.12).
  2 n   l g 
*c  2
2 

1  1  2 rt* 


1.491
2.16  3 0.467 rt*
*
u 
*c
1.491
1  0.467 rt*
(1.7)
(1.8)
(1.9)
rt*  rt 
(1.10)
*   
(1.11)
7
Chapter 1
Introduction
   g 
(1.12)
Hu and Jacobi [9] noted that the spacing between droplets or jets increases with increasing
tube diameter, decreases with increasing falling film flow rate and depends on the fluid
properties. Intertube distance causes first a reduction of the spacing between active sites and
then an increase, according to the same work. The results calculated by equation (1.7)
overpredicted their experimental results and in reference [10], Hu and Jacobi suggested
correlations function of film Reynolds and modified Galileo numbers. They proposed (1.13) with
Ref under 50, (1.14) with Ref over 100, and a general correlation, (1.15). Λ stands for the
dimensionless length scale, defined by equation (1.16). The experimental and numerical results
obtained by Jafar et al. [29] followed the trend described by Hu and Jacobi [10]. However, they
stated that the spacing between active sites decreases with increasing tube diameters.
*  0.836  - 0.863 Re f Ga *
*  0.75  - 85 Ga *
* 
14
(1.13)
14
0.836  - 0.863 Re f Ga *
(1.14)
14
 
14
  0.836  - 0.863 Re f Ga *
1

 
14
 
0.75  - 85 Ga *

  2 3





1 12
2




2 

1  1  2 rt* 


(1.15)
(1.16)
Christians [12] measured as well the active site spacing for the column mode with two
boiling enhanced tubes (Wolverine [30] Turbo-B5 and Wieland [31] Gewa-B5) and two
refrigerants (R134a and R236fa) and observed that this spacing was between λc and λu. The
departure site distance was independent of the tube studied, but was higher for R236fa than for
R134a (probably due to the lower surface tension and viscosity of R236fa). His measurements
were accurately predicted by the correlations (1.7) of Yung et al. [16], and (1.15) of Hu and
Jacobi [10] (deviation inside ±3%).
1.4.1.3. Flow patterns in jet mode and shape of the jets
As aforementioned, Hu and Jacobi [9] were the first to classify the jet mode (column mode)
into staggered pattern, Figure 1.3d, and inline pattern, Figure 1.3c. They observed that inline
pattern appeared with lower Ref than staggered pattern. With staggered pattern, in agreement
with references [8,14], crests (zones of thicker liquid films) occur between two jet impingements,
and valleys (thinner films) appear beneath these impingements. With inline jet pattern, low
Reynolds numbers lead to crests beneath the impingements (valleys between them) and high
Reynolds numbers lead to a similar film but with a smaller crest between the impingement zone
and the valley. Hu and Jacobi [9] analysed the shape of the jets (diameter), and observed that it
decreased as the distance between tubes increased.
1.4.2.
Transition between flow modes
Transitions between different flow patterns have been widely studied, but no general flow
map exists. Yung et al. [16] presented a correlation for the falling film flow rate of transition
between droplet and jet mode, (1.17), function of the instability wavelength λ, (1.7), the diameter
of primary drops dp, (1.18), and a coefficient c that depends on the fluid (3 for water and
alcohol). In contrast, Dhir and Taghavi-Tafreshi [32] found independent the transition of the fluid
properties. Mitrovic [8] established the transition between droplet and jet modes at Reynolds
numbers of 150 – 200 and between jet and sheet modes at 315 – 600. This differs from the
8
Chapter 1
Introduction
value proposed by Moalem and Sideman [27] for droplet-jet transition, 430 – 650. Ganic and
Roppo [14] stated that this transition depends not only on falling film flow rate, but also on tube
spacing. Another issue detailed in several works such as [9,11-13,18,32] is that transitions
occur differently when the film flow rate increases and when it decreases, i.e. hysteresis exists.
However, hysteresis is negligible according to [33].
  0.81 l    d p3 6  2    l 3 




(1.17)
d p  c   l g 
(1.18)
Hu and Jacobi [9] obtained experimental transitions between falling film flow modes for five
different fluids and realised that they depended on four dimensionless numbers: film Reynolds,
Galileo, Ohnesorge and dimensionless tube spacing (ratio between tube spacing and tube
diameter). However, they developed correlations as (1.19) which only took into account Ref and
Ga*. For engineering use, considering no hysteresis or intermediate flow modes, a1 and a2 for
the sheet-jet transition are 1.431 and 0.234, respectively, and for the droplet-jet transition are
0.084 and 0.302, respectively.
Re f  a1 Ga *a2
(1.19)
Honda et al. [17] studied experimentally the transitions with horizontal low-finned tubes in a
tube bundle with R113, methanol and n-propanol. They defined a dimensionless number K,
(1.20), which has a value for each transition and is independent of tube separation. Roques and
co-workers [18-20] developed flow maps with different water-ethylene glycol mixtures, plain
tubes and several enhanced tubes, which were: 3 low-finned tubes (19, 26 and 40 f.p.i.), 2
boiling tubes (Wolverine [30] Turbo-BII HP and Wieland [31] Gewa-B) and 3 condensation tubes
(Wolverine [30] Turbo-CSL, Wieland [31] Gewa-C and Hitachi [34] Thermoexcel-C). The authors
correlated their results by formulae based on (1.19) and compared with the transition values of
references [9,17]. a1 depends on the dimensionless tube spacing, s/dt, as expressed in (1.21).
K  Γ g ρl 1 4 σ 3 4
(1.20)
a1  b1  b2 s d t   b3 s d t 2  b4 s d t 3
(1.21)
Roques [21] studied the flow pattern transitions of R134a, under adiabatic and nonadiabatic conditions, with a plain tube and three boiling enhanced tubes (Wolverine [30] TurboBII HP, Wieland [31] Gewa-B and UOP [35] High-Flux). He stated that the distinction between
flow modes was complicated due to the low viscosity of R134a. He also correlated his
experimental data with formulae based on (1.19). The perturbation in the falling film caused by
nucleate boiling affects transitions, being needed a greater falling film flow rate to achieve the
same flow mode as under adiabatic conditions. Similarly, Christians [12] analysed the
transitions between flow modes for R134a and R236fa with two boiling enhanced tubes
(Wolverine [30] Turbo-B5 and Wieland [31] Gewa-B5), at three saturation temperatures.
Transitions are almost independent of saturation temperature, type of tube and refrigerant,
except for that between column/sheet and sheet mode, which occurred at higher Reynolds
number with the Gewa-B5 than with the Turbo-B5.
Wang and Jacobi [36] developed a theoretical approach to determine flow mode transitions
based on the thermodynamic equivalence of two flow modes at their transition. Their results
show that the Reynolds number at which these transitions occur depends not only on Ga*, but
also on tube spacing. The authors used previous experimental data to support their work, but
they realised about its limitations concerning hysteresis or the boundary between staggered and
inline jet modes.
9
Chapter 1
1.4.3.
Introduction
Entrainment
Vapour-liquid interaction may modify the falling film inside a horizontal tube bundle and the
wetting of the tubes downstream, deteriorating the heat transfer performance of the tube
bundle. Yung et al. [16] classified the causes of liquid entrainment as follows:


Deflection entrainment. A perpendicular vapour flow affects intertube flow.
Nucleate boiling entrainment. Nucleate boiling vapour bubbles break the sheet into
drops and entrain them forming a mist.
Stripping entrainment. A vapour flow with enough speed destabilises the falling film and
carries the resulting drops.
Splashing entrainment. Vapour flow entrains the drops generated through the
impingement of the liquid at the top of the tube.


Yung et al. [16] studied deflection entrainment for droplet and column modes separately. In
the first case they defined a critical angle, θ, and a real deflection angle, γ; equations (1.22) and
(1.23), respectively (Figure 1.4). While γ is smaller than θ, drops from one tube impact on the
following one but the complete wetting of the tube is not assured. Making both deflection angles
equal, the maximum vapour flow velocity without deflection greater than θ, ug, is obtained, (see
equation (1.24)). Higher vapour velocities and droplet diameters may lead to atomization of
droplets, making easier droplet entrainment.
Figure 1.4. Droplet deflection entrainment as described in reference [16]

  tan 1 1 2 P d t P d t   11 2

  tan 1   g ug2 3  l d dr g 





u g  3  l d dr g 2  g 1 2 P d t P d t  11 4
(1.22)
(1.23)
(1.24)
When column flow pattern exists, columns are defined with an effective diameter (1.25) to
simplify the model (s stands for the intertube spacing and λ can be calculated by equation (1.7)
with n=2). The resulting maximum vapour crossflow velocity for deflection angles lower than θ is
calculated by equation (1.26).
10
Chapter 1
Introduction
* 
d cl
 8   l  1 2 2 g s 1 4
(1.25)
12
* c  
u g   4 tan    g  cos d cl
d g  



2 g s 1 4
(1.26)
According to Yung et al. [16], if γ > θ within a tube bundle, the entrained liquid may impinge
on adjacent tubes and no decrease of the heat transfer performance should be observed.
Ilyushchenko et al. [37] studied analytically and experimentally drop entrainment within a tube
bundle and outside it and observed that it depends on the operation parameters and the tube
bundle size.
Czikk [38] studied deflection and entrainment with sheet mode. He tested ammonia in a
heat exchanger and measured deflection angles varying vapour flow rates and film Reynolds
numbers. He defined the critical angle with the ratio of tube diameter to pitch.
11
Chapter 1
1.5.
Introduction
DRY PATCHES AND FALLING FILM BREAKDOWN
The appearance of dry patches, i.e. breakdown of the falling film, has been widely studied
due to its adverse effect on the heat transfer performance and stability of the flow at falling film
evaporators. For sake of simplicity, in Table 1.1 we have included the main ideas on falling film
breakdown of several works from the literature.
Hsu et al. [39] affirmed that dry patches occur due to the shear of vapour flows. When
boiling or evaporation exist, the film becomes thinner and breakdown may happen. Moreover,
the surface tension at the interface and its variation with temperature may also lead to the
destruction of the falling film. Hartley and Murgatroyd [40] developed an analytical study about
dry patches on flat surfaces and with isothermal conditions. They obtained the minimum film
thickness and falling film flow rate that assure no film breakdown using two criteria: force
balance at the stagnation point (G at Figure 1.5) and minimum power (energy) in a laterally
unrestrained liquid film. They also stated that contact angle affects the formation of dry patches
and minimum falling film flow rate.
Figure 1.5. Dry patch formation and film breakdown on a plate, as described in reference [40]
Hartley and Murgatroyd [40] applied both criteria to a laminar film flowing vertically under
gravity, a case for which experimental data were available. A good agreement existed between
the minimum flow rate and film thickness calculated by the power criterion and the experimental
data from Dukler and Bergelin [41]. The comparison was also acceptable with the results from
Bessler [42].
El-Genk and Saber [43] incorporated the velocity distribution and the profile of stable liquid
rivulets (the columns of liquid surrounding dry patches, Figure 1.5) into the analytical model.
Zuber and Staub [44] considered the effect of heat flux on the appearance of dry patches and
noted that the forces present in the stagnation point are associated to the turning of kinetic
energy into static pressure, to surface tension, to thermocapillary and to evaporation.
Hartley and Murgatroyd [40] had already considered the first two. Thermocapillary effect
occurs due to the temperature difference at the interface, which causes a non-uniformity of the
surface tension and movement along the free surface [39]. With evaporation, vapour sucks up
the liquid that surrounds it, enlarging dry patches. A force balance at the stagnation point led
Zauber and Staub [44] to the minimum film thickness and minimum falling film flow rate that
prevented from the appearance of dry patches; and to the maximum heat flux at a surface, for a
given film thickness and falling film flow rate, that could be applied without causing the film
breakdown. They also stated that the contact angle (wettability) determines which force is
12
Chapter 1
Introduction
mainly involved in the stability of dry patches. In contrast, Zaitsev et al. [22] observed that the
breakdown of the film depends on thermocapillary forces and neglected the effect of the contact
angle at non-isothermal conditions. They defined a breakdown dimensionless criterion, Kmidp,
which depends on the q̇idp and fluid properties; and correlated it by equation (1.27), which is a
function of film Reynolds number. q̇dp stands for the heat flux needed to cause the first stable
dry patch in the film.
Kmidp   q idp d dT   c p   g 2 3   0.155 Re0.65
f


(1.27)
The breakdown phenomenon was also studied in falling films on horizontal tubes. Ganic
and Roppo [14] determined experimentally the breakdown heat flux ranges for plain tubes with
subcooled water and observed that they increased with increasing film Reynolds numbers and
with tube spacing (if droplet mode or splashing were not present). Similar experiments are
described by Ganic and Getachew [23] for water and ethanol on horizontal plain and porous
tubes. The authors of this work stated that the porous surface maintained the tube wet for
higher heat flux values. They also explained the breakdown phenomenon with the
thermocapillary effect, stating that the lower local temperature (higher surface tension) available
in the crests than in the valleys provokes the fluid transfer from the valleys to the crests.
Ganic and Getachew [23] and Chen et al. [45] conclude that enhanced surfaces on tubes
prevent dry patches from appearing. Chen et al. [45] also stated that with enhanced vertical
tubes and R11, the breakdown heat flux remained constant with Ref. Falling film breakdown
was also studied by Fujita and Tsutsui [24]. They first observed dryout at the bottom rows of the
bundle, since less falling film flow rate reached them due to evaporation on tubes placed
upstream. They correlated their experimental results on breakdown heat flux by equation (1.28).
q dryout  0.048 Re f
(1.28)
Roques [21] tested a plain tube and three boiling enhanced tubes (Wolverine [30] Turbo-BII
HP, Wieland [31] Gewa-B and UOP [35] High-Flux) to determine the appearance of dry patches
varying heat flux and film Reynolds number. The author considered that, with a fixed heat flux,
the dryout Reynolds number was related to the appearance of a dry patch at the middle of the
tube. The dryout Reynolds number was correlated by formulae such as (1.29). However, it is
clear that the first dry areas should appear at even higher Reynolds numbers. Ref,threshold
(threshold Reynolds number) indicates the lowest Ref for which no sharp decrease of the HTCs
occurs, and was defined as two times Ref,dryout. Plain tubes suffered film breakdown at higher
Ref than the enhanced tubes, which agrees with the conclusions from references [23,24,45].
Ref,dryout  e1 q  e2
(1.29)
Ribatski and Thome [25] changed the threshold Reynolds number criterion. They focused
on the significant decrease of the HTCs when film breakdown occurs. Equation (1.30) defines
mathematically the criterion developed. Kff is the falling film multiplier, (1.31) and separates the
effect of dryout on the HTCs from the effect of heat flux. The authors correlated the
experimental Ref,threshold obtained with R134a and a plain tube using equation (1.32).
1 n

K ff , j
n j 1
 0.05
1 n
 j 1 K ff , j
n
K ff , j 
K ff  hff hpb
(1.30)
(1.31)
13
Chapter 1
3 2 
Ref,threshold  6.93·105 q  l  v  hlv


 
Introduction
0.47
(1.32)
Habert [11] extended the study of the threshold Reynolds number using two refrigerants
(R134a and R236fa) with a plain, a condensation enhanced tube (Wieland [31] Gewa-C+LW),
and two boiling enhanced tubes (Wieland [31] Gewa-B4 and Wolverine [30] Turbo-EDE2). He
determined Ref,threshold with the criterion developed by Ribatski and Thome [25]. He observed no
effect of the refrigerant on the Ref,threshold and a delay in film breakdown when using enhanced
tubes. Although his results fitted correlation (1.29), developed by Roques [21], this equation
mismatches the adiabatic case, for which the threshold Reynolds number should be 0. Habert
formulated correlations with the general form of (1.33), which takes better into account the effect
the refrigerant properties on the Ref,threshold than (1.32). For the Gewa-C+LW tube, the reduced
pressure was also included in (1.33), multiplying the right term of the equation.
Ref,threshold  f1 q d t  l hlv f2
(1.33)
Threshold Reynolds number and the appearance of dry patches were also studied by
Christians [12] with two boiling enhanced tubes (Wolverine [30] Turbo-B5 and Wieland [31]
Gewa-B5) and R134a and R236fa. The criterion employed to define Ref,threshold was basically
that from Ribatski and Thome [25] or Habert [11]. As Habert, Christians stated that the influence
of the refrigerant viscosity on the threshold Reynolds is greater than the influence of the
difference between the refrigerant liquid and vapour densities, used by Ribatski and Thome
[25]. Therefore, the correlation defined by Christians [12], (1.34), follows the form of (1.33),
adding a geometric factor, Gt-s, different for each tube. The geometric factors were determined
correlating the pool boiling experimental HTCs gathered in references [11,12,21].
Re f,threshold  20.721q d t  l hlv 1.04 Gt0.175
s
14
(1.34)
Chapter 1
1.6.
Introduction
HEAT TRANSFER COEFFICIENTS: THEORETICAL AND ANALYTICAL WORKS
According to most theoretical works, falling film evaporation HTCs depend on the film
thermal region analysed. Kocamustafaogullary and Chen [46] or Liu et al. [47] distinguished two
regions. The heat transfer performance differs between regions only for tube bundles, according
to reference [46], defining a thermally developing region and a thermally developed region.
Kocamustafaogullary and Chen stated that HTCs depend on the position of the tube in the
bundle, decreasing from one tube to the next. Liu et al. [47] named the regions stagnation zone
and free film zone (Figure 1.6a).
Figure 1.6. Thermal regions in a falling film. a) Two regions (reference [47]). b) Three regions
(reference [48]). c) Four regions (reference [49])
Three regions were distinguished in the film around tubes in works such as [48,50]. Chyu
and Bergles [50] described a short impingement zone, with high HTCs; a larger thermal
developing zone, where the fluid is superheated and no evaporation occurs; and a fully
developed region, where evaporation at the interface exists and even nucleate boiling can take
place. Fujita and Tsutsui [48] stated that the existing regions are a developing region, a shorter
transition region and a developed region (Figure 1.6b). They differentiate between laminar and
turbulent falling films. Fujita and Tsutsui supported their model with the acceptable agreement
they found between it and their experimental results.
Chyu and Bergles [49] stated that the film is divided into four regions (Figure 1.6c) and
established correlations for the HTCs at each region. First, a stagnation region, where the liquid
reaches the tube, (1.35). Then, an impingement flow region, with high HTCs and where laminar
boundary layer, (1.36), or turbulent boundary layer, (1.37), can occur. They defined Rex as seen
in equation (1.38) and found the transition between laminar and turbulent regimes at 4.5·105.
After it, a thermal developing region, (1.39). Finally, a fully developed region, where evaporation
takes place at the liquid-vapour interface. They proposed two models to calculate the HTCs in
this region, but that taken from reference [51] agreed better with experimental results. This
model distinguished between laminar (1.40), wavy-laminar (1.41) and turbulent (1.42) regimes
in the film. The average HTC in the film is obtained by equation (1.43) and the size of each
region, in angular portion of tube, by equation (1.44). They also proved that at least the first
three regions must exist and that the fully developed region might not occur for very high falling
film flow rates.
15
Chapter 1
Introduction

hst  1.03 Pr 1 3 k d umax u j
 d x w  u j  w 0.5
(1.35)
him x k  0.73 Pr1 3 Re0.5
x
(1.36)
him x k  0.037 Pr1 3 Re0.8
x
(1.37)
Re x  x umax x  v
(1.38)
htd , im   td  
13
 2 
hfd 

 g
13
 2 
hfd 

 g


k  1.10 Re 1 3 ;  0.61  4 g



13
 2 
hfd 

 g
 td qtd ,0   td    im qtd ,0   im 
td   im Tl  Ts 

k  0.822 Re  0.22 ; 0.61  4 g


k  3.8  10  3 Pr 0.65 Re0.4 ;
(1.39)


3
  


3
  
1 11
(1.40)
1 11



 1450 Pr 1.06

 1450 Pr 1.06

(1.41)
(1.42)
h  hst st   him im  st    htd td  im    hfd 1  td  
(1.43)
13
 st  0.6 w rt ;  i  2 w rt ;  td  1   rt  3   4  g 5  



(1.44)
Barba and Felice [52] developed another theoretical approach considering non-boiling
conditions, constant film thickness and turbulent thin films on horizontal tubes. They provided a
dimensionless formula, (1.45), for the calculation of the average HTCs. Experimental data from
several authors deviated from these theoretical results a ±10% on average.
13
h  2 g 


16
k  0.046 Re0.18
Pr 0.47 ;1500  Re f  5000;1  Pr  5
f
(1.45)
Chapter 1
1.7.
Introduction
HEAT
TRANSFER
CORRELATIONS
COEFFICIENTS:
EXPERIMENTAL
WORKS
AND
The works found in the literature concerning the experimental determination of falling film
evaporation HTCs with refrigerants have been included in this section. Table 1.2 lists these
works, with the main ideas extracted from each.
Table 1.2. Review of experimental works on falling film evaporation HTCs
Author(s)
Fluid(s)
Tube(s)
Notes
and
R134a, R236fa
Plain, condensation
(Wieland Gewa-C+LW),
two boiling (Wieland
Gewa-B4, Wolverine
Turbo-EDE2)
Two facilities: 10 tube vertical array and three 10 tube
vertical arrays. Kff over the unity mainly with
Gewa-C+LW and Turbo-EDE2. Higher and less
scattered results with R134a than with R236fa. Kff
correlations for wet and partial dryout conditions.
Bundle effect exists and can be positive for HTCs.
Christians, Christians
and Thome [12,55,56]
R134a, R236fa
2 boiling (Wolverine
Turbo-B5, Wieland
Gewa-B5)
Test facilities from [10]. No bundle effect observed, no
distinction between one and three arrays of tubes.
Heat flux effect on HTCs negligible. Dry patches
deteriorate the performance of the process at low Ref
(under the onset value). Slightly higher HTCs for
Turbo-B5 than for Gewa-B5 and for R134a than for
R236fa. Correlations similar to those from [10], but
including a geometric tube factor.
R134a
Plain, three boiling
(Wolverine TurboBIIHP, Wieland
Gewa-B, UOP
High-Flux)
10 tube vertical array. HTCs constant with decreasing
Ref until a certain value, at which a sharp decrease
occurs (dry patches). Plain tube, HTCs increase with
heat flux. Enhanced tubes, HTCs decrease with heat
flux. Kff almost always over unity. Correlations for Kff
under wet conditions.
R11
Plain
Three types of low momentum liquid distribution. HTCs
independent of the feeding method.
Danilova et al. [57]
R12, R22, R113
Plain
Three HTC zones, function of heat flux. Low heat flux
range, evaporation dominates the process. High heat
flux range, nucleate boiling dominates. Medium heat
flux range, transition between both. Correlations for
HTCs in evaporation and boiling zones included.
Zeng et al. [58-60]
Ammonia
Plain, low-finned
Single tube and tube bundle experiments, spray
nozzles. Nucleate boiling dominance in the tests.
HTCs mainly increase with heat flux and saturation
temperatures. HTC correlations for both single and
tube bundle with plain and low-finned tubes.
Moeykens [61]
R123, R134a
Plain, two condensation
(Wieland Gewa-SC,
Wolverine Turbo-CII),
two boiling (Wieland
Gewa-SE, Wolverine
Turbo-B), two finned
(Wolverine-40 and
Wolverine-26)
Tests with single tube and tube bundles. Several types
of spray nozzles. Turbo-B tube bundles the most
suitable with R123. Condensation tubes lead to the
highest HTCs with R134a. Results with refrigerant-oil
mixtures.
Liu and Yi [62]
R11
Plain, low-finned and
roll-worked
Heat flux affects HTCs in the nucleate boiling zone,
not in low heat flux range. HTCs with enhanced tubes
up to 10 times those with plain tubes.
Tatara and Payvar [63]
R11
1024 f.p.m. finned
Spraying tube and dripping tube distribution devices.
50% higher HTCs with the former than with the latter.
Combination of the two distribution devices means no
additional improvement.
R141b
Plain, low-finned
Liquid catchers under the tubes to prevent dry
patches. HTCs improved mainly on the lowest row of
the tube bundle.
Habert, Habert
Thome [11,53,54]
Roques [21]
Fujita and Tsutsui [24]
Chang
and
Chang [64,65]
1.7.1.
Chiou,
Plain tubes (smooth tubes)
Danilova et al. [57] obtained falling film evaporation HTCs with R12, R22 and R113 on a
plain tube, and distinguished three HTC zones as a function of heat flux. In the low heat flux
range, evaporation dominates the process and HTCs depend mainly on the falling film flow rate,
increasing with it. The medium heat flux range is a transition zone, where evaporation and
nucleate boiling coexist and HTCs depend on heat flux and falling film flow rate. In the high heat
flux region, nucleate boiling is dominant and HTCs depend mainly on the heat flux. They
17
Chapter 1
Introduction
correlated the film evaporation and film boiling experimental HTCs by equations (1.46) and
(1.47), respectively. The dimensionless numbers needed are defined from equation (1.48) to
(1.54). ζ stands for the volumetric film flow rate.
Nuf,e  0.035 Re0.22
Re0.24
Pr 0.32 s dt 0.48
f,e
* f,e
(1.46)
Nuf,b  1.32  10 3 Re0.22
Kp 0.72 Pr 0.48
f,b
(1.47)
13
Nu f,e  h   2 g 


  
(1.48)
k

Nu f,b  h  g  l  v 1 2 k
(1.49)
Re f,e  4  
(1.50)
13
Re* f,e  q hlv  l    2 g 


(1.51)
Pr   
(1.52)
Ref,b  q hlv  l    g  l  v 1 2
(1.53)
Kp  ps   g  l  v 1 2
(1.54)
Fujita and Tsutsui [24] tested plain tube arrays with R11, using three types of liquid
distributors: a porous sintered tube (Figure 1.7a), a tube with small holes at the bottom (Figure
1.7b) and a plate with a row of small holes aligned with the array (Figure 1.7c). They stated that
when a complete wetting of the tubes existed, the worst HTCs appeared at the top tube of the
array due to the non-uniformity of the film on it. They also observed that the HTCs were
independent of the feeding method. They proposed a correlation for the calculation of the
Nusselt number for the first tube of the tube array, (1.55), and another for the rest of the tubes,
(1.56). Nusselt and Reynolds numbers are defined in (1.57) and (1.5), respectively.
Figure 1.7. Distribution methods used by Fujita and Tsutsui [24]. a) Sintered tube. b) Perforated
tube. c) Perforated plate
12
2 3
Nu   Re f
 0.008 Re f 0.3 Pr 0.25 


18
(1.55)
Chapter 1
Introduction
12
2 3
Nu   Re f
 0.01Re f 0.3 Pr 0.25 


13
Nu  h  2 g 


k
(1.56)
(1.57)
Zeng et al. [58-60] focused on the falling film evaporation of ammonia on plain tubes.
Experiments with a single plain tube show a HTC increase with increasing heat fluxes and
saturation temperatures, proving the dominance of nucleate boiling under the tested conditions.
Besides, HTCs varied with falling film flow rate, nozzle height and nozzle type only at the
highest saturation temperature tested. HTCs increased when the first two parameters increased
and were higher for the standard-angle nozzles than for the wide-angle nozzles. They
correlated their experimental results by (1.58), being Θ the dimensionless heat flux, (1.59), and
pred the reduced pressure (1.60). Nusselt and Reynolds numbers are calculated from (1.57) and
(1.5), respectively.
0.385 0.753
Nu  0.0518 Re0.039
Pr 0.278 pred

f
  q dt
Tc  Ts  k 
pred  ps pc
(1.58)
(1.59)
(1.60)
Zeng et al. analysed as well the heat transfer performance and bundle effect of tube
bundles, both square-pitch and triangular-pitch, with ammonia. They stated that spray
evaporation HTCs in a tube bundle can be up to 50% greater than under pool boiling. According
to the authors, impingement of spray explains the greater HTCs of the tubes of the top row,
regardless of the kind of tube bundle. They detected differences in spray evaporation HTCs
between both pitches only under certain conditions. Equations (1.61) and (1.62) predict the
experimental results for square-pitch and triangular-pitch tube bundles, respectively.
0.261 0.722
Nu  0.0495 Re f 0.00399 Pr 0.209 pred

(1.61)
0.456 0.704
Nu  0.0678 Re0.049
Pr 0.296 pred

f
(1.62)
Moeykens [61] includes experimental values of pool boiling and spray evaporation with
R134a and a multi-tube test facility with plain tubes. HTCs depended on heat flux and not on
feed flow rate (until the appearance of dryout), indicating the occurrence of nucleate boiling.
They achieved the best performance with the tube of smallest diameter. High-pressure drop
nozzles enhance heat transfer compared to low-pressure drop nozzles, but they need a greater
pumping power and number of nozzles.
1.7.2.
Enhanced tubes
Zeng and Chyu [58] analysed as well the heat transfer performance of spray evaporation of
ammonia with low-finned tubes. A single low-finned tube led to HTCs up to 2.5 times as high as
a plain tube. HTCs also increased with saturation temperature and heat flux, marking the
dominance of nucleate boiling. Single tube HTCs were correlated by (1.63). Nu is calculated by
equation (1.57), Re by equation (1.5), Θ by equation (1.59) and pred by equation (1.60).
Concerning low-finned tube bundles, both triangular-pitch and square-pitch, the highest HTCs
occurred at the top row, diminishing row by row. Tube bundle HTCs increased as well with heat
flux and saturation temperature, and were clearly higher for the square-pitch than for the
triangular-pitch tube bundle. The authors recommended (1.64) and (1.65) to predict HTCs of
square-pitch and triangular-pitch low-finned tube bundles, respectively.
19
Chapter 1
Introduction
0.323 1.034
Nu  0.0568 Re f 0.0058 Pr 0.193 pred

(1.63)
0.127 0.773
Nu  0.0622 Re f 0.00035 Pr 0.108 pred

(1.64)
0.179 0.758
Nu  0.00566 Re 0.034
Pr 0.147 pred

f
(1.65)
Liu and Yi [62] compared the performance of plain tubes and two types of enhanced tubes,
low-finned tubes and roll-worked tubes, with R11. Single tube HTCs were independent of Ref,
except for the low-finned tube and low Ref, at which a sharp HTC decrease was observed,
probably due to film breakdown. Convection prevailed at the low heat flux zone and they
detected no effect of heat flux on HTCs. In contrast, when nucleate boiling dominated, the effect
of heat flux was clear. HTCs achieved with the enhanced tubes were up to 10 times those with
the plain tube. The authors also tested an array of three roll-worked tubes and observed a
negligible difference among them in heat transfer performance.
Tatara and Payvar [63] developed a study with R11 and a small tube bundle of 1024 f.p.m.
enhanced tubes, two types of distribution devices (liquid drip tubes and spray tubes) and a
vapour inlet line. Spray tube distribution led to HTCs 50% greater than dripping distribution. The
combination of both distribution systems meant no additional improvement. The authors
observed no effect of heat flux on HTCs in the heat flux range studied, which coincides with the
convective heat flux range from Liu and Yi [62]. The overfeed ratio (ratio of liquid mass
distributed at the test facility to the liquid vaporised mass), was seen to have a positive influence
on the heat transfer performance. However, the authors advise against an overfeed excess,
which could lead to losing the advantage of falling film evaporators over flooded evaporators.
The behaviour of R123, a substitute refrigerant for R11, was analysed in Moeykens [61]
with triangular-pitch tube bundles of plain tubes, Turbo-CII condensation tubes and Turbo-B
boiling tubes (Wolverine [30]). The types of nozzles tested had a negligible effect on the heat
transfer performance. HTCs in the plain tube bundle increased slightly with heat flux, meanwhile
they diminished with heat flux for the Turbo-CII and increased first and then decreased for the
Turbo-B. Enhancement factors even greater than 10 were obtained with Turbo-B and between 3
and 6 with Turbo-CII. A row-by-row study was also conducted, observing that the HTCs
decreased slightly from row to row with plain and Turbo-B tube bundles, but they diminished
sharply in the Turbo-CII tube bundle. In conclusion, Moeykens recommended the use of TurboB tube bundles with R123.
Concerning the falling film heat transfer performance of R134a on horizontal tubes,
Moeykens [61] developed experiments with the multitube facilities and the following types of
tubes: plain tubes, two condensation tubes (Wieland [31] Gewa-SC and Wolverine [30] TurboCII), two boiling tubes (Wieland [31] Gewa-SE and Wolverine [21] Turbo-B), and two finned
tubes (Wolverine [30] 40 f.p.i. and 26 f.p.i.). HTCs were slightly influenced by heat flux, pointing
to the existence of simultaneous convective evaporation and nucleate boiling in the range
tested. The highest enhancement factors were achieved for condensation tubes (slightly over
3), followed by evaporation tubes (slightly under 3) and finned tubes (between 2 and 3 and
better with Wolverine [30] 26 f.p.i). He also compared the performance of circular spray nozzles
and square spray nozzles on a triangular-pitch arrangement of Wolverine [30] 40 f.p.i tubes. He
observed that HTCs depended on the nozzle orifice size. A row-by-row analysis was also
conducted, for with he defined the Row Performance Factor (RPF) using equation (1.66). The
RPF varied from one row to the next one, more steeply with higher heat fluxes, smaller orifice
sizes and lower feed flow rates, due to the inefficient distribution and the proneness to dryout of
these tubes. Spray evaporation HTCs were greater than pool boiling HTCs, except for those
tests with the lowest feed flow rates and high heat fluxes.
RPF  hr hbdl
(1.66)
Moeykens [61] employed a bundle test facility to study the bundle performance and the RPF
behaviour of 5 different triangular-pitch tube bundles using Wolverine [30] Turbo-CII, Turbo-B
20
Chapter 1
Introduction
and 40 f.p.i., Wieland [31] Gewa-SC and plain tubes; and of a Wolverine [30] Turbo-B squarepitch tube bundle, with R134a. Enhancement factors increased with decreasing feed flow rates
meanwhile dryout was avoided. The highest enhancement factors occurred for condensation
tubes Turbo-CII. In contrast, the HTCs with Gewa-SC and Wolverine [30] 40 f.p.i deteriorated in
the tube bundle due to dryout appearance and the RPF varied significantly with row depth. Such
effect was negligible with Turbo-CII and Turbo-B bundles. The authors found a small influence
of the bundle geometry over HTCs and RPF. Finally, the bundle HTCs with Turbo-CII under
spray evaporation were twice those under pool boiling with Turbo-B.
R134a falling film HTCs with enhanced tubes were further studied by Roques [21]. He
tested plain tubes and three types of boiling enhanced tubes (Wolverine [30] Turbo-BII HP,
Wieland [31] Gewa-B and UOP [35] High-Flux), placed in a 10 tube vertical array test facility.
Falling film HTCs remained practically constant when Ref decreased, until a certain value at
which they diminished sharply (Figure 1.8, continuous line) due to film dryout. HTCs increased
with heat flux only with the plain tube array and decreased with the rest, which is a similar trend
to that observed by the author under pool boiling and proves the dominance of nucleate boiling
on the falling film evaporation tests.
Figure 1.8. HTCs vs. film Re number in a single array, as described in reference [21], and bundle
effect, as observed in reference [11]
The falling film parameter or multiplier, Kff, defined in section 1.5 using equation (1.31), was
used by Roques [21] to compare pool boiling and falling film HTCs. Kff was over the unity for
almost every condition and tube tested without dryout. The falling film parameter without dryout
(Kff,wet) was correlated by equation (1.67). q̇crit stands for the critical heat flux (equation (1.68)),
and P0 stands for the reference pitch (22.25 mm). Roques and Thome [21,66] proposed
equation (1.69) to calculate the falling film parameter under dryout conditions, but the success
of the correlation was not the expected. Ref,threshold is obtained as explained in section 1.5,
multiplying by two Ref,dryout, (1.29).
K ff ,wet  1  i1 P P0  i 2  i 3q q c   i 4q qc 2 



 
(1.68)

(1.69)
q crit  0.131  g0.5 hlv g  l   g  l 0.25

(1.67)
K ff ,dryout  K ff ,wet Re f,threshold Re f
Yang and Wang [67] developed numerical simulations based on the research from Roques
[21] and on the Kff concept to obtain falling film HTCs in an evaporator. They studied two-passtube arrangements of similar tubes to those analysed in reference [21], R134a as working fluid
21
Chapter 1
Introduction
and with two distribution conditions, uniform/homogeneous liquid distribution and
heterogeneous distribution. The authors recommend a bottom-to-top arrangement evaporator
when uniform liquid feed exists, in terms of HTCs and Ref,threshold. The highest HTCs coefficients
occurred with the Wolverine [30] Turbo-EHP, but not the best Kff. They also proposed flooding
the bottom rows of the evaporator to improve the heat transfer performance. The simulation
stated that the evaporator performance diminishes and more dry-patches occur with
maldistribution of the refrigerant (defined by the flow maldistribution coefficient).
Habert and Thome [11,53] extended the existing database of HTCs with refrigerants and
tubes under falling film evaporation. They tested a condensation enhanced tube (Wieland [31]
Gewa-C+LW), two boiling enhanced tubes (Wieland [31] Gewa-B4 and Wolverine [30]
Turbo-EDE2), and a plain tube with R134a and R236fa. They used the experimental facility
from Roques [21], unmodified first and with two tube arrays in parallel later. Falling film HTCs
behaved similarly to those from Roques [21], increasing with heat flux with plain and
condensation tubes (Gewa-C+LW) and decreasing with boiling tubes (Gewa-B4 and TurboEDE2). The authors observed that Kff diminished as the heat flux increased under almost every
condition, but was greater than 1 with all the enhanced tubes (mainly with Gewa-C+LW and
Turbo-EDE2). R134a led to better and less scattered HTCs than R236fa. In addition, liquid
deflection, which was negligible with R134a, tended to occur with R236fa.
Habert and Thome used equation (1.70), defined by Ribatski and Thome [25], to correlate
the experimental HTCs obtained both in wet and partially wet conditions. F stands for the
apparent wet area fraction and was defined in reference [25] as the ratio between the tube
surface covered by the liquid film, Awet, to the total tube surface, Atotal (equation (1.71)).
hff  hwet F  hdry 1  F 
(1.70)
F  Awet Atotal
(1.71)
Ribatski and Thome [25] correlated F as a function of Ref, as stated in equation (1.72).
Habert and Thome [11,54] predicted accurately their results of apparent wet area using different
fitting constants for each tube-refrigerant combination studied. However, they stated that it
needs too many experimental constants and they proposed equation (1.73). They also
suggested the removal of hdry from correlation (1.70), since it is negligible compared to hwet.
Ribatski and Thome [25] defined equation (1.74) to substitute the formula previously proposed
by Roques [21] to calculate Kff,wet.
j
F  j1 Re f 2
Re f Re f, threshold
F 
1

Kff ,wet  m1 q ' q ' 'c m2
(1.72)
Re f  Re f,threshold
Re f  Re f,threshold
(1.73)
(1.74)
The modified test facility described in Habert [11] was used to study the bundle effect under
falling film with the same tubes and refrigerants. HTCs were maximum at a certain Ref, denoted
as Ref,peak (Figure 1.8, discontinuous line). However, these bundle results were very scattered
and in some cases very low due to the premature appearance of dry patches caused by the
liquid maldistribution in the bundle. Equation (1.75) correlates the bundle effect on those tubes
and conditions with no film breakdown. B stands for the empirical bundle factor, obtained by
equation (1.76). The fitting constants and Ref,peak depended on the tube-refrigerant combination.
Equation (1.75) was only satisfactory with plain tubes and both refrigerants.
hbdl  B harray
22
(1.75)
Chapter 1
B  1  o1 exp
Introduction

 o 2 Re f  Re f,peak
2
(1.76)
Additional falling film HTCs were included in the works developed by Christians and Thome
[12,55], obtained for Wolverine [30] Turbo-B5 and for Wieland [31] Gewa-B5 tubes with R134a
and R236fa. They developed their tests in the experimental facility used by Habert [11].
Contrary to the conclusions from [11,53], Christians and Thome found no bundle effect on the
falling film HTCs. In fact, they made no distinction between the results obtained using the array
arrangement or the bundle arrangement. Experimental HTCs were independent of heat flux or
film Reynolds number meanwhile no film breakdown occurred, confirming the trends detailed in
the works from Roques [21] or Habert and Thome [11,53]. The falling film HTCs were slightly
higher with Turbo-B5 tubes than with Gewa-B5 tubes, and with R134a than with R236fa.
Christians and Thome [12,56] proposed correlation (1.77) to predict the falling film HTCs
obtained and enclosed not only in their works, but also in references [11,21,55]. The correlation
depends on Gt-s (tube geometric factor, explained in section 1.5). Concerning the prediction of
the partial dryout falling film HTCs, F was calculated by (1.73), as defined by Habert and Thome
[11,54], and the HTCs were the result of multiplying it by hwet.



hwet d t k  9.623  10 4 q 2 d t  l hlv  l   g 


0.0328
Gt1.2449
s
(1.77)
The falling film multiplier, Kff, was also determined by Christians and Thome [12,55] with the
different tube-refrigerant combinations tested. Kff varied with heat flux, due to its influence on
pool boiling HTCs. Both refrigerants led to similar falling film multipliers. The correlation
proposed by Christians and Thome to predict Kff, (1.78), is also a function of Gt-s.


