Transcript
Page 1: Experimental investigations on boiling of n-pentane across a horizontal tube bundle: two-phase flow and heat transfer characteristics

Experimental investigations on boiling of n-pentane across ahorizontal tube bundle: two-phase ¯ow and heat transfer

characteristics

R. Roser, B. Thonon*, P. Mercier

Groupement ADEME/CEA pour la Recherche sur les Echangeurs Thermiques, CEA/Grenoble, DTP/GRETh, 17, rue des Martyrs,

38054 Grenoble Cedex 9, France

Received 14 January 1999; received in revised form 8 April 1999; accepted 9 April 1999

Abstract

This paper presents the heat transfer characteristics obtained from an experimental investigation on ¯ow boiling ofn-pentane across a horizontal tube bundle. The tubes are plain with an outside diameter of 19.05 mm and the bundlearrangement is inverse staggered with a pitch to diameter ratio of 1.33. The test conditions consist of reduced pressure

between 0.006 and 0.015, mass velocity from 14 to 44 kg/m2s, heat ¯ux up to 60 kW/m2 and vapor quality up to 60%.The convective evaporation is found to have a signi®cant e�ect on the heat transfer coe�cient, coexisting with nucleateboiling. An asymptotic model allows the prediction of the heat transfer data with a ®tted value of n=1.5. A strong

mass velocity e�ect is observed for the enhancement factor, implying that the correlations available from the literaturefor the convective evaporation will fail in predicting the present data. This e�ect decreases as the mass velocityincreases. # 1999 Elsevier Science Ltd and IIR. All rights reserved.

Keywords: Pentane; Boiling; Tube; Heat transfer; Heat transfer coe�cient

Etude expe rimentale de l'e bullition de n-pentane aÁ travers unfaisceau de tubes horizontal: e coulement diphasique et

caracte ristiques de transfert de chaleurRe sumeÂ

Cet article preÂsente les reÂsultats d'une eÂtude expeÂrimentale des caracteÂristiques de transfert de chaleur de l'eÂbullition den-pentane aÁ travers un faisceau de tubes horizontal. On a utilise des tubes lisses avec un diameÁtre exteÂrieur de 19,05 mm ;

la con®guration des tubes est en quinconce inverse avec une relation de 1,33 entre l'eÂcartement et le diameÁtre. Les condi-tions expeÂrimentales comprenaient : une pression reÂduite (entre 0,006 et 0,015), une vitesse massique de 14 aÁ 44 kg/m2s,un ¯ux thermique allant jusqu'aÁ 60 kW/m2 et une qualite de vapeur allant jusqu'aÁ 60%. On a eÂtabli que l'eÂvaporation

convective aÁ un e�et signi®catif sur le coe�cient de transfert de chaleur lors de l'eÂbullition nucleÂeÂe. Un modeÁle asympto-tique permet de preÂvoir les donneÂes de transfert de chaleur avec une valeur ajusteÂe de n=1,5. La vitesse massique a un e�etsur le facteur d'augmentation, ce qui montre que les correÂlations disponibles dans la litteÂrature ne seront pas ®ables pourpreÂvoir l'eÂvaporation convective dans le cas preÂsent. Cet e�et diminue en fonction de l'augmentation de la vitesse massique.

# 1999 Elsevier Science Ltd and IIR. All rights reserved.

Mots cleÂs: Pentane; Ebullition; Tube; Transfert de chaleur; Coe�cient de transfert de chaleur

0140-7007/99/$20.00 # 1999 Elsevier Science Ltd and IIR. All rights reserved.

PI I : S0140-7007(99 )00021-3

International Journal of Refrigeration 22 (1999) 536±547

www.elsevier.com/locate/ijrefrig

* Corresponding author.

E-mail addresses: [email protected] (R. Roser), [email protected] (B. Thonon)

Page 2: Experimental investigations on boiling of n-pentane across a horizontal tube bundle: two-phase flow and heat transfer characteristics

1. Introduction

Evaporators in which a boiling ¯uid ¯ows across ahorizontal tube bundle, like kettle reboilers, are widelyused as chiller-condensers in the refrigeration systems of

large ole®n and gas processing plants, where the refrig-erant is typically a hydrocarbon, such as propane orethane. The design of such equipment requires pressuredrop, void fraction and heat transfer correlations for

boiling two-phase ¯ow across tube bundles. The correla-tions available in the literature are limited to some givencouples of bundle geometry and ¯uid (mainly refriger-

ants), with moderate to high mass velocities. There is alack of data concerning typical operating conditions ofindustrial equipments: hydrocarbons as evaporating

¯uid with low mass velocity. The work by Goren¯o et al.[1,11,12] on boiling pure hydrocarbons and mixtureswere devoted to this subject, but the experiments wereperformed on a single tube (the bundle e�ect was simu-

lated by a ¯ow of bubbles produced in a tube located justbelow). The present investigation is part of an experi-mental program on the two-phase ¯ow and heat transfer

characteristics under the above industrial operating con-ditions. The current investigation concerns ¯ow boilingof n-pentane across a bundle of plain tubes, and will be

followed by testing di�erent types of enhanced tubesand di�erent hydrocarbons as the evaporating ¯uids.

