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

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  • Experimental investigations on boiling of n-pentane across ahorizontal tube bundle: two-phase flow 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 flow 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 flux up to 60 kW/m2 and vapor quality up to 60%.The convective evaporation is found to have a significant eect on the heat transfer coecient, coexisting with nucleateboiling. An asymptotic model allows the prediction of the heat transfer data with a fitted value of n=1.5. A strong

    mass velocity eect 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 eect decreases as the mass velocityincreases. # 1999 Elsevier Science Ltd and IIR. All rights reserved.

    Keywords: Pentane; Boiling; Tube; Heat transfer; Heat transfer coecient

    Etude experimentale de lebullition de n-pentane a` travers unfaisceau de tubes horizontal: ecoulement diphasique et

    caracteristiques de transfert de chaleurResume

    Cet article presente les resultats dune etude experimentale des caracteristiques de transfert de chaleur de lebullition den-pentane a` travers un faisceau de tubes horizontal. On a utilise des tubes lisses avec un diame`tre exterieur de 19,05 mm ;

    la configuration des tubes est en quinconce inverse avec une relation de 1,33 entre lecartement et le diame`tre. Les condi-tions experimentales comprenaient : une pression reduite (entre 0,006 et 0,015), une vitesse massique de 14 a` 44 kg/m2s,un flux thermique allant jusqua` 60 kW/m2 et une qualite de vapeur allant jusqua` 60%. On a etabli que levaporation

    convective a` un eet significatif sur le coecient de transfert de chaleur lors de lebullition nucleee. Un mode`le asympto-tique permet de prevoir les donnees de transfert de chaleur avec une valeur ajustee de n=1,5. La vitesse massique a un eetsur le facteur daugmentation, ce qui montre que les correlations disponibles dans la litterature ne seront pas fiables pourprevoir levaporation convective dans le cas present. Cet eet diminue en fonction de laugmentation de la vitesse massique.

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

    Mots cles: Pentane; Ebullition; Tube; Transfert de chaleur; Coecient 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) 536547

    www.elsevier.com/locate/ijrefrig

    * Corresponding author.

    E-mail addresses: roser@dtp.cea.fr (R. Roser), thonon@dtp.cea.fr (B. Thonon)

  • 1. Introduction

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

    large olefin 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 flow across tube bundles. The correla-tions available in the literature are limited to some givencouples of bundle geometry and fluid (mainly refriger-

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

    fluid with low mass velocity. The work by Gorenflo 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 eect was simu-

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

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

    followed by testing dierent types of enhanced tubesand dierent hydrocarbons as the evaporating fluids.

    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 configuration

    is representative of an industrial reboiler, but diers bythe presence of two vertical walls confining the flow. In

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

    operate with flammable fluids (hydrocarbons) under lowto moderate pressures (up to 16 bars). The operatingfluid (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 flowstraightener, enters the tube bundle where evaporation

    takes place after the boiling point is reached, and finallypasses 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 configuration reduces the two-phase flowinstabilities, allowing work with very low mass fluxes

    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 fitted with half-round solid tubes

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

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

    :h. Each

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

    directions, as shown in the left diagram of Fig. 2.The hydrocarbon flow 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 flow rate [kg/s]

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

    Q:

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

    1m2K]S Tube surface (5 tubes) [m2]T Temperature [K]U Overall heat transfer coecient [W/m2K]x Vapor quality

    Greek letters Heat transfer coecient [W/m2 K]" Void fraction2L Two-phase flow multiplierT Eective temperature dierence [K]Tw Wall-fluid temperature dierence [K]

    Subscripts1,2 Inside, outside tube

    c Cold fluid (hydrocarbon)cv Convectiveh Hot fluid

    i InletL Liquido Outletnb Nucleate boiling

    R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547 537

  • to the minimum cross-section area). The hot fluid tem-perature can be adjusted between 25 and 125C, 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 coecient,

    the heat flux, 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 fluid, aheat balance is performed for each of the 9 groups of

    tubes from the measurement of the mass flow 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 dierent 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 flow 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 dierent

    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 significant at low pressure.

    For each combination of pressure level and massvelocity, the global heat flux 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 experimental (schema en coupe vu de devant).

    Fig. 2. Test section schematic view and flow distribution arrangement.

    Fig. 2. Schema de la section dessai avec disposition de lecoulement.

    538 R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547

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

    were tested).