0.4585
q q c 0.6204 Gt0s.024
K ff  65.3 g d t 3 2  l   g q 


1.7.3.
(1.78)
Solutions to dry patches
The main inconvenient concerning falling film evaporation is the breakdown of the falling
film and dry patch appearance. If dryout occurs, the performance of spray evaporators
decreases, losing an advantage over flooded evaporators. Increasing the film flow rate or
decreasing the heat flux may prevent dryout. The implementation of liquid collectors or catchers
under the tubes (Figure 1.9) has been also proposed as a solution.
Figure 1.9. Tube bundle with liquid catchers, as described in references [64,65].
To our best knowledge, Chang and Chiou [64] were the first to mention liquid catchers for
falling film evaporators. They tested a tube bundle with five plain tubes under pool boiling, spray
23
Chapter 1
Introduction
evaporation without liquid catchers and spray evaporation with liquid catchers. They noticed that
at the narrow gap between tube and collector, the boiling process was different, with bubbles
that squeezed and flattened against the walls, then coalesced and caused intermittent small
dry-patches. HTCs improved sharply on the lowest row and were greater than under pool
boiling in the whole heat flux range tested. Chang [65] presented similar results with a bundle of
low-finned tubes. He observed a slight performance deterioration with liquid catchers at the tube
placed right beneath the distribution nozzle. Awad and Negeed [7] analysed mathematically the
improvement associated to the addition of liquid catchers under falling film and found that this
heat transfer enhancement was higher with larger gaps between tube and catcher. They carried
out the analysis at the gap considering pool boiling conditions and the correlation proposed by
Cooper [68].
Another possible solution to dry patches was studied by Chang and co-workers and
consists in distributing liquid refrigerant using sprays located inside the tube bundle, as can be
seen in references [69-72]. The authors state that spray evaporation outperforms pool boiling,
using R141b as refrigerant, both in triangular-pitch and square-pitch tube bundles, when
introduced into these bundles spraying tubes with orifices of 1 mm of diameter and 90º of cone
angle (Figure 1.10). They have also analysed the effect of the spraying incident angle on the
heat transfer performance of tube bundles, observing a maximum at 60º. Up to the date of
redaction of this PhD, the last work of this investigation group consisted in determining, both
theoretically and experimentally, the optimal cone angle for interior spraying tubes as a function
of the tube diameter and the distance between the spraying and the sprayed tubes.
a
b
Heater
Heater
Heater
Heater
N
Heater
N
Heater
Heater
Heater
Heater
Heater
Figure 1.10. Tube bundles with interior spraying tubes. a) Triangular-pitch (reference [69]).
b) Square-pitch (reference [70])
24
Chapter 1
1.8.
GENERAL CONSIDERATIONS
1.8.1.
Flow modes and transitions
Introduction
Up to five intertube flow patterns have been described, but mainly three are distinguished:
sheet, jet (column) and droplet modes. According to references [8,9,17,18], the flow pattern
depends on film flow rate and liquid properties (Dhir and Taghavi-Tafreshi [32] disagreed about
the latter). Concerning intertube distance, references [4,8] explained that sheet mode occurs
when this parameter is small, and changes to jet and droplet modes as it increases. In Roques
et al. [18] the effects of heat flux and nucleate boiling were also pointed out.
Habert [11] stated that sheet mode is the most convenient for falling film evaporation, since
it involves less possibilities of film breakdown and Hu and Jacobi [9,10] that the best HTCs are
achieved under this flow mode. However, higher refrigerant charges and pumping power are
needed to recirculate the excess liquid. Dryout may not occur under jet or droplet flow patterns if
the distance between column/droplet active sites is minimised. References [4,9,27] noted that
this distance depends on intertube spacing, film flow rate and fluid properties, increasing as the
first two increase and as the third decreases. In contrast, Ganic and Roppo [14] observed no
influence of intertube distance and film flow rate on it and Taghavi-Tafreshi and Dhir [15]
determined it depends only on viscosity.
1.8.2.
Film dryout
Film breakdown has been widely studied due to the important effect it has on the falling film
evaporator performance. References [11,21,24,40,44] defended the important role of film flow
rate on the film breakdown and references [11,21,24] of the liquid properties too. Moreover,
references [40,44] described different behaviours depending on the contact angle, in opposition
to the conclusions from Zaitsev et al. [22]. In references [11,21,24,44] the minimum film flow
rate to avoid film breakdown was seen to depend as well on heat flux. Normally, wetting
improves with enhanced tubes if compared to plain tubes, as stated in references [11,12,21,23].
However, some tubes such as low-finned or those with very complex external structures are not
recommended, since they restrict the liquid axial movement and are prone to dryout [53,58,62].
Dryout occurs primarily at the lowest tube rows inside tube bundles, due to the reduction of
the film flow rate caused by evaporation or liquid entrainment. Increasing the liquid overfeed has
been proposed as a solution to this problem, but other ideas have been suggested. Yang and
Wang [67] observed an improvement of the tube bundle performance by flooding the lowest
rows and Tatara and Payvar [63] analysed the effect of implementing extra distribution devices
within the tube bundle. According to references [64,65], HTCs were enhanced including liquid
catchers beneath the tubes, since dryout was prevented. Another solution is to include interior
spraying tubes in tube bundles, since it improves refrigerant distribution, minimizing the
appearance of dry patches (references [69-72]).
1.8.3.
Film flow rate
The effect film flow rate has on the falling film evaporation HTCs depends mainly on the
existence or not of nucleate boiling in the falling film, at least when no dry-patches occur. Under
non-boiling conditions, references [14,57] observed an increase of the HTCs with film flow rate.
In contrast, Chyu and Bergles [49] reported a HTC deterioration with falling film flow rate due to
thickening of the film. Under boiling conditions, no dependency between film flow rate and HTCs
was stated in references [11,21,57,61,62].
As mentioned above, low film flow rates may lead to dry patch formation and the authors
from references [11,21,24,62] noted that, when dry-patches exist, wetting improves by
increasing the film flow rate. Thus, the control of the film flow rate is important for the correct
performance of falling film evaporators (reference [63]). The chosen bundle geometry may also
facilitate liquid distribution. Normally, triangular-pitch leads to more compact evaporators and
square-pitch to more uniform refrigerant distribution. Zeng and co-workers [58,59,60] stated that
triangular-pitch plain tube bundles performed better, meanwhile with low-finned tubes, squarepitch bundles attained better HTCs. In contrast, Moeykens [61] observed no differences
between both arrangements.
25
Chapter 1
1.8.4.
Introduction
Heat flux
Under non-boiling conditions, HTCs remained constant with heat flux, as stated in
references [24,57,62]. However, Fujita and Tsutsui [24] affirmed that heat flux conditioned the
minimum film flow rate to prevent dry-patch formation. Under boiling conditions, the effect of
heat flux on HTCs depends mainly on the tube analysed. For plain tubes, references
[11,21,57,58,61,62] agreed that HTCs increase with heat flux. This trend is unclear for
enhanced surfaces. According to references [11,58,61,62], with condensation or low-finned
tubes, HTCs increase when the heat flux rises. Normally, with enhanced boiling tubes, HTCs
decrease or remain constant with heat flux (references [11,12,21,61]).
1.8.5.
Distribution method
Different refrigerant distribution methods were described and studied in the literature, and
they can be classified into low momentum and high momentum methods. Among the low
momentum solutions, it is worth pointing out:









Perforated tube. At the bottom without a stabilizing tube in reference [24] and with
stabilizing tube in references [8,9,10]. Perforated tube all around the surface used in
reference [63].
Open box with perforated bottom in reference [20].
Perforated plate in reference [24].
Perforated vertical narrow tanks and stabilizing tubes in reference [13].
Perforated rectangular box with foams inside and half tube with sharp edge in reference
[11,12,21,25,53,55].
Sintered tubes in reference [24].
Distribution tube with a slot at the top part in reference [49].
Tube-in-tube distributor in reference [57].
Distribution tray with a slot in reference [47,62].
High momentum solutions comprise spray nozzles, which were employed in references
[2,46,53,58,59,64,65]. Falling film HTCs and wetting of tubes improve with high momentum
distribution devices, particularly with liquids of low wettability. In addition, low momentum
distribution systems need a more precise alignment than spray nozzles. However, the liquid fed
with spray nozzles is difficult to quantify and a significant part of the fluid leaves the tube bundle.
A solution can be the use of square plume nozzles, which need less liquid excess to feed a
bundle but are more expensive (reference [61]).
1.8.6.
Enhanced tubes
Enhanced tubes delay the appearance of dry patches if compared to plain tubes
(references [21,23,24,45]). However, these enhanced surfaces should have as few axial liquid
movement restrictions as possible, to favour the refrigerant distribution on tubes. No specific
enhanced tubes exist for falling film, so the tubes tested were those prepared for processes
such as pool boiling or condensation, or low-finned tubes. Moeykens [61] stated that low-finned
tubes are prone to dryout and maldistribution, particularly as the number of fins per meter
increases. Pool boiling and condensation tubes lead to important enhancements in the HTCs
and the best solution depends on the refrigerant.
1.8.7.



26
Other considerations
Saturation temperature. References [57,58] state that HTCs increase when the
saturation temperature increases.
Nozzle height: Its small influence over HTCs is mainly reported. However, references
[14,61] agree that a slight increase of the HTCs can occur with nozzle height.
Vapour flow: The design of correct vapour outlets is of a great importance for two
reasons. First, the pernicious influence vapour entrainment can have on the liquid
distribution over tubes, according to references [16,39]. Second, the benefit vapour flow
may cause on the heat transfer performance of a tube bundle with falling film
evaporation, as stated in reference [63].
Chapter 1
1.9.
Introduction
CONCLUSIONS
This chapter encloses the results of works of the literature concerning falling film
evaporation of refrigerants on horizontal tubes. The main conclusions drawn are listed in the
following paragraphs.
Falling film evaporators for refrigeration systems can substitute satisfactorily flooded
evaporators due to their potential benefits in operation costs, safety, thermodynamic efficiency,
refrigerant charge or size. However, special attention must be paid to refrigerant distribution to
avoid dryout and deterioration of the HTCs.
A large number of parameters affect the performance of falling film evaporators, but authors
disagree about the effect of each of them. Those with a higher influence are heat flux, film flow
rate, geometry of the tube, refrigerant properties and distribution system.
Sheet mode between tubes is recommended to prevent film breakdown, but an important
pumping power may be needed to achieve it. Droplet or column intertube flow modes do not
necessarily lead to dryout.
The use of enhanced tubes improves falling film HTCs compared to plain tubes. In addition,
most enhanced tubes delay film breakdown, maintaining the surface wet. Only geometries that
limit liquid axial movement, such as low-finned tubes with a high concentration of fins, should be
avoided in these systems.
A large number of empirical correlations have been included in the literature, but the
accuracy of the predictions is normally limited to very specific experimental conditions.
27
Chapter 1
Introduction
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[52] D. Barba, R. Di Felice, Heat transfer in turbulent flow on a horizontal tube falling film
evaporator. A theoretical approach, Desalination. 51 (1984) 325-333.
[53] M. Habert, J.R. Thome, Falling-film evaporation on tube bundle with plain and enhanced
tubes—Part I: Experimental results, Experimental Heat Transfer. 23 (2010) 259-280.
[54] M. Habert, J.R. Thome, Falling-film evaporation on tube bundle with plain and enhanced
tubes—Part II: New prediction methods, Experimental Heat Transfer. 23 (2010) 281-297.
[55] M. Christians, J.R. Thome, Falling film evaporation on enhanced tubes, part 1:
Experimental results for pool boiling, onset-of-dryout and falling film evaporation, International
Journal of Refrigeration. 35 (2012) 300-312.
[56] M. Christians, J.R. Thome, Falling film evaporation on enhanced tubes, part 2: Prediction
methods and visualization, International Journal of Refrigeration. 35 (2012) 313-324.
[57] G.N. Danilova, V.G. Burkin, V.A. Dyundin, Heat transfer in spray-type refrigerator
evaporators. Heat Transfer Soviet Research. 8 (1976) 105-113.
[58] X. Zeng, M. Chyu, Heat transfer and fluid flow study of ammonia spray evaporators, Texas
Tech University, Lubbock, Texas, USA, 1995.
[59] X. Zeng, M. Chyu, Z.H. Ayub, Experimental investigation on ammonia spray evaporator
with triangular-pitch plain-tube bundle, Part I: tube bundle effect, International Journal of Heat
and Mass Transfer. 44 (2001) 2299-2310.
[60] X. Zeng, M. Chyu, Z.H. Ayub, Experimental investigation on ammonia spray evaporator
with triangular-pitch plain-tube bundle, Part II: evaporator performance, International Journal of
Heat and Mass Transfer. 44 (2001) 2081-2092.
[61] S.A. Moeykens, Heat transfer and fluid flow in spray evaporators with application to
reducing refrigerant inventory, Iowa State University of Science and Technology, Iowa, USA,
1994.
[62] Z. Liu, J. Yi, Enhanced evaporation heat transfer of water and R-11 falling film with the rollworked enhanced tube bundle, Experimental Thermal and Fluid Science. 25 (2001) 447-455.
[63] R. Tatara, P. Payvar, Measurement of spray boiling refrigerant coefficients in an integral-fin
tube bundle segment simulating a full bundle, International Journal of Refrigeration. 24 (2001)
744-754.
30
Chapter 1
Introduction
[64] T. Chang, J.S. Chiou, Spray evaporation heat transfer of R-141b on a horizontal tube
bundle, International Journal of Heat and Mass Transfer. 42 (1999) 1467-1478.
[65] T. Chang, Effects of nozzle configuration on a shell-and-tube spray evaporator with liquid
catcher, Applied Thermal Engineering. 26 (2006) 814-823.
[66] J. Roques, J.R. Thome, Falling films on arrays of horizontal tubes with R-134a, Part II: flow
visualization, onset of dryout, and heat transfer predictions, Heat Transfer Engineering. 28
(2007) 415-434.
[67] L. Yang, W. Wang, The heat transfer performance of horizontal tube bundles in large falling
film evaporators, International Journal of Refrigeration. 34 (2011) 303-316.
[68] M.G. Cooper, Saturation nucleate pool boiling - a simple correlation, in: Proceedings of the
first UK National Conference on Heat Transfer, 1984, pp. 785-793.
[69] T. Chang, C. Lu, J. Li, Enhancing the heat transfer performance of triangular-pitch shelland-tube evaporators using an interior spray technique, Applied Thermal Engineering. 29
(2009) 2527-2533.
[70] T. Chang, J. Li, C. Liang, Heat transfer enhancement of square-pitch shell-and-tube spray
evaporator using interior spray nozzles, Heat Transfer Engineering. 32 (2011) 14-19.
[71] R. Li, T. Chang, C. Liang, Effects of spray axis incident angle on heat transfer performance
of rhombus-pitch shell-and-tube interior spray evaporator, Journal of Mechanical Science and
Technology. 26 (2012) 681-688.
[72] T. Chang, L. Yu, Optimal nozzle spray cone angle for triangular-pitch shell-and-tube interior
spray evaporator, International Journal of Heat and Mass Transfer. 85 (2015) 463-472.
31
Chapter 2
Experimental facility
This chapter focuses on the experimental facility used to test pool boiling and spray
evaporation of refrigerants on horizontal tubes. We modified and prepared an existing
experimental facility to allow testing spray evaporation processes. First, the experimental setup
and the different devices involved in each test are described. Then, the distribution system used
for spray evaporation tests is detailed. After that, the acquisition data system, the sensors
employed and the software developed are explained. The chapter ends with the main
characteristics of the different tubes studied.
The modification of this experimental test rig was part of the project INC 841C INTESPRAY:
“Nuevo intercambiador de gran volumen con sistema de refrigeración por esprayado y sistema
de recirculación del fluido sobrante”, developed in collaboration with the company INTEGASA
and Xunta de Galicia. This project is included in a line of investigation in which we have studied
different heat transfer processes occurring in shell-and-tube heat exchangers and have
determined their HTCs.
The process of adapting the experimental test rig was developed in two stages. The first
stage is described in the paper Á.Á. Pardiñas, J. Fernández-Seara, S. Bastos and F.J. Uhía,
Diseño, construcción y validación de un equipo experimental para el estudio de la evaporación
en spray, included in the proceedings of the “VII Congreso Ibérico y V Congreso
Iberoamericano de Ciencias y Técnicas del Frío” (Tarragona, Spain, 2014) [1]. The second
stage is detailed in the paper Á.Á. Pardiñas, J. Fernández-Seara and R. Diz, Test rig for
experimental evaluation of spray evaporation heat transfer coefficients, of the 24th IIR
International Congress of Refrigeration (Yokohama, Japan, 2015) [2].
33
Chapter 2
2.1.
Experimental facility
EXPERIMENTAL SETUP PHILOSOPHY
Several works had been done in our laboratory to study heat transfer processes occurring in
shell-and-tube heat exchangers. The experimental test rig available in the laboratory (Figure
2.1) was designed for studying condensation and pool boiling of refrigerants.
Figure 2.1. Experimental test rig for condensation and pool boiling experiments
The experimental setup was redesigned in order to allow spray evaporation tests. These
tests consist in distributing the liquid refrigerant, in conditions very close to saturation, on the
tested tube/s, simulating the situation that occurs in spray evaporators.
The main modification developed was to include a liquid distribution system to distribute the
liquid refrigerant. The system was designed to allow testing different types of spreading devices.
Among the different possibilities, full cone nozzles have been selected. The equipment permits
different spacings between the nozzles, as well as choosing two distances between the nozzles
and the tubes. We can also compare the HTCs obtained when the tested tube receives the
liquid refrigerant directly from the nozzles and when the liquid refrigerant falls by gravity from a
conditioning tube above the tested one.
The equipment does not follow a typical vapour compression cycle. Instead, pool
boiling/spray evaporation and condensation occur at the same pressure and refrigerant flows
from one shell-and-tube heat exchanger to the other due to the differences of density between
liquid and vapour refrigerant. This configuration allows, on the one hand, testing very different
conditions and refrigerants and, on the other hand, discarding the effect of lubricants on HTCs.
The test rig is prepared for tubes of nominal external diameters up to 20 mm, but we tested
tubes of nominal external diameter 3/4” (19.05 mm), which are widely extended in shell-andtube heat exchangers. We chose tubes with plain and enhanced external surfaces, and the
material depends on the refrigerant used (compatibility refrigerant–material).
The compatibility with ammonia was the main consideration during the selection of
materials for building the experimental setup.
As previously mentioned, the working principle of the experimental facility allows testing a
wide range of condensation and evaporation conditions. We chose liquid temperatures between
0 and 10 ºC for our pool boiling and spray evaporation tests, common temperatures in water
chillers. This range of temperatures allowed using water as secondary fluid both for condensing
the vapour refrigerant at the condenser tubes and for vaporising the liquid at the evaporator
tubes. Water is very convenient since its properties are very accurately determined using the
temperatures measured.
34
Chapter 2
Experimental facility
The experimental facility stabilises the refrigerant pool temperature or the liquid distribution
temperature (boiling saturation pressure), for pool boiling and spray evaporation tests,
respectively. The distributed liquid refrigerant flow rate is also controlled accurately, maintaining
the rest of the conditions constant. The temperatures and flow rates of the secondary fluids can
also be regulated and stabilised at the values needed for each test.
The experimental setup allowed measuring the conditions (temperature, pressure and flow
rate) of the refrigerant and secondary fluids. Several sensors were also included to determine
the conditions of the distributed refrigerant.
A SolidWorks model was developed in order to introduce the modifications (mainly the
distribution system) in the existing test rig. An isometric view is shown in Figure 2.2.
Figure 2.2. Isometric view of the experimental test rig model
Figure 2.3 shows two photographs of the experimental setup once finished. The facility
does not follow completely the 3D model developed. In particular, the refrigerant pump position
was changed to improve its performance. The photographs also show the process of insulation,
which was carefully developed to minimise the heat transfer to the surroundings.
a
b
Figure 2.3. Photographs of the experimental facility. a) Front. b) Back
35
Chapter 2
Experimental facility
2.2.
EXPERIMENTAL FACITILITY DESCRIPTION
2.2.1.
Experimental facility
Figure 2.4 shows the layout of the experimental facility used for pool boiling and spray
evaporation tests. It consists mainly of a boiling test section, composed of a shell-and-tube
evaporator connected to a heating water loop; a condensation test section, composed of a
shell-and-tube condenser connected to a cooling water loop; and a refrigerant distribution
system.
Figure 2.4. Sketch of the experimental test rig
The condenser and the evaporator consist of a 6-mm-thick horizontal cylindrical body and
blind flanges made of stainless steel (AISI-316L). The condenser has an external diameter of
168.3 mm and an internal total length of 1895 mm. The evaporator has an external diameter of
200 mm and an internal total length of 1530 mm. Both ends of the tubes installed at the
condenser and evaporator protrude from the blind flanges.
36
Chapter 2
Experimental facility
The refrigerant distribution system consists mainly of a 12 l refrigerant tank, also made of
stainless steel (AISI-316L), an ammonia refrigerant pump, and a distribution tube with nozzles.
Independently of the test developed, liquid refrigerant vaporises on the evaporator tube/s
due to the heat transferred by the heating water that flows through it/them. The generated
vapour leaves the evaporator through 4 AISI 316L ports (inner/outer diameter 30/33 mm)
located at the top. Then, it flows through an AISI 316L stainless steel flexible hose (DN 40 mm)
and reaches the upper part of the condenser, where it enters through 4 AISI 316L ports
(inner/outer diameter 30/33 mm), to guarantee a proper vapour distribution.
Vapour condenses on the condenser tube/s, transferring heat to the cooling water that
circulates through it/them. Gravity drives the liquid refrigerant out from the condenser through a
single port and an AISI 316L pipe (inner/outer diameter 10/12 mm). At this point is where pool
boiling and spray evaporations tests differ.
In pool boiling tests, the refrigerant tank is left aside (V2 and V4 closed, and V1 in L position,
Figure 2.4), and the liquid refrigerant enters the evaporator through 4 ports placed at its bottom
part (AISI 316L). The liquid refrigerant forms a pool and floods the tested tube/s.
In spray evaporation tests, the distribution system is completely integrated into the
refrigerant loop (V2 and V4 open, and V1 in T position, Figure 2.4). The liquid refrigerant from the
condenser ends up in the refrigerant tank, where it is sucked by the refrigerant pump. Valves V 2
and V3 (Figure 2.4) are manually regulated to control the refrigerant distributed flow rate. After
this, the liquid refrigerant flows through an AISI 316L stainless steel duct (inner/outer diameter
15/18 mm), and is finally divided into two flows to enter the evaporator through both flanges.
This solution allows reducing the pressure drop and homogenising the flow rate distributed by
each nozzle.
An AISI 316L stainless steel distribution tube (inner/outer diameter 22/25 mm) is placed
inside the evaporator and receives the liquid refrigerant from the tubes that reach both flanges
of the evaporator. The distribution tube has threaded female connections (1/4”) where the
distribution nozzles are attached. A thorough explanation of the distribution tube and nozzles is
included in section 2.2.2.
The distribution nozzles spread liquid refrigerant on the tube/s at the evaporator. Part of the
refrigerant vaporises due to the heat transferred by the heating water flowing through the
evaporator tube/s and the excess liquid refrigerant leaves the evaporator through 4 AISI 316 L
ports placed at the bottom part of the evaporator and returns to the refrigerant tank.
The heating water loop, used to vaporise the liquid refrigerant at the evaporator, consists of
a water reservoir, a centrifugal pump and an electric boiler. Water from the reservoir is sucked
by the centrifugal pump and discharged into the electric boiler. The heating water flow rate is
controlled by means of two manually regulated valves and a bypass circuit to the tank. The
electric boiler (maximum 12 kW) heats the water and the heat delivered is regulated by a power
controller connected to a PC. The heating water leaves the electric boiler and flows through the
evaporator tube/s, transferring heat to the refrigerant. After leaving the tube/s, it closes the loop
by returning to the water reservoir.
The cooling water loop is in charge of condensing the vapour refrigerant on the condenser
tube/s. The main components of this cycle are a water reservoir, a centrifugal pump and a plate
heat exchanger. Water from the reservoir is sucked by the centrifugal pump and discharged to
the plate heat exchanger. The cooling water flow rate is controlled by means of two manually
regulated valves and a bypass circuit to the tank. In the plate heat exchanger, the cooling water
transfers heat to an auxiliary cooling loop. Then, it flows through the tube/s placed at the
condenser, absorbs heat from the refrigerant, and returns to the water tank.
Both the condenser and the evaporator are equipped with 6 sight glasses each, that allow
lighting, viewing and recording the processes that occur there. Figure 2.5 shows a photograph
of the recording equipment for pool boiling and spray evaporation processes.
37
Chapter 2
Experimental facility
Figure 2.5. Viewing and recording process for pool boiling and spray evaporation tests
2.2.2.
Distribution tube calculation
As explained in section 2.2.1, a distribution system was included in the experimental facility
to allow testing spray evaporation. The distribution system designed is a tube with threaded
female connections (1/4”) used to attach the spreading devices (nozzles). The following
paragraphs detail the design process of the system.
The distribution of refrigerant on the tube bundle of a spray evaporator is a key factor for its
correct performance, since the appearance of dry zones on the tubes may cause an important
deterioration of heat transfer. In the scientific literature, different distribution methods have been
proposed and studied, and they can be classified into low momentum and high momentum [3].
Liquid distribution with low momentum systems is mainly caused by the effect of gravity; i.e.
the liquid falls from the device to the surface (tube) placed directly beneath. Thus, the
distribution system must be placed over each and every column of the tube bundle, properly
aligned, in order to assure the liquid feed.
High momentum solutions include spray nozzles and these systems have been seen to
improve heat transfer and wetting of tubes. They seem more appropriate for industrial
equipment since alignment is not a critical issue and a same nozzle may distribute liquid to
more than one column of tubes. However, part of this liquid may leave the bundle and it is
difficult to quantify the fraction of the total flow rate that reaches each tube. The aptitude of
nozzles to be used in industrial equipment explains that these were chosen for the distribution
system of the experimental facility.
According to the Engineer’s Guide to Spray Technology [4], there are many types of
nozzles available in the market. They can be mainly classified into two groups, function of the
spray pattern produced by the nozzle: hollow cone nozzles and full cone nozzles. Hollow cone
nozzles produce an annulus of liquid; i.e. part of the area right beneath the nozzle receives no
liquid at all. On the other hand, full cone nozzles distribute liquid forming a spray that fills the
area covered completely and homogeneously, so they appear as the most appropriate for this
application.
From the different shapes of cones available in the market, we have selected circular
nozzles. Circular cone nozzles distribute liquid with axial symmetry, describing circles in those
planes perpendicular to the nozzle axis. Axial symmetry explains two of the main characteristics
of round cone nozzles. The first is that no specific positioning is needed in order to feed a
certain area. The second one concerns the necessity of overlapping a fraction of the liquid
distributed by two or more nozzles in order to feed an area (tube bundle). In addition, another
part of the flow rate leaves the bundle due to the same reason.
38
Chapter 2
Experimental facility
Concerning the cone angle, the possibilities are standard and wide angle nozzles. We have
chosen wide angle nozzles in order to cover the full length of the evaporator minimising the
number of nozzles needed.
Among the different kind of nozzles available in the market, HH14W (Spray Systems Co.)
fulfil the features of being full cone nozzles with a wide angle cone of circular shape. Table 2.1
(reference [5]) includes their main features and Figure 2.6a shows a picture of the selected
nozzles.
Table 2.1. Main characteristics of the chosen spray nozzles
Model
HH14W
Company
Spray Systems Co.
Type
Full cone
Shape
Circular
Nominal cone angle (º)
120
Nominal orifice diameter (mm)
3.58
Maximum free passage diameter (mm)
1.60
Nozzle pressure drop (kPa) function of the distributed
volumetric flow rate (m3/s)
PDnozzle  5.17·10 8 v 2.18
a
b
Figure 2.6. a) Circular wide angle full cone nozzles chosen. b) Nozzles connected to the distribution
tube
Once defined the kind of nozzles to be studied, we solved the problem of driving the
refrigerant to each of them with the distribution tube (Figure 2.6b). It has threaded female
connections (1/4”) to attach the nozzles, maintaining them at a fixed distance. However, it was
necessary to calculate the optimal distance between nozzles to cover the tested tube/s. The
optimisation method is a modification of another by Zeng and Chyu [6] and the following
assumptions are considered:


Homogeneous distribution of the fluid throughout the cone; i.e. if chosen a portion of the
total surface covered by a spray, the flow rate impinging on that surface is the result of
multiplying the total spray flow rate by the ratio of the chosen surface to the total surface
covered by the cone.
The spray cone of a nozzle is straight at the sides, unaffected by gravity in the range of
distances studied.
39
Chapter 2



Experimental facility
The shape of the cone is perfectly circular.
There is no interaction between the flows distributed by two or more nozzles that reach
a certain area.
The splashing rate is neglected.
In the experimental facility, the distribution tube should be placed in the vertical plane
containing the axis of the evaporator. If the tested tube is placed directly underneath, we have a
situation similar to that represented in Figure 2.7. An angle α, calculated following equation
(2.1), is defined by the tangents to the tested tube from the origin of the spray nozzle
(considered at the tip of the nozzle). The tube diameter, dt, was considered as 19.05 mm (3/4”)
and the distance from the tip of the nozzle, s, was set at 49.5 mm. This distance is constrained
by the evaporator dimensions.
b
a
Figure 2.7. Nozzle-tube system. a) Front view. b) Top view
sin 2  dt 2 s  dt 2
(2.1)
Considering a nozzle with a cone angle β, if β is greater than α, part of the fluid does not
impinge on the tube. The tangency spots are positioned at a vertical distance z’ from the origin
of the cone, calculated by equation (2.2). The diameter of the circle of spray at z’, dsp(z’), is
obtained by equation (2.3).
z'  s  dt 2 1  sin 2
(2.2)
dsp z'  2 z' tan 2
(2.3)
Taking into account the length of the evaporator, one nozzle is insufficient to distribute the
liquid refrigerant on the tube/s tested. When a distribution system consists of more than one
nozzle, the distance between them (between the threaded connections available in the
distribution tube) should be short enough to fully cover the surface with liquid, but minimising
the areas reached by two adjacent nozzles and the amount of refrigerant that leaves the
evaporator without touching the tube/s. This distance is the optimal distance, distopt in Figure
2.8, and it is calculated with equation (2.4). r(z’) is determined by equation (2.5).
40
Chapter 2
Experimental facility
Figure 2.8. Optimal distance between two adjacent nozzles, for the considered tube and distance
distopt  dsp z' 1  2 r z'2 dsp z'2
(2.4)
r z'  z' tan 2
(2.5)
For the chosen nozzles, distance to the tested tube and tube diameter, the distribution tube
was designed with threaded connections for 9 nozzles and 165 mm between the centres of two
adjacent connections.
A reasonable concern could be whether the flow rate is equally distributed by all the
nozzles. To discard this possibility we have calculated the pressure drop along the distribution
tube and nozzle connections and compared it with the pressure drop of the nozzles, provided by
the manufacturer. The ratio of the pressure drop of the nozzles to that along the distribution
tube is equal to or greater than 10. Taking into account that the liquid is introduced by both ends
of the evaporator, we calculated that the differences between the flow rates distributed by the
nozzles are lower than 5%.
41
Chapter 2
2.3.
Experimental facility
DATA ACQUISITION SYSTEM
The experimental setup is equipped with a data acquisition system based on a 16-bit data
acquisition card and a PC, 21 temperature sensors, 2 pressure transducers, 3 flow meters and
an active power transducer. The features and associated uncertainties of the different
measuring devices are shown in Table 2.2 and their layout in Figure 2.4.
The vapour temperature in the condenser is measured by means of 8 sensors (T01 – T08).
The vapour temperature in the evaporator is measured by means of 4 sensors (T09 – T12) and
the liquid temperature in the evaporator by means of another 4 sensors (T13 – T16). Another
sensor, T21, is placed in the refrigerant tank to measure the refrigerant temperature. These
sensors are A Pt100 inserted into stainless steel pockets of 100 mm of length and 3 mm of
diameter. The pressures in the condenser and in the refrigerant tank are measured using two
pressure transducers, P1 and P2, respectively. The mass flow rate and density of the liquid
refrigerant distributed during spray evaporation tests is measured by means of a Coriolis flow
meter (FMdist).
Temperature sensors, A Pt100 inserted into stainless steel pockets of 50 mm of length and
3 mm of diameter, are used in the heating and cooling water loops. T17 and T18 measure the
cooling water temperature at the inlet and outlet of the tubes placed in the condenser. T19 and
T20 measure the heating water temperature at the inlet and outlet of the tubes placed in the
evaporator. The cooling and heating water flow rates are measured by means of two
electromagnetic flow rates, FMcw and FMhw, respectively. Finally, an active power transducer
(qboiler) measures the electric power delivered to the heating water at the electric boiler.
The calibration test of the data acquisition system shows that the average uncertainty in
temperature measurement is within ±0.1 ºC.
Table 2.2. Features and accuracy of the different sensors used
Variable
Type
Measuring range
Accuracy
Temperatures
Pt100 A Desin
instruments SR-DZH
0 – 100 ºC
±0.1 ºC
Condenser pressure
Danfoss MBS-5150
0 – 2600 kPa
±0.3%·FS
Refrigerant tank
pressure
Danfoss AKS-33
0 – 1000 kPa
±0.8%·FS
Volumetric flow rates
Electromag. flow meter
SIEMENS SITRANS
M3100/M6000
0 – 3500 l/h
±0.25%·value
0 – 2190 kg/h
±0.25%·value
600 – 1200 kg/m3
±0.5 kg/m3
0 – 12000 W
±0.45%·value
Distributed refrigerant
mass flow rate
Distributed refrigerant
density
Electric power at the
electric boiler
Coriolis flow meter Micro
Motion ELITE CMF025
Active power transducer
Circutor CW-M
A computer programme prepared for spray evaporation, pool boiling and condensation tests
and developed in LabVIEW 8.5 software manages the data acquisition system. It repeats a loop
every 15 seconds and collects the values measured by each sensor. These values are shown in
the PC screen and can be saved in a .csv file for the data reduction process. The software was
also developed to calculate, show and chart the most important parameters. Figure 2.9 shows
the main screen of the programme developed for these experiments.
42
Chapter 2
Experimental facility
Figure 2.9. Main screen of the programme developed in LabVIEW 8.5
The programme allows regulating some of the most important parameters of the sensor by
means of PIDs. It controls the temperature of the distributed liquid refrigerant or pool of
refrigerant actuating over an analogue output of the acquisition card that drives an electronic
valve placed at the auxiliary cooling loop. Another analogue output is in charge of regulating the
mean heating water temperature (and therefore the logarithmic mean temperature difference at
the evaporator).
43
Chapter 2
2.4.
Experimental facility
ESPECIFICATIONS OF THE TUBES EMPLOYED
Five different commercially available tubes have been studied: two plain tubes, an integralfin tube and two 3D microfinned tubes. These tubes have been provided by INTEGASA, a heat
exchanger manufacturing company located in Vigo (Spain).
The plain tubes employed have 3/4” nominal external diameter and are made of copper
(Cu) and titanium (Ti). The copper tube (Figure 2.10a) has external and internal diameters of
18.87 and 16.75 mm, respectively and the titanium tube (Figure 2.10b) of 19.05 and 17.2 mm,
respectively.
a
b
Figure 2.10. Plain tubes used. a) Copper tube. b) Titanium tube
The tested 3D microfinned tubes are a Turbo-B and a Turbo-BII+, made of copper (Cu) and
commercialised by the company WOLVERINE TUBE INC. Both tubes have modified external
surface, designed for enhancing boiling heat transfer. Figure 2.11a and Figure 2.12b show the
external surfaces of the Turbo-B and the Turbo-BII+ tubes, respectively. Even though these
tubes are also available with smooth internal surface, the chosen tubes are also internally
enhanced, as can be seen in Figure 2.11b and Figure 2.12b. The main geometrical
characteristics of both tubes are included in Table 2.3.
a
b
Figure 2.11. Photographs of the Turbo-B tube. a) External surface. b) Cross section
44
Chapter 2
Experimental facility
a
b
Figure 2.12. Photographs of the Turbo-BII+ tube. a) External surface. b) Cross section
Table 2.3. Geometrical characteristics of the 3D microfinned tubes
Tube
Nominal
Turbo-B
Turbo-BII+
Catalogue number
54-9850035
59-4856525
Outer diameter (mm)
19.05
19.05
Wall thickness (mm)
0.889
Inner diameter (mm)
15.54
16.51
Outer diameter (mm)
18.87
18.87
Wall thickness (mm)
1.5
1.1
Minimum wall under fins (mm)
0.787
0.635
Root diameter (mm)
17.25
17.78
Nominal ridge height (mm)
0.381
0.39
Fin density (f.p.m.)
1575
1732
Nominal inner surface area (m2/m)
0.049
Actual inner surface area (m2/m)
0.070
0.0905
Nominal outer surface area (m2/m)
0.059
0.0585
Actual outer surface area (m2/m)
0.083
0.0984
Plain end
Outer finned section
Inner finned section
Areas
The tested integral-fin tube is a Trufin, made of titanium (Ti) and also commercialised by the
company WOLVERINE TUBE INC. From the different fin densities available, the chosen one
has 32 fins per inch (equivalent to 1250 fins per meter). Figure 2.13a shows the external
45
Chapter 2
Experimental facility
surfaces of the Trufin 32 f.p.i. tube and Figure 2.13b the inner surface, which in this case is
smooth. The main geometrical characteristics of the tube are included in Table 2.4.
a
b
Figure 2.13. Photographs of the Trufin 32 f.p.i. tube. a) External surface. b) Cross section
Table 2.4. Geometrical characteristics of the Trufin 32 f.p.i. tube
Tube
Trufin 32 f.p.i.
Outer diameter (mm)
19.05
Wall thickness (mm)
0.635
Fin thickness (mm)
0.965
Inner diameter (mm)
15.85 (16.45)
Minimum wall under fins (mm)
0.787
Root diameter (mm)
17.25
Fin pitch (mm)
0.8
Fin density (f.p.m.)
1250
Fin width base (mm)
0.5
Fin width tip (mm)
0.3
Fin flank angle (º)
4
Nominal inner surface area (m2/m)
0.0498
Nominal outer surface area (m2/m)
0.0598
Actual outer surface area (m2/m)
0.1535
Nominal
Outer finned section
Areas
The thermal conductivity of the copper employed is 386 W/m·K and its density 8890 kg/m3.
Concerning titanium, its thermal conductivity is 21.9 W/m·K and its density 4507 kg/m3.
46
Chapter 2
2.5.
Experimental facility
CONCLUSIONS
The experimental facility used to study pool boiling and spray evaporation on horizontal
tubes was described in this chapter. The sensors placed all over the test rig allow determining
the HTCs of such processes. The test rig consists mainly of a shell-and-tube evaporator,
connected to a heating water loop; a shell-and-tube condenser, connected to a cooling water
loop; and a liquid distribution system. Both heat exchangers work at a same pressure, with the
refrigerant flowing from one to another due to natural convection.
We focused specially on the liquid distribution system and on the way it was calculated and
designed. The system includes a tank, a refrigerant pump, and a distribution tube with wide
angle circular cone full nozzles. It allows testing different distributed liquid refrigerant flow rates
for the spray evaporation tests.
The types of tubes tested, all of ¾” (19.05 mm) nominal outer diameter, were two plain
tubes (titanium and copper), two 3D microfinned copper tubes (Turbo-B and Turbo-BII+) and a
2D finned titanium tube (Trufin 32 f.p.i.). We included the geometrical characteristics of the
tubes, as well as photographs of their inner and outer surfaces.
47
Chapter 2
Experimental facility
REFERENCES
[1] Á.Á. Pardiñas, J. Fernández-Seara, S. Bastos, F.J. Uhía, Diseño, construcción y validación
de un equipo experimental para el estudio de la evaporación en spray, in: Proceedings of the
VII Congreso Ibérico y V Congreso Iberoamericano de Ciencias y Técnicas del Frío, Tarragona,
Spain, 2014.
[2] Á.Á. Pardiñas, J. Fernández-Seara, R. Diz, Test rig for experimental evaluation of spray
evaporation heat transfer coefficients, in: Proceedings of the 24th IIR International Congress of
Refrigeration, Yokohama, Japan, 2015.
[3] J. Fernández-Seara, Á.Á. Pardiñas, Refrigerant falling film evaporation review: description,
fluid dynamics and heat transfer, Applied Thermal Engineering. 64 (2014) 155-171.
[4] Engineer’s Guide to Spray Technology, Spraying Systems Co., U.S.A., 2000.
[5] http://www.spray.com/cat75/hydraulic/files/31.html
[6] X. Zeng, M. Chyu, Heat transfer and fluid flow study of ammonia spray evaporators, Texas
Tech University, Lubbock, Texas, USA, 1995.
48
Chapter 3
Experimental methodology
This chapter describes the experimental methodology and the data reduction process to
determine pool boiling and spray evaporation HTCs for the different refrigerants and tubes
studied with the available experimental setup.
First, a short overview of the Wilson plot method to determine HTCs is done. After that, the
experimental methodology and conditions followed for each test are detailed, pointing out the
major differences between pool boiling and spray evaporation tests. Then, the calculation
methods to obtain the most important parameters, such as the refrigerant side HTCs or the
mass flow rates distributed on a certain surface, are described. Finally, the results of some
validation experiments are shown in order to support the experimental results obtained with this
experimental test rig and following this methodology and data reduction process.
Some of the main ideas detailed in this section were included in conference contributions
such as Á.Á. Pardiñas, J. Fernández-Seara, S. Bastos and F.J. Uhía, Diseño, construcción y
validación de un equipo experimental para el estudio de la evaporación en spray, included in
the proceedings of the “VII Congreso Ibérico y V Congreso Iberoamericano de Ciencias y
Técnicas del Frío” (Tarragona, Spain, 2014) [1]; Á.Á. Pardiñas, J. Fernández-Seara and R. Diz,
Test rig for experimental evaluation of spray evaporation heat transfer coefficients, from the 24th
IIR International Congress of Refrigeration (Yokohama, Japan, 2015) [2]; or Á.Á. Pardiñas, J.
Fernández-Seara, S. Bastos and R. Diz, Experimental boiling heat transfer coefficients of R134a on two boiling enhanced tubes, from the 8th World Conference on Experimental Heat
Transfer, Fluid Mechanics, and Thermodynamics (Lisbon, Portugal, 2013) [3].
49
Chapter 3
3.1.
Experimental methodology
CONVECTION HEAT TRANSFER COEFFICIENTS
Convection is the heat transfer mechanism that occurs between a solid and a fluid that have
different temperatures. Convection consists of simultaneous heat and mass transfer; i.e.
conduction takes place between the different fluid particles, but the energy transport is mainly
caused by the macroscopic fluid movement.
Describing convection from an analytical point of view is complex and involves mass,
momentum and energy equations, geometrical issues and fluid properties. Therefore, except for
those cases with simple geometries and fluid flow conditions, the study is faced using Newton’s
law of cooling. According to this law, convection heat flow is directly proportional to the surface
in contact with the fluid, A, by the convection HTC, h, by difference between the temperature of
the surface, Tsf, and the temperature of the bulk, Tbulk, as seen in equation (3.1).
q  A h Tsf  Tbulk 
(3.1)
Based on Newton’s law of cooling, for a certain geometry and fluid flow conditions, the
convection HTCs can be obtained experimentally by fixing a certain heat flow and measuring
the heat exchange area, and the temperature difference between the surface and the bulk.
However, this methodology requires measuring the temperature at the surface, which normally
varies from one point to another, and the existence of temperature sensors on it may modify the
fluid flow. This problem is even more challenging when the surface cannot be easily reached, as
normally happens with heat exchangers.
Wilson [4] proposed an alternative to this methodology which does not need placing
temperature sensors on the heat exchange surface. His method consists in determining the
overall thermal resistance of the whole heat exchange process, simple to obtain experimentally,
and separating it in the different thermal resistances of the process. With a proper design of
experiments, each HTC can be calculated.
In shell-and-tube condensers, for which the original method was proposed, the overall
thermal resistance, Rov, results from adding up the thermal resistances corresponding to outer
convection, Ro, to tube wall, Rw, to inner convection, Ri, and to fouling on the inner and outer
surfaces of the tube, Rfoul,i and Rfoul,o, respectively (equation (3.2)).
Rov  Ri  Rfoul,i  Rw  Rfoul,o  Ro
(3.2)
For a tube, taking into account the typical expressions for the convection and conduction
thermal resistances, the overall thermal resistance can be expressed as in equation (3.3),
where ho and hi stand for the outer and inner convection HTCs, respectively; do and di for the
outer and inner tube diameters, respectively; L for the length of the tube; and Ao and Ai the outer
and inner tube surfaces, respectively.
Rov 
lnd o d i 
1
1
 Rfoul,i 
 Rfoul,o 
hi Ai
2  kt L
ho Ao
(3.3)
The overall thermal resistance can be also calculated as a function of the overall HTC
referred to the inner/outer surface of the tubes, Ui/o, and the area corresponding to the
inner/outer diameter of the tube, Ai/o, as written in equation (3.4).
Rov 
1
U i / o Ai / o
(3.4)
Taking into account the conditions of condensation processes, Wilson considered that the
variations in the overall thermal resistance when changing the inner fluid flow rate are mainly
due to inner thermal resistance variations, being the remaining thermal resistances constant.
50
Chapter 3
Experimental methodology
Wilson observed that for a fully developed turbulent flow through a circular tube, the
convection HTC was directly proportional to what he called reduced velocity, ured, which
depended on the inner diameter of the tube and on the fluid properties. The inner convection
HTC could be obtained by equation (3.5), where C is a fitting constant and n and exponent
which should be determined experimentally.
hi  C ured n
(3.5)
If we combine equations (3.3) and (3.5) and group the constant thermal resistances we
obtain equation (3.6). This equation shows that the overall thermal resistance is a linear function,
and the experimental results are represented as in Figure 3.1.
R ov 
1
1
  R const
C Ai u n
red
(3.6)
Figure 3.1. Original Wilson plot
If a certain mass flow rate of cooling fluid, ṁcf, is used in the condenser, the thermal
resistance can be calculated dividing the logarithmic mean temperature difference at the
condenser, LMTD, by the heat flow exchanged, q, as stated in equation (3.7). The heat flow and
the LMTD can be calculated from experimental data following equations (3.8) and (3.9),
respectively. In the previous equations, Tv is the temperature of the vapour; Tcf,in and Tcf,out, are
the temperatures of the cooling fluid at the inlet and at the outlet of the tube, respectively; and
cp,fl, is the specific heat capacity of the cooling fluid.
Rov 
LMTD
q
(3.7)