2. Experimental apparatus and procedure

2.1. General description of the experimental apparatus

The experimental apparatus is shown in a cross-sec-tional schematic view in Fig. 1. The general con®guration

is representative of an industrial reboiler, but di�ers bythe presence of two vertical walls con®ning the ¯ow. In

this manner, the internal shellside recirculating ¯ow isavoided. Consequently, the mass ¯ow rate through thebundle can be controlled. The loop has been designed to

operate with ¯ammable ¯uids (hydrocarbons) under lowto moderate pressures (up to 16 bars). The operating¯uid (hydrocarbon) is pumped as saturated liquid fromthe shell of the boiler, then subcooled and re-entered to

the test section in the tube bundle channel, as shown inFig. 1. The subcooled liquid passes through a ¯owstraightener, enters the tube bundle where evaporation

takes place after the boiling point is reached, and ®nallypasses the weir level (the end of the channel walls) wherethe vapor separates from the liquid. The vapor, which

leaves the boiler by the top, is condensed and returnedto the shell where it mixes with the liquid pouring overthe weir. This con®guration reduces the two-phase ¯owinstabilities, allowing work with very low mass ¯uxes

which are representative of the typical industrial reboileroperating conditions.A schematic view of the test section, i.e. the vertical

channel containing the bundle, is shown in Fig 2. Thebundle geometry data are listed in Table 1. The innerwalls of the channel are ®tted with half-round solid tubes

in order to prevent ¯ow bypass. The heating power is sup-plied by a hot ¯uid (water-glycol solution) ¯owing insidethe tubes. Only the full tubes are heated (two or three

tubes per row, successively). The hot ¯uid ¯ow is dis-tributed in 9 pipes with equal mass ¯ow rates m

:h. Each

pipe supplies a group of 5 tubes (2 consecutive arrays of3 and 2 tubes) connected in series with alternative ¯ow

directions, as shown in the left diagram of Fig. 2.The hydrocarbon ¯ow rate can be varied up to 3000 l/h

(approximately 50 kg/m2s for light hydrocarbons related

Nomenclature

Amin Minimum cross section area A [m2]D Tube diameter [m]F Enhancement factor

G Mass velocity [kg/m2s]L Tube length [m]m:

Mass ¯ow rate [kg/s]

n Asymptotic model orderP Pitch between tube centers [m]p Pressure [Pa]

Q:

Heat rate [W]q Heat ¯ux related to outside tube surface [W/m2]Rw Wall heat transfer resistance [Wÿ1m2K]

S Tube surface (5 tubes) [m2]T Temperature [K]U Overall heat transfer coe�cient [W/m2K]x Vapor quality

Greek letters� Heat transfer coe�cient [W/m2 K]" Void fraction

�2L Two-phase ¯ow multiplier

�T E�ective temperature di�erence [K]�Tw Wall-¯uid temperature di�erence [K]

Subscripts1,2 Inside, outside tube

c Cold ¯uid (hydrocarbon)cv Convectiveh Hot ¯uid

i InletL Liquido Outletnb Nucleate boiling

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to the minimum cross-section area). The hot ¯uid tem-perature can be adjusted between ÿ25 and 125�C, pro-viding up to 70 kW (60 kW/m2 related to the apparentoutside tube surface).

The measurements performed on the test section areaimed at evaluating the outside heat transfer coe�cient,

the heat ¯ux, and the thermal and hydrodynamic con-ditions of boiling n-pentane. The measured variables areshown in Figs. 2 and 3. With respect to the hot ¯uid, aheat balance is performed for each of the 9 groups of

tubes from the measurement of the mass ¯ow rate (m:h)

and the inlet and outlet temperatures (Thi j� �;Tho j� �).Concerning the n-pentane, the measurements in the

bundle are the temperatures every two rows of tubes(Tc 1� �; . . . ;Tc 9� �), the pressure drop between the topand the bottom of the bundle, and the local void frac-

tion at di�erent positions along the linear motion of anoptical probe. The entrance conditions of the hydro-carbon are known from the measurement of the tem-

perature Tc 0� �, the pressure p 0� � and the mass ¯ow ratem:c.

2.2. Experimental conditions

The present experiment has been conducted withcopper plain tubes with an inside and outside diameter

of 15.7 and 19 mm, respectively. All the tubes havebeen treated by polishing the outside surface using 400grid emery paper. The rugosity measured at di�erent

positions of several tubes randomly selected had a meanvalue of Ra=0.4 mm. The hydrocarbon used was puren-pentane. The nominal experimental conditions are lis-

ted in Table 2. Note that the pressures tested are verylow. This is because the present investigation is aimed atstudying the convective heat transfer mechanism, whichis signi®cant at low pressure.

