on the generalized correlation equation of two...

On The Generalized Correlation EquationOf Two Phase Heat Transfer Coefficient

In Forced-Convection Boiling

Efrizon Umar*, M. Amarianto Kusumowardhoyo*** Research Centre for Nuclear Techniques, BATAN

** Mechanical Engineering Department, ITB

Abstract

On The Generalized Correlation Equation Of Two Phase Heat TransferCoefficient In Forced-Convection Boiling. Investigations of two-phase heattransfer in a horizontal pipe flow have led to a 'new generalized correlation for theheat transfer coefficients. The proposed correlation equation is

[ lO.8NuTP = 3.04 peJ [ BoJ 0.6

This correlation was tested against the existing and experimental data obtained ontwo-phase heat transfer covering the entire possible flow regimes in a horizontalpipe flow. The correlation produces satisfactory results.

INTRODUCTION

Successful design of heat exchanger requires accurate prediction of thelocal heat transfer coefficient for the boiling regime. However, asymmetrictopology or geometry of the flow introduces additional complications.Moreover, there also exists a variety of flow configurations known as flowpatterns which depends on the conditions of flow, heat flux, and channelgeometry. In the design of a heat exchanger it is desirable to know whatthe flow pattern or successive flow patterns are, so that a hydrodynamic orheat transfer theory appropriate to that particular pattern can be chosen.The patterns of flow boiling regime in a horizontal pipe have a descriptivename (Figure 1).

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Various correlation were reported [1-6]for heat transfer regimes in twophase flow systems, but there were little data and most of those availabledata give insufficient accurate information about the local heat transfercoefficient. Therefore, one should not be suprised that there exists, in theliterature, a multitude of equations purporting to describe the variouspossible heat transfer mechanism in a single evaporation process in a tube.

In the previous investigation [7,8], it was presented that the heattransfer coefficient of a two-phase flow in a horizontal pipe depend on eightprimary parameters :

f [Q/A, ~g, p, Cp, k, V, D, 11- ] •••••••••••••••••••••••••••••• (1)

hrP = heat transfer coefficient (W/m2.K)k = thermal conductivity (W/m.K)D = pipe diameter (m)Cp = constant pressure specific heat (J/kg.K)p = density (kg/m3)V = velocity (m/sec)Q/A = heat flux (W/m2s)hhf latent heat of evaporation (J/kg)11- = viscosity (kg/m.s) .

These parameters were formulated in four dimensionless groups, namelyNusselt number, Reynolds number, Prandtl number and Boiling number.The correlation equations are [7,8) :

[ ] OS[ rs[ T6hrP·D

p.V.D.

CP:~~~~

--=:' 3.2 -- ... (2)

k11-

[ fS2[ rs[ r62

hrP·D= 2.9 P.V~D CP.:

Q/A ... (3)-- k ~g'p.V

The fIrst equation is applied to the saturated flow boiling [7]and the secondequation to the slug to annular flow regime [8].

Each of those correlations has indicated that under forced boilingconditions, the flow exhibits a relatively large heat capacity effect per unitvolume of fluid conveyed in the tube and also a large unit thermalconvective conductance.

15

Based on the above results, t:Q.isinvestigation studied further the twophase heat transfer phenomena in a horizontal pipe. A general correlationequation for the two-phase heat transfer coefficient valid for the entire flowpatterns described in Figure 1 is proposed; a typical situation found in ahorizontal flow evaporator.

MATERIALS AND METHOD

Mixtures of ethanol and gasoline at various compositions were used inthe experiments. The compositions of the gasoline-ethanol mixtures were:100:0; 95:5; 90:10; 85:15; 80:20; and 60:40.

The experiment equation used an apparatus which was designed andconstructed by Kusumowardhoyo and Hardianto. Figure 2 shows theexperimental arrangements of the apparatus and the description of theapparatus has been presented in a previous work [7].

The correlation equation of a two-phase heat coefficient in a horizontalpipe is formed by applying the Buckingham Pi theorem. This theorem alsopresented in the work done by other authors [7,8].

RESULTS AND DISCUSSION

The experimental data can be used to verifY the heat transfermechanism postulate and, further, to form a basis for the development ofthe heat transfer correlation which will be discussed in this section. Theexperimental data for various ethanol concentrations in gasoline are shownin Tables 1-6.

Applying the Buckingham Pi Theorem, the resulting correlation,developed using the obtained experimental data, for the two-phase heattransfer coefficient is

0.8

NUn> = 3.04 [ Re Jand this can be rearranged to :

16

0.6

[ BoJ (4)

or

[ ] 0.83.04 Re.Pr : (5)

0.8

3.04 [ Pe ]

0.6.................... (6)

This equation can be written as a correlation between their parameters :

hrP = 3.04k

D[P.V.D.CPJ 0.8 IQlA ] 0.6k l!lrg.p.V

.......... (7)

. Where all properties, as indicated in the above correlation, must beevaluated at liquid conditions upstream of the saturated-boiling regime.