 cf c p,cf Tcf ,out  Tcf ,in
qm

(3.8)
51
Chapter 3
LMTD 
Experimental methodology
Tv  Tcf ,in   Tv  Tcf ,out 
 T T
ln v cf ,in
 Tv  Tcf ,out





(3.9)
If the reduced velocity exponent, n, is known, the different values of the thermal resistance
can be represented against 1/uredn and can be adjusted with a linear regression (equation (3.6)).
Then, the constant C and the ΣRconst are determined and the outer and inner HTCs are
calculated by equations (3.5) and (3.10), respectively. Wilson stated that the exponent n that
best adjusted his experimental results was 0.82.
ho 
1 Ao
 Rconst  Rfoul,i  Rt  Rfoul,o
(3.10)
The original Wilson method could be adapted to other heat exchangers under the following
hypothesis: the thermal resistance of one of the fluids remains almost constant as the other
varies. This first approach was modified by different authors in order to make it more accurate
and versatile, since that hypothesis is not always as valid as it seems. A thorough review of the
different works and modifications developed on this subject is included in Fernández-Seara et
al. [5].
52
Chapter 3
3.2.
Experimental methodology
BOILING EXPERIMENTS
In this subsection we explain the experimental procedure followed both for obtaining pool
boiling and spray evaporation HTCs with our experimental setup. The general methodology is
shown in the first part, meanwhile in the second part the special features concerning spray
evaporation tests are detailed.
3.2.1.
Pool boiling experiments
Prior to any set of tests (tube/fluid combination), we paid special care on removing
incondensable gases (air) from the refrigerant loop. Once removed the air and charged with
refrigerant, we checked that the temperature and pressure measurements at the refrigerant side
coincided with saturation conditions.
The pool boiling HTCs were calculated using the values of the sensors placed at the
evaporator section, including the refrigerant side (T13 to T16 in Figure 2.4) and the heating water
loop (T19 and T20 in Figure 2.4). The experiments were designed with the aim of obtaining the
refrigerant side HTCs at constant pool boiling temperatures and varying the heat flux as much
as possible.
Each test consisted in registering the values measured by the different sensors of the test
rig, keeping constant the mean heating water temperature and flow rate through the tube and
the refrigerant pool temperature. Except for special sets of experiments, which will be explained
when needed, a group of tests (constant pool temperature) started with the maximum mean
heating water temperature possible. When stationary conditions were achieved, data were
registered for a minimum of 15 minutes. After that, the mean heating water temperature was
lowered and fixed at the next testing condition. When finished a group of tests, a new was
began at another refrigerant pool temperature, repeating the procedure explained in the
previous lines.
The temperature of the pool of refrigerant was fixed by adjusting the heat absorbed by the
cooling water circulating through the condenser tubes. The mean heating water temperature
was adjusted by regulating the heat transferred to the heating water at the electric boiler
through Joule effect. The electric power at the electric boiler was controlled by means of a
power regulator and a PID.
The heating water flow rate was kept as high as possible to minimise the inner thermal
resistance at the evaporator tubes, reduce the uncertainty of the HTCs and homogenise the
boiling process along the tube (similar wall temperature conditions). The cooling water flow rate
was kept as low as possible to increase the cooling water temperature difference between the
inlet and the outlet of the condenser tube/s and to calculate with more accuracy the heat flow at
this heat exchanger.
The refrigerant pool temperatures considered for these tests, independently of the
refrigerant and tube utilised, were of 10, 7 and 4 ºC. These temperatures are typical in water
chiller units. Concerning the range of mean heating water temperatures, it depended on the
tube, the refrigerant and the pool temperature. Therefore, this range is indicated for each case
with the experimental results.
3.2.2.
Spray evaporation experiments
In spray evaporation experiments there are two new parameters to be considered: the
relative position between the tested tube and the distribution tube and the distributed liquid
refrigerant mass flow rate. In addition, instead of fixing the refrigerant pool temperature at the
evaporator, we fixed the temperature of the refrigerant at the tank (measured by sensor T21 in
Figure 2.4), which was in good agreement with the temperatures measured at the sensors
placed at the lowest part of the evaporator (T13 to T16 in Figure 2.4).
The relative position of the tested tube and the distribution tube was introduced as a new
experimental variable because other authors observed that the liquid droplet impingement effect
could enhance heat transfer [6]. Thus, we should expect differences in the heat transfer
performance between those tubes that receive refrigerant directly from the distribution devices
and those that are wetted by the excess liquid from the row of tubes placed above them.
53
Chapter 3
Experimental methodology
Therefore, we have designed two different spray evaporation tests to illustrate these two
possibilities, as depicted in Figure 3.2. The first tests (Figure 3.2 left), from now on ST tests,
consist in distributing the refrigerant directly from the nozzles to a tube, being the distance from
the tip of the nozzle to the centre of the tube 59 mm. In the second tests (Figure 3.2 right),
named SB tests, the refrigerant is distributed on the same tube (conditioning tube), forming a
film that falls to the tube placed underneath (distance of 45 mm between centres). No heating
water circulates through the conditioning tube to prevent liquid refrigerant from vaporising
before falling to the tested tube.
Figure 3.2. Types of spray evaporation tests. Left, liquid refrigerant on the tube directly from the
nozzle (ST tests). Right, liquid refrigerant from a conditioning tube (SB tests)
We started with ST tests. The liquid refrigerant distribution temperature was fixed and, for
each group of tests, the mean heating water temperature started at the maximum value
achievable by the experimental test rig. Then, the distributed liquid refrigerant flow rate was set
at the maximum of the experimental set points considered, which was different for each of the
refrigerants tested. When stationary conditions were achieved, data were registered for a
minimum of 15 minutes. After that, the distributed liquid refrigerant flow rate was lowered and
the process repeated. When all the flow rates were tested, the mean heating water temperature
was lowered and fixed at the next testing condition and the sequence of tests was repeated.
Once finished ST tests, we repeated the whole process with SB tests.
Most of the variables involved in the experiments were controlled as for pool boiling test.
Concerning the temperature of the distributed liquid refrigerant, it was fixed by adjusting the
heat absorbed by the cooling water that circulates through the condenser tubes. The liquid
refrigerant flow rate distributed was regulated manually by means of the two valves installed for
that purpose.
The temperature of the distributed liquid refrigerant considered for these tests,
independently of the refrigerant and tube utilised, was 10 ºC. The distributed liquid refrigerant
flow rates tested were a function of the refrigerant used. With R134a they were 1000 kg/h, 1250
kg/h and 1500 kg/h and with ammonia these were 450 kg/h, 550 kg/h, 650kg/h, 750 kg/h and
850 kg/h. The range of the mean heating water temperatures depended on the refrigerant and
on the distributed liquid refrigerant flow rate. Therefore, this range is indicated for each case
with the experimental results.
54
Chapter 3
Experimental methodology
3.3.
DATA REDUCTION
3.3.1.
Refrigerant side heat transfer coefficient determination
We have calculated the refrigerant side (spray evaporation and pool boiling) HTCs from the
data measured in the experimental facility and from the refrigerant and water properties from
REFPROP 8.0 Database [7].
Taking into account the working principle of the experimental test rig and the good
insulation applied, the heat flow transferred from the refrigerant to the cooling water at the
condenser tube/s, qcw, calculated by equation (3.11), should be equal to that transferred from
the heating water to the refrigerant at the evaporator tube/s, qhw, determined by equation (3.12).
In these equations, ṁcw and ṁhw stand for the mass flow rates of the cooling water and heating
water, respectively; cp,cw and cp,hw stand for the specific heat capacity of the cooling and heating
water (evaluated at the mean temperature of each loop), respectively; Tcw,in and Tcw,out stand for
the cooling water temperatures measured at the inlet and outlet of the tube/s at the condenser,
respectively; and Thw,in and Thw,out stand for the heating water temperatures measured at the inlet
and outlet of the tube/s at the evaporator, respectively.




 cw c p,cw Tcw,out  Tcw,in
qcw  m
 hw c p,hw Thw,in  Thw,out
qhw  m
(3.11)
(3.12)
Prior to including the refrigerant pump in the refrigerant cycle, the agreement between the
heat flow with (3.11) and (3.12) was very good, and pool boiling HTCs were calculated with the
heat flow at the condenser tubes. This was very convenient, since the heat flow at the
condenser was determined very accurately and the heating water flow rate could be kept high to
reduce the inner thermal resistance at the evaporation tubes and to homogenise the boiling
process. This method was applied to all the copper tubes under pool boiling.
However, the aforementioned condition was no longer satisfied with spray evaporation tests.
We installed an active power transducer and the heat flow at the evaporator tubes was seen to
match the electric power delivered to the heating water at the electric boiler. The uncertainty of
the electric power was also seen to be lower, and the HTCs were obtained with it.
The overall thermal resistance at the evaporator tube/s is calculated by equation (3.13),
where LMTDevap stands for the logarithmic mean temperature difference at the evaporator,
which is calculated by equation (3.14). In this last equation Tl is the liquid refrigerant
temperature, independently of the type of test developed, and Thw,in and Thw,out are the heating
water temperatures measured at the inlet and outlet of the tube/s at the evaporator, respectively
Rov,evap 
LMTDevap
LMTDevap 
(3.13)
qevap
Tl  Thw,in   Tl  Thw,out 
 Tl  Thw,in
ln
 Tl  Thw,out





(3.14)
The overall thermal resistance can be also calculated by adding all the thermal resistances
involved in the boiling process, as shown in equation (3.15). We neglect the effect of fouling at
the inner and outer surfaces of the tube/s, Rfoul,i and Rfoul,o, respectively, because the tubes were
thoroughly and regularly cleaned. Therefore, the overall thermal resistance can be obtained by
equation (3.16).
55
Chapter 3
Experimental methodology
Rov ,evap 
1
1
 Rfoul,i  Rw  Rfoul,o 
hi Ai
ho Ao
(3.15)
Rov ,evap 
1
1
 Rw 
hi Ai
ho Ao
(3.16)
Ai and Ao stand for the inner and outer heat exchange areas, respectively. We have also
tested tubes with enhanced surfaces and their heat exchange areas are very difficult to quantify
accurately. It is a common practice to calculate these areas using the nominal inner and outer
diameters of the original plain tubes. Independently of the type of enhanced tube, the areas are
calculated by equations (3.17) and (3.18). di and do are the inner and outer diameters of the
evaporator tube/s and L the length.
Ai   di L
(3.17)
Ao   do L
(3.18)
The thermal resistance of the tube wall, Rw, is determined by equation (3.19). In this
equation, kt is the tube wall thermal conductivity. The diameters of enhanced tubes are also
considered as the nominal diameters of the original plain tube.
Rw 
lndo di 
2  kt L
(3.19)
The inner convection HTC, hi, is also obtained from experimental data using typical
correlations for forced convection heat transfer in plain and enhanced tubes. This issue is
further explained in subsection 3.3.2.
Once determined all the variables included in the overall thermal resistance, the boiling
HTCs are calculated by reordering equation (3.16) in a convenient manner (equation (3.20)).
This equation is identical for plain tubes and enhanced tubes. For the latter, we talk about
boiling HTCs referred to the nominal outer surface.
ho 
1

1
 Rov,evap  Rt 
hi Ai


 Ao

(3.20)
The superheating of the tube wall, ΔTSH, is calculated using equation (3.21). Tw,o stands for
the temperature at the outer tube wall, which is obtained with equation (3.22).
TSH  Tw,o  Tl
Tw ,o  Tl 
3.3.2.
qevap
Ao ho
(3.21)
(3.22)
Inner heat transfer coefficients
In this study we focus on boiling HTCs on tubes, but in order to determine them precisely,
we need to properly characterise the thermal resistance of the process that occurs inside them.
General correlations can lead to uncertainties in the determination of secondary fluid HTCs.
Another option is the Wilson method and modifications, which have been frequently applied as
indirect tools to obtain accurate correlations for those HTCs.
56
Chapter 3
Experimental methodology
Previous studies were developed in our laboratory to determine the validity of employing a
general correlation, such as that of Petukhov [8], for forced convection HTCs in fully developed
turbulent flow through smooth tubes. These studies, detailed in the doctoral thesis of Uhía [9],
aimed to obtain the fitting constants for the inner HTCs using as functional form the
aforementioned Petukhov correlation, (3.23). The Darcy-Weisbach friction factor, f, is calculated
by (3.24). In these equations Ci stands for the Petukhov correlation fitting constant, Recw and
Prcw stand for the dimensionless Reynolds and Prandtl numbers of the water flowing in the tube,
kcw stands for the water thermal conductivity and di for the inner diameter of the tube.
hi , pl  Ci F Petukhov   Ci
f 8Recw
 k cw
Prcw

2
3


1.07  12.7 f 8  Prcw  1  d i


f  0.79 lnRecw   1.642



(3.23)
(3.24)
The closer Ci is to 1, the better the agreement between the experimental data and this
general correlation. Uhía [9] reported a deviation of 2.3% between them and, consequently,
considered Ci equal to the unity in his studies. Taking into account this study, which was
developed with basically the same experimental facility, we considered the same correlation in
order to determine the inner convection HTCs for our experimental studies with tubes of smooth
inner surface. The uncertainty was estimated as 5%.
Concerning the tubes with enhanced internal surface, Turbo-B and Turbo-BII+, the
manufacturer proposes the correlation by Sieder and Tate [10], equation (3.25), to calculate the
inner convection HTCs. The experimental constant, STC, is also proposed by the manufacturer.
0.058 and 0.075 are the STC values for the Turbo-B and Turbo-BII+ tubes, respectively.
.8 1 3   hw
hi ,en  STC Re0hw
Prhw 
 w
3.3.3.



0.14
 k hw

 di



(3.25)
Mass flow rate reaching the tubes
The distribution conditions of the nozzle devices are such that only part of the liquid
refrigerant spread reaches the studied tube/s. The procedure to determine this fraction is based
on a method described by Zeng and Chyu [11] and follows the study explained in subsection
2.2.2. For the sake of facilitating its understanding, it will be repeated here.
The following assumptions are considered:





Homogeneous distribution of the fluid throughout the cone; i.e. if chosen a portion of the
total surface covered by a spray, the flow rate impinging on that surface is the result of
multiplying the total spray flow rate by the ratio of the chosen surface to the total surface
covered by the cone.
The spray cone of a nozzle is straight at the sides, unaffected by gravity in the range of
distances studied.
The shape of the cone is perfectly circular.
There is no interaction between the flows distributed by two or more nozzles that reach
a certain area.
The splashing rate is neglected.
In the experimental facility, the distribution tube is placed in the vertical plane containing the
axis of the evaporator. If the tested tube is placed directly underneath, we have a situation
similar to that represented in Figure 3.3. An angle α is defined by the tangents to the tested tube
from the origin of the spray nozzle, which was considered at the tip of the nozzle, and is
calculated following equation (3.26). The tube diameter, dt, was considered as 19.05 mm (3/4”)
and the distance from the tip of the nozzle, which depends on the size of the evaporator shell,
was set at 49.5 mm.
57
Chapter 3
Experimental methodology
b
a
Figure 3.3. Nozzle-tube system. a) Front view. b) Top view
sin 2  dt 2 s  dt 2
(3.26)
Considering a nozzle with a cone angle β, if β is greater than α, part of the fluid does not
impinge on the tube. The tangency spots are positioned at a vertical distance z’ from the origin
of the cone, calculated by equation (3.27). The diameter of the circle of spray at z’, dsp(z’), is
obtained by equation (3.28).
z'  s  dt 21  sin 2
(3.27)
dsp z'  2 z' tan 2
(3.28)
Only that part of the spray cone between the tangents reaches the tube. Therefore, when
calculating the fraction of the total liquid that impinges on the tube, we should consider the area
of the intersection between the tube and the spray cone, projected on a plane normal to the
nozzle axis at the distance z’ from the origin of the spray cone. This area, Aproj(z’), striped in
Figure 3.3b, is obtained by equation (3.29). r(z’) and m(z’) are calculated by equations (3.30)
and (3.31), respectively.


Aproj z'  arcsin 2 r z' dsp z' dsp z'2 2  2 mz'r z'
(3.29)
r z'  z' tan 2
(3.30)
mz'  dsp z'2 4  r z'2
(3.31)
Taking into account the length of the evaporator, one nozzle is insufficient to distribute the
liquid refrigerant on the tube/s tested. When a distribution system consists of more than one
nozzle, the distance between them (between the threaded connections available in the
distribution tube) should be short enough to fully cover the surface with liquid, but minimising
the areas reached by two adjacent nozzles and the amount of refrigerant that leaves the
evaporator without touching the tube/s. This distance is the optimal distance, distopt in Figure
3.4, and it is calculated with equation (3.32). r(z’) is determined by equation (3.30).
58
Chapter 3
Experimental methodology
Figure 3.4. Optimal distance between two adjacent nozzles, for the considered tube and distance
distopt  dsp z' 1  2 r z'2 dsp z'2
(3.32)
For the chosen nozzles, distance to the tested tube and tube diameter, the distribution tube
was designed with threaded connections for 9 nozzles and 165 mm between the centres of two
adjacent connections.
The mass flow rate reaching the top of the tube under these conditions, ṁtop, is calculated
using equation (3.33). The projected area of the tube, An,proj, that can be achieved by the nozzle
system is determined with equation (3.34). Generally, this mass flow rate can be defined in a
dimensionless way by the Reynolds number, as seen in equation (3.35), where Γ stands for the
mass flow rate at the top of the tube per unit of tube length and per tube side (equation (3.36)).
 top  m
 dist An,proj z'  n  dsp z'2 4 
m


(3.33)
An,proj z'  2 r z'L
(3.34)
Re,top  4   l
(3.35)
  m top 2 L 
(3.36)
Finally, the mass flow rate reaching the top of the tube is compared with the amount of
liquid refrigerant per unit of time that vaporises during each experiment, ṁe, by the overfeed
ratio (OF in equation (3.37)). The vaporised mass flow rate is obtained with equation (3.38),
being hlv the refrigerant latent heat of vaporisation.
OF  m top m e
(3.37)
m e  qevap hlv
(3.38)
3.3.4.
Enhanced surface enhancement factor
To quantify the enhancement due to the use of enhanced surfaces, compared to a plain
tube, we defined the surface enhancement factor, EFsf. As shown in equation (3.39), it
compares the pool boiling HTCs for the enhanced surface with those for the corresponding plain
tube (same nominal outer diameter), at the same heat flux, q̇, pool temperature, Tl, and
refrigerant.
59
Chapter 3
Experimental methodology

EFsf  ho,en ho, pl
3.3.5.
q,Tl ,ref
(3.39)
Spray evaporation enhancement factor
According to several works from the literature, spray evaporation can lead to an
enhancement of the boiling heat transfer, if compared to pool boiling under similar conditions.
This enhancement is quantified by a spraying enhancement factor, EFsp,Γ, determined with
equation (3.40). It compares the spray evaporation HTCs, at a certain liquid refrigerant mass
flow rate, to those under pool boiling, at the same heat flux, q̇, refrigerant temperature, Tl, tube
and refrigerant. We have determined ho,pb in each case using the correlations obtained from our
own experimental data.


EFsp,  ho,sp, ho, pb 
q,Tl , ref , tube
60
(3.40)
Chapter 3
3.4.
Experimental methodology
UNCERTAINTY DETERMINATION
The simple presentation of the boiling HTCs leaves this information incomplete. By
presenting the uncertainties related to their determination, we give an idea of the quality and
reliability of these results. Uncertainty is a parameter associated with the estimated value of a
physical magnitude, measured or calculated, that indicates the range of values were the actual
value of this physical magnitude should be. In this work we have developed an uncertainty
determination procedure based on the Evaluation of measurement data – Guide to the
expression of uncertainty measurement (GUM) [12]. The results determined are included
throughout the document with their uncertainties as error bars. The determination of the
uncertainties of each parameter is detailed in Appendix A.
61
Chapter 3
3.5.
Experimental methodology
EXPERIMENTAL FACILITY VALIDATION
The experimental facility validation issues can be classified into those concerning the heat
flows, measured and calculated at the different loops of the experimental test rig and with the
different kinds of experiments; and those concerning spray distribution.
As aforementioned, prior to including the distribution system in the experimental test rig, the
pool boiling HTCs were determined by means of the heat flow transferred from the refrigerant to
the cooling water flowing through the condenser tubes. This was possible since the only heat
flows that existed in the refrigerant loop were the heat flow transferred from the heating water to
the refrigerant at the evaporator and the heat flow transferred from the refrigerant to the cooling
water at the condenser. The heat transfer from the ambient to the refrigerant was neglected due
to the convenient insulation of the test rig.
Figure 3.5, Figure 3.6 and Figure 3.7 compare the two heat flows at the condenser and
evaporator tubes, determined during the experiments with the copper plain tube, the copper
Turbo-B tube and the copper Turbo-BII+ tube, respectively. The average deviation for any of
these cases is close to 10% and the uncertainties, shown as error bars, are clearly lower at the
cooling water heat flow than at the heating water heat flow. More details on deviations and
uncertainties are given in Table 3.1.
4000
+10%
qcw [W]
3000
2000
1000
0
0
1000
2000
3000
4000
qhw [W]
Figure 3.5. Heat flow at the condenser vs. heat flow at the evaporator of R134a pool boiling
experiments developed with the cooper plain tube at the evaporator
62
Chapter 3
Experimental methodology
6000
+10%
5000
qcw [W]
4000
3000
2000
1000
0
0
1000
2000
3000
4000
5000
6000
qhw [W]
Figure 3.6. Heat flow at the condenser vs. heat flow at the evaporator of R134a pool boiling
experiments developed with the cooper Turbo-B tube at the evaporator
6000
+10%
5000
qcw [W]
4000
3000
2000
1000
0
0
1000
2000
3000
4000
5000
6000
qhw [W]
Figure 3.7. Heat flow at the condenser vs. heat flow at the evaporator of R134a pool boiling
experiments developed with the cooper Turbo-BII+ tube at the evaporator
63
Chapter 3
Experimental methodology
Table 3.1. Average and maximum deviation between the heat flows determined in the experiments
with the copper tubes and R134a under pool boiling; and average and maximum uncertainties of
these heat flows
Deviation between
heat flows [%]
Uncertainties qhw [%]
Uncertainties qcw [%]
Tube
Average
Maximum
Average
Maximum
Average
Maximum
Plain
12.2
35.2
40.7
108.9
4.2
7.1
Turbo-B
8.35
30.3
15.4
36.6
3.3
5.7
Turbo-BII+
11.2
32.3
16.5
46.8
3.1
3.8
When included the distribution system in the experimental test rig, we needed to change the
method to determine the overall thermal resistance and the HTCs. Considering the good
insulation of the heating water circuit, we assumed that, under stationary conditions, all the heat
flow absorbed by this fluid inside the electric boiler, measured through the active power
transducer, is transferred to the refrigerant in the evaporator by the heating water. We checked
this statement with validation tests, developed under pool boiling conditions, saturation
temperatures of 10 ºC and 5 ºC and using ammonia and the titanium plain tube. A particularity
of these tests is that we kept the heating water mass flow rate low in order to increase the
temperature difference of the heating water at the inlet and outlet and to calculate the heating
water heat flow accurately.
Figure 3.8 compares the electric power at the electric boiler and the heat flow of the heating
water at the evaporator tubes. The discrepancies between both are on average lower than 2.4%
and never greater than 8%. We concluded that the overall thermal resistance could be
accurately calculated using the electric power at the electric boiler. We also confirmed that the
uncertainties associated to the electric power at the electric boiler are lower than the
uncertainties of the heating water heat flow (on average ±1.5% and ±7.2%, respectively).
5000
+5%
4000
qboiler [W]
-5%
3000
2000
1000
0
0
1000
2000
3000
4000
5000
qhw [W]
Figure 3.8. Electric power at the electric boiler vs. heat flow at the evaporator obtained at the
specific validation experiments under pool boiling of ammonia and with a titanium plain tube
64
Chapter 3
Experimental methodology
We also checked the validity of the assumption with the results of the pool boiling tests with
ammonia (Figure 3.9 and Figure 3.10), spray evaporation with R134a (Figure 3.11) and spray
evaporation with ammonia (Figure 3.12). More details on average and maximum deviations and
uncertainties of the ammonia pool boiling tests and of the spray evaporation tests are included
in Table 3.2 and Table 3.3, respectively.
6000
5000
+5%
4000
qboiler [W]
-5%
3000
2000
1000
0
0
1000
2000
3000
4000
5000
6000
qhw [W]
Figure 3.9. Electric power at the electric boiler vs. heat flow at the evaporator obtained at the
ammonia pool boiling experiments with a titanium plain tube
6000
5000
+5%
-
qboiler [W]
4000
3000
2000
1000
0
0
1000
2000
3000
4000
5000
6000
qhw [W]
Figure 3.10. Electric power at the electric boiler vs. heat flow at the evaporator obtained at the
ammonia pool boiling experiments with a titanium Trufin 32 f.p.i.
65
Chapter 3
Experimental methodology
3000
+5%
-5%
qboiler [W]
2000
1000
0
0
1000
2000
3000
qhw [W]
Figure 3.11. Electric power at the electric boiler vs. heat flow at the evaporator obtained at the
R134a spray evaporation experiments with a copper plain tube
5000
+5%
4000
-5%
qboiler [W]
3000
2000
1000
0
0
1000
2000
3000
4000
5000
qhw [W]
Figure 3.12. Electric power at the electric boiler at the electric boiler vs. heat flow at the evaporator
obtained at the ammonia spray evaporation experiments with a titanium plain tube
66
Chapter 3
Experimental methodology
Table 3.2. Average and maximum deviation between the electric power and the heating water heat
flow determined in the experiments with the titanium tubes and ammonia under pool boiling; and
average and maximum uncertainties of the electric power and heat flow
Deviation between
heat flows [%]
Uncertainties qboiler [%]
Uncertainties qhw [%]
Tube
Average
Maximum
Average
Maximum
Average
Maximum
Plain
4.1
22.0
1.9
3.5
18.7
85.1
Trufin 32
f.p.i.
7.2
32.2
1.4
3.7
25.5
81.6
Table 3.3. Average and maximum deviation between the electric power and the heating water heat
flow determined in the experiments with the cooper and titanium tubes under spray evaporation;
and average and maximum uncertainties of the electric power and heat flow
Deviation between
heat flows [%]
Uncertainties qboiler [%]
Uncertainties qhw [%]
Tube
Average
Maximum
Average
Maximum
Average
Maximum
Copper
plain
2.8
10.5
0.5
1.3
11.7
17.6
Titanium
plain
6.7
36.6
1.4
2.6
20.3
79.3
Concerning the validation of the distribution system, we focused on two features: the
proximity to saturation conditions of the distributed refrigerant and the cone angles formed by
the nozzles.
Spray evaporation tests consisted in distributing the liquid refrigerant at conditions very
close to saturation, as occurs in vapour compression refrigeration systems with spray
evaporators. To validate this condition in our experimental facility, we compared the arithmetic
mean of the temperatures measured by the sensors placed at the low part of the evaporator
(T13 – T16 in Figure 2.4), to the saturation temperature that corresponds to the pressure
measured at the refrigerant tank (P2 in Figure 2.4). To calculate the latter, we used the
REFPROP 8.0 database [7]. There was a good agreement between both, independently of the
refrigerant, as shown in Figure 3.13 and Figure 3.14 for R134a and ammonia, respectively.
67
Chapter 3
Experimental methodology
12
Tl [ºC]
11
10
9
8
8
9
10
11
12
T(P2) [ºC]
Figure 3.13. Temperature of the distributed liquid R134a vs. saturation temperature at the pressure
in the refrigerant tank
12
Tl [ºC]
11
10
9
8
8
9
10
11
12
T(P2) [ºC]
Figure 3.14. Temperature of the distributed liquid ammonia vs. saturation temperature at the
pressure in the refrigerant tank
Regarding the spray cone angle, we checked that it was close to the value available in the
manufacturer catalogue, which for these nozzles is 120º. This is crucial in our experimental
facility, particularly if the determined angle is lower than the expected value, because it would
mean that dry patches may occur independently of the heat flux applied on the tube surface.
68
Chapter 3
Experimental methodology
To determine the cone angle we analysed the videos recorded of the different experiments.
At each distributed refrigerant flow rate, we analysed 3 randomly chosen snapshots. By means
of a video analyser tool we approximated the spray cone angle of each snapshot. For further
calculations we considered the arithmetic mean of the angles of the 3 snapshots with each flow
rate.
Figure 3.15 shows a picture for each flow rate condition with R134a as refrigerant. All of
them are very close to the manufacturer value (120º) and therefore the distribution system
worked as designed. The spray cone angles considered were 120º at 1000 kg/h, 122º at 1250
kg/h and 124º at 1500 kg/h. Figure 3.16 describes the analogous study with ammonia as
refrigerant and again the spray cone angles are equal to or greater than the manufacturer value.
In this case, the spray cone angles considered were 120º at 450 kg/h, 125º at 550 kg/h and
130º at 650 kg/h, 750 kg/h and 850 kg/h.
a
b
c
Figure 3.15. Spray cone angles obtained with R134a and different distributed flow rates.
a) 1000 kg/h. b) 1250 kg/h. c) 1500 kg/h
69
Chapter 3
Experimental methodology
a
b
c
d
e
Figure 3.16. Spray cone angles obtained with ammonia and different distributed flow rates.
a) 450 kg/h. b) 550 kg/h. c) 650 kg/h. d) 750 kg/h. e) 850 kg/h
70
Chapter 3
3.6.
Experimental methodology
CONCLUSIONS
In this section we have described the experimental methodology to determine refrigerant
pool boiling and spray evaporation HTCs on horizontal tubes. The methodology is based on the
separation of the thermal resistances that are part of the overall heat transfer process occurring
in heat exchangers.
The design of experiments focused on studying the boiling HTCs under temperature
conditions close to those found at water chillers, and with the largest range of heat fluxes
possible. We conceived a specific experimental methodology to analyse the influence of the
impingement effect on the HTCs with distribution of the liquid refrigerant.
After that, we have explained the calculation method to determine the HTCs from the
experimental data from the test rig. Experimental data obtained are mainly temperatures,
pressures, flow rates (mass and volumetric) and electric power. We have detailed the method to
estimate the fraction of liquid refrigerant reaching the studied tubes under spray conditions and
defined the enhancement factor to compare the HTCs calculated for different tubes and
different boiling process, at the same conditions.
The results from following subsections include uncertainties and these uncertainties prove
their quality and reliability. The determination of the uncertainties is based on the Guide to the
Expression of Uncertainty in Measurements [12].
Finally, we have performed validation experiments to check the assumptions considered at
the calculation process. The validation process was successful, as shown in the different charts
of this subsection. Therefore, the results obtained with this experimental facility and procedure,
included further in this document, result from a convenient and validated process.
71
Chapter 3
Experimental methodology
REFERENCES
[1] Á.Á Pardiñas, J. Fernández-Seara, S. Bastos, F.J. Uhía, Diseño, construcción y validación
de un equipo experimental para el estudio de la evaporación en spray, in: Proceedings of the
VII Congreso Ibérico y V Congreso Iberoamericano de Ciencias y Técnicas del Frío. Tarragona,
Spain, 2014.
[2] Á.Á Pardiñas, J. Fernández-Seara, R. Diz, Test rig for experimental evaluation of spray
evaporation heat transfer coefficients, in: Proceedings of the 24th IIR International Congress of
Refrigeration. Yokohama, Japan, 2015.
[3] Á.Á. Pardiñas, J. Fernández-Seara, S. Bastos, R. Diz, Experimental boiling heat transfer
coefficients of R-134a on two boiling enhanced tubes, in: Proceedings of the 8th World
Conference on Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics. Lisbon,
Portugal, 2013.
[4] E.E. Wilson, A basis of rational design of heat transfer apparatus, ASME Journal of Heat
Transfer. 37 (1915) 47-70.
[5] J. Fernández-Seara, F.J. Uhía, J. Sieres, A. Campo, A general review of the Wilson plot
method and its modifications to determine convection coefficients in heat exchange devices,
Applied Thermal Engineering. 27 (2007) 2745-2757.
[6] X. Zeng, M. Chyu, Z.H. Ayub, Experimental investigation on ammonia spray evaporator with
triangular-pitch plain-tube bundle, Part I: Tube bundle effect, International Journal of Heat and
Mass Transfer. 44 (2001) 2299-2310.
[7] E.W. Lemmon, M.O. McLinden, M.L. Huber, NIST Reference Fluid Thermodynamic and
Transport Properties Database (REFPROP), 8.0th ed. National Institute of Standards and
Technology, 2008.
[8] B.S. Petukhov, Heat Transfer and Friction Factor in Turbulent Pipe Flow with Variable
Physical Properties, Advanced Heat Transfer. 6 (1970) 503-564.
[9] F.J. Uhía, Aportaciones al Estudio de la Condensación de Refrigerantes Puros y Mezclas
sobre Tubos Lisos y Mejorados, 2010.
[10] E.N. Sieder, G.E. Tate, Heat Transfer and Pressure Drop of Liquids in Tubes, Industrial and
Engineering Chemistry. 28 (1936) 1429-1435.
[11] X. Zeng, M. Chyu, Heat transfer and fluid flow study of ammonia spray evaporators, Texas
Tech University, Lubbock, Texas, USA, 1995.
[12] Bureau International des Poids et Mesures, Joint Committee for Guides in Metrology
(JCGM), Evaluation of Measurement Data - Guide to the Expression of Uncertainty in
Measurement (GUM), 2008.
72
Chapter 4
Pool boiling of pure
refrigerants: R134a and
ammonia
This chapter explains the pool boiling HTCs determined with the experimental test rig and
procedure previously described. The refrigerants tested were R134a and ammonia, and the
tubes were made of copper and titanium, depending on the refrigerant-material compatibility;
and with plain and enhanced surfaces.
With each combination tube-refrigerant, we show the heat flux determined versus the tube
wall superheat to check in which area of the boiling curve our processes are. We also show how
pool boiling HTCs depend on heat flux and on the saturation temperature. In addition, with
ammonia we illustrate the effect of nucleation hysteresis on HTCs.
When possible, the HTCs obtained in this work are compared with those from works found
in the specialised literature. We also show the improvement in heat transfer performance
obtained, under the same conditions, with the different enhanced tubes.
We include a photographic report of the ammonia pool boiling processes on both the plain
and the enhanced tube. The pictures cover the full range of heat fluxes studied.
Some of the results here detailed appear in the journal paper Á.Á. Pardiñas, J. FernándezSeara, C. Piñeiro-Pontevedra and S. Bastos, Experimental Determination of the Boiling Heat
Transfer Coefficients of R-134a and R-417A on a Smooth Copper Tube, Heat Transfer
Engineering 35 (2014) 1424-1434 [1]. There are also other results in conference contributions
such as Á.Á. Pardiñas, J. Fernández-Seara, S. Bastos and R. Diz, Experimental boiling heat
transfer coefficients of R-134a on two boiling enhanced tubes, included in the proceedings of
the “8th World Conference on Experimental Heat Transfer, Fluid Mechanics, and
Thermodynamics” (Lisbon, Portugal, 2013) [2]; and Á.Á. Pardiñas, J. Fernández-Seara and R.
Diz, Experimental study on heat transfer coefficients of spray evaporation and pool boiling on
plain tubes, of the 24th IIR International Congress of Refrigeration (Yokohama, Japan, 2015) [3].
73
Chapter 4
4.1.
Pool boiling of pure refrigerants: R134a and ammonia
POOL BOILING OF R134a ON PLAIN TUBE
In this subsection, we present the results obtained with pool boiling tests of R134a on the
copper plain tube. We conducted tests with the pool of refrigerant at 10 ºC, 7 ºC and 4 ºC,
varying the LMTD at the evaporator from 3 K and 8.5 K (at steps of 0.5 K). With these
conditions, the heat flux ranged from 4800 W/m2 to 33200 W/m2. The velocity of the heating
water was 4 m/s, approximately, and the Reynolds number ranged from 47200 to 64100. Thus,
the flow was fully developed turbulent and the application of the correlation shown in subsection
3.3.2 for the plain tube was suitable. The heating water HTCs ranged from 12600 W/m2·K to
14600 W/m2·K, approximately.
4.1.1.
Refrigerant side heat transfer coefficients
Nukiyama [4] was the first to study and represent the boiling heat transfer curves (Figure
4.1) and that is the reason why the curves used to represent these processes are normally
called Nukiyama curves. Currently, it is more common to represent the surface superheating
instead of the surface temperature (Thome [5]). Nukiyama curves represent the trends of boiling
heat transfer regimes: natural convection, nucleate boiling, transition boiling and film boiling.
The curve in Figure 4.1 covers the first two regions, which are those expected in flooded
evaporators or spray evaporators, and, therefore, we focus on those two processes. Natural
convection is characterised by slight increases of the heat flux as the surface superheating
rises. At a certain point, called onset of nucleate boiling, this process starts to occur. In nucleate
boiling, a slight increase in the surface superheating leads to an important increase in heat flux.
This region is more interesting from a heat transfer point of view, as higher HTCs are expected
if kept the surface superheating constant.
Figure 4.1. Nukiyama boiling curve, Nichrome wire, d = 0.535 mm, water temperature = 100 °C
(reference [4])
Based on the Nukiyama general curve, we analysed the heat flux vs. surface superheating
curves of each tube-refrigerant combination tested. The reason is to detect in which region of
the curve is each test and to better understand the results. Figure 4.2 represents the boiling
curve of the pool boiling process of R134a on a smooth copper tube. From the lowest surface
superheating to the highest, the process is in the nucleate boiling region, independently of the
refrigerant pool temperature. Therefore, the heat flux increases rapidly with slight increase of
the surface superheating. If fixed the surface superheating, the heat flux is slightly higher if the
pool temperature increases.
74
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
40000
Tl 10 ºC
35000
Tl 7 ºC
30000
Tl 4 ºC
q/Ao [W/m2]
25000
20000
15000
10000
5000
0
0
1
2
3
4
5
6
7
ΔTSH [K]
Figure 4.2. Heat flux on the outer surface of the copper plain tube vs. surface superheating, under
R134a pool boiling conditions, with the different saturation temperatures tested
Figure 4.3 includes the pool boiling HTCs vs. the heat flux, obtained with the same tests. In
agreement with the tendencies presented in the previous paragraph, the higher the heat flux,
the higher the pool boiling HTCs. In addition, if fixed the heat flux, the HTCs are higher when
the R134a pool temperature increases. The average, maximum and minimum uncertainties
associated to the determination of these HTCs were ±5.9%, ±9.2% and ±4.3%, respectively.
7000
Tl 10 ºC
6000
Tl 7 ºC
Tl 4 ºC
ho [W/m2·K]
5000
4000
3000
2000
1000
0
0
5000
10000
15000
20000
25000
30000
35000
40000
q/Ao [W/m2]
Figure 4.3. R134a pool boiling HTCs vs. heat flux on the outer surface of the copper plain tube, with
the different saturation temperatures tested
We developed an experimental correlation with the pool boiling HTCs obtained with the
copper plain tube and R134a, shown in equation (4.1). The correlation depends on the heat
75
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
flux, q̇, and on the reduced pressure, pred (related to the saturation temperature), which were the
parameters varied and controlled during the experiments. The coefficient of determination of the
correlation is R2 = 0.99 and the average absolute deviation between the experimental data and
the correlation is 0.5%.
0.48
ho  44.9 q 0.57 pred
4.1.2.
(4.1)
Comparison with correlations
Many works from the specialised literature focus on the study of the HTCs of pool boiling of
refrigerants on tubes. In contrast with other processes, such as condensation on a tube or
forced convection inside a tube, pool boiling correlations differ importantly from one study to
another. The reason is the large number of parameters that have an important effect on this
process and that should be under control, such as heat flux, reduced pressure, tube roughness,
refrigerant surface tension, tube material, etc.
To properly apply some correlations from the literature, we determined the roughness of the
copper tube. The technique used was the profilometry (profilometer DEKTAK 150) and we
chose a random section of the tube, shown in Figure 4.4. We measured 10 profiles at the
external surface and the arithmetic averages of the absolute distances from the midlines to the
profiles, often denoted as Ra, appear in Table 4.1. From these experiments we determined the
mean Ra for the 10 profiles, which resulted to be 0.326416 µm. It is important to notice that the
resolution of the profilometer is 0.472 μm/sample, the same order of magnitude as the result
measured. Therefore, the roughness determination method should be improved.
Figure 4.4. Section of the copper tube chosen for the roughness determination
Table 4.1. Mean roughness height, Ra, per profile and arithmetic mean of Ra for the 10 profiles
76
Profile
Ra [µm]
Profile
Ra [µm]
1
0.28795
6
0.35028
2
0.29918
7
0.30707
3
0.29136
8
0.3544
4
0.31104
9
0.34509
5
0.27414
10
0.44365
Mean
0.326416
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
We selected well-known correlations of the literature to compare our experimental results.
These correlations were equation (4.2), of Stephan and Preusser [6]; equation (4.3), of Cooper
[7]; equation (4.4), of Ribatski and Saiz Jabardo [8]; and equation (4.5), of Gorenflo and
Kenning [9]. In these equations, kl stands for the thermal conductivity of the liquid refrigerant at
saturation conditions; dbubble for the bubble departure diameter (equation (4.6)); ρl and ρg for the
refrigerant density at liquid and gas saturation conditions, respectively; cp,l for the specific heat
capacity of the liquid refrigerant at saturation conditions; σ for the surface tension of the liquid
refrigerant at saturation conditions; hlv for the refrigerant latent heat of vaporization; q̇ for the
heat flux on the outer surface of the tube; Ts for the saturation temperature in Kelvin; M for the
molar mass of the refrigerant; pred for the reduced pressure; and g for the acceleration of gravity.
In addition, there are several constants in these equations, such as cw, that depends on the
material of the tube. For Cooper [7], this constant is 95 when the tube is of copper and 55 when
the tube is of stainless steel. For Ribatski and Saiz Jabardo [8], it equals 100 with copper, 95
with brass and 85 with stainless steel. Rp is the surface peak roughness, which according to
Kotthoff and Gorenflo [10] should be replaced by the mean roughness height, Ra, divided by
0.4. Finally, β stands for the contact angle and according to Stephan and Preusser [6] is 35º
with refrigerants.
0.1 k l   g
ho 
d b   l