    2.3. Data reduction

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

    under the following ideal conditions.

    . The liquid and vapor are saturated and underthermodynamic equilibrium.

    . The flow, from a macroscopic point of view, isone-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 first and the end rows of

    the bundle. With regard to the first 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 profilealong the bundle, as shown in the following. The tests

    have been arranged in sets of fixed 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 dierent tests, the

    n-pentane temperatures have been reduced to its dier-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 dierence. The later is repre-

    sented by the solid line in the figure. Let us consider thetest at x 9 35%. The temperature profile looks like atypical flow 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 profile. The entrance eectsare then assumed to be limited to the first 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 quitedierent. 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 first

    group of tubes. This is in clear disagreement with thetemperature profile in which the maximum is located in

    Table 1

    Bundle geometry

    Tableau 1

    Geometrie 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 groups2 rows/group)Number of tubes 45

    Minimum cross-section area Amin=6*(PD)*L=0.01886 m2

    Table 2

    Test conditions

    Tableau 2

    Conditions dessai

    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 1060 kW/m2

    Vapor quality 060%

    Fig. 3. Location of probes on the hydrocarbon flow.

    Fig. 3. Emplacements des capteurs mesurant lecoulement

    dhydrocarbures.

    R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547 539

  • the third group. Then, in this case, the entrance eectsare not only the subcooled state, but also a departurefrom the thermodynamic equilibrium. It is not clearwhether the later is due to an non-homogeneous flow 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 coecient 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 aected by theexit from the bundle (the heat transfer coecient isalways significantly 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 flux 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 flux 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 coecient and outside tubetemperature

    For each control volume j 19, an overall heattransfer coecient is calculated by:

    U j q j T j 1

    The eective temperature dierence is evaluated froma log mean formula:

    T j Thi j Tho j ln

    Thi j Tcm j Tho j Tcm j

    Tcm j Tc j Tc j 1 2

    2

    The external heat transfer coecient 2 j is thendeduced from the relation:

    U j 1S2S1

    1

    1 j S2Rw 1

    2 j 3

    The tube side heat transfer coecient 1 j is calculatedfrom the correlation of Gnielinsky [8]. Specific experi-mental tests were performed in order to fit a tube side

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

    Fig. 4. Volumes de controle pour lanalyse unidimensionnelle.

    Fig. 5. n-pentane temperature profile. Analysis of entrance

    eects. (The group of tubes n0 represents the temperatureTc 0 at the entrance of the bundle).Fig. 5. Profil de temperature du n-pentane. Eet de lentree du

    faisceau.

    540 R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547

  • 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 coecient. The

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

    fluid circulating inside tubes was 20% waterglycolsolution. Its physical properties were defined throughspecific measurements and fitted with respect to the

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

    the tube side heat transfer coecient 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 Tcm j 4

    2.3.4. Nucleate boiling and convective evaporation

    The variables treated in this section are applied to thecontrol volumes j=19. The notation j , which makesreference to the control volume number j, has beenomitted for a better clarity of the formulas.For flow boiling, the total heat flux is classically

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

    q qnnb qncv 1

    n 5

    Each component of the heat flux is related to a spe-cific heat transfer coecient but to the same tempera-

    ture dierence:

    q 2Tw 6

    qnb nbTw 7

    qcv cvTw 8

    The nucleate boiling heat transfer coecient 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 flux 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 flux qnb, the

    convective heat flux qcv and the convective heat transfercoecient cv can be evaluated from the above expres-sions and from the experimental values of Tw and q.The enhancement factor is defined as the ratio

    between the convective heat transfer coecient cv andthe heat transfer coecient L to the liquid phase flow-ing alone, i.e. with a mass rate equal to 1 x m: c:

    F cvL

    10

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

    flow 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 flux: Tw Tw j Tcm j and q q j .