The above correlation is valid over the entire flow regimes in ahorizontal pipe (Figure 1) and the result is shown in Figure 4. Therefore,it can be considered to represent a general correlation equation for twophase heat transfer coefficients of turbulent flow boiling in a pipe. Alsoplotted in Figure 4 are the existing experimental data taken from variousreferences [1,3,4,5,7]. Comparisons between experimental results andcalculated data using the proposed correlation of heat transfer coefficientis shown in Tables 7-12.

One may readily deduce from correlation equation [7] that, under flowboiling conditions, the thermal diffusivity ofthe flow is higher compared tothe ordinary liquid phase heating due to the formation of the vapor phase.Experiments show that such condition produces an increase in the heattransfer coefficient by approximately 100 % over the single phase heattransfer coefficient for the saturated flow boiling regime [7] and about140 % for the remainder or successive flow patterns, i.e slug to annularflow [8]. In a typical evaporator pipe, the slug to annular flow mayrepresent more than 75 % of the pipe length (Figure 1). Moreover, itappears that the viscosity effect is only of secondary importance andnegligible as compared to the above mentioned dominant effects due to thebubble agitation. In addition, physical properties do not vary significantlyalong the tube, because the unit surface conductance is usually large andthe variation of the bulk and wall temperature difference along the heatedof the tube is, therefore, small (Figure 3). However, due to boiling, onealways needs to account for the amount of liquid evaporated along theheated tube and, therefore, checking for the change ofthe liquid flow whichmay happened due to evaporation. This would, then, allow us to estimate

17

the ratio of the mass of the flowing liquid to the mass of the evaporatedfluid. The mass of the evaporated liquid is, strictly, affected by the amountof the applied heat flux and the latent heat of evaporation of the liquiditself.

Apparently, approaching the annular region, more liquid is evaporatedand, therefore, less liquid hold-up or more vapor void fraction is formed inthis region. The previous investigations have, however, successfullyaccounted for this varying hold-up or void fraction through the introductionof the boiling number [7,8].

It could be concluded that two-phase heat transfer coefficient forturbulent flow in forced-convection boiling depends on seven primaryparameters. The proposed correlation equation takes the form of

............................................ .(8)

One may quickly notice its analogous form to that of liquid metalheating [12]. The boiling number is essentially constant for a given heatflux and mass flow rate.

CONCLUSION

Two-phase heat transfer coefficient in forced convection boiling havebeen satisfactorily correlated by a new function of the type :

[ J8 [ rs3.04 Pe Bo ....... : (9)

The proposed correlation appears to be practical and simple to use in manydesigns and engineering applications because it does not involvecomplicated parameters such as varying vapor void fraction. The proposedcorrelation produces good agreement with experiments to within 13 % onthe average.

ACKNOWLEDGEMENT

The authors are grateful to Mr. Ranung and Mr. Indartono for theirexcellent technical assistance in this experiment.

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NOMENCLATURE

Bo = Boiling number, (Q/AIpVhrg)

Cp = Constant pressure specific heatD = Diameterhrg = Latent heat of evaporationk = Thermal conductivityNu = Nusselt number, (h.D/k)Pe = Peclet number, (PVDCp/k)Pr = Prandtl number, (CPJ!/k)Re = Reynolds number (PVD/J!)Q/A = Heat fluxV = VelocityJ! = Viscocityp = DensitySubscriptL = Liquid phaseTP = Two-phase.

REFERENCES

1. Y.G. COLLIER, Convective Boiling & Condensation, Mc.Graw HillBook Company, Tokyo, (1972)

2. W.M. ROHSENOW and HARRY CHOI, Heat, Mass, and MomentumTransfer, International Series in Engineering Prentice-Hall.Inc,Englewood CHfts, New Jersey, (1961)

3. J.W. ANDERSON and D.G. RICH, Evaporation of Refrigerant 22 inhorizontal 3/4 in tube, Ashrae Trans Vol 72, Part I, (1966) pp 22-36

4. J.G. LAVIN and E.H. YOUNG, A.J.Ch.E. Journal Vol II, (1965)

5. G.R. KUBANAK and D.G. MILETTI, ~at Transfer 1970, Vol 101,(1979) 447-452

6. U. GRIGOLL and E. HAHNE, Heat Transfer 1970, Vol V & VII,Elsevier Publishing Company, Amsterdam, (1971)

7. M.A. KUSUMOWARDHOYO and T. HARDIANTO, Two-phase heattransfer correlation for multicomponent mixtures in the saturated flowboilling regime, Int. J.Heat and Fluid Flow, (1985)