0.1565
 l c p,l

 k
l

0.371
 h d 2  2 c2 
lv
 d b q

b l p,l 



2
kl


 k l Tsat









 0.162 

k l2




  l c p2,l  d b 


0.35
(4.2)
0.674
0.120.2 logRp  logp 0.55 q 0.67
ho  cw M 0.5 pred
red
(4.3)
0.2
0.45 
ho  cw M  0.5 pred
 logpred  0.8 Ra0.2 q 0.9  0.3 pred
(4.4)
 q 
ho  href  
 q0 


0.3
0.95  0.3 pred
 k c

pw 

 k  cp

copper 



  Ra 
 

  Ra0 
2 15
(4.5)
0.25


2
d b  0.146  

 g  l   g 


1.4 pred
 0.7 p 0.2  pred 
red
1  pred


(4.6)
In Figure 4.5 we compare our experimental results with those from the aforementioned
correlations and in Table 4.2 we include the deviation range between our experimental data and
each correlation, as well as the arithmetic mean of the deviations between the predicted and the
experimental HTCs in absolute value. The figure shows that, except for Stephan and Preusser
[6] correlation, most of our experimental results are correlated within ±30%, being the
correlation from Gorenflo and Kenning [9] the one with the best agreement.
77
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
8000
Stephan and Preusser
Cooper
Ribatski and Saiz Jabardo
Gorenflo and Kenning
7000
hcorr [W/m2·K]
6000
+30%
+20%
+10%
-10%
-20%
5000
-30%
4000
3000
2000
1000
0
0
1000 2000 3000 4000 5000 6000 7000 8000
hexp [W/m2·K]
Figure 4.5. R134a pool boiling HTCs obtained with correlations vs. experimental pool boiling HTCs
from this work, with a copper plain tube and under the same conditions
Table 4.2. Comparison of the experimental pool boiling HTCs (R134a and copper plain tube) with
those calculated with correlations
Correlation
78
Arithmetic mean of the
Deviation range (%)
deviations in absolute value (%)
Stephan and Preusser
[6]
36.4
-44.3 – -31.1
Cooper [7]
20.2
8.2 – 29.5
Ribatski and Saiz
Jabardo [8]
27.5
-37.2 – -18.8
Gorenflo and Kenning
[9]
13.1
-29.6 – 9.0
Chapter 4
4.2.
Pool boiling of pure refrigerants: R134a and ammonia
POOL BOILING OF R134a ON ENHANCED SURFACES
In this subsection, we present the results obtained with the pool boiling tests of R134a on
two copper tubes with boiling enhanced surfaces, a Turbo-B and an Turbo-BII+. We conducted
tests with the pool of refrigerant at 10 ºC, 7 ºC and 4 ºC, varying the LMTD at the evaporator
from 1 K to 6 K (at steps of 0.5 K) with the Turbo-B tube, and from 1 K to 5 K (at steps of 0.5 K).
With these conditions, the heat flux ranged from 11100 W/m2 to 61400 W/m2 with the former,
and from 8900 W/m2 to 59800 W/m2 with the latter. With the Turbo-B tube, the velocity of the
heating water was 3.9 m/s and the Reynolds number ranged from 40000 to 55100. Thus, the
flow was fully developed turbulent and the application of the correlation shown in subsection
3.3.2 for the enhanced tube was suitable. With this tube, the heating water HTCs ranged from
22800 W/m2·K to 27000 W/m2·K, approximately. Concerning the Turbo-BII+ tube, the velocity of
the heating water was 3.5 m/s and the Reynolds number ranged from 37900 to 51200. Thus,
the flow was fully developed turbulent and the application of the correlation shown in subsection
3.3.2 for the enhanced tube was suitable. With this tube, the heating water HTCs ranged from
26600 W/m2·K to 31200 W/m2·K, approximately.
4.2.1.
Refrigerant side heat transfer coefficients on Turbo-B
Figure 4.6 represents the boiling curve of the pool boiling process of R134a on a Turbo-B
copper tube. From the lowest surface superheating to the highest, the process is in the nucleate
boiling region, independently of the refrigerant pool temperature. Therefore, the heat flux
increases rapidly with slight increase of the surface superheating. In addition, due to the
enhanced surface, the nucleate boiling process is achieved at surface superheating values as
low as 0.3 K. The effect of the refrigerant pool temperature is almost negligible on the curves.
70000
Tl 10 ºC
q/Ao [W/m2]
60000
Tl 7 ºC
Tle 4 ºC
50000
40000
30000
20000
10000
0
0
0.5
1
1.5
2
ΔTSH [K]
2.5
3
3.5
Figure 4.6. Heat flux on the outer surface of the copper Turbo-B tube vs. surface superheating,
under R134a pool boiling conditions, with the different saturation temperatures tested
Figure 4.7 represents the pool boiling HTCs vs. the heat flux, obtained under the same
conditions as in the previous case. In contrast with the results obtained with the plain tube, the
pool boiling HTCs decrease as the heat flux increases. The effect of the pool temperature on
the HTCs, if fixed the heat flux, is negligible. The average, maximum and minimum uncertainties
associated to the determination of these HTCs were ±11.9%, ±19.4% and ±8.4%, respectively.
79
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
45000
Tl 10 ºC
40000
Tl 7 ºC
ho [W/m2·K]
35000
Tl 4 ºC
30000
25000
20000
15000
10000
5000
0
0
10000
20000
30000
q/Ao
40000
50000
60000
70000
[W/m2]
Figure 4.7. R134a pool boiling HTCs vs. heat flux on the outer surface of the copper Turbo-B tube,
with R134a and with the different saturation temperatures tested
We developed an experimental correlation with the pool boiling HTCs obtained with the
copper Turbo-B tube and R134a, shown in equation (4.7). The correlation depends on the heat
flux, q̇, and on the reduced pressure, pred (related to the saturation temperature), which were the
parameters varied and controlled during the experiments. We observe in the correlation, as was
done with the experimental results, that the effect of the reduced pressure on the correlation is
very low (exponent 0.03). The coefficient of determination of the correlation is R2 = 0.94 and the
average absolute deviation between the experimental data and the correlation is 4.5%.
0.03
ho  3.3·105 q 0.25 pred
4.2.2.
(4.7)
Refrigerant side heat transfer coefficients on Turbo-BII+
Figure 4.8 represents the boiling curve of the pool boiling process of R134a on a Turbo-BII+
copper tube. The process is in the nucleate boiling region, independently of the surface
superheating and of the refrigerant pool temperature. Therefore, the heat flux increases rapidly
with slight increase of the surface superheating. In addition, due to the enhanced surface, the
nucleate boiling process occurs at surface superheating values as low as 0.5 K. The effect of
the temperature of the pool of refrigerant is almost negligible on the curves.
Figure 4.9 shows the pool boiling HTCs vs. the heat flux, obtained under the same
conditions as in the previous case. In contrast with the results obtained with the Turbo-B tube,
the pool boiling HTCs increase as the heat flux increases, up to a heat flux close to 30000
W/m2, and then remain constant. The effect of the pool temperature on the HTCs, if fixed the
heat flux, is not negligible at the low heat flux range (up to 30000 W/m2, approximately). The
average, maximum and minimum uncertainties associated to the determination of these HTCs
were ±9.4%, ±12.7% and ±8.0%, respectively.
80
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
70000
Tl 10 ºC
60000
Tl 7 ºC
Tl 4 ºC
q/Ao [W/m2]
50000
40000
30000
20000
10000
0
0
0.5
1
1.5
2
2.5
3
ΔTSH [K]
Figure 4.8. Heat flux on the outer surface of the copper Turbo-BII+ tube vs. surface superheating,
under R134a pool boiling conditions, with the different saturation temperatures tested
30000
25000
ho [W/m2·K]
20000
Tl 10 ºC
Tl 7 ºC
15000
Tl 4 ºC
10000
5000
0
0
10000
20000
30000
q/Ao
40000
50000
60000
70000
[W/m2]
Figure 4.9. R134a pool boiling HTCs vs. heat flux on the outer surface of the copper Turbo-BII+
tube, with the different saturation temperatures tested
We developed an experimental correlation, equation (4.8) with the pool boiling HTCs
obtained with the copper Turbo-BII+ tube and R134a. It depends on the heat flux, q̇, and on the
reduced pressure, pred, which were the parameters varied and controlled during the
experiments. The coefficient of determination of the correlation is R2 = 0.76 and the average
absolute deviation between the experimental data and the correlation is 5.2%.
81
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
0.04
ho  1.2·10 4 q 0.15 pred
4.2.3.
(4.8)
Comparison with experimental works from the literature
Several authors have studied the pool boiling HTCs of R-134a on several types of
enhanced boiling tubes, but we focused our comparison in the kind of tubes we tested (Turbo-B
and Turbo-BII). Webb and Pais [11] and Jung et al. [12] tested a Turbo-B tube with R-134a.
They observed that HTCs increase with heat flux with this kind of tube. On the other hand, the
pool boiling HTCs of Roques [13] and Tatara and Payvar [14], both studying a Turbo-BII HP
with R-134a, agreed neither in tendency nor in values. Roques [13] stated that the HTCs
decrease with heat flux and Tatara and Payvar [14] affirmed that the trend is the opposite.
Ribatski and Thome [15] stated that “there is no clear reason for such difference”, as the only
significant difference lay in the heating method.
In Figure 4.10, we compared the experimental HTCs obtained with the Turbo-B and TurboBII+ with those from the works of Webb and Pais [11], Jung et al. [12], Roques [13] and Tatara
and Payvar [14]. The minimum, maximum and mean deviations resultant from comparing these
correlations with our experimental HTCs for the Turbo-B and Turbo-BII+ (refrigerant pool
temperature of 4 ºC) are included in Table 4.3 and Table 4.4 respectively.
45000
40000
35000
ho [W/m2·K]
30000
25000
20000
15000
Turbo-B 4 ºC
Turbo-BII+ 4 ºC
Webb & Pais Turbo-B 4.4 ºC
Jung et al. Turbo-B 7 ºC
Tatara & Payvar Turbo-BIIHP 4.4 ºC
Roques Turbo-BIIHP 5 ºC
10000
5000
0
0
10000
20000
30000
40000
50000
q/Ao [W/m2]
Figure 4.10. R134a pool boiling HTCs vs. heat flux on the outer surface of the copper enhanced
tubes, both from our experimental results and from other works of the literature
As shown in Figure 4.10, the trend of our Turbo-B boiling HTCs agrees with that presented
by Roques [13] –obtained for a Turbo-BII HP tube– but differs from that obtained by Webb and
Pais [11] and Jung et al. [12], which also studied a Turbo-B; or Tatara and Payvar [14], who
tested a Turbo-BII HP. On the other hand, the Turbo-BII+ boiling HTCs we obtained behave
similarly to those of Webb and Pais [11], Jung et al. [12] or Tatara and Payvar [14], but the
results are slightly different.
82
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
Table 4.3. Comparison of the experimental pool boiling HTCs determined with R134a and the
copper Turbo-B tube with those from studies obtained with boiling enhanced tubes
Correlation
Arithmetic mean of the
deviations in absolute value (%)
Deviation range (%)
Webb and Pais [11]
35.3
-64.8 – -15.0
Jung et al. [12]
37.0
-65.8 – -17.1
Roques [13]
26.2
-42.8 – -18.0
Tatara and Payvar [14]
21.1
-31.5 – 30.9
Table 4.4. Comparison of the experimental pool boiling HTCs determined with R134a and the
copper Turbo-BII+ tube with those from studies obtained with boiling enhanced tubes
4.2.4.
Correlation
Arithmetic mean of the
deviations in absolute value (%)
Deviation range (%)
Webb and Pais [11]
25.5
-34.3 – -16.3
Jung et al. [12]
27.5
-36.0 – -18.4
Roques [13]
48.6
-11.0 – 180.3
Tatara and Payvar [14]
26.9
21.1 – 38.7
Surface enhancement factors
Figure 4.11 includes the surface enhancement factors achieved with the copper Turbo-B
tube vs. heat flux, with pool temperatures of 10 ºC, 7 ºC and 4 ºC. This parameter is highly
dependent of heat flux; as heat flux increases the surface enhancement factor decreases. The
effect of the pool temperature is more marked at the low heat flux range, where the EFsf is
higher as this temperature decreases. The surface enhancement factor is clearly over 1 under
every condition tested and reaches 11.8, being the average value 5.4.
Concerning the copper Turbo-BII+ tube, Figure 4.12 includes the surface enhancement
factors achieved with the copper Turbo-BII+ tube vs. heat flux with pool temperatures of 10 ºC,
7 ºC and 4 ºC. This parameter decreases as the heat flux decreases and is almost independent
of the pool temperature (excluding perhaps the lowest heat flux tested). The surface
enhancement factor ranges between 3.0 and 7.0, being the average value 4.7.
83
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
14
Tle 10 ºC
12
Tle 7 ºC
Tle 4 ºC
EFsf [-]
10
8
6
4
2
0
0
10000
20000
30000
40000
50000
60000
70000
q/Ao [W/m2]
Figure 4.11. Surface enhancement factor vs. heat flux on the outer surface of the copper Turbo-B
tube, with R134a and with the different saturation temperatures tested
8
Tl 10 ºC
7
Tl 7 ºC
6
Tl 4 ºC
EFsf [-]
5
4
3
2
1
0
0
10000
20000
30000
40000
50000
60000
70000
q/Ao [W/m2]
Figure 4.12. Surface enhancement factor vs. heat flux on the outer surface of the copper Turbo-BII+
tube, with R134a and with the different saturation temperatures tested
If compared between them, Turbo-B tube leads to a better heat transfer performance than
Turbo-BII+ if the heat flux is lower than a 30000 W/m2 (EFsf of 4.5, approximately). However, if
the heat flux is over this value, both tubes perform similarly and even the Turbo-BII+ prevails
over the Turbo-B.
84
Chapter 4
4.3.
Pool boiling of pure refrigerants: R134a and ammonia
POOL BOILING OF AMMONIA ON PLAIN TUBE
In this subsection, we present the results obtained with pool boiling tests of ammonia on the
titanium plain tube. We conducted tests with the pool of refrigerant at 10 ºC, 7 ºC and 4 ºC,
varying the LMTD at the evaporator from 4 K and 15 K (at steps of 1 K). With these conditions,
the heat flux ranged from 2800 W/m2 to 56600 W/m2. The velocity of the heating water was 2.4
m/s, approximately, and the Reynolds number ranged from 29400 to 45800. Thus, the flow was
fully developed turbulent and the application of the correlation shown in subsection 3.3.2 for the
plain tube was suitable. The heating water HTCs ranged from 8200 W/m2·K to 10200 W/m2·K,
approximately.
4.3.1.
Refrigerant side heat transfer coefficients
Figure 4.13 represents the boiling curve of the pool boiling process of ammonia on a
smooth titanium tube. Independently of the temperature of the pool of refrigerant, heat flux rises
with surface superheating throughout the studied range. At the low surface superheating region,
natural convection dominates the process and at the high surface superheating area nucleate
boiling occurs and heat flux increases rapidly with it. Figure 4.13 also shows that if the ammonia
pool temperature decreases, the transition between both regions occurs at a higher surface
superheating.
70000
Tl 10 ºC
60000
Tl 7 ºC
Tl 4 ºC
q/Ao [W/m2]
50000
40000
30000
20000
10000
0
0
1
2
3
4
5
6
7
8
ΔTSH [K]
Figure 4.13. Heat flux on the outer surface of the titanium plain tube vs. surface superheating,
under ammonia pool boiling conditions, with the different saturation temperatures tested
Figure 4.14 includes the pool boiling HTCs vs. the heat flux, obtained under the same
conditions as in the previous case. As the heat flux decreases, so do the pool boiling HTCs, and
if fixed the heat flux, the HTCs are higher when the ammonia pool temperature increases. The
average, maximum and minimum uncertainties associated to the determination of these HTCs
were ±4.2%, ±10.5% and ±1.6%, respectively.
85
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
10000
Tl 10 ºC
9000
Tl 7 ºC
8000
Tl 4 ºC
ho [W/m2·K]
7000
6000
5000
4000
3000
2000
1000
0
0
10000
20000
30000
40000
50000
60000
q/Ao [W/m2]
Figure 4.14. Ammonia pool boiling HTCs vs. heat flux on the outer surface of the titanium plain
tube, with the different saturation temperatures tested
We developed an experimental correlation with the pool boiling HTCs obtained with the
titanium plain tube and ammonia, shown in equation (4.9). The correlation depends on the heat
flux, q̇, and on the reduced pressure, pred, which were the parameters varied and controlled
during the experiments. The coefficient of determination of the correlation is R2 = 0.99 and the
average absolute deviation between the experimental data and the correlation is 5.0%.
.31
ho  87.35 q 0.77 p1red
4.3.2.
(4.9)
Comparison with correlations
We selected well-known correlations of the literature to compare our experimental results.
Three of them have already been presented in subsection 4.1.2, such as equation (4.2), of
Stephan and Preusser [6]; equation (4.3), of Cooper [7]; and equation (4.5), of Gorenflo and
Kenning [9]. For this refrigerant–tube combination we also included equation (4.10), of Mostinski
[16]. In addition to all the variables of the equations from subsection 4.1.2, in equation (4.10) pcrit
stands for the critical pressure (in kPa). We did not determine the roughness of the titanium
tube and we estimated it as for the copper tube (0.326416 µm). Cooper [7] gives cw values for
copper and stainless steel, but not for titanium, so we consider it equal to that for stainless steel.
0.69 q 0.7 1.8 p0.17  4 p1.2  10 p10 
ho  0.00417 pcrit

