s

f

A

n

f

o

t

-

n 5 kinematic viscosityr 5 density,Dr liquid-to-vapor density differencet 5 shear stressJ 5 extension of cooling surface orthogonal to condensate

flow

Subscripts

I 5 at vapor-liquid interfaceG 5 vaporL 5 liquid0 5 without suction, also saturated vapor

W 5 at cooling surfacez 5 local value

References@1# Joule, J. P., 1861, ‘‘On the Surface Condensation of Steam,’’ Philos. Tran

Soc. London,151, pp. 133–160.@2# Nusselt, W., 1916, ‘‘Die Oberfla¨chenkondensation des Wasserdampfes,’’

VDI, 60, pp. 541–546, 569–575.@3# Kruzhilin, G. N., 1937, ‘‘Improvement of the Nusselt Theory of Heat Trans

with Condensation,’’ J. Tech. Phys.,7, pp. 2011–2017.@4# Rohsenow, W. M., 1956, ‘‘Heat Transfer and Temperature Distribution

Laminar-Film Condensation,’’ Trans. ASME,78, pp. 1645–1648.@5# Labuntsov, D. A., 1956, ‘‘On the Influence of Convection and Inertia of Co

densate on Heat Transfer with Laminar Film Condensation,’’ Therm. Eng.,12,pp. 47–50.

@6# Parr, P. H., 1921, ‘‘The Water Film on Evaporating and Condensing TubeEngineer,131, pp. 559–561.

@7# Jakob, M., 1921, ‘‘Die Wasserhaut an Verdampfer-und Kondensarohren,’’ Z. VDI, 65, pp. 1244–1246.

@8# Rose, J. W., 1988, ‘‘Fundamentals of Condensation Heat Transfer: LamFilm Condensation,’’ JSME J. Ser. II,31, pp. 357–375.

@9# Rose, J. W., 1998, ‘‘Condensation Heat Transfer Fundamentals,’’ Trans.Chem. Eng.,76, Pt. A, pp. 143–152.

@10# Marto, J. P., 1998, ‘‘Condensation,’’ inHandbook of Heat Transfer, 3rd ed.,W. M. Rohsenow et al., ed., McGraw-Hill, New York.

@11# Cess, R. D., 1960, ‘‘Laminar-Film Condensation on a Flat Plate in thesence of a Body Force,’’ Z. Angew. Math. Phys.,11, pp. 426–433.

@12# Chen, M. M., 1961, ‘‘An Analytical Study of Laminar Film CondensatioPart 1-Flat Plate,’’ ASME J. Heat Transfer,83, pp. 48–54.

@13# Koh, J. C. Y., 1962, ‘‘Film Condensation in a Forced-Convection BoundaLayer Flow,’’ Int. J. Heat Mass Transf.,5, pp. 941–954.

@14# Shekriladze, I. G., and Gomelauri, V. I., 1966, ‘‘Theoretical Study of LaminFilm Condensation of Flowing Vapour,’’ Int. J. Heat Mass Transf.,9, pp.581–591.

@15# Webb, R. L., 1998, ‘‘Convective Condensation of Superheated VapoASME J. Heat Transfer,120, pp. 418–421.

@16# Stender, W., 1925, ‘‘Der Wa¨rmeubergang bei kondensierendem HeissdampZ. VDI, 69, pp. 905–909.

@17# Kutateladze, S. S., 1937, ‘‘On the Use of the Similarity Theory in the Procof Condensation of Saturated Vapor,’’ J. Tech. Phys.,7, pp. 282–293.

@18# Isachenko, V. L., 1977,Heat Transfer with Condensation, Energiya, Moscow.@19# Mills, A. F., 1999, Heat Transfer, 2nd edition, Prentice Hall, Englewood

Cliffs, NJ.@20# Sparrow, E. M., and Eckert, E. R. G., 1961, ‘‘Effects of Superheated Va

and Non-Condensable Gases on Laminar Film Condensation,’’ A.I.Ch.E. J7,pp. 474–477.

@21# Minkowycz, W. J., and Sparrow, E. M., 1966, ‘‘Condensation Heat Transfethe Presence of Noncondensables, Interfacial Resistance, Superheating,able Properties, and Diffusion,’’ Int. J. Heat Mass Transf.,9, pp. 1125–1144.