For each combination of pressure level and massvelocity, the global heat ¯ux has been varied from 10 to60 kW/m2 with an increasing step of 5 kW/m2 between

Fig. 1. Experimental apparatus (cross-sectional schematic

front view).

Fig. 1. Appareil expeÂrimental (scheÂma en coupe vu de devant).

Fig. 2. Test section schematic view and ¯ow distribution arrangement.

Fig. 2. ScheÂma de la section d'essai avec disposition de l'eÂcoulement.

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tests. In total, 95 test runs were performed (not all thecombinations of pressure, mass velocity and heat ¯ux

were tested).

2.3. Data reduction

2.3.1. Analysis and selection of the dataThe present work focuses on the study of ¯ow boiling

under the following ideal conditions.

. The liquid and vapor are saturated and under

thermodynamic equilibrium.. The ¯ow, from a macroscopic point of view, is

one-dimensional, upward.

The validity of the above ideal conditions has beenchecked for all the experiments, and the data out of ithave been rejected for the purpose of the present inves-

tigation. Each test has been analysed individually inorder to select the data, as explained in the following.The data rejected concern the ®rst and the end rows of

the bundle. With regard to the ®rst rows, there are twophenomena which make the local conditions far fromthe ideal: the subcooled state of the liquid at theentrance of the bundle and the non-homogeneous or

non-ideal two-phase mixture. These phenomena can bedetected by analysing the n-pentane temperature pro®lealong the bundle, as shown in the following. The tests

have been arranged in sets of ®xed pressure and massvelocity, and plotted together as shown in Fig. 5 (onlytwo tests are shown for a better clarity). In order toallow a proper comparison between di�erent tests, the

n-pentane temperatures have been reduced to its di�er-ence with respect to the temperature at the exit Tc 9� �. Inaddition, the hydrostatic pressure drop corresponding

to all liquid between the entrance and the exit of thebundle has been calculated and transformed into asaturated temperature di�erence. The later is repre-

sented by the solid line in the ®gure. Let us consider thetest at x 9� � � 35%. The temperature pro®le looks like atypical ¯ow boiling pattern with subcooled liquid at the

entrance: the temperature increases up to the saturatedtemperature (the boiling point) and then stays equal tothe last, which decreases due to the pressure drop. Theposition of the boiling point evaluated from the heat

balance is in agreement with the location of the max-imum in the temperature pro®le. The entrance e�ectsare then assumed to be limited to the ®rst and the sec-

ond group of tubes (the later is included to give reason-able margin), and consequently the data correspondingto these two groups are rejected. If we consider now the

test at x 9� � � 13%, we can see that the pattern is quitedi�erent. The temperature increases up to the thirdgroup, then fails within only one group, and recovers

approximately the same level of slope as the other tests(the same order of magnitude as the hydrostatic refer-ence, the solid line). The huge temperature dropbetween the third and the fourth group cannot be rela-

ted to the pressure drop under saturated conditions,because it is by far too high. Moreover, the boiling pointcalculated from the heat balance is located in the ®rst

group of tubes. This is in clear disagreement with thetemperature pro®le in which the maximum is located in

Table 1

Bundle geometry

Tableau 1

GeÂomeÂtrie du faisceau

Tube outside diameter D=19.05 mm

Tube length L=500 mm

Pitch to diameter ratio P/D=1.33

Arrangement Staggered inverse equilateral

Number of colums 5

Number of rows 18 (9 groups�2 rows/group)

Number of tubes 45

Minimum cross-section area Amin=6*(P±D)*L=0.01886 m2

Table 2

Test conditions

Tableau 2

Conditions d'essai

Fluid n-pentane

Pressure 0.2; 0.3 and 0.5 bar

Reduced pressure 0.006; 0.009 and 0.015

Mass velocity 14; 22; 30; 37 and 44 kg/m2 s

Global heat velocity 10±60 kW/m2

Vapor quality 0±60%

Fig. 3. Location of probes on the hydrocarbon ¯ow.

Fig. 3. Emplacements des capteurs mesurant l'eÂcoulement

d'hydrocarbures.

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the third group. Then, in this case, the entrance e�ectsare not only the subcooled state, but also a departurefrom the thermodynamic equilibrium. It is not clearwhether the later is due to an non-homogeneous ¯ow or

a liquid superheating due to the high compacity of thebundle. In any case, the data from the groups 1 to (andincluding) 5 have been rejected (the later is included to

give reasonable margin).Concerning the end rows, it has been observed for

some tests, a drop of the heat transfer coe�cient indi-

cating a dry-out. The data accepted for the analysis inthe present work are always below this point. Finally,the data concerning the end group of 5 tubes have been

rejected systematically because they are a�ected by theexit from the bundle (the heat transfer coe�cient isalways signi®cantly higher). For all the tests, it has beenchecked that the hydrocarbon entering the test section is

in subcooled liquid state. No tests have been performedunder saturated liquid at the entrance of the bundle,since the test facility does not allow the control of the

cooler with enough accuracy. All the data were collectedunder steady state conditions.On the whole, from the 855 set of data collected (1 set

per group of tubes � 9 groups � 95 tests), 429 have beenselected for the present analysis in accordance with theabove criteria.