red
red
red 

(4.10)
Figure 4.15 shows the pool boiling HTCs calculated with the aforementioned correlations
vs. the experimental ones for the titanium plain tube and ammonia. The deviation range and the
arithmetic mean of the absolute deviation between the predicted and the experimental HTCs
appear in Table 4.5. The figure shows the large scattering that exists between the correlations,
particularly for those of Cooper [7] and Gorenflo and Kenning [9]. The reason could lie in the
fact that the tube is made of titanium, a material that was not studied by any of them. The
correlation of Mostinski [16] has the best agreement with the experimental results, followed
closely by that of Stephan and Preusser [6].
86
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
12000
Stephan_Preusser +60%
Cooper
Mostinski
Gorenflo and Kenning
10000
+30%
+10%
hcorr [W/m2·K]
-10%
8000
-30%
6000
-60%
4000
2000
0
0
2000
4000
6000
8000
10000
12000
hexp [W/m2·K]
Figure 4.15. Ammonia pool boiling HTCs obtained with correlations vs. experimental pool boiling
HTCs from this work, with a titanium plain tube and under the same conditions
Table 4.5. Comparison of the experimental pool boiling HTCs (ammonia and titanium plain tube)
with those calculated with correlations
4.3.3.
Correlation
Arithmetic mean of the
deviation in absolute value (%)
Deviation range (%)
Stephan and Preusser
[6]
12.7
-17.3 – 20.5
Cooper [7]
70.4
28.4 – 101.6
Gorenflo and Kenning
[9]
44.2
-55.3 – -35.4
Mostinski [16]
10.7
-27.2 – 10.2
Hysteresis
Nucleation hysteresis is a process that occurs at pool boiling processes, and that consists in
a delay of the transition from natural convection to nucleate boiling, i.e. the surface
superheating is greater than that expected for a certain heat flux under nucleate boiling
(Poniewski and Thome, [17]). The existence of hysteresis in ammonia pool boiling is
documented in works such as that from Kuprianova [18].
87
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
70000
Tl 10 ºC Decrease
60000
Tl 10 ºC Increase
q/Ao [W/m2]
50000
40000
30000
20000
10000
0
0
1
2
3
4
5
6
7
8
ΔTSH [K]
Figure 4.16. Heat flux on the outer surface of the titanium plain tube vs. surface superheating,
under ammonia pool boiling conditions (10 ºC), with both decreasing and increasing heat flux tests
10000
Tl 10 ºC Decrease
Tl 10 ºC Increase
ho [W/m2·K]
8000
6000
4000
2000
0
0
10000
20000
30000
40000
50000
60000
q/Ao [W/m2]
Figure 4.17. Ammonia pool boiling HTCs vs. heat flux on the outer surface of the titanium plain
tube, for both decreasing and increasing heat flux tests, at a pool temperature of 10 ºC
With ammonia we developed tests to study nucleation hysteresis, i.e. we distinguished
between those results obtained decreasing the heat flux on the evaporator tube and those
obtained increasing the heat flux on the evaporator tube. Decreasing heat flux tests (explained
in subsection 3.2.1) started with the maximum mean heating water temperature possible. When
achieved steady state, we registered data for a minimum of 15 minutes. After that, we lowered
88
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
the mean heating water to the next testing condition and we repeated the process. In contrast,
increasing heat flux tests followed the opposite order, starting with the minimum mean heating
water temperature.
With the titanium plain tube and an ammonia pool temperature of 10 ºC, in the increasing
heat flux tests the transition surface superheating is considerably greater than in decreasing
heat flux tests, as shown in Figure 4.16. The effect of hysteresis on the pool boiling HTCs is
particularly important in the medium heat flux range, from 10000 W/m2 to 30000 W/m2, as
shown in Figure 4.17. In this region, the difference between the HTCs of analogous tests (same
logarithmic mean temperature difference at the evaporator) reaches a 54.2%.
4.3.4.
Photographic report
Prior to analysing the pictures shown in this subsection, it is important to point out that the
process photographed shows only a small part of the tube. We took the photographs following
an increasing heat flux order. The transition between natural convection and nucleate boiling, as
well as the length of the tube, implied that the situation could vary from a part of the tube to the
next. Therefore, both natural convection and nucleate boiling could coexist but it is not reflected
in the pictures.
a
b
c
d
e
f
Figure 4.18. Detail photographs of the ammonia pool boiling process on a titanium plain tube with
different heat fluxes on the outer surface and pool temperature of 10 ºC. a) 3300 W/m2.
b) 11000 W/m2. c) 19200 W/m2. d) 29900 W/m2. e) 42100 W/m2. f) 47900 W/m2
Figure 4.18 includes pictures of the pool boiling process of ammonia on the titanium plain
tube, at a saturation temperature of 10 ºC and different heat fluxes on the surface. Figure 4.18a
shows that with a heat flux of 3300 W/m2 the nucleate boiling process was barely active and
natural convection dominated. If the heat flux is higher, as can be seen in Figure 4.18b and c,
the density of nucleate boiling sites increases, as well as the diameter of the departing bubbles
89
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
(Figure 4.18d). In Figure 4.18e and f the nucleate boiling process is generalised all over the
tube surface, confirming the results shown in previous subsections.
At the low heat flux region (7700 W/m2) we also observed that nucleation sites were not
stable, and appeared and disappeared continually (Figure 4.19).
a
b
c
Figure 4.19. Unstable nucleation sites during an experiment at the transition between natural
convection and nucleate boiling (heat flux of 7700 W/m2)
90
Chapter 4
4.4.
Pool boiling of pure refrigerants: R134a and ammonia
POOL BOILING OF AMMONIA ON ENHANCED TUBE
In this subsection, we present the results obtained with pool boiling tests of ammonia on the
titanium integral-fin tube Trufin 32 f.p.i. We conducted tests with the pool of refrigerant at 10 ºC,
7 ºC and 4 ºC, varying the LMTD at the evaporator from 4 K and 15 K (at steps of 1 K). With
these conditions, the heat flux ranged from 3600 W/m2 to 60000 W/m2. The velocity of the
heating water with these tests was 2.6 m/s, approximately, and the Reynolds number ranged
from 30800 to 49300. Thus, the flow was fully developed turbulent and the application of the
correlation shown in subsection 3.3.2 for the plain tube was suitable. The heating water HTCs
ranged from 8900 W/m2·K to 11200 W/m2·K, approximately.
4.4.1.
Refrigerant side heat transfer coefficients on Trufin 32 f.p.i
Figure 4.20 represents the boiling curve of the pool boiling process of ammonia on the
titanium Trufin 32 f.p.i. tube. Independently of the temperature of the pool of refrigerant, heat
flux rises with surface superheating throughout the studied range. As shown with the plain tube,
the natural convection and the nucleate boiling areas appear, but the transition between them
occurs at a slightly lower surface superheating than with the plain tube (between 1 and 2 K).
70000
Tl 10 ºC Dec
60000
Tl 7 ºC Dec
Tl 4 ºC Dec
q/Ao [W/m2]
50000
40000
30000
20000
10000
0
0
1
2
3
4
5
6
7
ΔTSH [K]
Figure 4.20. Heat flux on the outer surface of the titanium Trufin 32 f.p.i. tube vs. surface
superheating, under ammonia pool boiling conditions, with the different saturation temperatures
tested
Figure 4.21 illustrates the pool boiling HTCs vs. the heat flux obtained in decreasing heat
flux order, with the titanium Trufin 32 f.p.i. tube and ammonia pool temperatures of 10 ºC, 7 ºC
and 4 ºC. In this case, HTCs also increase either if the heat flux or the ammonia pool
temperature is higher. The average, maximum and minimum uncertainties associated to the
determination of these HTCs were ±5.5%, ±14.0% and ±1.9%, respectively.
91
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
16000
Tl 10 ºC Dec
ho [W/m2·K]
14000
12000
Tl 7 ºC Dec
10000
Tl 4 ºC Dec
8000
6000
4000
2000
0
0
10000
20000
30000
40000
50000
60000
70000
q/Ao [W/m2]
Figure 4.21. Ammonia pool boiling HTCs vs. heat flux on the outer surface of the titanium
Trufin 32 f.p.i. tube, with the different saturation temperatures tested
We developed an experimental correlation with the pool boiling HTCs obtained with the
titanium Trufin 32 f.p.i. tube and ammonia, shown in equation (4.11). The correlation depends
on the heat flux, q̇, and on the reduced pressure, pred, which were the parameters varied and
controlled during the experiments. The exponents for both parameters agree with those
determined in equation (4.9) for the titanium plain tube. The coefficient of determination of the
correlation is R2 = 0.99 and the average absolute deviation between the experimental data and
the correlation is 5.5%.
.31
ho  110.46 q 0.77 p1red
4.4.2.
(4.11)
Surface enhancement factors
Figure 4.22 includes the surface enhancement factors achieved with the Trufin 32 f.p.i. tube
vs. heat flux, with pool temperatures of 10 ºC, 7 ºC and 4 ºC. It shows that this parameter,
generally, is independent of the heat flux. This conclusion is in agreement with the correlation
we obtained, which has the same exponents for both the heat flux and reduced pressure and
only the fitting constant changes. The effect of the ammonia pool temperature is more marked
at the low heat flux range, where the EFsf is clearly higher as this temperature decreases. The
surface enhancement factor is greater than or equal to 1 under every condition tested and
reaches 1.3, being the average value 1.2.
92
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
1.6
1.4
1.2
EFsf [-]
1.0
0.8
0.6
Tle 10 ºC
0.4
Tle 7 ºC
0.2
Tle 4 ºC
0.0
0
10000
20000
30000
40000
50000
60000
70000
q/Ao [W/m2]
Figure 4.22. Surface enhancement factor vs. heat flux if compared the titanium Trufin 32 f.p.i. tube
to the plain tube, with ammonia as refrigerant and with the different saturation temperatures tested
There are not many experimental works of the specialised literature focused on pool boiling
enhancement with ammonia as refrigerant. Djundin et al. [19] studied experimentally the HTCs
on a plain steel tube and several enhanced tubes. Mechanical grooves improved pool boiling
heat transfer between 30% and 60%. Djundin and co-workers also studied a porous aluminium
layer on the tube, which led to an enhancement of 40%; and a fluorocarbon layer with spots
placed randomly on the surface of the tube, which led to improvements between 300% and
400% if compared to the plain tube. Danilova et al [20] analysed ammonia pool boiling on
different horizontal steel tubes with aluminium coatings and, according to their results, these
coatings can improve heat transfer between 100% and 400% if compared to the plain tube used
as reference.
The enhancement factors obtained by Djundin et al. [19] with the grooved tube are very
similar to the improvement we achieved with our Trufin 32 f.p.i. tube. However, the rest of the
enhancement strategies from both works clearly outperform our results.
4.4.3.
Hysteresis
In a similar way we did with the titanium plain tube, we analysed the nucleation hysteresis
with ammonia and the titanium Trufin 32 f.p.i. tube. Figure 4.23 shows the heat flux vs. surface
superheating curves determined with the decreasing and increasing heat flux tests, at pool
temperatures of 10 ºC, 7 ºC and 4 ºC. In the increasing heat flux tests the transition surface
superheating is considerably greater than in decreasing heat flux tests. In addition, hysteresis is
higher as the pool temperature decreases, as depicted in Figure 4.23.
The effect of hysteresis on the pool boiling HTCs is particularly important in the medium
heat flux range, from 10000 W/m2 to 30000 W/m2, as shown in Figure 4.24. The difference
between the HTCs of analogous tests (same logarithmic mean temperature difference at the
evaporator) reaches 172%. This value is greater than the maximum difference determined with
the plain tube, which was 54%. This behaviour agrees with the conclusion stated in Poniewski
and Thome [17] concerning the higher effect of hysteresis on enhanced boiling surfaces than on
smooth surfaces.
93
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
70000
Tl 10 ºC Dec
Tl 10 ºC Inc
Tl 7 ºC Dec
Tl 7 ºC Inc
Tl 4 ºC Dec
Tl 4 ºC Inc
60000
50000
q/Ao [W/m2]
40000
30000
20000
10000
0
0
2
4
6
8
10
ΔTSH [K]
Figure 4.23. Heat flux on the outer surface of the titanium Trufin 32 f.p.i. tube vs. surface
superheating, under ammonia pool boiling conditions, with decreasing and increasing heat flux
tests and with the different saturation temperatures
16000
Tl 10 ºC Dec
Tl 10 ºC Inc
Tl 7 ºC Dec
Tl 7 ºC Inc
Tl 4 ºC Dec
Tl 4 ºC Inc
14000
12000
ho [W/m2·K]
10000
8000
6000
4000
2000
0
0
10000
20000
30000
q/Ao
40000
50000
60000
70000
[W/m2]
Figure 4.24. Ammonia pool boiling HTCs vs. heat flux on the surface of the titanium Trufin 32 f.p.i.
tube, for both decreasing and increasing heat flux tests, with the different saturation temperatures
While performing the increasing heat flux series at ammonia pool temperature of 10 ºC and
LMTD at the evaporator of 10 K, even though the conditions were stable, the heat flow at the
evaporator increased. Therefore, we conducted a special kind of experiment to check this trend.
This test consisted in reaching this specific condition following an increasing heat flux path and
maintaining it constant for a long period (more than 10 hours), as shown in Figure 4.25.
94
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
25
T [ºC]
20
15
10
Tl
Thw,mean
5
Thw,inlet
Thw,outlet
0
0
10000
20000
30000
40000
50000
t [s]
Figure 4.25. Temperatures of the pool of refrigerant and the heating water vs. time at the special
tests for studying the stability during hysteresis
70000
Tl 10 ºC Dec
60000
Tl 10 ºC Inc
Hysteresis
q/Ao [W/m2]
50000
40000
30000
20000
10000
0
0
1
2
3
4
5
6
7
ΔTSH [K]
Figure 4.26. Heat flux on the outer surface of the titanium Trufin 32 f.p.i. tube vs. surface
superheating, under ammonia pool boiling conditions (10 ºC), with decreasing and increasing heat
flux and hysteresis stability tests
Figure 4.26 shows the heat flux vs. surface superheating evolution of this experiment and
compares it to the increasing and decreasing heat flux series (ammonia pool temperature of 10
ºC). As shown in the chart, the heat flux increased and the surface superheating decreased,
even though the conditions were constant, starting from an experimental value close to the
95
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
increasing heat flux curve and ending at another close to the decreasing heat flux curve. This
result suggests that the effect of nucleation hysteresis diminishes as the time passes.
4.4.4.
Photographic report
Figure 4.27 includes pictures of the pool boiling process of ammonia on the titanium
Trufin 32 f.p.i. tube, at a saturation temperature of 10 ºC and different heat fluxes on the
surface. Figure 4.27a and b show that, with heat fluxes of 3700 W/m2 and 10200 W/m2, the
nucleate boiling process was barely active and natural convection dominated in the part of the
tube filmed. If the heat flux is higher, as can be seen in Figure 4.27c and d, the density of
nucleate boiling sites and diameter of the departing bubbles increase, and the nucleate boiling
process is generalised all over the tube surface. The boiling process is even more active in
Figure 4.27e and f, which agrees with the experimental HTCs determined.
96
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
a
b
c
d
e
f
Figure 4.27. Detail photographs of the ammonia pool boiling process on the titanium Trufin 32 f.p.i
tube with different heat fluxes on the outer surface and pool temperature of 10 ºC. a) 3700 W/m2.
b) 10200 W/m2. c) 17600 W/m2. d) 28400 W/m2. e) 38500 W/m2. f) 50600 W/m2
97
Chapter 4
4.5.
Pool boiling of pure refrigerants: R134a and ammonia
CONCLUSIONS
In this chapter we have shown the pool boiling HTCs obtained experimentally for this thesis.
The refrigerants studied were R134a and ammonia. With the former we tested copper tubes of
plain and enhanced surfaces (Turbo-B and Turbo-BII+); and with the latter we tested titanium
tubes of plain and enhanced surface (Trufin 32 f.p.i.).
We have observed that the vast majority of our experimental results are included in the
boiling region of the boiling curve, where the slope is steep and heat flux increases rapidly with
superheating.
Concerning the pool boiling HTCs, we have observed that they generally increase with
increasing saturation temperatures, being constant the heat flux. Another trend observed for all
the tubes except for Turbo-B is that pool boiling HTCs rise as the heat flux rises, independently
of the saturation temperature. This effect was clearer with the plain tubes.
With ammonia we also tested the influence of hysteresis on the nucleation process. We
confirmed its existence and that it is more important with the enhanced surface tested with
ammonia. However, our experiments have shown that increasing heat flux tests are timedependent, i.e. the HTCs obtained when the experimentation process follows an increasing
heat flux trend rise with time until they reach a value very close to that obtained with the
diminishing heat flux tests.
We have compared our experimental results with well-known correlations from different
works from the literature. In the case of plain tubes, the best agreement existed with Gorenflo
and Kenning [9] correlation with R134a and with Mostinski [16] correlation with ammonia.
The surface enhancement techniques were more effective with R134a than with ammonia.
With R134a, the surface enhancement factors were as high as 11.8 and 7 with the Turbo-B and
Turbo-BII+, respectively. In contrast, with ammonia the EFsf was never greater than 1.3.
Finally, we have included the photographic reports of the pool boiling of ammonia on the
plain tube and the Trufin 32 f.p.i. tube. The pictures show the increase of density of nucleation
sites and of the bubble diameters as the heat flux increases. The visual differences between
tubes are very slight, confirming the results determined experimentally.
98
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
REFERENCES
[1] Á.Á. Pardiñas, J. Fernández-Seara, C. Piñeiro-Pontevedra, S. Bastos, Experimental
determination of the boiling heat transfer coefficients of R-134a and R-417A on a smooth
copper tube, Heat Transfer Engineering. 35 (2014) 1424-1434.
[2] Á.Á. Pardiñas, J. Fernández-Seara, S. Bastos, R. Diz, Experimental boiling heat transfer
coefficients of R-134a on two boiling enhanced tubes, in: Proceedings of the 8th World
Conference on Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics. Lisbon,
Portugal, 2013.
[3] Á.Á. Pardiñas, J. Fernández-Seara, R. Diz, Experimental study on heat transfer coefficients
of spray evaporation and pool boiling on plain tubes, in: Proceedings of the 24th IIR International
Congress of Refrigeration. Yokohama, Japan, 2015.
[4] S. Nukiyama, The maximum and minimum values of the heat Q transmitted from metal to
boiling water under atmospheric pressure, International Journal of Heat and Mass Transfer. 27
(1984) 959-970.
[5] J.R. Thome, Boiling heat transfer on external surfaces, in: Wolverine Heat Transfer
Engineering Data Book III, 2009.
[6] K. Stephan, P. Preusser, Wärmeübergang und maximale Wärmestromdichte beim
Behältersieden binärer und ternärer Flüssigkeitsgemische. Chemie Ingenieur Technik. 51
(1979) 649-679.
[7] M.G. Cooper, Heat flow rates in saturated nucleate pool boiling - a wide ranging examination
using reduced properties, Advances in Heat Transfer. 16 (1984).
[8] G. Ribatski, J.M. Saiz Jabardo, Experimental Study of Nucleate Boiling of Halocarbon
Refrigerants on Cylindrical Surfaces, International Journal of Heat and Mass Transfer. 46
(2003) 4439-4451.
[9] D. Gorenflo, D.B.R. Kenning, Pool Boiling. Chapter H2, VDI Heat Atlas, second ed. Springer,
Berlin, 2010.
[10] S. Kotthoff, D. Gorenflo, Pool boiling heat transfer to hydrocarbons and ammonia: a stateof-the-art review, International Journal of Refrigeration. 31 (2008) 573-602.
[11] R.L. Webb, C. Pais, Nucleate pool boiling data for five refrigerants on plain, integral-fin and
enhanced tube geometries, International Journal of Heat and Mass Transfer. 35 (1992) 18931904.
[12] D. Jung, K. An, J. Park, Nucleate boiling heat transfer coefficients of HCFC22, HFC134a,
HFC125, and HFC32 on various enhanced tubes, International Journal of Refrigeration. 27
(2004) 202-206.
[13] J.F. Roques, Falling film evaporation on a single tube and on a tube bundle. Ph.D. thesis,
École Polytechnique Fédérale de Lausanne, 2004.
[14] R.A. Tatara, P. Payvar, Pool boiling of pure R134a from a single Turbo-BII-HP tube,
International Journal of Heat and Mass Transfer. 43 (2000) 2233-2236.
[15] G. Ribatski, J.R. Thome, Nucleate boiling heat transfer of R134a on enhanced tubes,
Applied Thermal Engineering. 26 (2006) 1018-1031.
[16] I.L. Mostinski, Application of the rule of corresponding states for calculation of heat transfer
and critical heat flux, Teploenergetika. 4 (1963) 66.
[17] M.E. Poniewski, J.R. Thome, Nucleate boiling on micro-structured surfaces. Heat Transfer
Research, Inc. (HITRI), Texas, 2008.
[18] A.V. Kuprianova, Heat transfer with pool boiling of ammonia on horizontal tubes, Kholod.
Tekh. 11 (1970) 40-44.
[19] V.A. Djundin, A.G. Soloviyov, A.V. Borisanskaja, J.A. Vol’nykh, Influence of the type of
surface on heat transfer in boiling, Kholod. Tekh. 5 (1984) 33-37.
99
Chapter 4
Pool boiling of pure refrigerants: R134a and ammonia
[20] G.N. Danilova, V.A. Djundin, A.V. Borishanskaya, A.G. Soloviyov, J.A. Vol’nykh, A.A.
Kozyrev, Effect of surface conditions on boiling heat transfer of refrigerants in shell-and-tube
evaporators, Heat Transfer-Soviet Research. 22 (1990) 56-65.
100
Chapter 5
Spray evaporation of pure
refrigerants: R134a and
ammonia
In this section we detail the experimental spray evaporation HTCs obtained with our
experimental setup and procedure. As with pool boiling, we tested R134a and ammonia, but the
tubes were only of plain surfaces, either of copper or titanium.
Each combination tube-refrigerant was tested for two different situations: with the liquid
refrigerant distributed directly on the tested tube (ST) and with the tested tube receiving liquid
refrigerant from a tube placed above it (SB). In this chapter, we show the heat flux determined
versus the tube wall superheat and the spray evaporation HTCs versus the heat flux, in both
cases as a function of the liquid refrigerant flow rate distributed. We also compare the
experimental results obtained with the tubes tested at the two situations to analyse the effect of
the refrigerant impingement on heat transfer.
A photographic report is included in this chapter of the spray evaporation processes
studied. The pictures cover different experimental conditions and describe processes such as
the formation of dry patches, which help to explain some of the results determined.
We also show the enhancement factors achieved by spray evaporation, if compared with
pool boiling, at the same testing conditions, refrigerant and tube surface.
Some of the results here detailed were stated in the conference contribution Á.Á. Pardiñas,
J. Fernández-Seara and R. Diz, Experimental study on heat transfer coefficients of spray
evaporation and pool boiling on plain tubes, from the 24th IIR International Congress of
Refrigeration (Yokohama, Japan, 2015) [1].
101
Chapter 5
5.1.
Spray evaporation of pure refrigerants: R134a and ammonia
SPRAY EVAPORATION OF R134a ON PLAIN TUBE
In this subsection, we present the results obtained with spray evaporation tests of R134a on
the copper plain tubes tested for both ST (direct distribution of the refrigerant) and SB
(distribution through conditioning tube) experiments. We conducted tests distributing the liquid
refrigerant at a temperature of 10 ºC, varying the LMTD at the evaporator from 4 K to 13 K (at
steps of 1 K). The distributed refrigerant mass flow rates were 1000 kg/h, 1250 kg/h and
1500 kg/h, which correspond to film flow rates per side and meter of tube of 0.0093 kg/m·s,
0.0116 kg/m·s and 0.0139 kg/m·s, respectively. With these conditions, the heat flux ranged from
4300 W/m2 to 28200 W/m2.The velocity of the heating water with these tests was between 0.7
m/s and 2.7 m/s (average 1.2 m/s) and the Reynolds number ranged from 9800 to 47900. Thus,
the flow was fully developed turbulent and the application of the correlation shown in subsection
3.3.2 for the plain tube was suitable. The heating water HTCs ranged from 3200 W/m2·K to
11000 W/m2·K, approximately.
5.1.1.
Spray evaporation heat transfer coefficients
Figure 5.1 shows the heat flux on the outer surface of the copper plain tube vs. surface
superheating, under ST spray evaporation tests and with a liquid R134a distribution
temperature of 10 ºC. Heat flux rises with surface superheating throughout the studied range,
independently of the series of tests considered. The rapid increase of heat flux with surface
superheating and the constant slope shows that the tests were in the nucleate boiling area.
35000
ST 0.0139 kg/m·s
30000
ST 0.0116 kg/m·s
q/Ao [W/m2]
25000
ST 0.0093 kg/m·s
20000
15000
10000
5000
0
0
2
4
6
8
10
12
ΔTSH [K]
Figure 5.1. Heat flux on the outer surface of the copper plain tube vs. surface superheating, under
R134a ST spray evaporation tests, with the different mass flow rates per side and per meter of tube
and with a refrigerant distribution temperature of 10 ºC
Following the results shown in the previous figure, we determined the spray evaporation
HTCs and represented them as a function of heat flux and mass flow rate of refrigerant per side
and meter of tube in Figure 5.2. Independently of the mass flow rate, spray evaporation HTCs
increase with heat flux throughout the experiments performed and they do it with a constant
slope from 1800 W/m2·K at 4300 W/m2 to 2800 W/m2·K at 28200 W/m2. The effect of the
refrigerant mass flow rate is almost negligible. The average, maximum and minimum
uncertainties associated to the determination of these HTCs were ±3.6%, ±5.1% and ±2.6%,
respectively.
102
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
3500
3000
ho [W/m2·K]
2500
2000
1500
1000
ST 0.0139 kg/m·s
ST 0.0116 kg/m·s
500
ST 0.0093 kg/m·s
0
0
5000
10000
15000
20000
25000
30000
35000
q/Ao [W/m2]
Figure 5.2. Spray evaporation HTCs vs. heat flux on the outer surface of the copper plain tube,
under R134a ST spray evaporation tests, with the different mass flow rates per side and per meter
of tube and with a refrigerant distribution temperature of 10 ºC
We developed an experimental correlation with the spray evaporation HTCs obtained with
ST tests, copper plain tube and R134a, shown in equation (5.1). The correlation depends on the
heat flux, q̇, and on the mass flow rate of refrigerant per side and per meter of tube, Γ, which
were the parameters varied and controlled during the experiments. The coefficient of
determination of the correlation is R2 = 0.98 and the average absolute deviation between the
experimental data and the correlation is 2.1%.
ho  391.68 q 0.21 0.04
(5.1)
Figure 5.3 shows the heat flux on the outer surface of the copper plain tube vs. surface
superheating, under SB spray evaporation tests and with a liquid R134a distribution
temperature of 10 ºC. Independently of the series of tests considered, heat flux rises with
surface superheating throughout the studied range, as happened with ST tests, but the values
are slightly lower than in that case. The constant and steep slope of the curve defined by heat
flux vs. surface superheating shows that the tests were in the nucleate boiling area.
Figure 5.4 describes the relation between SB spray evaporation HTCs with heat flux and
mass flow rate of refrigerant per side and meter of tube. Spray evaporation HTCs increase with
heat flux under the experimental conditions tested, independently of the mass flow rate, from
1600 W/m2·K at 5100 W/m2 to 2300 W/m2·K at 20500 W/m2. As with the ST experiments, the
effect of the refrigerant mass flow rate is almost negligible. The average, maximum and
minimum uncertainties associated to the determination of these HTCs were ±3.4%, ±4.6% and
±2.4%, respectively.
103
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
25000
SB 0.0139 kg/m·s
SB 0.0116 kg/m·s
20000
q/Ao [W/m2]
SB 0.0093 kg/m·s
15000
10000
5000
0
0
2
4
6
8
10
ΔTSH [K]
Figure 5.3. Heat flux on the outer surface of the copper plain tube vs. surface superheating, under
R134a SB spray evaporation test, with the different mass flow rates per side and per meter of tube
and with a refrigerant distribution temperature of 10 ºC
2500
ho [W/m2·K]
2000
1500
1000
SB 0.0139 kg/m·s
500
SB 0.0116 kg/m·s
SB 0.0093 kg/m·s
0
0
5000
10000
15000
20000
25000
q/Ao [W/m2]
Figure 5.4. Spray evaporation HTCs vs. heat flux on the outer surface of the copper plain tube,
under R134a SB spray evaporation tests, with the different mass flow rates per side and per meter
of tube and with a refrigerant distribution temperature of 10 ºC
We developed an experimental correlation with the spray evaporation HTCs obtained with
SB tests, copper plain tube and R134a, shown in equation (5.2). The correlation depends on the
heat flux, q̇, and on the mass flow rate of refrigerant per side and per meter of tube, Γ, which
were the parameters varied and controlled during the experiments. The coefficient of
104
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
determination of the correlation is R2 = 0.98 and the average absolute deviation between the
experimental data and the correlation is 1.9%.
ho  314.72 q 0.23 0.07
(5.2)
Figure 5.5 compares the spray evaporation HTCs vs. heat flux obtained with the tube
placed directly underneath the refrigerant distribution tube (ST tests) to those determined with
the tube that receives refrigerant from another placed over it (SB tests). The general trends
observed with heat flux and flow rates are similar, but the HTC values with the ST tests are
between 10.9% and 16.6% (average 13.2%) greater than with the second. The reason to this
could lie in a decrease of the liquid refrigerant mass flow rate of SB tests due to splashing on
the tube placed right above it. However, as seen in Figure 5.4, SB test HTCs are not affected by
the distributed mass flow rate. Another explanation to this difference could come from the liquid
droplet impingement effect. According to Zeng et al. [2] or Tatara and Payvar [3], high
momentum devices, as the nozzles we tested, improve the wetting of the target surface and the
high velocity of the liquid distributed enhances heat transfer.
3500
3000
ho [W/m2·K]
2500
2000
ST 0.0139 kg/m·s
ST 0.0116 kg/m·s
1500
ST 0.0093 kg/m·s
1000
SB 0.0139 kg/m·s
SB 0.0116 kg/m·s
500
SB 0.0093 kg/m·s
0
0
5000
10000
15000
20000
25000
30000
35000
q/Ao [W/m2]
Figure 5.5. Spray evaporation HTCs vs. heat flux on the outer surface of the copper plain tube,
under R134a ST and SB spray evaporation tests, with the different mass flow rates per side and per
meter of tube and with a refrigerant distribution temperature of 10 ºC
5.1.2.
Spray enhancement factors
Figure 5.6 illustrates the spray enhancement factor of R134a and plain copper tube vs. heat
flux, with ST experiments and as a function of the mass flow rate of refrigerant per side and
meter of tube. Spray evaporation enhances heat transfer if compared to pool boiling only in the
low heat flux range (up to 17500 W/m2), being the maximum enhancement factor of 1.7 (0.0139
kg/m·s and 4300 W/m2). At higher heat fluxes, pool boiling slightly outperforms spray
evaporation and the minimum enhancement factor is close to 0.9 (0.0093 kg/m·s and
27400 W/m2).
105
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
1.8
ST 0.0139 kg/m·s
1.6
ST 0.0116 kg/m·s
1.4
EFsp,Γ [-]
ST 0.0093 kg/m·s
1.2
1
0.8
0.6
0.4
0.2
0
0
5000
10000
15000
20000
25000
30000
q/Ao [W/m2]
Figure 5.6. Spray enhancement factors vs. heat flux on the outer surface of the copper plain tube,
under R134a ST spray evaporation tests, with the different mass flow rates per side and per meter
of tube and with a refrigerant distribution temperature of 10 ºC
1.6
SB 0.0139 kg/m·s
1.4
SB 0.0116 kg/m·s
EFsp,Γ [-]
1.2
SB 0.0093 kg/m·s
1
0.8
0.6
0.4
0.2
0
0
5000
10000
15000
20000
25000
q/Ao [W/m2]
Figure 5.7. Spray enhancement factors vs. heat flux on the outer surface of the copper plain tube,
under R134a SB spray evaporation tests, with the different mass flow rates per side and per meter
of tube and with a refrigerant distribution temperature of 10 ºC
Similarly, Figure 5.7 includes the spray enhancement factor of R134a and plain copper tube
vs. heat flux, with SB experiments and as a function of the mass flow rate of refrigerant per side
and meter of tube. The enhancement achieved with SB tests is lower in this case than with ST
106
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
tests. In fact, the surface enhancement factor is greater than or equal to 1 only up to a heat flux
of 12500 W/m2, approximately. The maximum and minimum enhancement factors obtained
under these conditions are 1.4 (0.0139 kg/m·s and 5000 W/m2) and 0.8 (0.0093 kg/m·s and
20100 W/m2), respectively.
In the PhD thesis developed by Roques [4], the author also compares the HTCs obtained
with pool boiling and falling film evaporation (low momentum distribution device) of R134a on a
tube bundle of copper tubes of the same diameter as ours. The HTCs presented in this work for
both processes are greater than our results. In the case of falling film (spray evaporation) the
explanation to this difference could lie in the film Reynolds number, which in some of our
experiments is lower than the dryout onset Reynolds number. However, there is not an
apparent explanation in the case of pool boiling. In the PhD thesis, the author states that the
spray enhancement factor ranges from 1 to 1.5, very close to the range we determined (except
when dry patches dominated on the tube surface).
Another interesting work concerning spray evaporation of R134a on copper tubes is that
from Moeykens [5]. The HTCs obtained by this author, shown in Figure 5.8, are in the same
range of values of our own and they were obtained under similar experimental conditions. As
we observe in the figure, pool boiling outperforms spray evaporation at a heat flux between
20000 and 25000 W/m2. This heat flux is close to that corresponding to a spray enhancement
factor of 1 in our ST tests.
Figure 5.8. Spray evaporation and pool boiling HTCs vs. heat flux of R134a on the outer surface of
a copper plain tube obtained by Moeykens [5]
5.1.3.
Photographic report
Figure 5.9 includes pictures of the flow mode that occurs when distributing R134a on the
copper plain tube as a function of the mass flow rate of refrigerant distributed, at a saturation
temperature of 10 ºC and under nearly adiabatic conditions (negligible heat flux). The distance
between actives sites among the range of distributed mass flow rates tested remains almost
unchanged. With mass flow rates of 0.0093 kg/m·s and 0.0116 kg/m·s (Figure 5.9a and Figure
5.9b, respectively) the distance is 8.5 mm, approximately; and with a mass flow rate of
0.0139 kg/m·s it is 7.5 mm. The difference between the pictures lies in the intertube flow mode.
Meanwhile with the lowest mass flow rate droplets occur (Figure 5.9a), columns appear with the
other two (Figure 5.9b and Figure 5.9c) and we talk about a droplet-column mode.
107
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
a
b
c
Figure 5.9. Dripping active sites with R134a and the copper plain tube as a function of the mass
flow rate per side and per meter of tube, Γ, under nearly adiabatic conditions. a) Γ = 0.0093 kg/m·s.
b) Γ = 0.0116 kg/m·s. c) Γ = 0.0139 kg/m·s
The distribution system with nozzles involves that the active sites move longitudinally.
Therefore, the determination of the distance between active sites from the pictures was
complicated and varied from snapshot to snapshot. We compared these distances with those
calculated using equation (5.3), developed by Yung et al. [6] and based on the Taylor instability
theory. According to the authors of that work, n = 2 with thin films. The values obtained with this
equation are 8 mm, and therefore in between the ones we determined.
  2 n   l g 
(5.3)
In Figure 5.10, we also focused on the falling film flow mode keeping fixed the mass flow
rate of refrigerant at 0093 kg/m·s and varying the heat flux. An increase in the heat flux leads to
an increase of the distance between active sites, particularly when it goes from 12200 W/m2 to
27400 W/m2. We conducted a similar analysis with the mass flow rate of 0.0139 kg/m·s, as
seen in Figure 5.11, and the conclusion is similar. To explain this behaviour we must focus on
the overfeed factor, OF, defined in subsection 3.3.3 as the ratio of the mass flow rate reaching
the top of the tube to the mass flow rate that vaporises. As the heat flux increases, the OF factor
decreases and, therefore, there is less liquid refrigerant left after boiling to drip from the tube
and several dripping sites should merge in order to form a new dripping site.
From the previous figures we can also conclude that dry patches are present in our R134a
and copper tube spray evaporation tests, especially as the heat flux increases. We have a
closer look to that effect in the pictures included in Figure 5.12. Figure 5.12a shows the film with
Γ = 0.0139 kg/m·s and heat flux of 4400 W/m2, which covers the surface on the tube. In
contrast, when the heat flux increases to 12700 W/m2 the film breaks down and certain regions
of the tube are uncovered by liquid refrigerant (Figure 5.12b). As we increase the heat flux and
decrease the mass flow rate on the tube, the dry fraction of the tube increases (Figure 5.12c,
Γ = 0.0093 kg/m·s and heat flux of 20400 W/m2) and at certain conditions the wet areas are
limited to very small patches (Figure 5.12d, Γ = 0.0093 kg/m·s and heat flux of 27400 W/m2).
108
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
a
b
c
Figure 5.10. Dripping active sites with R134a and the copper plain tube as a function of heat flux, q̇,
with mass flow rate per side and per meter of tube, Γ = 0.0093 kg/m·s. a) q̇ = 4300 W/m2.
b) q̇ = 12200 W/m2. c) q̇ = 27400 W/m2
a
b
c
Figure 5.11. Dripping active sites with R134a and the copper plain tube as a function of heat flux, q̇,
with mass flow rate per side and per meter of tube, Γ = 0.0139 kg/m·s. a) q̇ = 4400 W/m2.
b) q̇ = 12700 W/m2. c) q̇ = 28200 W/m2
109
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
a
b
c
d
Figure 5.12. Dry patches on the copper plain tube with R134a. a) Γ = 0.0139 kg/m·s and
q̇ = 4400 W/m2. b) Γ = 0.0139 kg/m·s and q̇ = 12700 W/m2. c) Γ = 0.0093 kg/m·s and q̇ = 20400 W/m2.
c) Γ = 0.0093 kg/m·s and q̇ = 27400 W/m2
We employed the correlation from Ribatski and Thome [7], equation (5.4), to determine the
maximum Reynolds number at which dryout occurred in their tests, Ref,threshold. In the equation, q̇
stands for the heat flux on the outer surface of the tube, ρl and ρl stand for the densities of the
liquid and vapour refrigerant, respectively, and hlv stands for the refrigerant latent heat of
vaporisation.
3 2 
Ref,threshold  6.93·105 q  l  v  hlv


 
0.47
(5.4)
We considered the conditions of heat flux from the pictures shown in Figure 5.12. With
q̇ = 4400 W/m2 (Figure 5.12a), the dryout onset Reynolds number is 237, which is just what we
have at the top of the tube, 236, confirming the non-dryout conditions. With q̇ = 12700 W/m2
(Figure 5.12b), the dryout onset Reynolds number from the correlation is 392, much higher than
the Reynolds number at the top, 236. Therefore, dry patches are expected, even when the
overfeed factor is 7 under these conditions. Similarly, with q̇ = 20400 W/m2 (Figure 5.12c) and
q̇ = 27400 W/m2 (Figure 5.12d) the determined film Reynolds numbers, 157 and 158,
respectively, are clearly lower than the dryout onset Reynolds numbers, 489 and 562,
respectively. Consequently, the correlation predicts the appearance of the dry patches observed
in those figures.
110
Chapter 5
5.2.
Spray evaporation of pure refrigerants: R134a and ammonia
SPRAY EVAPORATION OF AMMONIA ON PLAIN TUBE
In this subsection, we present the results obtained with spray evaporation tests of ammonia
on the titanium plain tubes tested for both ST (direct distribution of the refrigerant) and SB
(distribution through conditioning tube) experiments. We conducted tests distributing the liquid
refrigerant at a temperature of 10 ºC, varying the LMTD at the evaporator from 4 K to 15 K (at
steps of 1 K). The distributed refrigerant mass flow rates were 450 kg/h, 550 kg/h, 650 kg/h,
750 kg/h and 850 kg/h, which correspond to film flow rates per side and meter of tube of
0.0042 kg/m·s, 0.0051 kg/m·s, 0.0061 kg/m·s, 0.0071 kg/m·s and 0.0078 kg/m·s, respectively.
With these conditions, the heat flux ranged from 2600 W/m2 to 44400 W/m2.The velocity of the
heating water with these tests was 2.4 m/s, approximately, and the Reynolds number ranged
from 31900 to 43700. Thus, the flow was fully developed turbulent and the application of the
correlation shown in subsection 3.3.2 for the plain tube was suitable. The heating water HTCs
ranged from 8500 W/m2·K to 10000 W/m2·K, approximately.
5.2.1.
Spray evaporation heat transfer coefficients
Figure 5.13 shows the heat flux on the outer surface of the titanium plain tube vs. surface
superheating, under ST spray evaporation tests and with a liquid ammonia distribution
temperature of 10 ºC. Heat flux rises with surface superheating throughout the studied range,
independently of the series of tests considered. In contrast with pool boiling tests, the slope of
each set of data is almost constant, pointing out that nucleate boiling occurs with much lower
surface superheating values than under pool boiling (subsection 4.3.1). We observe that with
the lowest mass flow rates tested (Γ = 0.0042 kg s-1 m-1 and Γ = 0.0051 kg s-1 m-1) the slope of
the curves decreases if the heat flux is high. This effect shows a heat transfer deterioration,
which could be caused by the dryout of the film on the tube.
50000
ST 0.0078 kg/m·s
45000
ST 0.0071 kg/m·s
q/Ao [W/m2]
40000
ST 0.0061 kg/m·s
35000
ST 0.0051 kg/m·s
30000
ST 0.0042 kg/m·s
25000
20000
15000
10000
5000
0
0
1
2
3
4
5
6
ΔTSH [K]
Figure 5.13. Heat flux on the outer surface of the titanium plain tube vs. surface superheating,
under ammonia ST spray evaporation tests, with the different mass flow rates per side and per
meter of tube and with a refrigerant distribution temperature of 10 ºC
Concerning the spray evaporation HTCs, we represented them in Figure 5.14 vs. heat flux
and as a function of the mass flow rate distributed. At the low heat flux range (up to
10000 W/m2, approximately) HTCs increase rapidly from 5000 W/m2·K to 8000 W/m2·K,
approximately, independently of the film flow rate per side and meter of tube (Γ). With higher
heat fluxes, the results depend on Γ. On the one hand, the HTCs at tests developed with Γ from
0.0061 kg/m·s to 0.0078 kg/m·s keep increasing as the heat flux increases. On the other hand,
with Γ = 0.0051 kg/m·s, HTCs remain almost constant as heat flux rises, and with
111
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
Γ = 0.0042 kg/m·s they even decrease. The average, maximum and minimum uncertainties
associated to the determination of these HTCs were ±9.1%, ±14.2% and ±6.6%, respectively.
14000
12000
ho [W/m2·K]
10000
8000
6000
ST 0.0078 kg/m·s
4000
ST 0.0071 kg/m·s
ST 0.0061 kg/m·s
2000
ST 0.0051 kg/m·s
ST 0.0042 kg/m·s
0
0
10000
20000
30000
40000
50000
q/Ao [W/m2]
Figure 5.14. Spray evaporation HTCs vs. heat flux on the outer surface of the titanium plain tube,
under ammonia ST spray evaporation tests, with the different mass flow rates per side and per
meter of tube and with a refrigerant distribution temperature of 10 ºC
Figure 5.14 also indicates that, if fixed the heat flux, spray evaporation HTCs deteriorate as
the refrigerant Γ decreases. For instance, at a heat flux of approximately 20000 W/m2, the spray
evaporation HTCs with Γ = 0.0078 kg/m·s and Γ = 0.0061·kg/m·s are respectively 20.3% and
12.0% higher than with Γ = 0.0042 kg/m·s. At higher heat fluxes, these percentages increase,
reaching 57.4% and 38.6% with a heat flux of 35000 W/m2, approximately.
The appearance of dry patches on the tubes could explain this effect. Dry patches are areas
of the tubes uncovered by the liquid refrigerant due to incorrect or insufficient refrigerant
distribution. The negative effect on the average HTCs increases as the fraction of dry patches
rises and this fraction increases as the film flow rate decreases, if fixed the heat flux. We
confirmed the appearance of dry patches visually and we show and explain the images taken in
subsection 5.2.3.
We developed an experimental correlation with the spray evaporation HTCs obtained with
ST tests, titanium plain tube and ammonia, shown in equation (5.5). The correlation depends on
the heat flux, q̇, and on the mass flow rate of refrigerant per side and per meter of tube, Γ, which
were the parameters varied and controlled during the experiments. We obtained the correlation
with the three highest mass flow rates tested to guarantee that it represents complete wetting
conditions. The coefficient of determination of the correlation is R2 = 0.94 and the average
absolute deviation between the experimental data and the correlation is 4.9%.
ho  3180.22 q 0.25 0.3
(5.5)
Figure 5.15 shows the heat flux on the outer surface of the titanium plain tube vs. surface
superheating, under SB spray evaporation tests and with a liquid ammonia distribution
temperature of 10 ºC. As happened in the previous tests, heat flux rises with surface
superheating throughout the studied range, independently of the series of tests considered.
Nucleate boiling also occurs at lower surface superheating values than under pool boiling
(subsection 4.3.1), independently of Γ. However, the slopes of the curves at Γ = 0.0042 kg/m·s
112
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
and Γ = 0.0051 kg/m·s are clearly lower than with the other three mass flow rates and this effect
is again caused by the appearance of dry patches on the tested tube.
50000
SB 0.0078 kg/m·s
q/Ao [W/m2]
45000
SB 0.0071 kg/m·s
40000
SB 0.0061 kg/m·s
35000
SB 0.0051 kg/m·s
SB 0.0042 kg/m·s
30000
25000
20000
15000
10000
5000
0
0
1
2
3
4
5
6
7
8
ΔTSH [K]
Figure 5.15. Heat flux on the outer surface of the titanium plain tube vs. surface superheating,
under ammonia SB spray evaporation tests, with the different mass flow rates per side and per
meter of tube and with a refrigerant distribution temperature of 10 ºC
The spray evaporation HTCs obtained with SB spray evaporation experiments vs. the heat
flux on outer surface of the titanium tube, with ammonia as refrigerant and the different mass
flow rates distributed appear in Figure 5.16. Γ determines the dependence between heat fluxes
and spray evaporation HTCs. When Γ = 0.0042 kg/m·s, the HTCs increase with heat flux only
up to 5900 W/m2 and then decrease sharply and remain constant. The same happens when
Γ = 0.0051 kg/m·s, but the change of trend occurs at higher heat flux (15600 W/m2). With the
remaining mass flow rates, the increasing tendency lasts up to heat fluxes over 20000 W/m2
and then spray evaporation HTCs remain constant The average, maximum and minimum
uncertainties associated to the determination of these HTCs were ±6.8%, ±13.1% and ±3.8%,
respectively.
As happened with ST tests, Figure 5.16 indicates that, if fixed the heat flux, spray
evaporation HTCs deteriorate as the refrigerant Γ decreases. For instance, at a heat flux of
approximately 20000 W/m2, the spray evaporation HTCs with Γ = 7.8·10-3 kg/m·s and
Γ = 6.1·10-3 kg/m·s are respectively 92.4% and 73.9% higher than with Γ = 4.2·10-3 kg/m·s. With
an approximate heat flux of 30000 W/m2, these percentages reach 72.4% and 66.6%. Dry
patches seem to be the reason of the HTC deterioration, but the process could not be recorded
under SB tests due to the limitations of the viewing sections.
113
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
9000
8000
ho [W/m2·K]
7000
6000
5000
4000
SB 0.0078 kg/m·s
3000
SB 0.0071 kg/m·s
2000
SB 0.0061 kg/m·s
1000
SB 0.0051 kg/m·s
SB 0.0042 kg/m·s
0
0
10000
20000
30000
40000
50000
q/Ao [W/m2]
Figure 5.16. Spray evaporation HTCs vs. heat flux on the outer surface of the titanium plain tube,
under ammonia SB spray evaporation tests, with the different mass flow rates per side and per
meter of tube and with a refrigerant distribution temperature of 10 ºC
We developed an experimental correlation with the spray evaporation HTCs obtained with
SB tests, titanium plain tube and ammonia, shown in equation (5.6). The correlation depends on
the heat flux, q̇, and on the mass flow rate of refrigerant per side and per meter of tube, Γ, which
were the parameters varied and controlled during the experiments. Due to the appearance of
dry patches, particularly when Γ = 0.0042 kg/m·s, the correlation was obtained with the three
highest mass flow rates tested. The coefficient of determination of the correlation is R2 = 0.84
and the average absolute deviation between the experimental data and the correlation is 6.4%.
ho  913.43 q 0.23 0.07
(5.6)
Figure 5.17 compares the spray evaporation HTCs vs. heat flux obtained with the tube
placed directly underneath the refrigerant distribution tube (ST tests) to those determined with
the tube that receives refrigerant from another placed over it. The HTC values with the first tests
are between 20.7% and 56.6% (average 38.7%) greater than with the second. Therefore, the
enhancement effect due to droplet impingement stated by Zeng et al. [2] or Tatara and Payvar
[3] appeared again with this refrigerant.
We compared our experimental results with those calculated with equation (5.7), as shown
in Figure 5.18. This equation correlates the experimental results included in Zeng and Chyu [8]
of spray evaporation with ammonia as refrigerant and distribution with high momentum devices
(nozzles). Θ stands for the dimensionless heat flux, obtained with (5.8). Our results are clearly
underestimated by the correlation and the disagreement is greater than 60% with more than half
of our results. The cause for this disagreement is not clear, since the heat flux range and the
mass flow rates distributed are similar.
114
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
14000
12000
ho [W/m2·K]
10000
8000
6000
ST 0.0078 kg/m·s
ST 0.0061 kg/m·s
ST 0.0042 kg/m·s
SB 0.0078 kg/m·s
SB 0.0061 kg/m·s
SB 0.0042 kg/m·s
4000
2000
0
0
10000
20000
30000
40000
50000
q/Ao [W/m2]
Figure 5.17. Spray evaporation HTCs vs. heat flux on the outer surface of the titanium plain tube,
under ammonia ST and SB spray evaporation tests, with the different mass flow rates per side and
per meter of tube and with a refrigerant distribution temperature of 10 ºC
0.385 0.753
Nu  0.0518 Re0.039
Pr 0.278 pred