@22# Minkowycz, W. J., and Sparrow, E. M., 1969, ‘‘Effect of SuperheatingCondensation Heat Transfer in a Forced Convection Boundary Layer,’’ InHeat Mass Transf.,12, pp. 147–154.

@23# Ferreira, S. M. M., 1973, ‘‘Forced Convection Condensation of Vapor FlowAround a Circular Cylinder: Effect of the Presence of Inert Gas, GravitatField and Superheating,’’ Chem. Eng. J.,6, pp. 81–90.

@24# Fujii, T., 1991,Theory of Laminar Film Condensation, Springer, Berlin.@25# Mitrovic, J., 1998, ‘‘The Nusselt Condensation and Nonisothermality,’’ Int.

Heat Mass Transf.,41, pp. 4055–4061.@26# Sadasivan, P., and Lienhard, J. H., 1987, ‘‘Sensible Heat Correction in La

nar Film Boiling and Condensation,’’ ASME J. Heat Transfer,109, pp. 545–547.

@27# Schlichting, H., 1979,Boundary-Layer Theory, McGraw-Hill, New York.@28# Bird, R. B., Stewart, W. E., and Lightfoot, E. N., 1960,Transport Phenomena,

Wiley, New York.@29# Webb, D. R., 1990, ‘‘Multicomponent Condensation,’’ Proceedings of the

International Heat Transfer Conference, Vol. 1, pp. 287–304.@30# Mitrovic, J., and Gneiting, R., 1996, ‘‘Kondensation von Dampfgemischen

Forschung im Ingenieurwesen, Vol. 62, Springer-Verlag, New York, pp.1–10, 33–42, and 81–89.

196 Õ Vol. 122, FEBRUARY 2000

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Predicting the Influence ofCompressibility and Thermal andFlow Distribution Asymmetry on theFrequency-Response Characteristicsof Multitube Two-PhaseCondensing Flow Systems

C. J. KobusVisiting Assistant Professor, Mem. ASME, OaklandUniversity, Rochester, MI 48309e-mail: cjkobus@oakland.edu

G. L. WedekindJohn F. Dodge Professor of Engineering, Mem. ASME,Oakland University, Rochester, MI 48309e-mail: wedekind@oakland.edu

B. L. BhattProfessor and Associate Dean of Engineering andComputer Science, Mem. ASME, Oakland University,Rochester, MI 48309e-mail: bhatt@oakland.edu

An equivalent single-tube model concept was extended to predicthe frequency-response characteristics of multitube two-phasecondensing flow systems, complete with the ability to predict theinfluence of compressibility and thermal and flow distributionasymmetry. The predictive capability of the equivalent single-tubemodel was verified experimentally with extensive data that encom-passed a three-order-of-magnitude range of frequencies, and awide range of operating parameters.@S0022-1481~00!00601-0#

Keywords: Condensation, Heat Transfer, Heat Exchangers, Two-Phase, Unsteady

IntroductionThe research presented in this paper is associated with the in

fluence of compressibility on the frequency-response characteris-tics of multitube condensing flow systems. To the best knowledgeof the authors, the archival literature does not contain any theo-retical models for predicting the frequency-response characteris-tics of such systems. There is also very little experimental data.Filling these knowledge gaps is the focus of this research.

Kobus et al. @1# extended the predictive capability of theequivalent single-tube model to predict the frequency-responsecharacteristics of multitube condensing flow systems when com-pressibility effects are negligible. The influence of compressibilityon transient flow surges in multitube condensing flow systemswas investigated by Wedekind et al.@2#. The effects of compress-ibility on a single-tubecondensing flow system had also beenstudied earlier~@3#!. Given the complexity of the physical mecha-nisms involved, and the fact that most of them are coupled insome way, a significant step is involved between successfully

Contributed by the Heat Transfer Division for publication in the JOURNAL OFHEAT TRANSFER. Manuscript received by the Heat Transfer Division, Aug. 25,1998; revision received, Aug. 23 1999. Associate Technical Editor: M. Kaviany.