2.3.2. Heat balance, heat ¯ux and vapor qualityA heat balance is performed for each of the 9 groups

of tubes, giving the total heat rate Q:j� � delivered by the

group j. The tube bundle is divided in 9 control volumesCV j� � corresponding to each of the 9 groups of tubes asshown in Fig. 4. The horizontal boundaries of the con-

trol volumes are coincident with the locations of thetemperature probes Tc 1� � to Tc 9� �. Because of the highcompactness of the bundle, there is no horizontal line

crossing between two consecutive rows and then thecontrol volumes cuts across the tubes. The heat rates

corresponding to each control volume Q:

CV j� � are eval-uated from the heat rates Q

:j� � by interpolation. The

mean heat ¯ux q j� � for each control volume is calculatedfrom the heat rate Q

:CV j� �. The thermodynamic vapor

quality x j� � on the top boundary of each control volumej is deduced from a heat balance involving all the con-trol volumes from 1 to j.

2.3.3. Heat transfer coe�cient and outside tubetemperature

For each control volume j �1±9, an overall heattransfer coe�cient is calculated by:

U j� � � q j� ��T j� � �1�

The e�ective temperature di�erence is evaluated froma log mean formula:

�T j� � � Thi j� � ÿ Tho j� �ln

Thi j� � ÿ Tcm j� �Tho j� � ÿ Tcm j� �� �

Tcm j� � � Tc j� � � Tc jÿ 1� �2

�2�

The external heat transfer coe�cient �2 j� � is thendeduced from the relation:

U j� � � 1

S2

S1

1

�1 j� � � S2Rw � 1

�2 j� ��3�

The tube side heat transfer coe�cient �1 j� � is calculatedfrom the correlation of Gnielinsky [8]. Speci®c experi-mental tests were performed in order to ®t a tube side

Fig. 4. Control volumes for one-dimensional analysis.

Fig. 4. Volumes de controÃle pour l'analyse unidimensionnelle.

Fig. 5. n-pentane temperature pro®le. Analysis of entrance

e�ects. (The `group of tubes' n�0 represents the temperature

Tc 0� � at the entrance of the bundle).Fig. 5. Pro®l de tempeÂrature du n-pentane. E�et de l'entreÂe du

faisceau.

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heat transfer correlation using the Wilson plot method.The tests were conducted using outside enhanced tubesunder high pressure and high mass velocity, in order toobtain a high external heat transfer coe�cient. The

values obtained from the ®tted correlation were veryclose to the ones predicted by the general correlation ofGnielinsky [8], so the last was ®nally adopted. The hot

¯uid circulating inside tubes was 20% water±glycolsolution. Its physical properties were de®ned throughspeci®c measurements and ®tted with respect to the

temperature. In all the tests performed in the presentwork, the hot ¯uid ¯owrate was more or less the same.The Reynolds number was approximately 35,500, and

the tube side heat transfer coe�cient 11,500 W/m2K.Finally, a mean value of the outside tube wall tempera-ture Tw j� � is deduced from:

q j� � � �2 j� � Tw j� � ÿ Tcm j� �� � �4�

2.3.4. Nucleate boiling and convective evaporation

The variables treated in this section are applied to thecontrol volumes j=1±9. The notation j� �, which makes

reference to the control volume number j, has beenomitted for a better clarity of the formulas.For ¯ow boiling, the total heat ¯ux is classically

assumed to have two components: convective evapora-tion and nucleate boiling. According to the recommen-dations of Webb et al. [15] for ¯ow boiling across abank of tubes, the asymptotic model has been adopted:

q � qnnb � qncv

ÿ �1n �5�

Each component of the heat ¯ux is related to a spe-ci®c heat transfer coe�cient but to the same tempera-

ture di�erence:

q � �2�Tw �6�

qnb � �nb�Tw �7�

qcv � �cv�Tw �8�

The nucleate boiling heat transfer coe�cient is calcu-lated from:

�nb � a qnb� �b �9�

which is the usual form of the correlations for nucleatepool boiling available in the literature. It should benoted that the heat ¯ux involved here is not the total,but only the nucleate boiling component. Several corre-

lations for nucleate pool boiling on a single horizontaltube have been tested for the evaluation of the para-meters a and b. The nucleate boiling heat ¯ux qnb, the

convective heat ¯ux qcv and the convective heat transfercoe�cient �cv can be evaluated from the above expres-sions and from the experimental values of �Tw and q.The enhancement factor is de®ned as the ratio

between the convective heat transfer coe�cient �cv andthe heat transfer coe�cient �L to the liquid phase ¯ow-ing alone, i.e. with a mass rate equal to 1ÿ x� �m: c:

F � �cv

�L�10�

The heat transfer coe�cient �L is evaluated using thecorrelations of Gnielinsky et al. [9] for forced convective

¯ow through a bank of plain tubes.The above expressions have been applied for each

group of tubes j using the corresponding experimentalvalues of the wall superheat and total heat ¯ux: �Tw �Tw j� � ÿ Tcm j� � and q � q j� �.