    3. Results and analysis

    3.1. Profiles of hydrocarbon temperature and heat

    transfer coecient

    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 thefigure). The temperature rises on the first 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 eect was observed in this test, according to the

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

    throughout the bundle, a significant increase of the heattransfer coecient 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 first step, in Fig. 7(a), the heat transfer coecient

    2 j is plotted versus the heat flux 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 figure):

    2 aqb 11

    From this pattern, one could conclude that the heattransfer coecient depends mainly on the heat flux, and

    R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547 541

  • 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 significant 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], Gorenflo [10] and Cooper [4])

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

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

    values compared to the other three. The solid line in thefigures represents the fitted expression (11) to theexperimental data. As said, the heat transfer coecient

    for single tube pool boiling is well under the experi-mental. Moreover, the value of the exponent b for theexperimental correlation (b0.35) is lower than thevalue for pool boiling (b0.67, except for Gorenflo [10]were b is greater and varies with pressure). Furthermore,the eect of pressure seems to be much less significant inour tests than for single tube pool boiling, as can be seen

    in Fig. 7(e), where the fitted 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 flow boiling through a bank of plain tubes by usingthe expression (11). They found also a significantunderestimation 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 coecient is plotted versus

    the heat flux for a set of tests with fixed conditions ofpressure and mass velocity. Each line in the figurerepresents the data obtained for one test, i.e. one heat

    rate, which is equivalent to one vapor quality at the exitx 9 . The dierent dots in each line represent the dier-ent control volumes in the bundle (the heat transfercoecient rising with the height in the bundle). The fig-

    ure clearly shows a significant eect 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 significant,despite the apparent exclusive part of the heat flux sug-gested by Fig. 7(a). In fact, this appearance is due to the

    link between the heat flux, the heat transfer coecientand the vapor quality. The rise of the heat transfercoecient 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 flux.In Fig. 9 the ratio between the nucleate boiling heat

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

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

    the total heat flux. This trend is in agreement with thewell known increase of the nucleate boiling heat transfercoecient with pressure.

    3.3. Asymptotic model and convective heat transfer

    3.3.1. Asymptotic model

    The asymptotic model defined by the set of Eqs. (5)(10) has been adopted for the evaluation of the totalheat transfer coecient, accounting for convective eva-

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

    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 profile. (b) Heat flux,

    heat transfer coecient and vapor quality.

    Fig. 6. (a) Profil de temperature de lhydrocarbure. (b) Flux

    thermique, coecient de transfert de chaleur et qualite de la

    vapeur.

    542 R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547

  • Fig. 7. (a) Heat transfer coecient vs total heat flux for all the data (npb: correlation of Cornwall et al. [3] for nucleate pool boiling).

    (b) Heat transfer coecient vs total heat flux for p=0.2 bar. Comparison with single tube pool boiling correlations. (c) Heat transfer

    coecient vs total flux for p=0.3 bar. Comparison with single pool boiling correlations. (d) Heat transfer coecient vs total heat for

    p=0.5 bar. Comparison with single tube pool boiling correlations. (e) Heat transfer coecient vs total heat flux for all the data (npb:

    correlation of Cornwell et al. [3] for nucleate pool boiling). Eect of pressure on the experimental fitted correlation (lower: 0.2 bar,

    intermediate: 0.3 bar, upper: 0.5 bar).

    Fig. 7 (a) Coecient de transfert de chaleur en fonction du flux thermique total (correlation de Cornwell et al. [3] pour lebullition nucleee

    libre). (b) Coecient de transfert de chaleur en fonction du flux thermique pour une pression de 0,2 bar. Comparaison avec les correla-

    tions de lebullition libre a` tube unique. (c) Coecient de transfert de chaleur en fonction du flux thermique pour une pression de 0,3 bar.

    Comparaison avec les correlations de lebullition libre a` tube unique. (d) Coecient de transfert de chaleur en fonction du flux thermique

    pour une pression de 0,5 bar. Comparaison avec les correlations de lebullition libre a` tube unique. (e) Coecient de transfert de chaleur

    en fonction du flux thermique pour toutes les donnees (correlation de Cornwell et al. [3] pour lebullition nucleee libre). Eet de la pression

    sur la correlation trouvee experimentalement (courbes inferieures : 0,2 bar ; courbes intermediaires : 0,3 bar ; courbes superieures : 0,5 bar).

    R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547 543

  • the present analysis: Cornwell et al. [3] and Gorenflo[10]. The other, Stephan et al. [13] and Cooper [4], arenot considered [the first 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 first for the calculation of nb. The data havebeen arranged in dierent sets of experiments corre-sponding to a fixed pressure and a fixed 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 fixed 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 fittedvalue 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 quantifiedby fitting 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 Gorenflo [10] for the calculation of nb. Thevalue of n giving the best correlation between F and x

    Fig. 8. Heat transfer coecient vs total heat flux for fixed

    pressure and mass velocity and dierent heat rates.