Transactions of the ASME

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modeling the frequency-response characteristics in a single-condenser, and having the same level of success when thedenser is multitube. The major purpose of this research, then,investigate the requirements for extending the equivalent sintube model so that it can successfully predict the influencecompressibility on the frequency-response characteristics fomultitube system, and to verify the model by comparing its pdictions with experimental data.

Formulation of Governing Differential EquationsThe formulation of the governing differential equations, inclu

ing the effects of compressibility, was presented in previoussearch~@2#!, but solved for the case oftransient flow surges.Therefore, details of the development of these governing eqtions will not be repeated here. The solution of the equatiohowever, will be presented for the special case of a sinusoinlet vapor flowratemt,i(t).

Equivalent Single-Tube Model . The equivalent single-tubemodel is based on the system mean void fraction model, whica one-dimensional, two-fluid, distributed parameterintegral modeldeveloped in previous research~@2#!. It represents a way of modeling the transient characteristics of the effective point of coplete condensationh(t). The system mean void fraction modincorporates the concept of a system mean void fractiona. Thedifferential equation governing the effective point of complecondensation for a representativej th tube,h j (t), obtained fromthe conservation of mass and energy principles~@2#!, is expressedas follows:

tc, j

dh j~ t !

dt1h j~ t !5xi

~h82h!

f q, j Pj

g jmt,i~ t ! (1)

where

tc, j5r8~h82h!aAt, j

f q, j Pj

. (2)

In the above equations,f q, j represents the spatially averaged heflux for a representativej th tube,xi the inlet flow quality,At, j andPj the tube cross-sectional area and periphery, respectively,r8 and (h82h) the saturated vapor density and heat of vaporition.

The system mean void fractiona is defined in terms of thelocal area void fractiona(z,t), and represents the integral form othe mean value theorem. The particular void fraction model uis that of Zivi @4#, chosen for its simplicity, yet is sufficientlyaccurate for these types of condensing flow problems. Howeany void fraction-flow quality relationship that is valid over thfull range of flow qualities would yield similar results. It waestablished in previous early research that the system meanfraction is essentially time invariant. This has the effect of uncpling the conservation of mass and energy principles in the tphase region from the transient form of the momentum principthus, only the steady-state form of the momentum principlerequired. The system mean void fractiona can therefore be expressed as

a[1

h~ t ! Ez50

h~ t !

a~z,t !dz

51

~12a!1

a

xi~12a!2 LnU a

a1~12a!xiU; a5~r/r8!2/3.

(3)

The equivalent single-tube model is an approximation tenique that has been shown to be successful in predicting vartransient characteristics associated with multitube condenflow systems~@2,1#!. This approximation technique has the effeof reducing the equations governing the multitube system, wh

Copyright © 2Journal of Heat Transfer

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contain complex summations~@2#!, to an approximation where thesummations are eliminated. The resulting approximation hasappearance of being an equivalent single-tube condensingsystem, but where the associated parameters are weighteddeterminable multitube parameters. The equivalent single-tmodel contains an equivalent single-tube condensing flow systime constanttc,s which is a weighted average of the condensiflow system time constants of each of the individual tubestc, j ,thus

tc,s5(j 51

n

g jtc, j5tc,1 (j 51

n

g jb j ; b j5 f q,l / f q, j (4)

where the flow distribution parameterg j is defined as the fractionof the total mass flowrate entering tubej. In general, 0<g j<1. Aflow distribution parameterg j51/n signifies flow distributionsymmetry in ann-tube system. The parameterb j is the heat fluxratio between a reference tube~usually designated as tube 1! andthe j th tube in the system. In general,b j>0. b j51 signifies ther-mal symmetry of the multitube system. In this phase of the modevelopment, both the thermal and flow distribution parameare treated as parameters in the classical sense~@2#!.

Outlet Liquid Flowrate. The differential equation governingthe transient outlet liquid flowratemt,o(t) is the same as thapresented in the aforementioned research; thus,

t f ,s

dmt,o~ t !

dt1mt,o~ t !5$@~r/r8!21#xi11%mt,i~ t !

2@~r/r8!21#(j 51

nf q, j Pjh j~ t !

~h82h!(5)

where

t f ,s5S r

r8D H S r8

r D $@~r/r8!21#xi11%Vu,t1V2f1Vp,effJ g* k0* .