3. Results and analysis

3.1. Pro®les of hydrocarbon temperature and heat

transfer coe�cient

A typical set of data for one test is shown in Figs. 6(a)

and 6(b). The hydrocarbon enters the bundle in sub-cooled liquid state (corresponding to group 0 on the®gure). The temperature rises on the ®rst rows of tubesdue to sensible heating, reaches a peak corresponding

approximately to the boiling point, then decreases dueto the pressure drop under saturated state (no non-idealmixture e�ect was observed in this test, according to the

analysis discussed previously referring to Fig. 5). Theso-called bundle e�ect is visible in Fig. 6(b): althoughthe inlet temperature of the hot ¯uid is mainly the same

throughout the bundle, a signi®cant increase of the heattransfer coe�cient is observed with the increase of thevapor quality from the bottom to the top of the bundle[each dot in Fig. 6(b) corresponds to a group of tubes

with increasing row number from the left to the right, asin Fig. 6(a)].

3.2. Heat transfer mechanisms

As a ®rst step, in Fig. 7(a), the heat transfer coe�cient

�2 j� � is plotted versus the heat ¯ux q j� � for all the data,without distinction of pressure, mass velocity or vaporquality. A fairly good correlation seems to be achieved

with the usual type of expression for pool boiling (thethick line on the ®gure):

�2 � aqb �11�

From this pattern, one could conclude that the heattransfer coe�cient depends mainly on the heat ¯ux, and

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not on the hydrodynamics; this is to say that the dom-

inating heat transfer mechanism should be nucleateboiling, and not convective evaporation. However, theuse of correlations for single tube pool boiling results in

a signi®cant underestimation of the experimental data.This is shown in Figs. 7(b) to (d) where four of thesecorrelations based on the expression (11) (Cornwell etal. [3], Stephan et al. [13], Goren¯o [10] and Cooper [4])

are checked for each of the three tested pressures. Asigni®cant scatter is observed between them. Whereasthe correlations of Cornwell et al. [3] and Stephan et al.

[13] are similar, the correlation of Goren¯o [10] giveslower values at low pressure and low heat ¯ux. Thecorrelation of Cooper [4] seems to give overestimated

values compared to the other three. The solid line in the®gures represents the ®tted expression (11) to theexperimental data. As said, the heat transfer coe�cient

for single tube pool boiling is well under the experi-mental. Moreover, the value of the exponent b for theexperimental correlation (b�0.35) is lower than thevalue for pool boiling (b�0.67, except for Goren¯o [10]

were b is greater and varies with pressure). Furthermore,the e�ect of pressure seems to be much less signi®cant inour tests than for single tube pool boiling, as can be seen

in Fig. 7(e), where the ®tted expressions (11) are plottedtogether with the correlation of Cornwell et al. [3] forthe three tested pressures.Dowlati et al. [7] also correlated their data for R-113

in ¯ow boiling through a bank of plain tubes by usingthe expression (11). They found also a signi®cantunderestimation of their data by the use of the correla-

tions for pool boiling, as well as an exponent b less than0.67.In Fig. 8, the heat transfer coe�cient is plotted versus

the heat ¯ux for a set of tests with ®xed conditions ofpressure and mass velocity. Each line in the ®gurerepresents the data obtained for one test, i.e. one heat

rate, which is equivalent to one vapor quality at the exitx 9� �. The di�erent dots in each line represent the di�er-ent control volumes in the bundle (the heat transfercoe�cient rising with the height in the bundle). The ®g-

ure clearly shows a signi®cant e�ect of the vapor qual-ity. The same trends have been obtained for all thecombinations of pressure and mass velocity tested. The

convective heat transfer mechanism is then signi®cant,despite the apparent exclusive part of the heat ¯ux sug-gested by Fig. 7(a). In fact, this appearance is due to the

link between the heat ¯ux, the heat transfer coe�cientand the vapor quality. The rise of the heat transfercoe�cient observed for each test between the bottom

and the top of the bundle is a consequence of anincrease of the vapor quality, and not directly of the riseof the heat ¯ux.In Fig. 9 the ratio between the nucleate boiling heat

¯ux, calculated from the Eqs. (7) and (9), and the totalheat ¯ux is plotted versus the measured total heat ¯ux.The ®gure suggests that the nucleated boiling accounts

only for a minor part of the total heat transfer. Thee�ect of pressure is also shown: the lower the pressure,the lower the part of the nucleate boiling, compared to

the total heat ¯ux. This trend is in agreement with thewell known increase of the nucleate boiling heat transfercoe�cient with pressure.