f
  q dt
5.2.2.
Tc  Ts  k 
(5.7)
(5.8)
Spray enhancement factors
Figure 5.19 illustrates the spray enhancement factor of ammonia and plain titanium tube vs.
heat flux, with ST experiments and as a function of the mass flow rate of refrigerant per side
and meter of tube. Spray evaporation enhances heat transfer if compared to pool boiling under
every condition tested. This statement is particularly true in the low heat flux range (up to
20000 W/m2). The maximum spray enhancement factor is 6.2 (0.0042 kg/m·s and 2600 W/m2)
and the minimum 1.1 (0.0042 kg/m·s and 35200 W/m2).
Similarly, Figure 5.20 includes the spray enhancement factor of ammonia and plain titanium
tube vs. heat flux, with SB experiments and as a function of the mass flow rate of refrigerant per
side and meter of tube. In this case there are some conditions, particularly with
Γ = 0.0042 kg/m·s and Γ = 0.0051 kg/m·s, at which pool boiling outperforms spray evaporation,
i.e. the spray enhancement factor is lower than 1. The maximum and minimum enhancement
factors obtained under these conditions are 5.6 (0.0042 kg/m·s and 2500 W/m2) and 0.8
(0.0042 kg/m·s and 29800 W/m2), respectively.
Our experimental results concerning spray enhancement are in agreement with Zeng and
Chyu [8], who observed that spray evaporation HTCs in a tube bundle can be up to a 50%
greater than under pool boiling.
115
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
12000
10000
hcorr [W/m2·K]
8000
6000
-60%
4000
2000
0
0
2000
4000
6000
8000
10000
12000
hexp [W/m2·K]
Figure 5.18. Spray evaporation HTCs obtained with the correlation of Zeng and Chyu [8] vs. our
experimental spray evaporation HTCs with ammonia and a titanium plain tube
7
ST 0.0078 kg/m·s
6
ST 0.0071 kg/m·s
ST 0.0061 kg/m·s
EFsp,Γ [-]
5
ST 0.0051 kg/m·s
ST 0.0042 kg/m·s
4
3
2
1
0
0
10000
20000
30000
40000
50000
q/Ao [W/m2]
Figure 5.19. Spray enhancement factors vs. heat flux on the outer surface of the titanium plain
tube, under ammonia ST spray evaporation tests, with the different mass flow rates per side and
per meter of tube and with a refrigerant distribution temperature of 10 ºC
116
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
6
SB 0.0078 kg/m·s
5
SB 0.0071 kg/m·s
EFsp,Γ [-]
SB 0.0061 kg/m·s
4
SB 0.0051 kg/m·s
SB 0.0042 kg/m·s
3
2
1
0
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
q/Ao [W/m2]
Figure 5.20. Spray enhancement factors vs. heat flux on the outer surface of the titanium plain
tube, under ammonia SB spray evaporation tests, with the different mass flow rates per side and
per meter of tube and with a refrigerant distribution temperature of 10 ºC
5.2.3.
Photographic report
Figure 5.21 includes pictures of the flow mode that occurs when distributing ammonia on
the titanium plain tube as a function of the mass flow rate of refrigerant distributed, at a
saturation temperature of 10 ºC and under adiabatic conditions (no heat flux). As the mass flow
rate distributed increases from 0.0042 kg/m·s (Figure 5.21a) to 0.0061 kg/m·s (Figure 5.21b)
the distance between active dripping sites decreases from 35.8 mm to 25.4 mm, approximately,
and the shape of the falling liquid is in between columns and drops. Liquid columns become
more clear in Figure 5.21c, taken with Γ = 0.0078 kg/m·s, but the distance between the columns
increased slightly (26.5 mm). However, in between the columns of this last situation, active
dripping sites are present.
The determination of the distance between active sites from the pictures was very
complicated since the active sites move longitudinally due to the characteristics and direction of
the flow caused by the nozzles. Taking into account this, we compared them with the distances
calculated using equation (5.4), developed by Yung et al. [6] and based on the Taylor instability
theory. According to the authors of that work, ammonia films are considered thin films and,
therefore, n = 2. The values obtained with this equation are 19.5 mm, and therefore in the same
order of magnitude than the ones we obtained, particularly with the highest mass flow rates.
In Figure 5.22, we also focused on the falling film flow mode keeping fixed the mass flow
rate of refrigerant at 0.0051 kg/m·s and varying the heat flux. An increase in the heat flux leads
to slight differences in the distance between active sites, but the dripping rate decreases. Figure
5.23 shows an analogous study, but developed with a mass flow rate of refrigerant at
0.0071 kg/m·s. In this case, the increase of heat flux has a negligible effect on both the dripping
rate and the distance between active sites. To explain this different behaviour we focus on the
overfeed factor, OF, defined in subsection 3.3.3 as the ratio of mass flow rate reaching the top
of the tube to the mass flow rate that vaporises. OF is much lower with 0.0051 kg/m·s, and
therefore there is less liquid refrigerant left after boiling to drip from the tube.
117
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
a
b
c
Figure 5.21. Dripping active sites with ammonia and the titanium plain tube as a function of the
mass flow rate per side and per meter of tube, Γ, under adiabatic conditions. a) Γ = 0.0042 kg/m·s.
b) Γ = 0.0061 kg/m·s. c) Γ = 0.0078 kg/m·s
a
b
c
Figure 5.22. Dripping active sites with ammonia and the titanium plain tube as a function of heat
flux, q̇, with mass flow rate per side and per meter of tube, Γ = 0.0051 kg/m·s. a) q̇ = 10000 W/m2.
b) q̇ = 24800 W/m2. c) q̇ = 38800 W/m2
118
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
a
b
c
Figure 5.23. Dripping active sites with ammonia and the titanium plain tube as a function of heat
flux, q̇ with mass flow rate per side and per meter of tube, Γ = 0.0071 kg/m·s. a) q̇ = 10200 W/m2.
b) q̇ = 25600 W/m2. c) q̇ = 44400 W/m2
We expected the existence of dry patches on the tube due to the HTCs we obtained. We
confirmed them visually. Figure 5.24 includes four photographs taken at our experimental facility
to illustrate dryout. With Γ = 4.2·10-3 kg/m·s and no heat flux on the surface (Figure 5.24a) the
film is unperturbed. In contrast, dry patches appeared with the same film flow rate and a heat
flux on the surface of 35200 W m-2 (Figure 5.24b). Figure 5.24c and Figure 5.24d represent
analogous situations with Γ = 7.1·10-3 kg/m·s, but dry areas do not occur at this film flow rate.
a
b
c
d
Figure 5.24. Dry patches on the titanium plain tube with ammonia. a) Γ = 0.0042 kg/m·s and
q̇ = 0 W/m2. b) Γ = 0.0042 kg/m·s and q̇ = 35200 W/m2. c) Γ = 0.0071 kg/m·s and q̇ = 0 W/m2.
c) Γ = 0.0071 kg/m·s and q̇ = 44400 W/m2
We employed the correlation from Ribatski and Thome [7], equation (5.4), to determine the
maximum Reynolds number at which dryout occurred in their tests. We considered the
conditions of heat flux from the pictures shown in Figure 5.24. With q̇ = 35200 W/m2 (Figure
5.24b), the dryout onset Reynolds number is 236, which is clearly greater than the one we
119
Chapter 5
Spray evaporation of pure refrigerants: R134a and ammonia
determined from our experimental measurements, 110.3. Therefore, the existence of dryout is
in agreement with their correlation. With q̇ = 44400 W/m2 (Figure 5.24d), the dryout onset
Reynolds number from the correlation is 263, again higher than that we obtained, 183.
However, in this case we did not observe or confirm dryout in our experiments.
Finally, we also checked visually that in our experiments nucleate boiling occurred. In the
pictures taken of the pool boiling processes (subsections 4.3.4 and 4.4.4) bubbles can be easily
visualised in the liquid that surrounds the tube. In contrast, the thin film around the tubes under
spray evaporation makes difficult viewing nucleate boiling. However, we detected bubbles in the
drops that fell from the tube, as can be seen in all the pictures from Figure 5.25.
a
b
c
d
Figure 5.25. Nucleate boiling and bubbles entrained by drops on the titanium plain tube with
ammonia. a) Γ = 0.0051 kg/m·s and q̇ = 31700 W/m2. b) Γ = 0.0061 kg/m·s and q̇ = 33000 W/m2.
c) Γ = 0.0071 kg/m·s and q̇ = 34600 W/m2. c) Γ = 0.0078 kg/m·s and q̇ = 44300 W/m2
120
Chapter 5
5.3.
Spray evaporation of pure refrigerants: R134a and ammonia
CONCLUSIONS
In this chapter we have shown the spray evaporation HTCs obtained experimentally for this
thesis. The refrigerants studied were R134a and ammonia. With the former we tested copper
tubes of plain external surface and with the latter titanium tubes of plain external surface.
We have observed that the vast majority of our experimental results were included in the
boiling region of the boiling curve, where the slope is steep and heat flux increases rapidly with
superheating. However, the slope is slightly slower in some cases, pointing out the existence of
dry patches.
Concerning the spray evaporation HTCs with R134a and the copper tube, we have
observed that they generally increase if the heat flux is higher, independently of the mass flow
rate of the film per side and meter of tube. We have also observed that the effect of the mass
flow rate on the HTCs is negligible.
The spray evaporation heat transfer coefficients obtained with R134a and the tube placed
directly underneath the refrigerant distribution tube (ST tests) are, on average, 13.2% greater
than those determined with the tube that receives refrigerant from the conditioning tube (SB
tests), if kept the heat flux and distributed mass flow rate constant. The heat transfer
enhancement occurs due to the liquid droplet impingement effect.
We compared spray evaporation and pool boiling, with R134a, under similar conditions. We
have observed that spray evaporation enhances heat transfer only if the heat flux is low (lower
than 20000 W/m2) and this enhancement has never been higher than 60%. These results
concerning enhancement are in line with what Roques [4] or Moeykens [5] stated.
An analysis of the photographs taken during the experiments allowed confirming the
existence of dry patches on the tubes and explained the heat transfer deterioration found.
Dryout occurred even when the distributed refrigerant was significantly greater than the amount
of refrigerant that vaporised on the tube (overfeed rates well over 1).
Concerning the spray evaporation HTCs with ammonia and the titanium tube, we have
observed that they depend on both the heat flux and the mass flow rate of refrigerant per side
and meter of tube. Generally, they increase as the heat flux increases, but this trend was even
opposite under conditions of high heat flux and low mass flow rate.
We observed that the spray evaporation heat transfer coefficients obtained with ammonia
and the tube placed directly underneath the refrigerant distribution tube (ST tests) are, on
average, 38.7% higher than those determined with the tube that receives refrigerant from the
conditioning tube (SB tests). Droplet impingement effect is responsible of this effect.
From the comparison of spray evaporation and pool boiling of ammonia on the plain tube,
we have concluded that spray evaporation enhances importantly heat transfer. Spray
enhancement factors are well over 1, particularly when the refrigerant on the tested tube arrives
directly from the nozzles (ST tests). The maximum enhancement factor was over 6 and the best
results occurred in the low heat flux range (up to 20000 W/m2). Zeng and Chyu [8] stated as
well that spray evaporation with ammonia enhances heat transfer, even though in lower
magnitude than what we observed. Our results are underpredicted by their experimental
correlation.
We have analysed the snapshots taken when conducting the tests and the most important
conclusion is that dry patches occurred under certain conditions. Dryout explains some of the
tendencies we obtained from our experimental results.
121
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Spray evaporation of pure refrigerants: R134a and ammonia
REFERENCES
[1] Á.Á. Pardiñas, J. Fernández-Seara, R. Diz, Experimental study on heat transfer coefficients
of spray evaporation and pool boiling on plain tubes, in: Proceedings of the 24th IIR International
Congress of Refrigeration, Yokohama, Japan, 2015.
[2] X. Zeng, M. Chyu, Z.H. Ayub, Experimental investigation on ammonia spray evaporator with
triangular-pitch plain-tube bundle, Part I: Tube bundle effect, International Journal of Heat and
Mass Transfer. 44 (2001) 2299-2310.
[3] R. Tatara, P. Payvar, Measurement of spray boiling refrigerant coefficients in an integral-fin
tube bundle segment simulating a full bundle, International Journal of Refrigeration. 24 (2001)
744-754.
[4] J.F. Roques, Falling film evaporation on a single tube and on a tube bundle, Ph.D. thesis,
École Polytechnique Fédérale de Lausanne, Switzerland, 2004.
[5] S.A. Moeykens, Heat transfer and fluid flow in spray evaporators with application to reducing
refrigerant inventory, Iowa State University of Science and Technology, Iowa, USA, 1994.
[6] D. Yung, E.N. Ganić, J.J. Lorenz, Vapor/liquid interaction and entrainment in falling film
evaporators, Journal of Heat Transfer. 102 (1980) 20-25.
[7] G. Ribatski, J.R. Thome, Experimental study on the onset of local dryout in an evaporating
falling film on horizontal plain tubes, Experimental Thermal and Fluid Science. 31 (2007) 483493.
[8] X. Zeng, M. Chyu, Heat transfer and fluid flow study of ammonia spray evaporators, Texas
Tech University, Lubbock, Texas, USA, 1995.
122
Chapter 6
Optimisation of the nozzle
distribution system in shelland-tube evaporators
In this chapter we focus on the distribution of liquid on spray (falling film) shell-and-tube
evaporators. It starts with an analysis of different systems, proposed mainly in patents, to
distribute refrigerant on the tube bundles. This analysis suggests that most of the existing
systems are based on low momentum techniques. As a result, we study the layout to optimize
refrigerant distribution with nozzles (high momentum devices). The optimization study is based
on geometry and trigonometry and completes and delves into previous research found in the
specialized literature on this topic.
The study starts with the definition of the spray cone formed by full cone nozzles and of the
area of a general tube from the bundle reached by the nozzle. It continues calculating the
optimal position of the nozzles for a particular tube bundle and how this optimal position must
be adapted as a function of the actual length of the tube bundle.
To continue, in this chapter we present the computer programme developed to apply the
previously described model to real tube bundles. We also include a parametric analysis to show
how the different distribution indicators are affected by parameters such as the tube bundle
pattern, the distance between tubes, the nozzle cone angle or the number of nozzle systems.
123
Chapter 6
6.1.
Optimisation of the nozzle distribution system in shell-and-tube evaporators
INTRODUCTION
The distribution of refrigerant on the tube bundle of an evaporator is a key factor for its
correct performance, since the appearance of dry zones on the tubes may cause an important
deterioration of heat transfer. In the scientific literature, different distribution methods have been
proposed and studied, and they can be classified into low momentum and high momentum.
As explained in section 1.8.5, several low momentum solutions distribute liquid by the effect
of gravity; i.e. it falls from the device to the surface (tube) placed directly beneath. This means
that the distribution system must be placed over each and every column of the tube bundle,
properly aligned, in order to assure the liquid feed. In contrast, high momentum solutions (spray
nozzles) distribute the liquid with a much higher velocity. These systems have been seen to
improve heat transfer and wetting of tubes, and they seem more appropriate for industrial
equipment, since alignment is not a critical issue and a same nozzle may distribute liquid to
more than one column of tubes inside the bundle. However, a part of this liquid may leave the
bundle and it is difficult to quantify which fraction of the flow rate reaches each tube.
Independently of the kind of method used, there has been great effort to optimise the
distribution systems for shell-and-tube evaporators, as shows the large list of patents available
on the topic. One of the first approaches we have found is that from Hartfield and Sanborn [1],
in the United States Patent number US 5,561,987. The authors claimed a distribution system
which can be classified into the low momentum group and that includes also a liquid-vapour
separator (Figure 6.1). In the patent, they state several possible configurations for the
distribution device itself, which go from a tree of tubes with orifices to wavy-shaped plates that
should increase the size of the droplets that reach the evaporator tubes.
Figure 6.1. Combined liquid distribution system and liquid-vapour separator from reference [1]
The previous work describes the necessity of immersing the last rows of tubes of the
evaporator tube bundle in liquid refrigerant, since film breakdown is more likely to occur on
them. This idea is further described in patent US 5,839,294, where Chiang et al. [2] claim the
invention of a system combining pool boiling and spray evaporation. According to the authors,
the liquid is distributed by the spray dispensers due to the refrigerant flow loop differential
pressure. In addition, the system leads to a refrigerant charge reduction without any pump or
similar system for recirculation. However, oil recovery from the evaporator seems an important
issue of this loop which was not considered or mentioned by the authors.
Gupte [3] presents the main distribution challenges to be faced as a function of the pattern
of the tube bundle. Staggered tube bundles, which are very typically used in shell-and-tube heat
exchangers to reduce their size, have a very high pressure drop of the refrigerant vapour, which
explains that inline tube bundles appear as an option. In addition, the liquid flow rate distributed
in staggered tube patterns spreads out among more tubes than with inline tube bundles, which
means that dry patches are more likely to appear in the first case. However, according to Gupta,
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Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
inline tube bundles have also more complex distribution systems and part of the refrigerant may
leave the bundle without reaching any tube. In this patent, the author suggests an inline pattern
distribution system to direct the refrigerant from the nozzles.
Liu and Liu [4] claimed in the United States patent US 2008/0149311 A1 that a main issue
concerning spray evaporators is to maximize the number of tubes dedicated to heat transfer in
the shell. To do so they propose several layouts of the tubes all over the shell and, in between
the tubes, distribution units (plates) of different shapes with holes or slots. Liu et al. [5] suggest
an extended distributor system to improve wetting. To finish with this kind of low dripping
distributors, Christians et al. [6] propose a different configuration (Figure 6.2) that includes
channels aligned with each and every tube column. The authors also state that, in order to
homogenise distribution, these channels could be filled with a porous media. Vapour slots are
also present in the system to evacuate the vapour fraction that comes with the liquid refrigerant.
Figure 6.2. Distribution system proposed in patent US 2014/0366574 A1 [6]
As seen up to this moment, the main distribution devices on the aforementioned works were
of low momentum type. However, there is an important innovative work concerning nozzles for
refrigerant distribution in tube bundles, as seen in reference [7]. Chang and Yu show the
possibility of introducing tubes with nozzles machined in their wall throughout the tube bundle.
In this way, if the nozzles are properly positioned, dry patches are more likely to be prevented.
In addition, liquid impingement, which has been seen to have a positive effect on heat transfer,
occurs all over the tube bundle and not only on the uppermost row of tubes. The main
disadvantage of this system lies in the fact that one of each 4 positions of the tube bundle
where a heat transfer tube should be, is occupied by a nozzle tube.
The control of the vapour flow is another important issue concerning refrigerant distribution,
as reviewed in section 1.4.3. In the United States patent US 6,293,112 B1, Moeykens et al. [8]
suggest different tube bundle layouts to form vapour channels that should allow vapour
drainage from it. De Larminat et al. [9] propose an alternative to solve this problem, which
consists in covering the distribution system and tube bundle with a hood. Thus, cross flow
should be prevented. The authors also claim that this hood should minimize the amount of liquid
droplets entrained that reach the suction line.
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Chapter 6
6.2.
Optimisation of the nozzle distribution system in shell-and-tube evaporators
AIM OF THE STUDY AND PREVIOUS CONSIDERATIONS
From the analysis shown in the previous subsection we concluded that there is a general
trend of focusing on low momentum distribution techniques. These techniques lead to very
complicated structures and layouts of the shell, where groups of tube bundles and distributors
are placed. From our point of view, the reason why nozzles are underused is due to the
challenge of positioning them to achieve a homogeneous and complete distribution, minimising
the liquid that leaves the tube bundle without reaching any of its tubes. This challenge motivated
the study presented in this section, which main aim was to optimise the nozzle system or
systems needed for a certain tube bundle. To satisfy this we developed a mathematical model
based on the geometry of the spray cones that result from using nozzles when distributing
refrigerant.
When designing the refrigerant distribution system with spray nozzles, a designer should
take into account several considerations. The system should cover all the available surface of
the tube bundle seen from above. Moreover, the distribution has to be homogeneous, i.e., each
column of tubes of the tube bundle should receive a similar fraction of the whole flow rate
distributed. Thus, dry patches may be prevented by distributing the proper amount of liquid
without involving high overfeed on other columns and high recirculation rates of excess liquid.
Furthermore, the fraction of the flow rate that reaches an area where two or more adjacent
nozzles distribute refrigerant (overlapping) or where there are no tubes (fluid lost) should be
minimum. Further issues to take into consideration could be minimising the number of nozzles
systems (groups of nozzles placed at the same plane), minimising the total number of nozzles
used, etc.
Taking into account these considerations, the selection of the type of nozzle to be used is
crucial. According to the Engineer’s guide to spray technology [10], there are plenty of different
nozzle types available in the market, which can be mainly classified into hollow cone nozzles
and full cones nozzles. This classification attends to the spray pattern produced by the nozzle.
Hollow cone nozzles produce an annulus of liquid; i.e. part of the area right beneath this type of
nozzles receives no liquid at all. On the other hand, full cone nozzles distribute liquid forming a
spray that fills the area covered completely and homogeneously. Thus, the characteristics of
this last option makes it appropriate for this application.
Full cone nozzles produce sprays with different shapes depending on the manufacturer, but
the most common ones are round cone nozzles and square cone nozzles. Round cone nozzles
distribute liquid with axial symmetry, describing circles in every plain normal to the longitudinal
nozzle axis. This kind of symmetry leads to two of the main characteristics of round cone
nozzles. The first is that no specific alignment is needed in order to feed a certain area, which is
very convenient from the point of view of industrial processes or heat exchangers. The second
one concerns the necessity of overlapping a fraction of the liquid distributed by two or more
nozzles in order to feed an area (tube bundle). In addition, another part of the flow rate leaves
the bundle due to the same reason.
In contrast, square cone nozzles produce cones without axial symmetry, describing squares
instead of circles in every plain perpendicular to the nozzle axis. Therefore, the shape of the
cone at the fed zone depends on the positioning angle of the nozzle and these nozzles require
a certain alignment process to work in the expected manner. However, the main advantage of
square over round nozzles is also associated with their non-axial symmetry. If the system is
properly designed, no overlapping is needed in order to feed a certain bundle, which means that
the flow rate arriving to the bundle is more uniform. Moreover, the shape of the spray adapts
better to tube bundles and the flow rate that leaves the bundle is minimised.
In the following chapters, round and square full cone nozzles and the sprays produced by
them will be further studied.
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Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
6.3.
GEOMETRIC CALCULATIONS
6.3.1.
Characterisation of the spray produced by a full cone nozzle
The first issue that must be defined in order to characterise geometrically a spray is the
determination of the origin of the spray, O, which should correspond to the place of spray where
the size of the cone is 0. If we analyse the size of the spray (diameter in case of a circular
nozzle) at the tip of the nozzle it is not equal to 0 and technically cannot be considered as origin.
According to references [10,11], the origin of the cone, for calculation considerations, is placed
at the orifice or outlet of the nozzle, which is a few millimetres upstream from the tip. However,
for the sake of simplicity in the representation of the different cases, the origin (O in Figure 6.3)
appears at the tip of the nozzle and is considered at a generic position (xO,yO,0).
Figure 6.3. Representation of the spray cone produced by a spray nozzle and coordinate systems
used throughout the study
The interest in defining geometrically a spray is to determine whether a point of the space
receives liquid from a nozzle or not. This definition will be later applied to tube bundles in heat
exchangers and to determine the flow rate distributed to each tube or portion of tube. In order to
define the geometry of a spray full cone, we considered the following assumptions:




The spray flow distributed by a nozzle is treated as a whole, and not as individual drops
or jets of liquid.
Homogeneous distribution of the fluid throughout the cone; i.e. if chosen a portion of the
total surface covered by a spray, the flow rate impinging on that surface is the result of
multiplying the total spray flow rate by the ratio of the chosen surface to the total surface
covered by the cone.
The spray from a nozzle is straight at the sides, unaffected by gravity in the range of
distances studied.
The shape of the cones is a perfect circle/square.
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Chapter 6



Optimisation of the nozzle distribution system in shell-and-tube evaporators
Square nozzle cones are considered perfectly aligned.
There is no interaction between the flows distributed by two or more nozzles that reach
a certain area.
The splashing rate is neglected.
Taking into account these hypothesis, any point from the spray cone can be defined as a
function of three parameters: z, θ and α, as represented in Figure 6.3. Each of these
parameters varies in a range that depends on the nozzle spray pattern and shape. As
previously stated, the most suitable nozzles at evaporators are those with full cone pattern, due
to the necessity of a homogeneous distribution. Among them, round and square nozzles will be
analysed from now on.
The vertical distance from the origin of the spray to a certain point of space reached by it, z,
which ranges from 0 to infinite for both kind of nozzles. α represents the angle formed by the
trajectory from the origin of the spray to any point reachable by the spray cone and the plane
x=0. It ranges from -β/2 to β/2, where β corresponds to the nozzle maximum spray angle.
Finally, the limits for θ, which defines the angular position in the cone, depend on the previous
parameters and on the type of nozzle.
For round cone nozzles, θ is between -arccos(tan(α)/tan(β/2)) and arccos(tan(α)/tan(β/2))
when α > 0, and between arccos(tan(α)/tan(β/2)) and -arccos(tan(α)/tan(β/2)) when α < 0. For
square cone nozzles, θ ranges from -arctan(tan(β/2)/tan(α)) to arctan(tan(β/2)/tan(α)) when
α > 0, and from arctan(tan(β/2)/tan(α)) to -arctan(tan(β/2)/tan(α)) when α < 0. When α = 0,
neither of the nozzles can be defined using θ as third parameter, i.e. the point is indeterminate.
The solution to this is to approach α = 0 either by limiting at the left or the right of it.
The conversion from the aforementioned definition of the nozzle, with z, θ and α, to a
definition with Cartesian coordinates is the same for either round or square nozzles, and is done
through equation (6.1).
x  xo  z tan ;
y  y o  z tan tan ;
z
(6.1)
For a general situation of a nozzle distributing liquid on a tube randomly positioned, as
shown in Figure 6.4, only if the tube (represented as a circle) is positioned in between the angle
described by β it receives liquid from that nozzle.
Figure 6.4. Representation of a nozzle spreading refrigerant on a general tube
The geometrical models developed in this study are based on the previous study from Zeng
and Chyu [11], but there is a main difference at this point between our study and theirs that
conditions the rest of it. According to Zeng and Chyu, the tube from Figure 6.4 would receive
128
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
liquid from the nozzle on all its upper surface. From our point of view, that would only be true if
the distance between the tube and origin of the spray, z1, were infinite. Our statement lies in the
fact that any part of the spray cone that is out of the angle formed by the tangents from the
spray origin to the tube is lost for that tube. In Figure 6.4 we represent one of those tangents,
which “touches” the tube at a distance z’ from the nozzle. At that distance, the “diameter” of the
spray cone is calculated with equation (6.2). The “diameter” represents a real diameter in the
case of circular full cone nozzles and the side of the square in case of square full cone nozzles.
dsp z'  2 z' tan 2
6.3.2.
(6.2)
Optimal position of adjacent nozzles and 1 nozzle system
As stated in section 6.2, due to the axial symmetry of round full cone nozzles, they need to
be positioned in a certain manner that leads to the full coverage of the heat transfer tube or tube
bundle, minimising the flow that is not useful (lost out of the tube bundle or overlapped with an
adjacent nozzle. This issue does not occur with square full cone nozzles, and that is the reason
why we will first focus on the former.
In Figure 6.5 we represent a generic tube bundle, projected on a plane normal to the nozzle
axis at a distance z’ from the origin of the sprays. z’ coincides with the distance in the z axis
between the origin of spray and the points of tangency of the external tubes of the uppermost
row of the tube bundle. If there is only one nozzle system (row of nozzles), it could happen that
the distance between adjacent nozzles (distnozzle in Figure 6.5) leads to a small area of bundle
fed by two nozzles, but also leads to uncovered or unreached areas (Auncovered in Figure 6.5a).
Thus, we do not fulfil the consideration stated in section 6.2 concerning the need of covering all
the reachable area of the bundle.
b
Auncovered
Auseless,2
distnozzle
distnozzle
a
Auseless,1
distnozzle
distnozzle
Auseful
dsp(z )
dsp(z )
wbdl
wbdl
Figure 6.5. Position between adjacent nozzles. a) Distance greater than the optimal. b) Distance
lower than the optimal
The opposite situation is shown in Figure 6.5b, where the distance between adjacent
nozzles leads to spray cones that fully cover the first row of the tube bundle, but with a high
fraction of overlapping between them (Auseless,2).
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Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
There should be an optimal distance at which all the considerations are fulfilled. This
optimal situation is graphically shown in Figure 6.6, where adjacent nozzles intersect exactly at
the limit of the tube bundle, defined by the tangencies of the tubes placed at the edges of the
uppermost row of the bundle. The area of each spray nozzle that is neither lost nor overlapped
(Auseful) has a square shape. This last statement will be mathematically verified in the following
paragraphs.
distnozzle
Auseless,2
Auseless,1
distnozzle
Auseful
dsp(z )
wbdl
Figure 6.6. Optimal distance between adjacent nozzles
The objective of the nozzle system is to cover the first row of the tube bundle minimising the
“useless” area. This could be mathematically expressed with the ratio of useless area, RAuseless,
as shown in equation (6.3). Auseful can be obtained with equation (6.4), where wbdl(z’) stands for
the width of the tube bundle at a plane normal to the spray nozzle axis at z’ from the spray cone
origin. Asp(z’) is the area covered by the spray produced by one nozzle at the same plane,
calculated with equation (6.5).
z'  Asp z'  Auseful z'  1  Auseful z'
A
RAuseless  useless
Asp z'
Asp z'
Asp z'
(6.3)
Auseful z'  w bdl z' distnozzle
(6.4)


Asp z'   d sp z' 2 2
(6.5)
If we consider that the tangent from the origin of the spray to the external tubes of the first
row forms an angle α with the plane that contains the spray nozzle row, x = 0, equation (6.6) is
true. In addition, there is a right-angled triangle formed by wbdl(z’)/2, distnozzle/2 and dsp(z’)/2.
Thus, equation (6.3) can be rearranged, resulting in equation (6.7).
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Chapter 6
z' 
Optimisation of the nozzle distribution system in shell-and-tube evaporators
d sp z'
2 tan 2

RAuseless  1 
w bdl z'
2 tan 
4
 tan2  2
(6.6)
tan  tan2  2  tan2  
(6.7)
The ratio of useless area depends on α, and therefore we derived equation (6.7) and equal
it to 0 to calculate the possible minimum. We evaluated the second derivative with this possible
minimum and verified that in the range where α occurs, (-β/2, β/2). The second derivative in that
range is always positive. The value of α that minimises the ratio is shown in equation (6.8). With
this equation and the previous ones we prove that the optimal distnozzle is equal to wbdl(z’) and
can be calculated by (6.9). nt,1 stands for the number of tubes of the first of the first row of the
tube bundle; distt,r stands for the distance in the x axis between the centres of consecutive tubes
of the same row of the tube bundle; and dt stands for the outer diameter of the tubes.
tan  
2 tan 2
2
(6.8)


distnozzle  w bdl z'  nt,1  1 distt,r  dt sin
(6.9)
The fact that the optimal distnozzle is equal to wbdl(z’) points out that the optimal shape of the
useful area (Auseful in Figure 6.6) is a square. Thus, we can easily conclude that the optimal
distance between square shape nozzles should be exactly the same as with circular shape
nozzles, but without any useless areas (RAuseless = 0).
6.3.3.
Optimal position of adjacent nozzles and multiple nozzle systems
The use of a singular nozzle system simplifies the distribution, but can be inefficient from
several points of view. First, for wide tube bundles, the distance between the nozzles and the
tube bundle to optimise distribution would be very high and a large part of the shell of the heat
exchanger would be wasted. In addition, the minimum RAuseless with 1 nozzle system is 0.363,
high compared with other possibilities that will be analysed in this subsection.
When a distribution system consists of more than 1 nozzle system, overlapping can occur
between 3 or more adjacent nozzles. This would deteriorate the distribution of refrigerant and
rapidly increase the RAuseless, and therefore it must be prevented. To achieve that, the
intersection between more than 2 adjacent nozzles should be punctual, as shown in Figure 6.7.
Having multiple nozzle systems involves not only optimising the distance between nozzles
of the same nozzle system, but also the distance between nozzles systems and how these are
positioned. According to Zeng and Chyu [11], the nozzle pattern can be square (Figure 6.7a) or
following an equilateral triangle (Figure 6.7b). Zeng and Chyu state that the latter makes better
use of the liquid refrigerant than the former, i.e. RAuseless is lower with the triangular pattern.
However, the geometrical model is slightly different in that study and, thus, we include our own
mathematical proof.
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Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
b
distnozzle
distnozzle
a
distnozzle
Auseful
Auseful
dsp(z )
dsp(z )
distsyst
distsyst
wbdl
wbdl
Figure 6.7. Position between adjacent nozzles of multi nozzle systems. a) Nozzles in a square
nozzle pattern. b) Squares in a equilateral triangle nozzle pattern
If the nozzles are positioned following a square pattern, the situation is similar to that
described for 1 nozzle system (section 6.3.2). The useful part of the area covered by each spray
cone describes a square inscribed in the circle and α depends on the nozzle angle β as stated
in equation (6.8). In this case the optimal distance between nozzles of the same system,
distnozzle, is a function of the number of nozzle systems, nsyst, and is also equal to the distance
between nozzle systems, distsyst, as calculated with equation (6.10).



dist nozzle  distsyst  nt ,1  1 distt ,r  d t sin nsyst
(6.10)
The RAuseless for this pattern, calculated with equation (6.11) and independent of the number
of nozzle systems, equals 0.363. This equation is solved taking into account the right-angled
triangle formed by distnozzle, distsyst and dsp(z’).
z'  1  distnozzle distsyst  1  2  0.363
A
RAuseless  1  useful
Asp z'

 d z' 2 2
 sp

(6.11)
If the nozzles are positioned following an equilateral triangle pattern, the situation is shown
in Figure 6.7b. The useful part of the area covered by each spray cone depends on the relative
position of the nozzle system to the whole distribution system. If the nozzle system is internal
(surrounded by two nozzle systems) the useful part is the hexagon inscribed in the circle formed
by the spray cone. If the nozzle is external, the hexagon is truncated by the limit of the tube
bundle. Thus, RAuseless should evaluate both possibilities. The method we propose consists in
considering the summation of the useful area of one nozzle of each nozzle system (striped area
in Figure 6.7b) and divide it by the summation of the area of the cone of spray of each of these
nozzles at z’ from the origin of the sprays (equation (6.12)). wbdl(z’) stands for the width of the
tube bundle at the plane normal to the nozzle axis at z’ from the spray cone origin and is a
result of equation (6.9). However, in this case (triangular nozzle pattern) the distance between
nozzles of the same nozzle system, distnozzle, is not equal to wbdl(z’).
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Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
z'  1  w bdl z' distnozzle
A
RAuseless  1  useful
Asp z'
n
 d z' 2 2
syst
 sp

(6.12)
If we apply trigonometry to Figure 6.7b, we observe that the relation expressed in equation
(6.13) is true. Rearranging this equation, the optimal relation between both angles is that from
equation (6.14). Solving triangles we calculate distnozzle with equation (6.15), which depends on
the number of nozzle systems, nsyst. If combined the 4 previous equations, we observe that
RAuseless depends on nsyst as pointed out in equation (6.16).
z' 
dsp z'
2 tan 2
tan  

dsp z' sin 6 
2 tan 
(6.13)
tan 2
2
distnozzle 
(6.14)
w bdl z'
3 nsyst  1 3

RAuseless  1 

(6.15)
3  3 nsyst  1 
2  nsyst 
(6.16)
Finally, equation (6.17) evaluates the optimal distance between nozzle systems if nozzles
are positioned following the equilateral triangular pattern.
distsyst  tan 6
distnozzle
3 distnozzle

2
6
(6.17)
Table 6.1 compares the useless areas of the optimal distribution systems as a function of
the number of nozzles systems and of the nozzle pattern. On the one hand, when the pattern is
square, RAuseless is independent of nsyst. On the other hand, when the pattern follows an
equilateral triangle, RAuseless diminishes as the number of nozzle systems increases. Therefore,
we conclude that the equilateral triangle nozzle pattern outperforms the square nozzle pattern if
the nsyst is greater than 1. The theoretical minimum of RAuseless is 0.173, obtained applying the
limit as nsyst approaches the infinity in equation (6.16).
Table 6.1. RAuseless as a function of the nozzle pattern and the number of nozzle systems
RAuseless
nsyst
Square nozzle pattern
Triangle nozzle pattern
1
-
2
0.311
0.265
3
0.363
4
0.242
5
0.228
∞
0.173
133
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
The question of the suitability of one nozzle pattern or another with square full cone nozzles
does not require a further analysis, since the square nozzle pattern adapts perfectly to the spray
cone of these nozzles. In contrast, an equilateral triangle nozzle pattern would lead to
overlapping of the sprays from adjacent nozzles systems.
6.3.4.
Repositioning of the distribution systems and their nozzles
From the optimal distance between nozzles of the same nozzle system, calculated in the
two previous subsections, it is possible to calculate the number of nozzles per system, nnozzle,
needed to distribute liquid on a tube bundle of length Lbdl. For square nozzles or systems with
one row of circular nozzles, it comes from equation (6.18). Unless the quotient inside the ceiling
function in equation (6.18) is an integer, the distance between these nozzles needs to be
recalculated by equation (6.19). Equation (6.20) evaluates nnozzle for circular nozzles and more
than one nozzle system and equation (6.21) recalculates the distance between them.
nnozzle  ceiling Lbdl distnozzle 
(6.18)
distnozzle, rec  Lbdl nnozzle
(6.19)
nnozzle  ceiling Lbdl distnozzle  0.5
(6.20)
distnozzle, rec  Lbdl nnozzle  0.5
(6.21)
distnozzle,rec
distnozzle,rec
Lbdl
The new situation is that the distnozzle,rec is lower than or equal to the optimal, independently
of the distribution system or nozzle. In case it is lower and if kept the distance between the
centre of any tube of the first row and the origin of the sprays, z1, there would be overlapping
and fluid loss (only with circular nozzles) as shown in Figure 6.5b. This situation is unavoidable
with square nozzles, since any change in their position or a decrease of z1 would lead to
uncovered regions of the tube bundle that should be accessible from the nozzles. Concerning
circular nozzles, we propose a method to rearrange them, reducing overlapping and fluid loss.
dsp,rec(z rec)
distsyst,rec
wbdl
Figure 6.8. Recalculation of the position between adjacent circular nozzles and their nozzle
systems
134
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
The method is iterative and starts assuming that the accessible area from the new nozzle
system should have the same width as the optimal one, i.e. wbdl remains constant. Another aim
of the recalculation is to have punctual intersections between every three adjacent spray cones
at z’rec, as shown in Figure 6.8. Solving triangles we reach equation (6.22), which indicates how
wbdl depends on dsp,rec(z’rec) and distnozzle,rec. If we rearrange it, we obtain a second degree
equation, from which is possible to determine dsp,rec(z’rec).
 d sp,rec z'rec    distnozzle,rec 
 
 
w bdl  nsyst  1 
 
2
2


 
dsp,rec z'rec 
 nsyst  1
2


2

2
(6.22)

In case of having more than one nozzle system, the distance between them, distsyst,rec, is
calculated with equation (6.23). At this point it is possible to recalculate the spray angle αrec,
described by tangent from the origin of a nozzle to the most external tube of the first row of the
tube bundle, with equation (6.24).
distsyst,rec 
dsp,rec z'rec 
2



  
 rec  arctan tan 
2
  



 dsp,rec z'rec    distnozzle,rec 

 
 
 

2
2

 

2
 dsp,rec z'rec    distnozzle,rec 


 

 

2
2

 

dsp,rec z'rec 
2
2
2
(6.23)
2








(6.24)
If we introduce αrec in equation (6.9), we recalculate the width of the surface accessible from
the rearranged distribution system, wbdl,rec. If wbdl,rec differs from wbdl, assumed at the beginning
of the iteration, in more than a certain tolerated value, we repeat the process with the
recalculated width. Once the difference is lower than the stated tolerance, we consider valid the
rearranged nozzle system/s. In addition, equation (6.25) allows calculating the distance in the z
axis between the origin of the sprays and the centre of any tube of the first row, z1.
z1 
dsp,rec z'rec 
 
2 tan 
2
d
 t cos rec 
2
(6.25)
If we assume that all the flow inside the limits of the tube bundle (inside wbdl) will eventually
reach a tube, we can calculate the actual RAuseless of the resulting distribution system with
equation (6.26).
z' 
A
w z'  distnozzle
RAuseless  1  useful rec  1  bdl rec
Asp z'rec 
nsyst  dsp z'rec  2 2

6.3.5.

(6.26)
Liquid distribution from a nozzle to a generic tube. Limit angles
Once evaluated the optimal distribution systems for the tube bundle as a whole, it is
interesting to determine how much liquid reaches each tube of the tube bundle or each column
of tubes. Figure 6.9 represents a situation where the lth nozzle from the kth nozzle system
generates a spray cone with origin in Ok,l and distributes liquid on a generic tube from the mth
135
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
row and nth column of the tube bundle. The upper part of Figure 6.9 shows a view of the system
from the side (perpendicular to the tube axis) and the lower part shows a top view
(perpendicular to the nozzle axis). The axis of the tube is positioned at horizontal and vertical
distances xk,l,m,n and zk,l,m,n from the origin of the spay cone, respectively.
x
y
α
z
Ok,l
zk,l,m,n
αlim,th,1(k,l,m,n)
αlim,th,2(k,l,m,n)
φlim,th,1(k,l,m,n)
Om,n
xk,l,m,n
x
z
φlim,th,2(k,l,m,n)
θ
dt
y
Ok,l
Figure 6.9. Theoretical limit angles from a given nozzle to a generic tube
If we consider a plane parallel to y = 0 containing Ok,l and assume that the nozzle angle β =
180º (π rad) and that there are no obstacles in between the nozzle and the tube, this tube
receives liquid directly from the nozzle in an area limited by the tangents from the origin of the
spray to the tube. The angles described by these tangents and the nozzle axis, and with these
assumptions, are denoted as theoretical αlim. αlim,th,1(k,l,m,n) and αlim,th,2(k,l,m,n) are calculated with
equations (6.27) and (6.28), respectively. They correspond to analogous angles on the tube
surface, named as φlim,th,1(k,l,m,n) and φlim,th,2(k,l,m,n) and determined with equations (6.29) and
(6.30), respectively.


dt 2
lim, th,1(k ,l ,m,n )  arctan xk ,l ,m,n zk ,l ,m,n  arcsin
 x2
 zk2,l ,m,n
 k ,l ,m,n





(6.27)


dt 2
lim, th,2(k ,l ,m,n )  arctan xk ,l ,m,n zk ,l ,m,n  arcsin
2
 x
 zk2,l ,m,n
 k ,l ,m,n





(6.28)


lim, th,1(k,l ,m,n )  lim, th,1(k,l ,m,n )  3 2
136


(6.29)
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
lim, th,2(k,l ,m,n )   lim, th,2(k,l ,m,n )   2
(6.30)
These theoretical limit angles are true if the assumptions previously stated are true.
However, real nozzles or actual tube bundles do not fulfil these assumptions. In the following
paragraphs we explain the method proposed to determine the real limit angles from that nozzle
to the tube.
As aforementioned, we assumed that nozzle had a nozzle angle β equal to 180º (π rad).
This means that any tube of the bundle is accessible from any nozzle. However, the typical
commercial nozzles have nozzle angles between 30º and 120º. Thus, there are tubes that
receive no liquid from a particular nozzle. Figure 6.10 shows the different situations that can
occur between the nozzle and the tube.
x
y
α
z
zk,l,1,n
Ok,l
Tube
m,n
Tube
m,n+1
Tube
m,n+2
Tube
m,n+3
Figure 6.10. Effect of the nozzle angle on the limit angles from a nozzle to a generic tube
First, the tube positioned at the mth row and nth column has its theoretical limit angles
outside the interval formed by –β/2 and β/2. This means that the tube is inaccessible from that
nozzle. Second, the tube positioned at the mth row and nth+1 column has one of its theoretical
limit angles (αlim,th,1(k,l,m,n+1)) outside the interval formed by –β/2 and β/2 and another one inside it
(αlim,th,2(k,l,m,n)). Consequently, the tube is partially reachable from the nozzle. The real limit
angles are not equal to the theoretical limit angles, or at least not both of them. αlim,r,1(k,l,m,n+1) is in
this case equal to –β/2. Third, the tubes positioned in the mth row and nth+2 and nth+3 columns
have both theoretical limit angles inside the interval formed by –β/2 and β/2. Thus, these tubes
are totally accessible from this nozzle and the real limit angles are equal to theoretical limit
angles.
At this stage, it is necessary to check if there is any interaction (another tube) between the
studied tube and the nozzle. Figure 6.10 shows the ideal situation where there are no
interactions between them. Figure 6.11 describes several forms of blocking that may occur
between the tubes of a tube bundle. The continuous lines represent the real limits of the spray
and the dotted lines represent the theoretical ones, in case they differ from the real ones.
137
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
x
y
α
z
zk,l,1,n
Ok,l
Tube
m,n
Tube
m,n+2
Tube
m+1,n+1
Tube
m,n+4
Tube
m+1,n+3
Figure 6.11. Effect of the interaction between tubes on the limit angles from a nozzle to a generic
tube
The first kind of interaction appears between tubes of the same row, Tube m,n and Tube
m,n+2 in Figure 6.11. The tube that is closer to the nozzle covers part of the theoretical
accessible area of the further one. Thus, the greater real limit angle of Tube m,n is equal to the
lower theoretical angle of Tube m,n+2. It is even more common that tubes from an upper row
cover the direct distribution of refrigerant from the nozzle, as happens with Tube m+1,n+1 and
Tube m,n+2, or with Tube m+1,n+3 and Tube m,n+4. In the first of them, the real interval is
different from the theoretical and ranges from the greater theoretical limit of Tube m,n+2 and its
greater theoretical angle. In the second of these interactions, the real interval of Tube m+1,n+3
ranges from its lower theoretical angle and the lower theoretical limit angle of Tube m,n+4.
Another situation, not represented in Figure 6.11, occurs a tube is completely blocked by
another and it does not receive any liquid directly from the nozzle.
At this point of the analysis, we already know the real limit angles from the given nozzle to
the tube at the mth row and nth column, αlim,real,1(k,l,m,n) and αlim,real,2(k,l,m,n). These spray angles need
to be translated into tube angles, φlim,real,1(k,l,m,n) and φlim,real,2(k,l,m,n), which are more convenient to
determine the percentage of the total flow rate distributed by the nozzle that reaches directly the
tube. The trigonometry used to achieve this translation is explained in the following paragraphs
and making use of Figure 6.12.
x
y
α
z
zk,l,m,n
Ok,l
T
Om,n
φlim,real,1(k,l,m,n)
φlim,th,2(k,l,m,n)
xk,l,m,n
Figure 6.12. Definition of the real limit tube angles from the real spray limit angles
138
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
Equation (6.31) shows the relation between αlim,real,1(k,l,m,n) and φlim,real,1(k,l,m,n) in this generic
case. A and B also depend on αlim,real,1(k,l,m,n) and on the relative position between the nozzle and
the tube as detailed in equations (6.32) and (6.33), respectively. If we rearrange equation (6.31)
we obtain equation (6.34), used to obtain φlim,real,1(k,l,m,n). The procedure to determine
φlim,real,2(k,l,m,n) from αlim,real,2(k,l,m,n) is analogous.




d
A  t sin lim, real,1(k,l ,m,n )
2
tan lim, real,1(k ,l ,m,n ) 
dt
B  cos lim, real,1(k ,l ,m,n )
2