(6)

The compressible flow system time constantt f ,s incorporatesfluid properties, system vapor volumes, and flow resistances~@2#!.For the case where the effects of compressibility are negligit f ,s50, Eq. ~5! reduces to an algebraic equation identical to thobtained in the work of Kobus et al.@1#. Also, for the case of asingle-tube condenser,n51, Eq.~5! reduces to the governing differential equation that appears in the work of Bhatt and Wedek@3#.

A solution of Eq. ~5! is obtained by first solving the set oequations represented by Eq.~1!, then substituting these solutioninto the summation in Eq.~5!, and then solving. As mentioneearlier, this was carried out in previous work where the inlet florate to the condensing flow systemmt,i(t) produces transient flowsurges~@2#!. In this current work, however, the inlet flowrate issinusoidal function of the form

mt,i~ t !5m1a* cos~vt ! (7)

wherea* and v are the amplitude and angular frequency of tinlet flowrate oscillations, respectively, andm is the mean flow-rate about which the oscillations occur. Carrying out the solutithe frequency-response characteristics of the transient outlet liflowrate, mt,o(t), for an n-tube condensing flow system, can bexpressed by the following generalized, yet comparably simexpressions:

Gm5H 11$@~r/r8!21#xi11%2~vtc,s!2

@11~vt f ,s!2#@11~vtc,s!

2# J 1/2

(8)

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Fig. 1 Strip chart record of measured outlet liquid and inletvapor flowrates for an oscillatory inlet vapor flowrate

Table 1 Physical properties and parameters

Dataset

a@ #

tc,1@s#

V2f,1

@cm3#V2f,2

@cm3#

k0*@N s

/cm2kg#tc,s@s#

t f ,s@s#

1fr-618b 0.831 0.79 245 — 67.7 0.79 0.91fr-620 0.831 0.79 245 — 364.4 0.79 5.11fr-620b 0.830 0.81 244 — 19.3 0.81 0.22fr-623 0.830 0.79 120 120 16.3 0.79 0.22fr-707 0.830 0.81 123 123 57.7 0.81 0.92fr-707b 0.830 0.81 123 123 312.4 0.81 5.02fr-714b 0.826 0.84 98 343 265.5 2.09 5.0

198 Õ Vol. 122, FEBRUARY 2000

Fm5tan21

3H H F S r

r8D21Gxi11J ~vtc,s!2@~vtc,s!1~vt f ,s!#

@12~vtc,s!~vt f ,s!#

11H F S r

r8D21Gxi11J ~vtc,s!@~vtc,s!1~vt f ,s!#

@12~vtc,s!~vt f ,s!#

J .

(9)

For the case where the effects of compressibility are negligit f ,s50, Eqs.~8! and~9! reduce to Eqs.~1! and~2! in the researchof Kobus et al.@1#. Note that the above solution is greatly simpfied by the equivalent single-tube model, where the summatioEq. ~5! is eventually assimilated by the definition of the condening flow system time constanttc,s , Eq. ~4!.

Experimental VerificationAs was pointed out in earlier research~@2#!, a two-tube con-

densing flow system with significant thermal asymmetry may vwell represent a worst-case situation for the equivalent single-tmodel. For this reason, and to keep the experimental appartractable, experimental verification was carried out using a palel two-tube configuration.

Experimental Apparatus and Measurement Uncertainties.The experimental apparatus used in the present research is sito that used by Kobus et al.@1#. Therefore, the details will not berepeated here. Uncertainties in the experimental measuremwere also discussed in detail in the aforementioned research,will not be repeated. The experimental data pertaining to the gcharacteristics had an average maximum uncertainty of610 per-

6320

Fig. 2 Influence of compressibility on frequency-response characteristics of outlet liquid flow-rate relative to inlet vapor flowrate for a two-tube condensing flow system; comparison ofexperimental data with equivalent single-tube model „equivalent single-tube model …

Transactions of the ASME

Journal of Heat

Fig. 3 Influence of thermal and flow distribution asymmetry on frequency-response charac-teristics of outlet liquid flowrate relative to inlet vapor flowrate for a two-tube condensing flowsystem; comparison of experimental data with predictions of equivalent single-tube model„equivalent single-tube model …

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cent, whereas the uncertainty associated with the phase shiftacteristics was slightly higher at615 percent. A sample stripchart trace of the inlet and outlet flowrate variations,mt,i(t) andmt,o(t), respectively, for the two-tube system is shown in Fig. 1demonstrates the clarity and repeatability of the experimemeasurements.