3.3. Asymptotic model and convective heat transfer

3.3.1. Asymptotic model

The asymptotic model de®ned by the set of Eqs. (5)±(10) has been adopted for the evaluation of the totalheat transfer coe�cient, accounting for convective eva-

poration and nucleate boiling. The convective liquidheat transfer coe�cient (�L) is calculated using the cor-relation of Gnielinsky et al. [9] for single-phase ¯ow

across a bank of plain tubes. If a single tube pool boil-ing correlation is adopted for the evaluation of �nb, theonly unknowns are the order n of the asymptotic modeland the enhanced factor F. If a value of n is assumed, an

experimental value of F can be deduced from the data.Of course, the latter will depend on the choice of thecorrelation for �nb. Two correlations have been tested in

Fig. 6. (a) Hydrocarbon temperature pro®le. (b) Heat ¯ux,

heat transfer coe�cient and vapor quality.

Fig. 6. (a) Pro®l de tempeÂrature de l'hydrocarbure. (b) Flux

thermique, coe�cient de transfert de chaleur et qualite de la

vapeur.

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Fig. 7. (a) Heat transfer coe�cient vs total heat ¯ux for all the data (npb: correlation of Cornwall et al. [3] for nucleate pool boiling).

(b) Heat transfer coe�cient vs total heat ¯ux for p=0.2 bar. Comparison with single tube pool boiling correlations. (c) Heat transfer

coe�cient vs total ¯ux for p=0.3 bar. Comparison with single pool boiling correlations. (d) Heat transfer coe�cient vs total heat for

p=0.5 bar. Comparison with single tube pool boiling correlations. (e) Heat transfer coe�cient vs total heat ¯ux for all the data (npb:

correlation of Cornwell et al. [3] for nucleate pool boiling). E�ect of pressure on the experimental ®tted correlation (lower: 0.2 bar,

intermediate: 0.3 bar, upper: 0.5 bar).

Fig. 7 (a) Coe�cient de transfert de chaleur en fonction du ¯ux thermique total (correÂlation de Cornwell et al. [3] pour l'eÂbullition nucleÂeÂe

libre). (b) Coe�cient de transfert de chaleur en fonction du ¯ux thermique pour une pression de 0,2 bar. Comparaison avec les correÂla-

tions de l'eÂbullition libre aÁ tube unique. (c) Coe�cient de transfert de chaleur en fonction du ¯ux thermique pour une pression de 0,3 bar.

Comparaison avec les correÂlations de l'eÂbullition libre aÁ tube unique. (d) Coe�cient de transfert de chaleur en fonction du ¯ux thermique

pour une pression de 0,5 bar. Comparaison avec les correÂlations de l'eÂbullition libre aÁ tube unique. (e) Coe�cient de transfert de chaleur

en fonction du ¯ux thermique pour toutes les donneÂes (correÂlation de Cornwell et al. [3] pour l'eÂbullition nucleÂeÂe libre). E�et de la pression

sur la correÂlation trouveÂe expeÂrimentalement (courbes infeÂrieures : 0,2 bar ; courbes intermeÂdiaires : 0,3 bar ; courbes supeÂrieures : 0,5 bar).

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the present analysis: Cornwell et al. [3] and Goren¯o[10]. The other, Stephan et al. [13] and Cooper [4], arenot considered [the ®rst because of the similarity with

Cornwell et al. [3] and the second because it gives over-estimated values of �nb, as discussed previously withrespect to Fig. 7(b) to 7(d)].

The correlation of Cornwell et al. [3] has been con-sidered ®rst for the calculation of �nb. The data havebeen arranged in di�erent sets of experiments corre-sponding to a ®xed pressure and a ®xed mass velocity,

and the enhancement factor F has been plotted versusthe local vapor quality x for a value of n varying from 1to 10. It has been observed that F and x are notably well

correlated for a ®xed value of n=1.5, as can be seen inFigs. 10 to 12. Moreover, this value is the same for all thesets, suggesting that n is independent on the pressure and

on the mass velocity. If n moves away from the ®ttedvalue n=1.5, the correlation between F and x declines

very quickly, disappearing almost completely for highvalues of n. This is clearly shown in Fig. 13 for a valueof n=3. It has to be noted that in the above analysis the

level of correlation between F and x has been quanti®edby ®tting an exponential function to each set of tests(each combination of pressure and mass velocity).The same analysis has been performed using the cor-

relation of Goren¯o [10] for the calculation of �nb. Thevalue of n giving the best correlation between F and x

Fig. 8. Heat transfer coe�cient vs total heat ¯ux for ®xed

pressure and mass velocity and di�erent heat rates.

Fig. 8. Coe�cient de transfert de chaleur en fonction du ¯ux

thermique pour des pressions et de la vitesse massique reÂgleÂes et

divers rendements thermiques.

Fig. 9. Ratio between nucleate boiling and total heat ¯ux vs

total heat ¯ux.

Fig. 9. Relation entre l'eÂbullition nucleÂeÂe et les ¯ux thermiques

totaux en fonction du ¯ux thermique total.

Fig. 10. F factor vs vapor quality (P=0.5 bar). �nb:correlation

of Cornwell et al. [3] for single tube pool boiling. Order of the

asymptopic model: n=1.5.