A  xk2,l ,m,n  zk2,l ,m,n sin  m(k,l ,m,n )  lim, real,1(k,l ,m,n )

(6.31)

B  xk2,l ,m,n  zk2,l ,m,n cos  m(k,l ,m,n )  lim, real,1(k,l ,m,n )
(6.32)




  tan 

B A 
lim,
real
,
1
(
k
,
l
,
m
,
n
)




dt
dt 

lim, real,1(k ,l ,m,n )  arcsin 

 

2
2 


 cos lim, real,1( k ,l ,m,n )  lim, real,1(k ,l ,m,n ) 




6.3.6.
(6.33)

(6.34)

Liquid flow rate reaching a generic tube
At this stage, the interest lies in calculating the amount of liquid that reaches the tube from
the nozzle, ṁ(k,l,m,n). The method proposed is numerical and was designed for its implementation
in the computer program described in section 6.4. It consists in adding up the ratios of the finite
differential areas reached by the nozzle, ΔA(k,l,m,n,o), to the total area of the spray cone at a
certain distance of the origin of the spray, Asp(k,l,o), and multiplying the result by the total flow rate
distributed by the nozzle, ṁ(k,l), as stated in equation (6.35).
 (k,l ,m,n )  m
 ( k ,l )
m
ndiv 1 A
(k ,l ,m,n,o )

o 1
Asp(k,l ,o )
(6.35)
A generic differential area of the tube reached by the nozzle appears striped in Figure 6.13.
The first assumption for its calculation is to consider a sufficiently small tube angle step
(Δφ(k,l,m,n) in Figure 6.13). It is fair to approximate the differential area by a quadrilateral and
calculate its area with equation (6.36). The Cartesian coordinates depend on the relative
position between the nozzle and the tube, and on the tube angle, φ(k,l,m,n,o). This angle is
necessarily between φlim,real,2(k,l,m,n) and φlim,real,1(k,l,m,n). The equations needed for obtaining these
Cartesian coordinates are shown from (6.37) to (6.42). In case of using square full cone
nozzles, equation (6.41) and (6.42) are substituted by (6.43) and (6.44), respectively.
139
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
x
α
y
xk,l,m,n,o
zk,l,m,n,o
zk,l,m,n
zk,l,m,n,o+1
z
xk,l,m,n,o+1
φ(k,l,m,n,o)
xk,l,m,n
Figure 6.13. Representation of the differential area of a tube accessible from a nozzle
A(k ,l ,m,n,o )  x k ,l ,m,n,o  x k ,l ,m,n,o 1 
 y 
 y k,l ,m,n,o    y k,l ,m,n,o 1  y k,l ,m,n,o 1 
k ,l ,m,n,o

 


2

d
x k ,l ,m,n,o  x k ,l ,m,n  t sin  k ,l ,m,n,o
2


d
x k ,l ,m,n,o 1  x k ,l ,m,n  t sin  k ,l ,m,n,o  
2

d
zk ,l ,m,n,o  zk ,l ,m,n  t cos  k ,l ,m,n,o
2
(6.36)
(6.37)



d
zk ,l ,m,n,o 1  zk ,l ,m,n  t cos  k ,l ,m,n,o  
2
(6.38)
(6.39)

(6.40)
y k,l ,m,n,o   zk2,l ,m,n,o tan 2  2  xk2,l ,m,n,o
(6.41)
y k,l ,m,n,o 1   zk2,l ,m,n,o 1 tan2  2  xk2,l ,m,n,o 1
(6.42)
y k,l ,m,n,o  zk,l ,m,n,o tan 2
(6.43)
y k,l ,m,n,o 1  zk,l ,m,n,o 1 tan 2
(6.44)
The area of the spray cone at a distance of the origin of the spray, Asp(k,l,o), also depends on
the kind of nozzles used. Equation (6.45) evaluates the area for circular full cone nozzles, and
equation (6.46) for square full cone nozzles.
140
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
 zk ,l ,m,n,o 1  zk ,l ,m,n,o

Asp,(k ,l ,o )   
tan 2
2


z
z

Asp,(k,l ,o )  4 k,l ,m,n,o 1 k ,l ,m,n,o tan 2
2


2
(6.45)
2
(6.46)
If we assume that the flow rate coming from a nozzle to a tube is unaffected by the flow
reaching the same tube from another nozzle and that the flows are cumulative, we obtain all the
flow rate that reaches a generic tube, ṁ(m,n) with equation (6.47). If we follow equation (6.48), we
calculate the flow rate distributed on each column of tubes, ṁ(n).
 (m,n ) 
m
 (n ) 
m
nsyst nnozzle

k 1
 m (k,l ,m,n )
(6.47)
l 1
nrow
 m (m,n )
,m 1
(6.48)
Finally, we developed a dimensionless column factor, Fcol(n) to evaluate how evenly
distributed the liquid among the different columns of the tube bundle is. For the calculation of
this column factor we use equation (6.49). In this equation, ṁmin represents the minimum among
the mass flow rates received by any of the columns of the tube bundle. The closer this factor is
to the unity in all the columns of the tube bundle, the better distributed the fluid is along the tube
bundle and the less overfeed on some columns is needed to prevent dryout on others.
Fcol(n ) 
 (n )
m
 min
m
(6.49)
141
Chapter 6
6.4.
Optimisation of the nozzle distribution system in shell-and-tube evaporators
PROGRAMME FOR THE CALCULATION OF HEAT EXCHANGERS
The calculation methods described in the previous section are tedious and repetitive,
particularly if the heat exchanger is large and has an important number of tubes. Consequently,
we developed a programme in MATLAB software where the characteristics of the tube bundle
(number of tubes, distance between them, type of pitch, etc.) are introduced, and returns the
layout of different optimal distribution systems and how the flow is distributed on the different
tubes and columns of tubes.
6.4.1.
Inputs
The inputs that the user can introduce in the programme are mainly associated with the
dimensions, disposition and number of tubes of the tube bundle. The list of inputs and their
explanation is:











Tube diameter (in meters).
Type of pitch. It is possible to select between inline (Figure 6.14a) and staggered
tube layout (Figure 6.14b).
Number of tube rows.
Number of tubes per row (number of columns). If the chosen pitch is staggered,
even rows have a tube less than odd rows.
Horizontal pitch. It is a factor that defines the distance between consecutive tubes
of the same row by multiplying the diameter of the tube (see Figure 6.14).
Vertical pitch. It is a factor that defines the distance between consecutive rows by
multiplying the diameter of the tube (see Figure 6.14).
Type of nozzle. The possible choices are circular full cone nozzles and square full
cone nozzles.
Nozzle angle vector (β). In this vector the user introduces the cone angles of the
nozzles to be evaluated by the programme. The default values included in the
vector are 60º, 90º and 120º.
Maximum number of nozzle systems. The user must define the maximum number
of nozzle systems (rows of spray nozzles) to be considered by the programme.
Tube length. Length of the tubes dedicated to heat exchange.
Expected shell diameter. Input that the programme uses to discard solutions that
need a large distance between the spray nozzles and the tube bundle.
Phor·dt
a
Phor·dt
b
Phor·dt/2
Tube
1,3
Tube
1,ncol
Tube
2,1
Tube
2,3
Tube
2,ncol
Pver·dt
Pver·dt
Pver·dt
Tube
1,1
Tube
1,1
Tube
1,3
Tube
2,2
Tube
3,1
Tube
2,4
Tube
3,3
Tube
nrow-1,2
Tube
nrow,1
Tube
nrow,3
Tube
nrow,ncol
Tube
nrow,1
Tube
1,ncol
Tube
3,ncol
Tube
nrow-1,4
Tube
nrow,3
Tube
nrow,ncol
Figure 6.14. Position and numbering of the tubes in the bundle. a) Inline tube pattern. b) Staggered
tube pattern
142
Chapter 6
6.4.2.
Optimisation of the nozzle distribution system in shell-and-tube evaporators
Calculation process
The calculation process programmed follows the ideas described in subsection 6.3. We
have included a flow chart in Figure 6.15 to summarise it. Once the inputs are introduced, the
programme selects the first spray cone angle of the vector and starts studying the distribution
with one nozzle system. Then, it calculates the number of nozzles needed for that inputs and
the best relative position between the bundle and the nozzles. After that, it determines the limit
angles, both theoretical and real, for each tube and from each of the spray nozzles. These
angles allow calculating the percentage of the flow rate distributed by the nozzles that reaches
each tube and each column of tubes. The next step is to increase the number of nozzle systems
in one unit (up to the maximum, nsyst,max) and to repeat the process. If the maximum is reached,
the programme checks the spray nozzle vector, selects the next value (if any) and does over
the calculations.
INPUTS
Spray nozzle β
Nozzle systems nsyst
Position of the nozzles and tube bundle
Limit angles
% flow rate per tube and
column
YES
Maximum nozzle
systems?
NO
YES
Another nozzle
angle?
NO
OUTPUTS
Figure 6.15. Flow chart of the calculation process of the programme
6.4.3.
Outputs
The outputs that the programme returns can be classified into graphical outputs and data
outputs. Similar graphics to that shown in Figure 6.16 are obtained for each of the possible
143
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
spray nozzle angle-nozzle systems combinations. They represent the tube bundle and the
expected shell, as well as the origin of the different spray nozzles and the cones they produce.
Figure 6.16. 3D-plot of the tube bundle, the shell and the spray cones for each solution
Another graphical output from the programme is the graph shown in Figure 6.17. This graph
represents the real limit angles for each tube of the bundle and for a representative nozzle of
each nozzle system. It gives the user an idea on the distribution of the liquid on the different
columns, particularly interesting with staggered pitch tube bundles, and of the possible
interactions between tubes.
Figure 6.17. 2D representation of the real limit angles for each tube of the bundle and for a
representative nozzle of each nozzle system
144
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
Finally, the programme registers the most important data outputs in a .xls file. The list of
saved variables includes:






Input values.
Vector of spray nozzle angles.
Distances between nozzle systems and between spray nozzles of the same nozzle
system.
Relative position between the distribution system and the tube bundle.
Number of spray nozzles per nozzle system and total number of nozzles of the heat
exchanger.
Percentage of the total flow rate distributed that reaches each tube directly from the
distribution system.
145
Chapter 6
6.5.
Optimisation of the nozzle distribution system in shell-and-tube evaporators
PARAMETRIC ANALYSIS
We used the programme developed to perform a parametric analysis to study how the
different inputs (tube bundle and spray nozzle characteristics) affect the even distribution of the
liquid on a bundle consisting of 8 rows of tubes and 8 tubes per row and with a length of 1 m. In
this subsection we detail the inputs considered and the range of values for each of them, as well
as the results attained and the discussion of these results.
6.5.1.
Input parameters
We analysed the effect of varying part of the variables that the programme includes, listed
in subsection 6.4.1. Others were kept constant to simplify the analysis. Among the variables that
remained constant is the outer diameter of the tubes, at 3/4” (19.05 mm); the number of rows of
the bundle, at 8; the number of tubes of each row, at 8 (staggered tube bundles have 7 tubes if
the row is even numbered); the length of the shell-and-tube heat exchanger, at 1 m; and the
type of nozzle, considered as circular full cone nozzle throughout the analysis. The nozzle
angles studied were 60º, 90º and 120º, available with almost any manufacturer. The tube
patterns were both inline and staggered. The horizontal and vertical pitches, depended on the
tube pattern, as shown in Table 6.2. Those combinations from Table 6.2 that are in black are
incompatible. Finally, the number of nozzle systems was 1, 2 or 3.
Table 6.2. Horizontal and vertical pitches analysed in the parametric analysis
TUBE BUNDLE
INLINE PITCH
Horizontal Pitch
6.5.2.
STAGGERED PITCH
(60º)
STAGGERED PITCH
(45º)
Vertical Pitch
1.25
1.25
1.08
1.5
1.5
1.3
2
2
1.73
1
Results
Figure 6.18 shows the percentage of the total flow rate distributed that reaches the inline
tube bundles considered, as a function of the number of nozzle systems, the horizontal pitch of
the tube bundle and the cone angle of the spray nozzles. Generally, this percentage increases if
the horizontal pitch decreases, as there is a smaller amount of liquid that flows in between the
columns of tubes. The other trend observed is that the amount of liquid reaching the tubes rises
with the smallest spray nozzles (60º). The effect of the number of nozzles systems on the
percentage of flow reaching the tubes depends on the rest of variables, but it is normally higher
with 1 and with 3 nozzle systems than with 2 nozzles systems.
Similarly, Figure 6.19 depicts the situation with the different staggered tube bundles
analysed. The fraction of the distributed liquid that does not reach any tube of the bundle
diminishes as the nozzle cone angle decreases. The percentage of flow reaching the tubes is
maximum with 1.5 horizontal pitch bundles, if kept constant the other parameters. Excluding the
situation of 60º spray cone angles, the liquid reaching the tubes increases if the vertical pitch
decreases, independently of the number of nozzle systems and with 2 of horizontal pitch.
146
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
Percentage flow reaching tube bundle [%]
100%
90%
80%
70%
60%
50%
Inline_1.25_β = 60º
Inline_1.25_β = 90º
Inline_1.25_β = 120º
Inline_1.5_β = 60º
Inline_1.5_β = 90º
Inline_1.5_β = 120º
Inline_2_β = 60º
Inline_2_β = 90º
Inline_2_β = 120º
40%
0
1
2
3
4
nsyst [-]
Figure 6.18. Percentage of the total flow rate distributed that reaches the inline tube bundles
considered, as a function of the number of nozzle systems, the horizontal pitch of the tube bundle
and the cone angle of the spray nozzles
Percentage flow reaching tube bundle [%]
100%
90%
80%
70%
60%
Staggered_1.25_1.08_β = 60º
Staggered_1.25_1.08_β = 120º
Staggered_1.5_1.3_β = 90º
Staggered_2_1.73_β = 60º
Staggered_2_1.73_β = 120º
Staggered_2_1_β = 90º
50%
40%
30%
0
1
Staggered_1.25_1.08_β = 90º
Staggered_1.5_1.3_β = 60º
Staggered_1.5_1.3_β = 120º
Staggered_2_1.73_β = 90º
Staggered_2_1_β = 60º
Staggered_2_1_β = 120º
2
3
4
ndist [-]
Figure 6.19. Percentage of the total flow rate distributed that reaches the staggered tube bundles
considered, as a function of the number of nozzle systems, the horizontal pitch of the tube bundle
and the cone angle of the spray nozzles
From the previous figures we concluded that 60º cone angle nozzles are the best from the
point of view of increasing the flow rate reaching the bundle. However, in Figure 6.20 we
observe that the distance between the nozzles and the first row of tubes of the bundle that
147
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
optimises the distribution system is clearly greater with these nozzles than with 90º or 120º
nozzles. This can be an important limitation in shell-and-tube evaporators, as it reduces the
amount of tubes that can be introduced in a shell of a certain diameter. z1 also increases as the
horizontal pitch increases, since the width of a bundle with 8 tubes per row is also higher. The
solution to decrease this distance is to add nozzle systems, as shown in Figure 6.20, because
they share the width of the tube bundle.
0.35
HP = 1.25_β = 60º
HP = 1.25_β = 90º
HP = 1.25_β = 120º
HP = 1.5_β = 60º
HP = 1.5_β = 90º
HP = 1.5_β = 120º
HP = 2_β = 60º
HP = 2_β = 90º
HP = 2_β = 120º
0.3
z1 [m]
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
nsyst [-]
Figure 6.20. Optimal distance between the first row of tubes and the nozzles (spray cone origin) as
a function of the number of nozzle systems, the horizontal pitch of the tube bundle and the cone
angle of the spray nozzles
The method used to calculate the optimal number of nozzles and the distances between
them, explained in subsection 6.3, considers the bundles as a whole. Thus there are no
differences between inline and staggered bundles.
Figure 6.21 includes the number of nozzles needed by each of the distribution systems
analysed. The nozzle angle, β, has a negligible effect on this parameter, in agreement with the
equations included in subsections 6.3.2 and 6.3.3. The increase of z1 that occurs as the
horizontal pitch rises, explained in previous paragraphs, leads to an increase of the optimal
distance between nozzles of the same nozzle system and, thus, to a reduction of the number of
nozzles needed. The final conclusion drawn from Figure 6.21 is that the number of nozzles
needed for a certain bundle increases proportionally to the number of nozzle systems.
The results shown up to this stage state that there should be a compromise between the
percentage of flow reaching the tube bundle, which is highest with 60º spray nozzles and 1
nozzle system, and the necessary distance between the nozzles and the tube bundle, which is
shortest, and therefore most convenient, with 120º spray nozzles, 3 nozzles systems and 1.25
horizontal pitch. However, the most important issue to consider when deciding on the best
option is to have an even distribution on the different columns of the bundle. The best way to
study this is through the dimensionless column factor, defined at the end of subsection 6.3.6.
The results of this parameter as a function of all the variables considered are stated in the
following figures and paragraphs.
148
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
45
HP = 1.25_β = 60º
HP = 1.25_β = 90º
HP = 1.25_β = 120º
HP = 1.5_β = 60º
HP = 1.5_β = 90º
HP = 1.5_β = 120º
HP = 2_β = 60º
HP = 2_β = 90º
HP = 2_β = 120º
40
35
nozzles [-]
30
25
20
15
10
5
0
0
1
2
3
4
nsyst [-]
Figure 6.21. Optimal number of nozzles of the whole distribution system as a function of the
number of nozzle systems, the horizontal pitch of the tube bundle and the cone angle of the spray
nozzles
Figure 6.22 includes the dimensionless column factor vs. the position of the column of tubes
for an inline tube bundle of 1.25 horizontal pitch and 1.25 vertical pitch, as a function of the
number of nozzle systems and of β. As a reminder, due to the definition of the bundle and
taking into account that it is of inline type, there are tubes only in odd columns. The best
distribution system according to this factor is that with 60º nozzles and 1 nozzle system,
because its column factor is always in the range between 1 and 1.29. Those distribution
systems with 90º nozzles seem also very convenient, independently of the number of
distribution systems. In these cases Fcol is never higher than 1.35 and, therefore, the liquid is
fairly well distributed all over the tube bundle. In contrast, this dimensionless number increases
when β = 120º and reaches values close to 1.7.
A similar situation is shown in Figure 6.23 with an inline tube bundle with horizontal pitch of
1.5 and vertical pitch of 1.5. The performance of distribution systems with 120º nozzles
improves for this tube bundle, which is wider. The options with 60º and 90º nozzles and 1
nozzle system are also convenient from the point of view of the dimensionless column factor,
with maximums of 1.32 and 1.3, respectively.
149
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
1.8
1.6
Fcol [-]
1.4
1.2
1
0.8
β = 60º & nsyst = 1
β = 60º & nsyst = 2
β = 60º & nsyst = 3
β = 90º & nsyst = 1
β = 90º & nsyst = 2
β = 90º & nsyst = 3
β = 120º & nsyst = 1
β = 120º & nsyst = 2
β = 120º & nsyst = 3
0.6
0
2
4
6
8
10
12
14
16
Column [-]
Figure 6.22. Dimensionless column factor vs. the numbering of the column of tubes, for an inline
pattern bundle with horizontal pitch of 1.25 and vertical pitch of 1.25, and as a function of the
number of nozzle systems and the cone angle of the spray nozzles
2
1.8
Fcol [-]
1.6
1.4
1.2
1
0.8
β = 60º & nsyst = 1
β = 60º & nsyst = 2
β = 60º & nsyst = 3
β = 90º & nsyst = 1
β = 90º & nsyst = 2
β = 90º & nsyst = 3
β = 120º & nsyst = 1
β = 120º & nsyst = 2
β = 120º & nsyst = 3
0.6
0
2
4
6
8
10
12
14
16
Column [-]
Figure 6.23. Dimensionless column factor vs. the numbering of the column of tubes, for an inline
pattern bundle with horizontal pitch of 1.5 and vertical pitch of 1.5, and as a function of the number
of nozzle systems and the cone angle of the spray nozzles
The wider the tube bundle, the worse the dimensionless column factor, as we observe if we
compare the results for an inline tube bundle of Phor = 2 and Pver = 2, shown in Figure 6.24, to
those from previous figures. The best solutions are again those with β = 60º and β = 90º nozzles
150
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
and 1 nozzle system. The maximum dimensionless column factor for any of these solutions
never exceeds 1.44.
2.6
2.4
2.2
2
Fcol [-]
1.8
1.6
1.4
1.2
1
0.8
0.6
β = 60º & nsyst = 1
β = 60º & nsyst = 2
β = 60º & nsyst = 3
β = 90º & nsyst = 1
β = 90º & nsyst = 2
β = 90º & nsyst = 3
β = 120º & nsyst = 1
β = 120º & nsyst = 2
β = 120º & nsyst = 3
0.4
0
2
4
6
8
10
12
14
16
Column [-]
Figure 6.24. Dimensionless column factor vs. the numbering of the column of tubes, for an inline
pattern bundle with horizontal pitch of 2 and vertical pitch of 2, and as a function of the number of
nozzle systems and the cone angle of the spray nozzles
15
β = 60º & nsyst = 1
β = 60º & nsyst = 2
β = 90º & nsyst = 1
β = 90º & nsyst = 3
β = 60º & nsyst = 3
12
Fcol [-]
9
6
3
0
0
2
4
6
8
10
12
14
16
Column [-]
Figure 6.25. Dimensionless column factor vs. the numbering of the column of tubes, for a
staggered pattern bundle with horizontal pitch of 1.25 and vertical pitch of 1.08 (60º angle), and as
a function of the number of nozzle systems and the cone angle of the spray nozzles
151
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
The dimensionless column factor scattering increases significantly with staggered tube
bundles, as shown in the subsequent figures. Figure 6.25 includes the results with a tube
bundle of Phor = 1.25 and Pver = 1.08. As can be observed, not all the possible distribution
systems are represented. The explanation to this fact is that there are cases that have
dimensionless column factors very high or even infinite (when there is a column of tubes of the
bundle that is inaccessible from the nozzles). This may occur with subsequent figures.
The general idea drawn from Figure 6.25 is that staggered tube bundle layout is
inconvenient for the distribution with spray nozzles, independently of the nozzle angle or the
number of nozzle systems. The best option is that with 1 nozzle system of 60º devices for which
the maximum Fcol is 5.02, but the recirculation needed to provide enough liquid to all the
columns is not assumable even for this case.
The situation improves slightly when the horizontal pitch of the staggered tube bundle
increases to 1.5 and the vertical pitch to 1.3, as shown in Figure 6.26. The most convenient
options occur for the distribution systems with 60º nozzles, for which the dimensionless column
factor is never greater than 3. However, the distribution is not as even as it should be to have an
efficient system, with a small pumping power and minimum refrigerant charge.
15
β = 60º & nsyst = 1
β = 60º & nsyst = 2
β = 60º & nsyst = 3
β = 90º & nsyst = 1
β = 90º & nsyst = 3
β = 120º & nsyst = 3
12
Fcol [-]
9
6
3
0
0
2
4
6
8
10
12
14
16
Column [-]
Figure 6.26. Dimensionless column factor vs. the numbering of the column of tubes, for a
staggered pattern bundle with horizontal pitch of 1.5 and vertical pitch of 1.3 (60º angle), and as a
function of the number of nozzle systems and the cone angle of the spray nozzles
Figure 6.27 depicts that a further improvement is achieved with the staggered tube bundle
of 2 of horizontal pitch and 1.73 of vertical pitch. It is possible to have maximum dimensionless
factor lower than 3 not only with 60º nozzles, but also with 90º nozzles and 1 or 3 nozzle
systems. If the staggered tube bundle has the same horizontal pitch and 1 of vertical pitch these
factor diminish, as shown in Figure 6.28. Thus, under these situations it is possible and even
convenient to have a staggered tube bundles. Of course, the main drawback of increasing the
horizontal pitch is that the compactness of staggered tube bundles, their main advantage, is
partially lost.
152
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
12
β = 60º & nsyst = 1
β = 90º & nsyst = 1
β = 120º & nsyst = 2
10
β = 60º & nsyst = 2
β = 90º & nsyst = 2
β = 120º & nsyst = 3
β = 60º & nsyst = 3
β = 90º & nsyst = 3
Fcol [-]
8
6
4
2
0
0
2
4
6
8
10
12
14
16
Column [-]
Figure 6.27. Dimensionless column factor vs. the numbering of the column of tubes, for a
staggered pattern bundle with horizontal pitch of 2 and vertical pitch of 1.73 (60º angle), and as a
function of the number of nozzle systems and the cone angle of the spray nozzles
6
5
β = 60º & nsyst = 1
β = 60º & nsyst = 2
β = 60º & nsyst = 3
β = 90º & nsyst = 1
β = 90º & nsyst = 2
β = 90º & nsyst = 3
β = 120º & nsyst = 1
β = 120º & nsyst = 2
β = 120º & nsyst = 3
Fcol [-]
4
3
2
1
0
0
2
4
6
8
10
12
14
16
Column [-]
Figure 6.28. Dimensionless column factor vs. the numbering of the column of tubes, for a
staggered pattern bundle with horizontal pitch of 2 and vertical pitch of 1 (45º angle), and as a
function of the number of nozzle systems and the cone angle of the spray nozzles
To summarise these results we prepared Table 6.3 and Table 6.4, which include the
maximum column factors, Fcol,max, for the different distribution systems and with all the inline and
153
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
staggered tube bundles studied, respectively. The best solution for each tube bundle is
highlighted in bold letters.
Table 6.3. Maximum dimensionless column factor for each inline tube bundle as a function of the
horizontal and vertical pitch, the number of nozzle systems and the cone angle of the spray
nozzles
INLINE TUBE
BUNDLE
Fcol,max
β = 60º
Phor
β = 90º
β = 120º
Pver
nsyst=1 nsyst=2 nsyst=3 nsyst=1 nsyst=2 nsyst=3 nsyst=1 nsyst=2 nsyst=3
1.25
1.25
1.29
1.42
1.54
1.35
1.29
1.33
1.69
1.69
1.45
1.5
1.5
1.32
1.61
1.83
1.30
1.54
1.66
1.39
1.22
1.23
2
2
1.44
2.10
2.44
1.35
1.99
2.31
1.61
1.51
1.74
Table 6.4. Maximum dimensionless column factor for each staggered tube bundle as a function of
the horizontal and vertical pitch, the number of nozzle systems and the cone angle of the spray
nozzles
STAGGERED
TUBE BUNDLE
Fcol,max
β = 60º
Phor
β = 90º
β = 120º
Pver
nsyst=1 nsyst=2 nsyst=3 nsyst=1 nsyst=2 nsyst=3 nsyst=1 nsyst=2 nsyst=3
6.94
∞
74.76
22.91
10.56 356.50
7.70
∞
17.79
12.03
2.79
3.63
4.07
3.74
17.12
5.62
9.49
2.09
2.56
2.61
2.62
4.15
3.93
3.52
1.25
1.08
5.23
5.57
5.71
11.95
1.5
1.3
2.92
2.96
3.00
2
1.73
2.89
2.86
2
1
1.77
2.11
154
∞
Chapter 6
6.6.
Optimisation of the nozzle distribution system in shell-and-tube evaporators
CONCLUSIONS
In this chapter we have shown a state of the art of different distribution systems patented
and applied in spray evaporators. We have observed that the main focus was on systems with
low momentum devices. Due to the potential benefits on HTCs and on wetting of using high
momentum devices, in this chapter we have focused on the optimization of distribution systems
with spray nozzles for shell-and-tube evaporators.
The next stage of this chapter has been the study, using geometry and trigonometry, of the
optimal distribution system as a function of the tube bundle dimensions and the characteristics
of the nozzles used. We have also detailed the process followed to determine the percentage of
liquid distributed by a given spray nozzle that reaches a generic tube, defining concepts such as
those of the theoretical and real limit angles from a nozzle to a tube or the dimensionless
column factor.
We have also developed a parametric analysis with the computer programme prepared for
optimising distribution systems. The inputs for the study have been: 1-meter-long tube bundle, 8
rows and 8 tubes per row (7 for even rows in staggered pitch layout), different horizontal and
vertical pitches, inline and staggered tube bundle pattern, 3 different spray nozzle angles, etc.
We have observed that, in general, 60º nozzles lead to an even distribution and more efficient
use of the liquid distributed. However, they require a larger distance between the spray nozzles
and the first row of the tube bundle to optimise distribution and, thus, there is an important part
of the shell that must be clear of tubes. The performance of systems with 90º nozzles is slightly
lower, but the distance required is also shorter and they are convenient from that point of view.
We have determined that the even distribution of liquid on the different columns of inline
tube bundles is easier than when the pattern is staggered. In fact, staggered tube bundles seem
unsuitable for this kind of distribution systems with nozzles and without intermediate devices.
Only when the horizontal pitch between tubes of the same row was high (2 in this case), we
have observed a convenient distribution between the different columns. However, an increase
of this horizontal pitch leads to the loss of compactness of staggered bundles, which is the main
advantage of such tube pattern.
155
Chapter 6
Optimisation of the nozzle distribution system in shell-and-tube evaporators
REFERENCES
[1] J.P. Hartfield, D.F. Sanborn, Falling film evaporator with vapor-liquid separator, US
5,561,987, October 8, 1996.
[2] R.H.L. Chiang, J.L. Esformes, E.A. Huenniger, Chiller with hybrid falling film evaporator, US
5,839,294, November 24, 1998.
[3] N.S. Gupte, Heat exchanger of the type of a falling-film evaporator having refrigerant
distribution system, E.P. 1 030 154 B1, 06.04.2005.
[4] C.H. Liu, C.C. Liu, Spray type heat Exchange device, US 2008/0149311 A1, June 26, 2008.
[5] C.C. Liu, Y.Z. Hu, H.T. Cheng, Spray type heat-exchanging unit, US 8,561,675 B2, October
22, 2013.
[6] M. Christians, J.L. Esformes, S. Bendapudi, M. Bezon, X. Qiu, S.P. Breen, Evaporator and
liquid distributor, US 2014/0366574, December 18, 2014.
[7] T.B. Chang, L.Y. Yu, Optimal nozzle spray cone angle for triangular-pitch shell-and-tube
interior spray evaporator, International Journal of Heat and Mass Transfer. 85 (2015) 463-472.
[8] S.A. Moeykens, J.W. Larson, J.P. Hartfield, H.K. Ring, Falling film evaporator for a vapor
compression refrigeration chiller, US 6,293,112 B1, September 25, 2001.
[9] P. De Larminat, L. Le Cointe, J.F. Judge, S. Kulankara, Falling film evaporator, US
7,849,710 B2, December 14, 2010.
[10] Engineer’s Guide to Spray Technology, Spraying Systems Co., U.S.A., 2000.
[11] X. Zeng, M. Chyu, Heat transfer and fluid flow study of ammonia spray evaporators, Texas
Tech University, Lubbock, Texas, USA, 1995.
156
Chapter 7
General conclusions and future
works
This chapter begins with the main conclusions drawn from the theoretical and experimental
studies developed for this thesis.
This document finishes with a brief explanation of the future works that will be developed to
continue with this line of research focused on HTC determination in phase change processes
(condensation and evaporation/boiling).
157
Chapter 7
7.1.
General conclusions and future works
GENERAL CONCLUSIONS
The conclusions we have drawn from the different works developed during this study are
listed below.
1. We have performed a thorough literature review on the main characteristics and
particularities of the boiling process of refrigerants on horizontal tubes when the refrigerant is
distributed on the tubes by means of different devices, such as nozzles, perforated plates, etc.
We have analysed the main variables that have an effect on this process, normally called spray
or falling film evaporation.
2. We have modified an existing experimental setup which had been designed to determine
HTCs of condensation and pool boiling of refrigerants on horizontal tubes. The modification we
have developed consisted in including a liquid refrigerant distribution system that was
specifically dimensioned and built for this experimental test rig. The system includes a tank, a
refrigerant pump, and a distribution tube with wide angle circular full cone nozzles.
3. We have designed an experimental methodology based on the separation of thermal
resistances to study boiling HTCs of refrigerants on horizontal tubes, both under flooded or
refrigerant distribution conditions. We have conceived a specific experimental methodology to
analyse the influence of the impingement effect on HTCs with distribution of the liquid
refrigerant. We have also developed a systematic methodology to determine the uncertainties of
the different variables measured and calculated, based on the Guide to the Expression of
Uncertainty in Measurements (GUM). The different assumptions considered for this
experimental methodology have been successfully validated with specific tests.
4. We have shown the pool boiling HTCs obtained with R134a as refrigerant and copper
tubes of plain and enhanced outer surfaces (Turbo-B and Turbo-BII+ of Wolverine Tube Inc.).
The vast majority of our experimental results are included in the nucleate boiling region of the
boiling curve. Pool boiling HTCs increase both with saturation temperatures (reduced pressure)
and with heat flux (except for Turbo-B). We have compared our plain tube results with wellknown correlations found in works of the specialised literature and we have observed the large
discrepancies that exist among them, confirming how difficult it is to determine accurately the
HTCs associated to this process.
5. The pool boiling tests developed with ammonia on titanium tubes with plain and integralfin (Trufin 32 f.p.i.) outer surfaces have covered both the natural convective and nucleate boiling
regions of the boiling curve. The HTCs obtained increase with increasing heat fluxes and
saturation temperatures. We have also tested the influence of hysteresis on the nucleation
process. We have confirmed its existence and that it is more important with the integral-fin tube
than with the plain tube. However, our experiments have shown that increasing heat flux tests
are time-dependent, i.e. the HTCs obtained when the experimentation process follows an
increasing heat flux trend rise with time until they reach a value very close to that obtained with
the diminishing heat flux tests, even when the test conditions remained constant. Our pool
boiling HTCs with ammonia have been complemented with photographic reports that confirm
the main experimental results.
6. The surface enhancement techniques under pool boiling have been more effective with
R134a than with ammonia. With R134a, the surface enhancement factors have been as high as
11.8 and 7 with the Turbo-B and Turbo-BII+, respectively. In contrast, with ammonia, the EFsf
has never been greater than 1.3.
7. We have studied spray evaporation with R134a and copper plain tube and we have
observed that the HTCs generally increase if the heat flux is higher, independently of the mass
flow rate of the film per side and meter of tube. We have also observed that the effect of the
mass flow rate on the HTCs is negligible. The spray evaporation HTCs obtained with R134a
and the tube placed directly underneath the refrigerant distribution tube (ST tests) are, on
average, 13.2% greater than those determined with the tube that receives refrigerant from the
conditioning tube (SB tests), if kept the heat flux and distributed mass flow rate constant. The
heat transfer enhancement occurs due to the liquid droplet impingement effect. We have
compared spray evaporation and pool boiling, with R134a, plain copper tube and under similar
conditions and we have observed that spray evaporation enhances heat transfer only in the low
158
Chapter 7
General conclusions and future works
heat flux range. The enhancement has never been greater than 60% and the results are in line
with other works from the specialised literature. An analysis of the photographs taken during the
experiments have confirmed the existence of dry patches on the tubes and explained the heat
transfer deterioration found at the high heat flux range.
8. We have performed spray evaporation tests with ammonia and titanium plain tubes and
we have noted that the HTCs depend on both the heat flux and the mass flow rate of refrigerant
per side and meter of tube. Generally, they increase with increasing heat fluxes, but this trend is
even opposite under conditions of high heat flux and low mass flow rate. We have observed that
the spray evaporation HTCs obtained with ammonia and the tube placed directly underneath
the refrigerant distribution tube (ST tests) are, on average, 38.7% higher than those determined
with the tube that receives refrigerant from the conditioning tube (SB tests). Droplet
impingement effect is responsible of this effect. From the comparison of spray evaporation and
pool boiling of ammonia on the plain tube, we have concluded that spray evaporation enhances
importantly heat transfer, particularly in the low heat flux range. Spray enhancement factors
have been over 1 under almost every condition and have reached values over 6. The
photographic report of the process has verified the existence of dry patches under certain
conditions that coincide with the lowest spray enhancement factors.
9. The experimental results obtained made clear the importance of having a proper
distribution of the liquid refrigerant on the tubes of spray evaporators. Thus, we have developed
a computer programme, based on a geometric study, to optimise the design of liquid distribution
systems with spray nozzles.
10. We have performed a parametric analysis with the programme developed for a tube
bundle of a given number of rows, tubes per row and length. We have observed that, in general,
60º nozzles lead to an even distribution and efficient use of the distributed liquid. However, they
require a large distance to the first row of the bundle to optimise distribution and, thus, there is
an important part of the shell that must be clear of tubes. The performance of systems with 90º
nozzles is slightly lower, but the distance required is also shorter and they are convenient from
this point of view. We have also determined that the even distribution of liquid on the different
columns of inline tube bundles is easier than when the pattern is staggered. In fact, staggered
tube bundles seem unsuitable for this kind of distribution systems with nozzles and without
intermediate devices. Only when the horizontal pitch between tubes of the same row was high
(2 in this case), we have observed a convenient distribution between the different columns.
However, an increase of this horizontal pitch leads to the loss of compactness of staggered
bundles, which is the main advantage of such tube pattern.
159
Chapter 7
7.2.
General conclusions and future works
FUTURE WORKS
The line of research in which this work is enclosed continues in our laboratory. Some of the
works that will be developed in the future are listed below.
1. Different tubes with enhanced outer surfaces will be tested under pool boiling conditions.
The refrigerants on which we will focus in future studies are natural refrigerants, particularly
ammonia. At this moment we are conducting slight modifications in the test rig to extend the test
conditions to lower temperatures and, thus, have a larger range of saturation
temperatures/reduced pressures.
2. Spray evaporation tests will be performed with the same enhanced tubes used for pool
boiling tests. We will also study the process with different spray nozzles, such as square full
cone nozzles, or low momentum distribution devices.
3. We will design an auxiliary test rig to conduct the experimental validation of the
programme developed for the optimisation of the distribution system.
4. We will continue with the condensation tests that were developed during previous stages
of this line of research by testing new enhanced surfaces for ammonia.
160
Appendix A
Uncertainty determination
In this appendix we detail the uncertainty analysis prepared for the most important
parameters and fluid properties. It is based on the application of the general uncertainty
propagation expression, as stated in the Evaluation of measurement data – Guide to the
expression of uncertainty measurement (GUM). The output of this appendix is normally
expressed with the results determined in form of error bars.
161
Appendix A
A.1.
Uncertainty determination
GENERAL FEATURES
The simple presentation of the boiling HTCs leaves this information incomplete. By
including the uncertainties related with their determination, we give an idea of the quality and
reliability of these results. Uncertainty is a parameter associated with the estimated value of a
physical magnitude, measured or calculated, that indicates the range of values were the actual
value of this physical magnitude should be. In this work we have developed an uncertainty
determination procedure based on the Evaluation of measurement data – Guide to the
expression of uncertainty measurement (GUM).
According to the GUM, a certain physical magnitude or measurand can be directly
measured or determined from other quantities by a certain function. These other quantities can
be also treated as measurands and they are classified depending on their origin: measured or
from external sources.
If a measurand, xk, is the result of n independent determinations xki, a convenient estimation
of the measurand is the arithmetic mean of these independent determinations, as seen in
equation (A.1).
xk 
1 n i
x
n i 1 k
(A.1)
The uncertainty can be classified into two categories: type A and type B. On the one hand,
type A uncertainty, uA(xk), results from the statistical analysis of a series of measurements. On
the other hand, type B uncertainty, uB(xk) is any other component of the uncertainty, including
previously measured data, manufacturer specifications, data from calibration reports, etc. The
total uncertainty of the magnitude, u(xk), results from adding the previous two (equation (A.2)).
u xk 2  u A xk 2  uB xk 2
(A.2)
The best estimation of the type A uncertainty is the experimental standard deviation of the
mean, calculated with equation (A.3).
u A x k  
n
2
1
  x ki  x k 
n n  1 i 1
(A.3)
Type B uncertainties are detailed for each situation, since they depend on the experimental
sensors utilised or the correlations considered. As a general fact, type B uncertainties from
experimental devices, uB,sensor, are estimated from the manufacturer specifications and
considering a uniform distribution in the device uncertainty range, ±a, as seen in equation (A.4).
uB,sensor xk   a
3
(A.4)
When the measurand, for instance y, is not directly measured, but calculated from others by
a certain function f, the uncertainty of this measurand results from the law of propagation of
uncertainty. The general equation to determine this uncertainty is (A.5).
 f
u y    
k  x k
2

 u x k 2

(A.5)
In following paragraphs, the determination of the uncertainties associated with the different
physical magnitudes is detailed. The number of measurements n was of 100 for all the
experiments developed.
162
Appendix A
A.2.
Uncertainty determination
Uncertainties of directly measured measurands
A.2.1. Uncertainty of temperatures
The estimation of the temperature is obtained by the arithmetic mean of the measured
values, following equation (A.1). The uncertainty of the temperature is determined using the
general equation (A.2), being type A and B uncertainties calculated with the general equations
(A.3) and (A.4), respectively. All the temperature sensors used in the test rig are Pt100 A Class
thermorresistances (Table 2.2). Taking into account the manufacturer specifications and the
calibration process, we considered the device uncertainty range of ±0.1 K.
A.2.2. Uncertainty of refrigerant pressures
The estimation of the pressure is obtained by the arithmetic mean of the measured values,
following equation (A.1). The uncertainty of the pressure is determined using the general
equation (A.2), being type A and B uncertainties calculated with the general equations (A.3) and
(A.4), respectively. The pressure transducers used in the test rig are of high accuracy sensors
(Table 2.2). Taking into account the manufacturer specifications, we considered the device
uncertainty range of approximately ±8 kPa.
A.2.3. Uncertainty of water volumetric flow rates
The estimation of the volumetric flow rate is obtained by the arithmetic mean of the
measured values, following equation (A.1). The uncertainty of the volumetric flow rate is
determined using the general equation (A.2), being type A and B uncertainties calculated with
the general equations (A.3) and (A.4), respectively. The volumetric flowmeter used in the test rig
are electromagnetic flow meters (Table 2.2). Taking into account the manufacturer
specifications, we considered the device uncertainty range of ±0.5% of the measured value.
A.2.4. Uncertainty of the electric power at the electric boiler
The estimation of the electric power delivered to the heating water at the electric boiler is
obtained by the arithmetic mean of the measured values, following equation (A.1). The
uncertainty of the electric power is determined using the general equation (A.2), being type A
and B uncertainties calculated with the general equations (A.3) and (A.4), respectively. The
power meter used in the test rig is an active power transducer (Table 2.2). Taking into account
the manufacturer specifications, we considered the device uncertainty range of ±0.45% of the
measured value.
A.2.5. Uncertainty of the distributed liquid refrigerant mass flow rate
The estimation of the distributed liquid refrigerant mass flow rate is obtained by the
arithmetic mean of the measured values, following equation (A.1). The uncertainty of the mass
flow rate is determined using the general equation (A.2), being type A and B uncertainties
calculated with the general equations (A.3) and (A.4), respectively. The flow meter used in the
test rig is a Coriolis Effect mass flow meter (Table 2.2). Taking into account the manufacturer
specifications, we considered the device uncertainty range of ±0.25% of the measured value.
A.2.6. Uncertainty of the distributed liquid refrigerant density
The estimation of the distributed liquid refrigerant density is obtained by the arithmetic mean
of the measured values, following equation (A.1). The uncertainty of the density is determined
using the general equation (A.2), being type A and B uncertainties calculated with the general
equations (A.3) and (A.4), respectively. The density sensor used in the test rig is the Coriolis
Effect mass flow meter (Table 2.2). Taking into account the manufacturer specifications, we
considered the device uncertainty range of ±0.5 kg/m3.
A.2.7. Uncertainty of lengths and diameters
The lengths, distances and diameters were measured only once, and therefore we consider
the measured value as the best estimation. As a consequence, there are no uncertainties type
A. The uncertainty is only of type B. Concerning lengths and distances, the measuring device
was a meter tape and the uncertainty range is ±0.001 m. For the diameters the measurements
were conducted with a calliper and the uncertainty range is ±0.00005 m.
163
Appendix A
A.3.
Uncertainty determination
Propagated uncertainties
A.3.1. Uncertainty of the mean heating water temperature
The mean heating water temperature is calculated by equation (A.6). The arithmetic mean
of the values calculated with this equation is the best estimation. Applying the law of
propagation of uncertainties (equation (A.5)), we determine the uncertainty of this physical
magnitude, as shown in equation (A.7). The partial derivatives needed are calculated in
equation (A.8).
Thw 
Thw,in  Thw,out
2
2
(A.6)
 Thw 

 u Thw,in 2   Thw
u Thw  
 Thw,in 
 Thw,out







2

 u Thw,out 2




(A.7)
Thw
Thw

 0.5
Thw,in Thw,out
(A.8)
A.3.2. Uncertainty of the heating water temperature difference between inlet and outlet
The heating water temperature difference between inlet and outlet is calculated by equation
(A.9). The arithmetic mean of the values calculated with this equation is the best estimation.
Applying the law of propagation of uncertainties (equation (A.5)), we determine the uncertainty
of this physical magnitude, as shown in equation (A.10). The partial derivatives needed are
calculated in equation (A.11).
Thw  Thw,in  Thw,out
(A.9)
2
 Thw 

 u Thw,in 2   Thw
u Thw   
 Thw,in 
 Thw,out





2

 u Thw,out 2



Thw
Thw

1
Thw,in
Thw,out

(A.10)
(A.11)
A.3.3. Uncertainty of the heating water properties
Heating water properties are obtained using REFPROP 8.0 database, as previously stated.
The estimations of the water properties are obtained by the arithmetic mean of the calculated
values, following equation (A.1), and their uncertainties by equation (A.2). In this case, type A
uncertainty occurs due to the propagation of the uncertainty of the mean heating water
temperature (equations (A.12), (A.14), (A.16) and (A.18)). Type B uncertainty depends on the
formulae employed by REFPROP to calculate the properties (equations (A.13), (A.15), (A.17)
and (A.19)).