In calculating the compressible flow system time constantt f ,sthe total upstream vapor volume in the two-tube system wascm3, while that in the single-tube system was 486 cm3. The testsections were copper tubes with an inside diameter of 0.80All of the forthcoming experimental data were run at constconditions of m54.31 g/s, xi51.0, f q,1511.1 kW/m2, and at acondensing pressure of approximately 690 kPa, which in tyields a liquid-to-vapor density ratio (r/r8)533.7. Table 1 listsother relevant parameters associated with the calculations nesary to predict the frequency-response characteristics in therent research.

Experimental Verification of Equivalent Single-TubeModel. The theoretical predictions of the equivalent single-tumodel, Eqs.~6! and~7!, for the frequency-response characteristof a two-tube condensing flow system, are compared with expmental data for several different condensing flow conditions.

Influence of Compressibility.Similar to what was done byKobus et al.@1#, frequency-response tests were carried outtially with a two-tube condenser. But this time the effects of copressibility were made to be more significant. The results, alwith the theoretical predictions of the present compressequivalent single-tube model, are depicted in Fig. 2. Note the vdramatic attenuating effect that compressibility can have onfrequency-response characteristics; the experimental data c

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sponding to the most significant compressibility,t f ,s55.0 s, hav-ing roughly a quarter the maximum amplitude in the gain~one-half the gain in decibels, db! to that of the experimental datcorresponding to the lowest magnitude of compressibility,t f ,s50.26 s. The agreement between the experimental data andcompressible equivalent single-tube model predictions are seebe exceptionally good over the entire three-order-of-magnitrange of frequencies.

As a further means of model verification, the compressiequivalent single-tube model was used to design a test fosingle-tube condenser, which theoretically would yield the exsame frequency-response characteristics as that of the twocondenser, even though the refrigerant flowrate in each of thetubes was different from what it was for the single-tube codenser. The results of the designed experiments are superimpin Fig. 2. The equivalent single-tube model predicts thatfrequency-response characteristics of symmetric or asymmmultitube systems are identical to that of a single-tube systemlong as the equivalent condensing system time constanttc,s andthe compressible flow system time constantt f ,s for the multitubesystem are the same astc andt f for a single-tube system. As cabe seen from the figure, the measured frequency-response chteristics were virtually identical for both the single- and the twtube condensers, as the equivalent single-tube model predict

Influence of Thermal and Flow Distribution AsymmetThermally and hydrodynamically asymmetric experimental dare depicted in Fig. 3 for a two-tube condenser for the case whthere is considerable compressibility. One set of data depictscondition where thermal and flow distribution symmetry wpresent~b51.0, g50.5!; the other set of experimental data posessed significant thermal and flow distribution asymmetry

FEBRUARY 2000, Vol. 122 Õ 199

s

r

c

a

.

sa

a

a

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-

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s

tween the two tubes~b252.09,g150.4!. Note the significant in-fluence of thermal and flow distribution asymmetrSuperimposed in the figure is the frequency response predictethe compressible equivalent single-tube model. It is importannote that there is no empiricism or ‘‘curve fitting’’ involved in thequivalent single-tube model predictions. All of the parameterEqs. ~8! and ~9! are known or determined analytically~@2#!.Again, the agreement between the experimental data andequivalent single-tube model is seen to be quite good for bothsymmetric and asymmetric conditions, even at the higher frequcies. The incompressible equivalent single-tube model was inpable of predicting the attenuating effects of compressibility~@1#!.More experimental data are available at other levels of compribility by referring to the work of Kobus@5#. As can be seen, theagreement between the experimental data and the compresequivalent single-tube model is again exceptionally good overentire range of frequencies presented, which represents threders of magnitude.