Fig. 10. Relation entre le facteur f et la qualite de la vapeur

(P=0,5 bar). �nb : correÂlation de Cornwell et al. [3] pour pour

l'eÂbullition libre et un tube simple. Ordre du modeÁle asymptotique :

n=1,5.

Fig. 11. F factor vs vapour quality (P=0.3 bar). �nb: correla-

tion of Cornwell et al. [3] for single tube pool boiling. Order of

the asymptotic model: n = 1.5.

Fig. 11. Relation entre le facteur f et la qualite de la vapeur

(P=0,3 bar). �nb : correÂlation de Cornwell et al. [3] pour pour

l'eÂbullition libre et un tube simple. Ordre du modeÁle asympto-

tique : n=1,5.

544 R. Roser et al. / International Journal of Refrigeration 22 (1999) 536±547

Page 10: Experimental investigations on boiling of n-pentane across a horizontal tube bundle: two-phase flow and heat transfer characteristics

has been found to be dependent on the pressure: n=2.2for p=0.5 bar and n=1.2 for p=0.3 bar. At the lowerpressure, p=0.2 bar, the value of n has no e�ect on theplot of F against x. This is because the values of �nb

predicted by the correlation of Goren¯o [10] are so lowcompared to the total heat transfer coe�cient that thecontribution of the nucleate boiling is no signi®cant.

In any case, the best level of correlation between Fand x obtained using the correlation of Cornwell et al.[3] is signi®cantly higher than the one obtained using thecorrelation of Goren¯o [10]. For this reason, the ®rst

has been selected.The ®tted value of n=1.5 di�ers from the value n=3

proposed by Webb et al. [15] for R-113 boiling on dif-

ferent tube bundles. However, it is not clear whether intheir investigations these authors have ®tted the value ofn to the experimental data or this value has been ®xed

previously. In any case, the adoption of n=3 for thepresent data leads to a very poor correlation between Fand x. On the other hand, the present results do not

agree with the model proposed by Cornwell [2], in whichn ! 1 (implying no superposition of nucleate boilingand convective evaporation). On the contrary, the pre-sent results indicate clearly that the two heat transfer

mechanisms coexist. It should be noted that the modelof Cornwell [2] was ®tted for R-113 with relatively highmass velocities, but the author observed that the model

failed for the few data collected under low mass velo-cities, which is the case of the present work.

3.3.2. Enhancement factorAs quoted above, a notably good correlation between

F and x is observed in Figs. 10±12. However, an e�ect of

the mass velocity appears clearly: the correlationbetween F and x depends on the mass velocity. This is asigni®cant result, implying that the F factor can not becorrelated only to the vapor quality and the ¯uid den-

sities (the last are practically constant for a ®xed pres-sure in our experiment). Consequently, all thecorrelations recommended up to now for the evaluation

of the F factor (see the review of Webb et al. [15]), whichare based only on the above variables, fail into predict-ing the present data.

Another interesting trend can be observed in these®gures: as the mass velocity increases, the curves seemsto concur to a single correlation, suggesting that themass velocity e�ect is signi®cant only for low values of

G.There is no available data in the literature related to

the mass velocity e�ect on the enhanced factor F. The

only data concerning a ¯ow boiling under low massvelocities are those from the work of Webb et al. [14].Unfortunately, these authors did not focus their work

on the study of the enhancement factor. However, thepresent results are consistent with the observations ofDowlati et al. [5±7] concerning the pressure drop in

vertical two-phase ¯ows through di�erent banks oftubes. A strong mass velocity e�ect was observed on thetwo-phase ¯ow multiplier �2

L for low mass velocities,both for adiabatic air-water and R-113 boiling ¯ows

(the e�ect was signi®cant for G < 200 kg/m2s for the®rst case and G < 100 kg/m2s for the second). More-over, the authors observed that the mass velocity e�ect

Fig. 13. F factor vs vapour quality (P=0.3 bar). �nb: correla-

tion of Cornwell et al. [3] for single tube pool boiling. Order of

the asymptotic model: n=3.

Fig. 13. Relation entre le facteur f et la qualite de la vapeur

(P=0,3 bar). �nb : correÂlation de Cornwell et al. [3] pour

l'eÂbullition libre et un tube simple. Ordre du modeÁle asympto-

tique : n=3.

Fig. 12. F factor vs vapour quality (P=0.2 bar). �nb: correla-

tion of Cornwell et al. [3] for single tube pool boiling. Order of

the asymptotic model: n=1.5.

Fig. 12. Relation entre le facteur f et la qualite de la vapeur

(P=0,2 bar). �nb : correÂlation de Cornwell et al. [3] pour pour

l'eÂbullition libre et un tube simple. Ordre du modeÁle asympto-

tique : n=1,5.