u A  hw    hw Thw  u Thw   hw Thw
uB hw   0.0001hw
164

(A.12)
(A.13)
Appendix A
Uncertainty determination




u A  hw    hw Thw  u Thw   hw Thw

(A.14)
uB hw   0.01hw




(A.15)




u A c p,hw  c p,hw Thw  u Thw  c p,hw Thw

(A.16)
uB c p,hw  0.001 c p,hw

(A.17)



u A k hw   k hw Thw  u Thw  k hw Thw

(A.18)
uB khw   0.015 khw
(A.19)
A.3.4. Uncertainty of the heating water mass flow rate
The heating water mass flow rate is calculated by equation (A.20). The arithmetic mean of
the values calculated with this equation is the best estimation. Applying the law of propagation
of uncertainties (equation (A.5)), we determine the uncertainty of this physical magnitude, as
shown in equation (A.21). The partial derivatives needed are calculated in equations (A.22) and
(A.23).
 hw  hw v hw
m
 m
u m hw    hw
  hw
(A.20)
2

 m
 u  hw 2   hw

 v hw
2

 u v hw 2

(A.21)
 hw
m
 v hw
 hw
(A.22)
 hw
m
  hw
v hw
(A.23)
A.3.5. Uncertainty of the heating water heat flow
The heating water heat flow is calculated by equation (A.24). The arithmetic mean of the
values calculated with this equation is the best estimation. Applying the law of propagation of
uncertainties (equation (A.5)), we determine the uncertainty of this physical magnitude, as
shown in equation (A.25). The partial derivatives needed are calculated in equations (A.26),
(A.27) and (A.28).
qhw  m hw c p,hw Thw
 q
u qhw    hw
 hw
 m
2


 hw 2   qhw
 u m
 c p,hw


(A.24)
2

 u c p,hw 2   qhw
 T

hw




2

 u Thw 2

(A.25)
165
Appendix A
Uncertainty determination
q hw
 c p,hw Thw
 hw
m
(A.26)
qhw
 m hw Thw
c p,hw
(A.27)
qhw
 hw
 c p,hw m
Thw
(A.28)
A.3.6. Uncertainty of heat exchange areas
The heat exchange areas, either of the inner or the outer surface of a plain tube, are
calculated by equation (A.29). The lengths, distances and diameters were measured only once,
and therefore we consider the area calculated as the best estimation. Applying the law of
propagation of uncertainties (equation (A.5)), we determine the uncertainties of these physical
magnitudes, as shown in equation (A.30). The partial derivatives needed are calculated in
equations (A.31) and (A.32).
Ai / o   d i / o L
 A
u Ai / o    i / o
 d i / o
(A.29)
2

 A
 u d i / o 2   i / o
 L

2

 u L 2

(A.30)
Ai / o
L
d i / o
Ai / o
L
(A.31)
  di / o
(A.32)
A.3.7. Uncertainty of the heating water heat fluxes
The heating water heat fluxes, referred either to the inner and outer surfaces, are calculated
by equation (A.33). The arithmetic means of the values calculated with these equations are the
best estimation. Applying the law of propagation of uncertainties (equation (A.5)), we determine
the uncertainties of these physical magnitudes, as shown in equation (A.34). The partial
derivatives needed are calculated in equations (A.35) and (A.36).
qhw,i / o  qhw,i / o Ai / o
 q hw,i / o
u q hw,i / o  
 qhw


q hw,i / o
qhw
166
 1 Ai / o
(A.33)
2

 q
 u qhw 2   hw,i / o

 A
i /o


2

 u Ai / o 2


(A.34)
(A.35)
Appendix A
Uncertainty determination
qhw
  qhw Ai2/ o
Ai / o
(A.36)
A.3.8. Uncertainty of the cooling water mean temperature
The mean cooling water temperature is calculated by equation (A.37). The arithmetic mean
of the values calculated with this equation is the best estimation. Applying the law of
propagation of uncertainties (equation (A.5)), we determine the uncertainty of this physical
magnitude, as shown in equation (A.38). The partial derivatives needed are calculated in
equation (A.39).
Tcw 
Tcw,in  Tcw,out
(A.37)
2
2
 Tcw 

 u Tcw,in 2   Tcw
u Tcw  
 Tcw,in 
 Tcw,out



 


2

 u Tcw,out 2




Tcw
Tcw

 0.5
Tcw,in Tcw,out
(A.38)
(A.39)
A.3.9. Uncertainty of the cooling water temperature difference between outlet and inlet
The cooling water temperature difference between outlet and inlet is calculated by equation
(A.40). The arithmetic mean of the values calculated with this equation is the best estimation.
Applying the law of propagation of uncertainties (equation (A.5)), we determine the uncertainty
of this physical magnitude, as shown in equation (A.41). The partial derivatives needed are
calculated in equation (A.42).
Tcw  Tcw,out  Tcw,in
2
(A.40)
 Tcw 

 u Tcw,in 2   Tcw
u Tcw   
 Tcw,in 
 Tcw,out





2

 u Tcw,out 2



Tcw
Tcw

1
Tcw,out
Tcw,in

(A.41)
(A.42)
A.3.10. Uncertainty of the cooling water properties
Cooling water properties are obtained using REFPROP 8.0 database, as previously stated.
The estimations of the water properties are obtained by the arithmetic mean of the calculated
values, following equation (A.1), and their uncertainties by equation (A.2). In this case, type A
uncertainty occurs due to the propagation of the uncertainty of the mean heating water
temperature (equations (A.43), (A.45), (A.47) and (A.49)). Type B uncertainty depends on the
formulae employed by REFPROP to calculate the properties (equations (A.44), (A.46), (A.48)
and (A.50)).




u A  cw    cw Tcw  u Tcw   cw Tcw

(A.43)
167
Appendix A
Uncertainty determination
uB cw   0.0001cw

(A.44)



u A cw    hw Tcw  u Tcw   hw Tcw

(A.45)
uB cw   0.01cw




(A.46)




u A c p,cw  c p,cw Tcw  u Tcw  c p,cw Tcw

(A.47)
uB c p,cw  0.001c p,cw

(A.48)



u A k cw   k cw Tcw  u Tcw  k cw Tcw

(A.49)
uB kcw   0.015 kcw
(A.50)
A.3.11. Uncertainty of the cooling water mass flow rate
The cooling water mass flow rate is calculated by equation (A.51). The arithmetic mean of
the values calculated with this equation is the best estimation. Applying the law of propagation
of uncertainties (equation (A.5)), we determine the uncertainty of this physical magnitude, as
shown in equation (A.52). The partial derivatives needed are calculated in equations (A.53) and
(A.54).
 cw  cw v cw
m
 
 cw    mcw
u m
 
 cw
(A.51)
2
 cw

 m
 u  cw 2  

 v cw
2

 u v cw 2

(A.52)
 cw
m
 v cw
 cw
(A.53)
 cw
m
  cw
v cw
(A.54)
A.3.12. Uncertainty of the cooling water heat flow
The cooling water heat flow is calculated by equation (A.55). The arithmetic mean of the
values calculated with this equation is the best estimation. Applying the law of propagation of
uncertainties (equation (A.5)), we determine the uncertainty of this physical magnitude, as
shown in equation (A.56). The partial derivatives needed are calculated in equations (A.57),
(A.58) and (A.59).
qcw  m cw c p,cw Tcw
 q
u qcw    cw
 cw
 m
168
2


 cw 2   qcw
 u m
 c p,cw


(A.55)
2

 u c p,cw 2   qcw
 T

cw




2

 u Tcw 2

(A.56)
Appendix A
Uncertainty determination
qcw
 c p,cw Tcw
 cw
m
(A.57)
qcw
 m cw Tcw
c p,cw
(A.58)
qcw
 cw
 c p,cw m
Tcw
(A.59)
A.3.13. Uncertainty of the liquid refrigerant mean temperature
Independently of the type of experiments, pool boiling or spray evaporation, the liquid
refrigerant mean temperature is calculated by equation (A.60). The arithmetic mean of the
values calculated with this equation is the best estimation. Applying the law of propagation of
uncertainties (equation (A.5)), we determine the uncertainty of this physical magnitude, as
shown in equation (A.61). The partial derivatives needed are calculated in equation (A.62).
T T T T
Tl  13 14 15 16
4
(A.60)
2
2
 Tl 
 Tl 
 u T13 2    
 u T16 2
u Tl   

T

T
 13 
 16 
(A.61)
Tl
Tl

 0.25
T13
T16
(A.62)
A.3.14. Uncertainty of the temperature difference at each end of the evaporator section
The temperature difference at each end of the evaporator section is calculated by equation
(A.63). The arithmetic mean of the values calculated with this equation is the best estimation.
Applying the law of propagation of uncertainties (equation (A.5)), we determine the uncertainty
of this physical magnitude, as shown in equation (A.64). The partial derivatives needed are
calculated in equation (A.65).
Tend,1/ 2  Thw,in / out  Tl
(A.63)
 Tend,1/ 2
u Tend,1/ 2  
 Thw,in / out


Tend,1/ 2
Thw,in / out


Tend,1/ 2
Tl
2
2

 Tend,1/ 2 
 u Thw,in / out 2  
 u Tl 2




T
l



1


(A.64)
(A.65)
A.3.15. Uncertainty of the logarithmic mean temperature difference at the evaporator
The logarithmic mean temperature difference at the evaporator is calculated by equation
(A.66). The arithmetic mean of the values calculated with this equation is the best estimation.
Applying the law of propagation of uncertainties (equation (A.5)), we determine the uncertainty
of this physical magnitude, as shown in equation (A.67). The partial derivatives needed are
calculated in equations (A.68) and (A.69).
169
Appendix A
LMTD 
Uncertainty determination
Tend,1  Tend,2

ln Tend,1 Tend,2
2

(A.66)
2
 LMTD 


 u Tend,1 2   LMTD  u Tend,2 2
u LMTD  
 Tend,1 
 Tend,2 







 



ln Tend,1 Tend,2  Tend,1  Tend,2 Tend,1
LMTD

Tend,1
ln Tend,1 Tend,2 2



 
(A.68)

 ln Tend,1 Tend,2  Tend,1  Tend,2 Tend,2
LMTD

Tend,2
ln Tend,1 Tend,2 2
 
(A.67)

(A.69)
A.3.16. Uncertainty of the overall thermal resistance at the evaporator
The overall thermal resistance at the evaporator is calculated by equation (A.70). The
arithmetic mean of the values calculated with this equation is the best estimation. Applying the
law of propagation of uncertainties (equation (A.5)), we determine the uncertainty of this
physical magnitude, as shown in equation (A.71). The partial derivatives needed are calculated
in equations (A.72) and (A.73).
Rov 
LMTD
qevap
(A.70)
2
2
 Rov 
2  Rov 
u Rov   
u qevap 2
 u LMTD  
 qevap 
 LMTD 


(A.71)
Rov
1

LMTD qevap
(A.72)
Rov
LMTD

2
qevap
qevap
(A.73)


A.3.17. Uncertainty of the heating water Reynolds number in the evaporator tube
The heating water Reynolds number in the evaporator tube is calculated by equation (A.74).
The arithmetic mean of the values calculated with this equation is the best estimation. Applying
the law of propagation of uncertainties (equation (A.5)), we determine the uncertainty of this
physical magnitude, as shown in equation (A.75). The partial derivatives needed are calculated
in equations (A.76), (A.77), (A.78) and (A.79).
Rehw 
170
4 v  hw
  hw d i
(A.74)
Appendix A
Uncertainty determination
2
u Rehw  
  Rehw
  Rehw 

 u v 2  
 v 
  hw
  Rehw
 
 d i
2

 u  hw 2 

2

  Rehw
 u d i 2  

  hw
2
(A.75)

 u  hw 2

 Rehw
4  hw

v
 d i  hw
(A.76)
 Rehw
4v

 hw
 d i  hw
(A.77)
 Rehw
4  hw v

d i
 d i 2 hw
(A.78)
 Rehw 4  hw v

2
 hw
 d i  hw
(A.79)
A.3.18. Uncertainty of the heating water Prandtl number
The heating water Prandtl number is calculated by equation (A.80). The arithmetic mean of
the values calculated with this equation is the best estimation. Applying the law of propagation
of uncertainties (equation (A.5)), we determine the uncertainty of this physical magnitude, as
shown in equation (A.81). The partial derivatives needed are calculated in equations (A.82),
(A.83) and (A.84).
Prhw 
c p,hw  hw
(A.80)
k hw
2
  Prhw 

 u c p,hw 2    Prhw
 
 c p,hw 
 hw


u Prhw  
2
  Prhw 
 u k hw 2
 
 k hw 


2

 u  hw 2 

(A.81)
 Prhw hw

c p,hw k hw
(A.82)
 Prhw c p,hw

 hw
k hw
(A.83)
171
Appendix A
Uncertainty determination
c p,hw  hw
 Prhw

k hw
k2
(A.84)
hw
A.3.19. Uncertainty of the Darcy-Weisbach friction factor
The Darcy-Weisbach friction factor with a plain tube is calculated by equation (A.85). The
arithmetic mean of the values calculated with this equation is the best estimation. The
uncertainty of this physical magnitude is calculated applying the propagation of uncertainties
(equation (A.5)) and adding the uncertainty due to the use of the model to calculate it, which
was estimated from our own experience and results as 5% of the calculated value (equation
(A.86)). The partial derivatives needed are calculated in equations (A.87) and (A.88).
f  0.79 lnRehw   1.642
 f
u f   
  Rehw
(A.85)
2

 f
 u Rehw 2  

  mod f
2

 u mod f 2

(A.86)
f
0.79
 2 0.79 lnRehw   1.643
 Rehw
Rehw
(A.87)
f
1
 mod f
(A.88)
A.3.20. Uncertainty of the heating water Nusselt number with plain tube
The heating water Nusselt number with plain tube is calculated by equation (A.89). The
arithmetic mean of the values calculated with this equation is the best estimation. The
uncertainty of this physical magnitude is calculated applying the propagation of uncertainties
(equation (A.5)) and adding the uncertainty due to the use of the model to calculate it, which
was estimated from our own experience and results as 5% of the calculated value (equation
(A.90)). The partial derivatives needed are calculated in equations (A.91), (A.92), (A.93) and
(A.94).
Nui , pl 
f 8Rehw Prhw
23
1.07  12.7 f 8 0.5  Prhw  1



u Nui , pl 
Nui , pl
 Rehw
172

 Nui , pl

  Re
hw

(A.89)

2

 Nui , pl
 u Rehw 2  

 f


 Nui , pl
 
  Prhw




2
2

 u f 2 


 Nu
i , pl
u Prhw 2  
  mod
Nu i , pl

f 8Prhw
23
1.07  12.7 f 80.5  Prhw  1


2



2
 u mod
Nu i , pl


(A.90)
(A.91)
Appendix A
Nui , pl
f

Uncertainty determination
1



 f 2  2 3  
1.07  12.7    Prhw  1  
 

8 
Rehw Prhw 

1



12
.
7
f
f
 Pr 2 3  1   2




 8 
16  hw


23
8 1.07  12.7 f 8 0.5  Prhw  1 



2
1
1

1 3 

 f 2  2 3 
 f  2 2 Prhw 

f Rehw 1.07  12.7    Prhw  1  12.7 Prhw  

3


8 
8
Nui , pl



2
 Prhw
23
8 1.07  12.7 f 80.5  Prhw  1 



Nui , pl
 mod Nui , pl
(A.92)
1
(A.93)
(A.94)
A.3.21. Uncertainty of the heating water Nusselt number with enhanced tubes
The heating water Nusselt number with plain tube is calculated by equation (A.95). The
arithmetic mean of the values calculated with this equation is the best estimation. The
uncertainty of this physical magnitude is calculated applying the propagation of uncertainties
(equation (A.5)) and adding the uncertainty due to the use of the model to calculate it, which
was estimated from our own experience and results as 5% of the calculated value (equation
(A.96)). The partial derivatives needed are calculated in equations (A.97), (A.98), (A.99),
(A.100) and (A.101).
 
.8 1 3   Thw 
Nui ,en  STC Re0hw
Prhw 

  Twall  
0.14
(A.95)
2
2
 Nui ,en 
 Nui ,en 

 u Rehw 2  
 u Prhw 2 
  Re

  Pr

hw 
hw 


 Nui ,en
u Nui ,en   
  Thw


2
    
 Nu
i ,en

  mod Nu
i ,en

Nui ,en
2

 Nui ,en 
 u  Thw 2  
 u  Twall 2 
  T



wall 


2

(A.96)


2
 u mod
Nu i ,en


 
 0.2 1 3   Thw 
 0.8 STC Rehw
Prhw 

 Rehw
  Twall  
0.14
(A.97)
173
Appendix A
Nui ,en
 Prhw

13
Nui ,en

 Twall
.8 Pr
0.14 STC Re0hw
hw





0.86
1
 2 3   Thw 
.8
STC Re0hw
Prhw 

3
  Twall  

Nui ,en
 Thw
Uncertainty determination
 Twall
0.14
 Thw
13


Nui ,en
 mod Nu i ,en

.8 Pr
 0.14 STC Re0hw
 Thw
hw
0.14
(A.98)
0.14  Twall 0.86
 Twall 0.28
1
(A.99)
(A.100)
(A.101)
A.3.22. Uncertainty of the heating water convection HTC in tubes
Either with plain tubes or enhanced tubes, the heating water convection HTC in tubes is
calculated by equation (A.102). The arithmetic mean of the values calculated with this equation
is the best estimation. Applying the law of propagation of uncertainties (equation (A.5)), we
determine the uncertainty of this physical magnitude, as shown in equation (A.103). The partial
derivatives needed are calculated in equations (A.104), (A.105) and (A.106).
hi , pl / en 
Nui , pl / en k hw
di
(A.102)
2
2
 hi , pl / en 
 h


 u Nui , pl / en 2   i , pl / en  u k hw 2 
 k

 Nui , pl / en 
hw 


u hi , pl / en  
2
 hi , pl / en 
 u d i 2
 


d
i






hi , pl / en
k
 hw
Nui , pl / en
di
hi , pl / en
k hw
hi , pl / en
d i


(A.103)
(A.104)
Nui , pl / en
di
Nui , pl / en k hw
d i2
(A.105)
(A.106)
A.3.23. Uncertainty of the inner thermal resistance
Either with plain tubes or enhanced tubes, the inner thermal resistance is calculated by
equation (A.107). The arithmetic mean of the values calculated with this equation is the best
estimation. Applying the law of propagation of uncertainties (equation (A.5)), we determine the
uncertainty of this physical magnitude, as shown in equation (A.108). The partial derivatives
needed are calculated in equations (A.109) and (A.110).
174
Appendix A
Ri , pl / en 
Uncertainty determination
1
(A.107)
hi , pl / en Ai
2
2
 Ri , pl / en 
 R

 u hi , pl / en 2   i , pl / en  u Ai 2
u Ri , pl / en  
 A

 hi , pl / en 
i






Ri , pl / en
hi , pl / en
Ri , pl / en
Ai




(A.108)
1
(A.109)
Ai hi2, pl / en
1
(A.110)
hi , pl / en Ai2
A.3.24. Uncertainty of the tube wall thermal resistance
Either with plain tubes or enhanced tubes, the tube wall thermal resistance is calculated by
equation (A.111). The arithmetic mean of the values calculated with this equation is the best
estimation. Applying the law of propagation of uncertainties (equation (A.5)), we determine the
uncertainty of this physical magnitude, as shown in equation (A.112). The partial derivatives
needed are calculated in equations (A.113), (A.114) and (A.115).
Rt 
ln d o d i 
2  kt L
 R
u Rt    t
 d o
(A.111)
2

 R
 u d o 2   t
 d i

2
2

 R 
 u d i 2   t  u L 2
 L 

(A.112)
Rt
1

d o 2  k t L d o
(A.113)
Rt
1

d i
2  kt L d i
(A.114)
Rt  lnd o d i 

L
2  k t L2
(A.115)
A.3.25. Uncertainty of the outer thermal resistance
Either with plain tubes or enhanced tubes and neglecting fouling thermal resistances, the
outer thermal resistance is calculated by equation (A.116). The arithmetic mean of the values
calculated with this equation is the best estimation. Applying the law of propagation of
uncertainties (equation (A.5)), we determine the uncertainty of this physical magnitude, as
shown in equation (A.117)The partial derivatives needed are calculated in equation (A.118).
Ro, pl / en  Rov  Ri , pl / en  Rt
(A.116)
175
Appendix A
Uncertainty determination
2
2
 R

 Ro, pl / en 

 u Rov 2   o, pl / en  u Ri , pl / en 2 
 R

 Ri , pl / en 
ov 



u Ro, pl / en 
2
 Ro, pl / en 



u Rt 2

Rt




Ro, pl / en

Rov
Ro, pl / en
Ri , pl / en

Ro, pl / en
Rt


1
(A.117)
(A.118)
A.3.26. Uncertainty of the outer convection HTC on tubes
Either with plain tubes or enhanced tubes, the outer (refrigerant side) convection HTC on
tubes is calculated by equation (A.119). The arithmetic mean of the values calculated with this
equation is the best estimation. Applying the law of propagation of uncertainties (equation
(A.5)), we determine the uncertainty of this physical magnitude, as shown in equation (A.120).
The partial derivatives needed are calculated in equations (A.121) and (A.122).
ho, pl / en 
1
(A.119)
Ao Ro, pl / en
2
2
 ho, pl / en 
2  ho, pl / en 




u ho, pl / en  
u
A

u Ro, pl / en 2
o




A

R
o


 o, pl / en 


ho, pl / en
Ao
ho, pl / en
Ro, pl / en



1
Ro, pl / en Ao2

(A.120)
(A.121)
1
Ao Ro2, pl / en
(A.122)
A.3.27. Uncertainty of the temperature at the inner tube wall
The temperature at the inner tube wall is calculated by equation (A.123). The arithmetic
mean of the values calculated with this equation is the best estimation. Applying the law of
propagation of uncertainties (equation (A.5)), we determine the uncertainty of this physical
magnitude, as shown in equation (A.124). The partial derivatives needed are calculated in
equations (A.125), (A.126), (A.127) and (A.128).
Tw ,i  Thw 
176
qevap
hi ,pl / en Ai
(A.123)
Appendix A

 Tw ,i

 T
 hw

u Tw ,i 
Tw ,i
Thw
 
2


 Tw ,i 
T
 u hi ,pl / en 2   w ,i

 A
 hi ,pl / en 
i




qevap
Tw ,i
hi ,pl / en
Ai
2
2

2  Tw ,i 
 u Thw  
u qevap 2 




q

 evap 



(A.124)
2

 u Ai 2

1
Tw ,i
Tw ,i
Uncertainty determination
(A.125)
1
(A.126)
hi ,pl / en Ai

qevap
(A.127)
hi2,pl / en Ai
qevap
(A.128)
Ai2 hi ,pl / en
A.3.28. Uncertainty of the temperature at the outer tube wall
The temperature at the outer tube wall is calculated by equation (A.129). The arithmetic
mean of the values calculated with this equation is the best estimation. Applying the law of
propagation of uncertainties (equation (A.5)), we determine the uncertainty of this physical
magnitude, as shown in equation (A.130). The partial derivatives needed are calculated in
equations (A.131), (A.132) and (A.133).
Tw ,o  Tw ,i  Rt qevap
2
(A.129)
2
2
 Two 
 T

T
 u qevap 2   w ,o  u Rt 2
u Tw ,o   w ,o  u Tw ,i 2  
 R 
 Tw ,i 
 qevap 
t 







Tw ,o
Tl
Tw ,o
qevap
Tw,o
Rt




1
 Rt
 qevap
(A.130)
(A.131)
(A.132)
(A.133)
A.3.29. Uncertainty of the superheating at the outer tube wall
The superheating at the outer tube wall is calculated by equation (A.134). The arithmetic
mean of the values calculated with this equation is the best estimation. Applying the law of
propagation of uncertainties (equation (A.5)), we determine the uncertainty of this physical
177
Appendix A
Uncertainty determination
magnitude, as shown in equation (A.135). The partial derivatives needed are calculated in
equation (A.136).
TSH  Tw,o  Tl
(A.134)
 TSH
u TSH   
 Tw ,o

2


 u Tw ,o 2   TSH
 T

l




2

 u Tl 2

(A.135)
TSH
TSH

1
Tw,o
Tl
(A.136)
A.3.30. Uncertainty of the enhanced surface enhancement factor
The enhanced surface enhancement factor under pool boiling is calculated by equation
(A.137). The arithmetic mean of the values calculated with this equation is the best estimation.
Applying the law of propagation of uncertainties (equation (A.5)), we determine the uncertainty
of this physical magnitude, as shown in equation (A.138). The partial derivatives needed are
calculated in equations (A.139) and (A.140).


EFsf  ho,en ho, pl 
q,Tl , ref
2
(A.137)

 EFsf 
 u ho,en 2   EFsf
u EFsf   
 ho,en 
 ho, pl





2

 u ho, pl 2




(A.138)
EFsf
1

ho,en ho, pl
(A.139)
EFsf ho,en

ho, pl
ho2, pl
(A.140)
A.3.31. Uncertainty of the spray evaporation enhancement factor
The spray evaporation enhancement factor is calculated by equation (A.141). The
arithmetic mean of the values calculated with this equation is the best estimation. Applying the
law of propagation of uncertainties (equation (A.5)), we determine the uncertainty of this
physical magnitude, as shown in equation (A.142). The partial derivatives needed are
calculated in equations (A.143) and (A.144).


EFsp,  ho,sp, ho, pb 
q,Tl , ref , tube
2
(A.141)
2
 EFsp, 
 EFsp, 
 u ho,sp, 2  
 u ho, pb 2
u EFsp,  
 ho,sp, 
 ho, pb 






178




(A.142)
Appendix A
EFsp,

ho,sp,
EFsp,
ho, pb

Uncertainty determination
1
(A.143)
ho, pb
ho,sp,
(A.144)
ho2, pb
A.3.32. Uncertainty of the distance from the tip of the nozzle to the tangents on the tubes
The distance from the tip of the nozzle to the tangents on the tubes is calculated by
equation (A.145). The distances and diameters were measured only once, and therefore we
consider the calculated distance as the best estimation. Applying the law of propagation of
uncertainties (equation (A.5)), we determine the uncertainty of this physical magnitude, as
shown in equation (A.146). The partial derivatives needed are calculated in equations (A.147)
and (A.148).
zs
do s
2s  d o
(A.145)
2
2
 z 
 z 
 u d o 2
u z     u s 2  

d
 s 
 o
(A.146)
d o 22
z
 1
s
s  d o 22
(A.147)

z
1
s
s2

 

d o 2  s  d o 2 s  d 22 
o


(A.148)
A.3.33. Uncertainty of the spray cone diameter at the distance z from the tip of the nozzle
The spray cone diameter at the distance z from the tip of the nozzle is calculated by
equation (A.149). The distances and diameters were measured only once, and therefore we
consider the calculated diameter as the best estimation. Applying the law of propagation of
uncertainties (equation (A.5)), we determine the uncertainty of this physical magnitude, as
shown in equation (A.150). The partial derivatives needed are calculated in equations (A.151)
and (A.152). Even though the nozzle angle β was stated by the manufacturer, we developed
validation experiments to check them (see section 3.5). From these experiments we concluded
that the nozzle angle depends on the refrigerant, and we also observed that it is not completely
constant during the experiments. We also evaluated the uncertainty of the nozzle angle through
video recording, which was estimated in ±2º.
d sp z   2 z tan 2
(A.149)
 d sp z  
 u z 2
u d sp z   

 z 


2
(A.150)
179
Appendix A
d sp z 
z
d sp z 

Uncertainty determination
 2 tan 2

(A.151)
z
(A.152)
2
cos  2
A.3.34. Uncertainty of the angle formed by the tangents to the tube from the nozzle
The angle formed by the tangents to the tube from the nozzle is calculated by equation
(A.153). The distances and diameters were measured only once, and therefore we consider the
calculated angle as the best estimation. Applying the law of propagation of uncertainties
(equation (A.5)), we determine the uncertainty of this physical magnitude, as shown in equation
(A.154). The partial derivatives needed are calculated in equations (A.155) and (A.156).
 d 2 

  2 arcsin o

 s  do 2 
 
u    
 d o


d o


s
(A.153)
2
2

  
2
 u d o 2  
 u s 

s



(A.154)
s
2
 do 2  
d
  s  o
1  
2
 s  do 2  



2
(A.155)
d o
2
2
 d 2  
d 
  s  o 
1   o
2 
 s  do 2  
(A.156)
A.3.35. Uncertainty of the projected tube radius at a distance z from the tip of the nozzle
The projected tube radius at a distance z from the tip of the nozzle is calculated by equation
(A.157). The distances and diameters were measured only once, and therefore we consider the
calculated value as the best estimation. Applying the law of propagation of uncertainties
(equation (A.5)), we determine the uncertainty of this physical magnitude, as shown in equation
(A.158). The partial derivatives needed are calculated in equations (A.159) and (A.160).
r z   tan 2 z
(A.157)
 r z  
2  r z    2
u r z   
 u    
 uz




 z 
(A.158)
r z 
z


2 cos2  2
(A.159)
2
180
2
Appendix A
Uncertainty determination
r z 
 tan 2
z
(A.160)
A.3.36. Uncertainty of the projected tube lengthwise dimension at a distance z from the
tip of the nozzle
The projected tube lengthwise dimension at a distance z from the tip of the nozzle is
calculated by equation (A.161). The lengths, distances and diameters were measured only
once, and therefore we consider the area calculated as the best estimation. Applying the law of
propagation of uncertainties (equation (A.5)), we determine the uncertainty of this physical
magnitude, as shown in equation (A.162). The partial derivatives needed are calculated in
equations (A.163) and (A.164).
mz   d sp z 2 4  r z 2
2
(A.161)
2
 mz  
 mz  
2


 u r z 2
u mz  
u d sp z   
 d sp z  



r
z




mz 

d sp z 
mz 

r z 


(A.162)
d sp z 
(A.163)
4 d sp z 2 4  r z 2
 r z 
(A.164)
d sp z 2 4  r z 2
A.3.37. Uncertainty of the projected area of tube reached from the distribution system
The projected area of tube reached from the distribution system is calculated by equation
(A.165). The lengths, distances and diameters were measured only once, and therefore we
consider the area calculated as the best estimation. Applying the law of propagation of
uncertainties (equation (A.5)), we determine the uncertainty of this physical magnitude, as
shown in equation (A.166). The partial derivatives needed are calculated in equations (A.167)
and (A.168).
An,tw z   2 r z  L
(A.165)
z  
 An,tw z  
 A
 u r z 2   n,tw
u An,tw z   
u L 2



L
 r z  




An,tw z 
r z 
An,tw z 
L
2
2
(A.166)
 2L
(A.167)
 2 r z 
(A.168)
A.3.38. Uncertainty of the spray cone area of n nozzles at a distance z
The spray cone area of n nozzles at a distance z is calculated by equation (A.169). The
distances and diameters were measured only once, and therefore we consider the area
181
Appendix A
Uncertainty determination
calculated as the best estimation. Applying the law of propagation of uncertainties (equation
(A.5)), we determine the uncertainties of these physical magnitudes, as shown in equation
(A.170). The partial derivative needed is calculated in equation (A.171).
An,sp z   n

d sp z 2
4
(A.169)
 An,sp z  
 u d sp z  2
u An,sp z   
 d sp z  



2

An,sp z 
d sp z 
n


(A.170)

d sp
2
(A.171)
A.3.39. Uncertainty of the mass flow rate reaching the top of the tube
The mass flow rate reaching the top of the tube is calculated by equation (A.172). The
arithmetic mean of the values calculated with this equation is the best estimation. Applying the
law of propagation of uncertainties (equation (A.5)), we determine the uncertainties of these
physical magnitudes, as shown in equation (A.173). The partial derivatives needed are
calculated in equation (A.174), (A.175) and (A.176).
 top  m
 dist
m


 top 
um
An,tw z 
An,sp z 
 top
 m

 m

 dist
(A.172)
2
 top  2
 m

2
 u An,tw z  2 
 dist   
 u m

 An,tw z  





 top  2
 m

 u An,sp z  2

 An,sp z  




m top
An,tw z 

m dist An,sp z 
m top
An,tw z 
 top
m
An,sp z 


(A.173)
m dist
An,sp z 
 dist An,tw z 
m
An,sp z 2
(A.174)
(A.175)
(A.176)
A.3.40. Uncertainty of the film flow rate at each side per meter of tube
The film flow rate at each side per meter of the tube is calculated by equation (A.177). The
arithmetic mean of the values calculated with this equation is the best estimation. Applying the
law of propagation of uncertainties (equation (A.5)), we determine the uncertainties of these
physical magnitudes, as shown in equation (A.178). The partial derivatives needed are
calculated in equation (A.179) and (A.180).
182
Appendix A

Uncertainty determination
 top
m
(A.177)
2L
 
u    
 m

 top
2
2

 um
 top 2     u L 2

 L 



(A.178)

1

m top 2 L
(A.179)
 m top

L
2 L2
(A.180)
A.3.41. Uncertainty of the liquid refrigerant properties
Liquid refrigerant properties are obtained using REFPROP 8.0 database, as previously
stated. The estimations of the liquid refrigerant properties are obtained by the arithmetic mean
of the calculated values, following equation (A.1), and their uncertainties by equation (A.2). In
this case, type A uncertainty occurs due to the propagation of the uncertainty of the liquid
refrigerant water temperature (equations (A.181), (A.183), (A.185), (A.187) and (A.189)). Type
B uncertainty depends on the formulae employed by REFPROP to calculate the properties
(equations (A.182), (A.184), (A.186), (A.188) and (A.190)).
u A  ref    ref Tl  u Tl    ref Tl 
(A.181)
uB R134a   0.0005 R134a ; uB R717   0.0002 R717;
(A.182)
u A ref   ref Tl  u Tl   ref Tl 
(A.183)
uB R134a   0.015 R134a ; uB R717   0.005 R717;
(A.184)


u A c p,ref  c p,ref Tl  u Tl   c p,ref Tl 



(A.185)

uB c p,R134a  0.01c p,R134a ; uB c p,R 717  0.02 c p,R 717;
(A.186)
u A k ref   k ref Tl  u Tl   k ref Tl 
(A.187)
uB kR134a   0.05 kR134a ; uB kR717   0.002 kR717;
(A.188)


u A hlv,ref  hlv,ref Tl  u Tl   hlv,ref Tl 



(A.189)

uB hlv,R134a  0.05 hlv,R134a ; uB hlv,R717  0.002 hlv,R717;
(A.190)
A.3.42. Uncertainty of the film flow Reynolds number at the top of the tube
The film flow Reynolds number at the top of the tube is calculated by equation (A.191). The
arithmetic mean of the values calculated with this equation is the best estimation. Applying the
law of propagation of uncertainties (equation (A.5)), we determine the uncertainties of these
183
Appendix A
Uncertainty determination
physical magnitudes, as shown in equation (A.192). The partial derivatives needed are
calculated in equation (A.193) and (A.194).
Re,top 
4
ref
(A.191)
  Re,top
u Re,top  




 Re,top

 Re,top
 ref


2

  Re,top
 u  2  

 
ref


2

 u  ref 2


4
(A.192)
(A.193)
ref
 4
(A.194)
2
 ref
A.3.43. Uncertainty of the liquid refrigerant overfeed ratio
The liquid refrigerant overfeed ratio is calculated by equation (A.195). The arithmetic mean
of the values calculated with this equation is the best estimation. Applying the law of
propagation of uncertainties (equation (A.5)), we determine the uncertainties of these physical
magnitudes, as shown in equation (A.196). The partial derivatives needed are calculated in
equation (A.197), (A.198) and (A.199).
OF 
m top
(A.195)
qevap hlv,ref
2
2
2
 OF 
 OF 
2  OF 
2





u OF  
u mtop 
u qboiler   
u hlv 2

 m
 qevap 
 top 
 hlv 




(A.196)
OF
1


mtop qevap hlv
(A.197)
m top
OF

qevap q 2
evap hlv
(A.198)
m top
OF

2
hlv q
evap hlv
(A.199)
184