ConclusionsIt seems appropriate to emphasize the significance of the de

of agreement between all of the single- and the two-tube expmental data presented, and the predictive capability of the cpressible equivalent single-tube model. The experimental drepresent both single- and two-tube condensers, with diffeflowrates, heat fluxes, having a wide range of compressibilityfects, as well as significant thermal and flow distribution asymmtries. The equivalent single-tube model is seen to predict thefects of all of these different system characteristics very well, oa three order of magnitude range of frequencies.

The experimental data not only confirm the predictive capaity of the equivalent single-tube model, they demonstrate itscuracy and its wide range of application. This confirming expemental data also establishes the applicable frequency range odynamic viability of the system mean void fraction model, whiis an integral part of the equivalent single-tube model. The tvalue of the equivalent single-tube model can only be appreciwhen consideration is given to the complexity of the numerophysical mechanisms involved, and the remarkable accuracsuch a relatively simple model; a model which can be solved,graphically demonstrated, on typical ‘‘spread-sheet’’ software

AcknowledgmentsThe authors would like to acknowledge the National Scien

Foundation, Thermal Transport and Thermal Processing ProgDivision of Chemical and Transport Systems, for its part in tsupport of this research under Grant No. CTS-9420853. Theport of the NASA/Michigan Space Grant Consortium is alsoknowledged.

References@1# Kobus, C. J., Wedekind, G. L., and Bhatt, B. L., 1998, ‘‘Application of a

Equivalent Single-Tube Model for Predicting Frequency-Response Charaistics of Multitube Two-Phase Condensing Flow Systems With ThermalFlow Distribution Asymmetry,’’ ASME J. Heat Transfer,120, No. 2, pp. 528–530.

@2# Wedekind, G. L., Kobus, C. J., and Bhatt, B. L., 1997, ‘‘Modeling the Chacteristics of Thermally Governed Transient Flow Surges in Multitube TwPhase Condensing Flow Systems With Compressibility and Thermal and FDistribution Asymmetry,’’ ASME J. Heat Transfer,119, No. 3, pp. 534–543.

@3# Bhatt, B. L., and Wedekind, G. L., 1980, ‘‘Transient and Frequency RespoCharacteristics of Two-Phase Condensing Flows: With and Without Cpressibility.’’ ASME J. Heat Transfer,102, pp. 495–500.

@4# Zivi, S. M., 1964, ‘‘Estimation of Steady-State Steam Void Fraction by Meaof the Principle of Minimum Entropy Production,’’ ASME J. Heat Transfe86, p. 247.

@5# Kobus, C. J., 1998, ‘‘Application of the System Mean Void Fraction ModelFormulating an Equivalent Single-Tube Model for Predicting Various Trasient and Unstable Flow Phenomena Associated with Horizontal MultitTwo-Phase Condensing Flow Systems With and Without the Effects of Cpressibility, Inertia, and Thermal and Flow Distribution Asymmetry,’’ Ph.thesis,Oakland University, Rochester, MI.

200 Õ Vol. 122, FEBRUARY 2000

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An Experimental Study ofElectrohydrodynamic InductionPumping of a Stratified Liquid ÕVaporMedium

M. Wawzyniak1

J. Seyed-YagoobiG. L. MorrisonDepartment of Mechanical Engineering, Texas A&MUniversity, College Station, TX 77843-3123

Electrohydrodynamic induction pumping of a stratified liquid/vapor medium is quantitatively assessed utilizing Laser DoppleAnemometry. Data are presented suggesting that pumping is duto both interfacial and bulk effects. Values of turbulence intensityassociated with this type of flow are briefly discussed for the vari-ous cases studied.@S0022-1481~00!00401-1#

Keywords: Electric Fields, Heat Transfer, Pumps, Stratified,Two-Phase

IntroductionElectrohydrodynamic induction pumping is based on charges

induced in the fluid and delayed at a gradient or discontinuity ofthe electric conductivity. A traveling electric wave then attracts orrepels these induced charges, leading to fluid motion. Electrohydrodynamic pumps are generally lightweight, produce no vibra-tions, require little to no maintenance, are easily controllable byadjusting the applied voltage, and have low power consumptionThey are also useful for the enhancement of heat transfer, as aincrease in mass transport often translates to an augmentationthe heat transfer.