    Fig. 8. Coecient de transfert de chaleur en fonction du flux

    thermique pour des pressions et de la vitesse massique reglees et

    divers rendements thermiques.

    Fig. 9. Ratio between nucleate boiling and total heat flux vs

    total heat flux.

    Fig. 9. Relation entre lebullition nucleee et les flux thermiques

    totaux en fonction du flux thermique total.

    Fig. 10. F factor vs vapor quality (P=0.5 bar). nb:correlationof 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 : correlation de Cornwell et al. [3] pour pourlebullition libre et un tube simple. Ordre du mode`le 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 : correlation de Cornwell et al. [3] pour pourlebullition libre et un tube simple. Ordre du mode`le asympto-

    tique : n=1,5.

    544 R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547

  • 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 eect on theplot of F against x. This is because the values of nbpredicted by the correlation of Gorenflo [10] are so lowcompared to the total heat transfer coecient that thecontribution of the nucleate boiling is no significant.

    In any case, the best level of correlation between Fand x obtained using the correlation of Cornwell et al.[3] is significantly higher than the one obtained using thecorrelation of Gorenflo [10]. For this reason, the first

    has been selected.The fitted value of n=1.5 diers 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 fitted the value ofn to the experimental data or this value has been fixed

    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 fitted 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. 1012. However, an eect of

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

    sities (the last are practically constant for a fixed 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 thesefigures: as the mass velocity increases, the curves seemsto concur to a single correlation, suggesting that themass velocity eect is significant only for low values of

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

    the mass velocity eect on the enhanced factor F. The

    only data concerning a flow 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. [57] concerning the pressure drop in

    vertical two-phase flows through dierent banks oftubes. A strong mass velocity eect was observed on thetwo-phase flow multiplier 2L for low mass velocities,both for adiabatic air-water and R-113 boiling flows

    (the eect was significant for G < 200 kg/m2s for thefirst case and G < 100 kg/m2s for the second). More-over, the authors observed that the mass velocity eect

    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 : correlation de Cornwell et al. [3] pourlebullition libre et un tube simple. Ordre du mode`le 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 : correlation de Cornwell et al. [3] pour pourlebullition libre et un tube simple. Ordre du mode`le asympto-

    tique : n=1,5.

    R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547 545

  • decays as the value of G is increased. The mass velocityeect on the F factor and on the 2L 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 flow boiling through a bank of plain tubes

    with low mass velocity and low reduced pressure:

    . Convective evaporation plays a significant 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 significant mass velocity eect has beenobserved for the F factor. This eect decreases asthe mass velocity G increases, and is expected to

    disappear for high enough values of G. The massvelocity eect on F is probably linked to the sameeect on 2L observed by Dowlati et al. [57]reflecting an analogy between heat and momen-

    tum transfer.. The mass velocity eect 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 final output of each channel, i.e.including the entire system: probe+extension wire+data acquisition system.

    The experimental uncertainty on the heat flux q j , theheat transfer coecient 2 j and the vapor quality x j has been evaluated taking into account fixed 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 P0;P1 Endress+Hauser PMC 731 Ceramic sensorDierential pressure transducer P Endress+Hauser PMD 130 Ceramic sensor

    Flowmeter m:c Rosemount MicroMotion DS 100 S Mass flowmeter

    Flowmeter m:h Endress+Hauser Promag 33 Volumetric flowmeter

    Temperature probes Thij 19Thoj 19 Endress+Hauser Pt100 DINIEC751 Platinum RTD 2 wires,class B 1.6 mm O.D.

    Temperature probes Tcj 09 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

    Precision des mesures

    Temperature 0.1 K

    Pressure 0.2%

    Outside tube flow rate 0.2%

    Inside tube fluid flow rate 0.5%

    546 R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547

  • lation of Gnielinsky [8] for the evaluation of 1 j . Thelast has been evaluated as 10%. The maximum fixederrors 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 flux, the heat transfercoecient and the vapor quality evaluated as quotedabove are shown in Fig. 14.

    For the heat flux and the vapor quality, the uncer-tainty comes mainly from the assumed 0.1 K max-imum fixed error in the inside tube temperature probes

    from which heat balances are performed. For the out-side tube heat transfer coecient, the 10% uncer-tainty in the inside tube heat transfer coecient carriesalso a significant weight.

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    Fig. 14. Erreurs experimentales.

    R. Roser et al. / International Journal of Refrigeration 22 (1999) 536547 547

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