R. Roser et al. / International Journal of Refrigeration 22 (1999) 536±547 545

Page 11: Experimental investigations on boiling of n-pentane across a horizontal tube bundle: two-phase flow and heat transfer characteristics

decays as the value of G is increased. The mass velocitye�ect on the F factor and on the �2

L parameter are prob-ably the consequence of the same hydrodynamic phenom-

ena according to heat and momentum transfer analogy.The above analysis suggests that a proper evaluation

of the convective vaporization for low mass velocities

requires the use of other variables than the vapor qual-ity. The use of the void fraction, and then the velocitiesof liquid and vapor, will be probably more successful.

The evaluation of the void fraction is then an essentialtask. This is part of the current investigation performedin GRETh laboratory.

4. Conclusions

The present investigation leads to the following mainconclusions related to the heat transfer characteristics ofn-pentane in ¯ow boiling through a bank of plain tubes

with low mass velocity and low reduced pressure:

. Convective evaporation plays a signi®cant part onthe total heat transfer.

. An asymptotic model has been tested using thecorrelations of Cornwell et al. [3] for nucleateboiling and Gnielinsky et al. [9] for liquid convec-

tion. A value of n=1.5 has been found to give avery good correlation between the enhancementfactor and the vapor quality.

. A signi®cant mass velocity e�ect has beenobserved for the F factor. This e�ect decreases asthe mass velocity G increases, and is expected to

disappear for high enough values of G. The massvelocity e�ect on F is probably linked to the samee�ect on �2

L observed by Dowlati et al. [5±7]re¯ecting an analogy between heat and momen-

tum transfer.. The mass velocity e�ect on the F factor implies

that the available correlations from the literature

fail in predicting the present data. It is suggested

that the use of the void fraction instead of thevapor quality would be more successful for thecalculation of the convective heat transfer.

Acknowledgements

This project is partially supported by the Commission

of the European Communities within the framework ofthe Non Nuclear Energy Program JOULE III, contractN� JOE3-CT97-0061 (DG 12 - WSMN).

Appendix: Instrumentation and experimental uncertainty

The instrumentation related to the measurementsconsidered in this work is listed in Table 3. All the tem-perature probes (RTDs and thermocouples) were cali-

brated using an isothermal bath system. The calibrationwas performed for the ®nal output of each channel, i.e.including the entire system: probe+extension wire+data acquisition system.

The experimental uncertainty on the heat ¯ux q j� �, theheat transfer coe�cient �2 j� � and the vapor quality x j� �has been evaluated taking into account ®xed and vari-

able uncertainties in all the measured quantities onwhich they depend. The uncertainty in �2 j� � alsoincludes the uncertainty related to the use of the corre-

Table 3

Instrumentation

Tableau 3

Instrumentation

Variables involved Manufacturer Model Type

Absolute pressure transducers P�0�;P�1� Endress+Hauser PMC 731 Ceramic sensor

Di�erential pressure transducer �P Endress+Hauser PMD 130 Ceramic sensor

Flowmeter m:c Rosemount MicroMotion DS 100 S Mass ¯owmeter

Flowmeter m:h Endress+Hauser Promag 33 Volumetric ¯owmeter

Temperature probes Thi�j� � 1ÿ9Tho�j� � 1ÿ9 Endress+Hauser Pt100 DINIEC751 Platinum RTD 2 wires,

class B 1.6 mm O.D.

Temperature probes Tc�j� � 0ÿ9 ThermoEst K-Type 3 wires,

class 2 1.0 mm O.D.

Data acquisition system all FLUKE Helios I

Table 4

Fixed uncertainty in the measurements

Tableau 4

PreÂcision des mesures

Temperature 0.1 K

Pressure 0.2%

Outside tube ¯ow rate 0.2%

Inside tube ¯uid ¯ow rate 0.5%

546 R. Roser et al. / International Journal of Refrigeration 22 (1999) 536±547

Page 12: Experimental investigations on boiling of n-pentane across a horizontal tube bundle: two-phase flow and heat transfer characteristics

lation of Gnielinsky [8] for the evaluation of �1 j� �. Thelast has been evaluated as �10%. The maximum ®xederrors for all the measurements are show in Table 4. Thevariable uncertainty in the measured values comes from

their slight oscillation in time around the mean valueunder steady state conditions. It has been evaluatedfrom 12 successive samples at 40 s intervals.

The uncertainties in the heat ¯ux, the heat transfercoe�cient and the vapor quality evaluated as quotedabove are shown in Fig. 14.

For the heat ¯ux and the vapor quality, the uncer-tainty comes mainly from the assumed �0.1 K max-imum ®xed error in the inside tube temperature probes

from which heat balances are performed. For the out-side tube heat transfer coe�cient, the �10% uncer-tainty in the inside tube heat transfer coe�cient carriesalso a signi®cant weight.

References

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heat transfer of propane/n-butane mixtures at a single tube

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ference, Brighton, UK, 1994, Vol 5, pp. 69±74.

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Fig. 14. Experimental uncertainties.

Fig. 14. Erreurs expeÂrimentales.

R. Roser et al. / International Journal of Refrigeration 22 (1999) 536±547 547


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