Melcher @1# provided the first theoretical model of electrohy-drodynamic induction pumping due to charges at a liquid/air in-terface. He then presented an improved version of his theoreticamodel which also described the pumping of a liquid/liquid inter-face ~@2#!. This theory was recently examined in more detail byWawzyniak and Seyed-Yagoobi@3,4#. The above theoretical mod-els are built around a number of simplifying assumptions leadingto a linear velocity profile~Couette flow!, the most significant ofwhich are that: ~1! flow is laminar, isothermal, and one-dimensional,~2! charges are induced and consequently an electricforce is present only at the interface, and~3! the pressure is con-stant in the direction of motion. It will later be shown that theseassumptions are not met and that improvements have to be mato the existing theoretical model of Wawzyniak and Seyed-Yagoobi @3,4# to accurately describe and predict the phenomenaencountered in two-phase flow electrohydrodynamic inductionpump.

For this experimental study, induction pumping of a stratifiedliquid/vapor medium is carried out. Specifically, velocity and tur-bulence intensity measurements inside a liquid film of HCFC-123are conducted by means of a one-dimensional LDA system afunctions of location, frequency, and voltage.

1Current address: Behr GmbH& Co., Abt.E-T, Postfach 30 09 20, 70449Stuttgart, Germany.

Contributed by the Heat Transfer Division for publication in the JOURNAL OFHEAT TRANSFER. Manuscript received by the Heat Transfer Division, Dec. 1, 1998;revision received, Aug. 1, 1999. Associate Technical Editor: P. Ayyaswamy

Transactions of the ASME

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Experimental Setup and ProcedureThe details of the experimental setup and procedure are g

in Wawzyniak@5#. The AC power supply utilized in this study icapable of generating sine, square, and triangle waves at voltof 0–12 kV ~zero to peak! and frequencies of 0–13 Hz. Thpumping channel with a rectangular cross-section width of 50and a height of 36 mm is milled directly into a single piecePVC ~see Fig. 1!. Two straight sections measuring 390 mmlength are connected by half-round sections with a centerlinedius of 150 mm. The pump is equipped with three view poalong one of the straight pumping sections. These view portslocated at 37.5, 195.0, and 352.5 mm from the start of the strasection, respectively. Each view port measures 45 mm in width25 mm in height and extends from the bottom of the pumpchannel up. The pumping channel is covered with a plate mfrom high-density polyethylene, which is equipped with portsa pressure transducer, a vacuum gauge, and two thermocoprobes. The pumping channel and support lines are initievacuated to a vacuum better than 250mm of mercury. The ap-paratus is then charged with refrigerant HCFC-123.

Two integrated electrode boards are mounted into the bottof the two straight sections of the induction pump. Each boarschematic of which is shown in Fig. 1, measures 50 mm in wid390 mm in length, and 1.5 mm in thickness. The board laminat

Copyright © 2Journal of Heat Transfer

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made from the epoxy resin FR-4, a material commonly usedprinted circuit boards, while the electric lines are tin covered cper. The top of each board features 39 electrodes and the boholds the three bus lines. The electrodes are 1 mm wideextend across the entire width of the board, and subsequenttrodes are spaced 10 mm apart~center to center!. To completelyeliminate the possibility of direct charge injection~@5#!, a coatingof epoxy 0.8 mm in thickness was applied to the top surfaceboth electrode plates. This material was compatible withworking fluid. The three bus lines running along the length of tboard are also 1 mm in width, but they are located 17 mm freach other~center to center! with the second bus line placed in thmiddle of the board. The first, second, and third bus linesconnected to electrodes 1, 4, 7, . . . 2, 5, 8,. . . , and 3, 6, 9, . . . ,respectively, by means of through-plated holes. The bus lineturn are linked to the high-voltage power supply.

The one-dimensional LDA system measures the main velocomponent and turbulence intensity in thex-direction ~see Fig. 1for the definition ofx, y, andz-directions!. Light from an argon-ion laser is passed through a prism, with the green color comnent (l5514 mm), being used for the measurement. The opttrain consists of a polarization unit, a Bragg cell,3.753 beam expander, and a lens with a focal length of 450 mLight reflected from particles in the flow is collected in an on-ax

Fig. 1 Schematic of electrohydrodynamic induction pump and electrode plate

000 by ASME FEBRUARY 2000, Vol. 122 Õ 201