19

8. E. UMAR, Majalah BATAN, Vol XXI, (3-4) (1989)

9. E.R: ECKERT and R.M. DRAKE, Heat and Mass Transfer, SecondEdition, Mc.Graw Hill Book Company, New York (1959)

10. B.D. THOMAS, Advances in Chemical Engineering, Vol II AcademicPress, New York, (1968)

11. J.P. HOLMAN, Heat Transfer, Fourth Edition, MC.Graw Hill BookCompany, New York, (1975)

12. F. KREITH, Principles of heat transfer, Third Edition, IntextEducational Publishers, New York, (1973)

13. F .M.WHITE, Fluid Mechanics, MC.GrawHill Kogukuskha Ltd, (1979)

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Table 1. Experimental data for 100 % gasoline

GQ/A T. - Tbhrg

(kg/m2.s)(Qlm2)(OC)(J/kg)

129.8

20066.0438.5946423

129.8

21139.9239.0945488129.8

23032.4940.5945024

129.8

27046.4241.5941809129.8

28812.9943.0940431

169.9

18834.8839.0952189169.9

20640.5842.0948760

169.9

23167.7745.5946423169.9

26192.3748.5943646169.9

28964.8550.0937431169.9

32251.9852.0932830

T. = surface wall tem}?eratureTb = bulk temperatur8 uf fluid


GQ/A1'. - Thhrg

(kg/m2.s)(Qlm~eC)(J/kg)

130.4

18452.2536.01075011

130.4

22561.0139.01069714

130.4

23622.0140.01066461

130.4

23685.6744.51064834130.4

26923.0746.51063750

130.429791.1150.01062123

170.6

18255.9730.51076582

170.6

19637.9336.51074488

170.6

23838.8639.01070798

170.6

26531.8343.51068087170.6

29906.4947.01067545170.6

31974.8046.51064834

21

22


G Q/AT. - Tbhrg

(kg/m2.s)(Q/m~(OC)(J/kg)

130.9

15950.2734.01322422130.9

17523.8735.01320957130.9

21823.6138.01314625130.9

26728.1242.01310267130.9

28912.4744.51307295130.9

31167.1056.51304630

171.4

15124.0030.51325619171.4

18518.5634.51320957171.4

21226.7937.01317918171.4

25121.3540.51313959171.4

27700.2642.01311960171.4

31966.8445.01309295


G Q/AT. - Tb. hrghrg(kg/m2.s)

(Q/m~("C)(J/kg)

131.5

15519.2331.51389674131.5

17350.1333.01386292131.5

21421.0936.01383554131.5

26390.5839.51378651131.5

28717.5041.51374447131.5

33193.6342.51371644

172.1

15203.5828.01389674172.1

18141.2429.51385615172.1

21826.2635.51384255172.1

26598.1438.01380752172.1

29515.9139.51378651172.1

31729.5140.01375148


GQ/AT. - Tbhrg

(kg/m2.s)(Q/m~("C)(J/kg)

132.1

14292.4431.51295950

132.1

17773.8733.51293424

132.1

21104.7736.01290191132.1

25603.4438.51286922132.1

28967.5041.01283652132.1

32338.8543.51280382

172.8

16812.3331.01300387

172.8

18518.5632.01297843172.8

22023.2035.01295318172.8

27167.1039.01294055

172.8

28899.2039.51290845172.8

31467.5041.01287671

. Table 6. Experimental data for 60 % gasoline

GQ/AT. - Thhrg

(kg/m2.s)(Q/m~(OC)(J/kg)

134.4

15218.16331.51389674

134.4

18508.6233.01386292

134.4

21393.2336.01383554

134.427218.1739.51378651

134.4

29613.3941.51374447

134.4

32903.1842.51371644

175.8

14547.7428.01389674

175.8

18857.5529.51385615

175.8

22568.9635.51221245

175.8

26945.6238.01380752

175.8

29888.5939.51378651

175.8

33344.8240.01375148

23

24

Table 7. Comparisons between experimental results and those calculated

using the proposed correlation for 100 % g~oline 0 % ethanol

Heat Transfer Coefficient (kW/m2.K)

Experimental

Correlation% Difference

0.521

0.5628.1

0.568

0.5595.50.569

0.6137.70.652

0.6763.70.671

0.7044.90.531

0.5330.30.559

0.5640.9

0.6110.6150.7

0.668

0.6812.0

0.7060.7131.0

0.7710.7943.0


using the proposed correlation for 100 % gasoline 0 % ethanol


Experimental


0.469

0.41112.30.494

0.43611.80.574

0.49713.50.636

0.56311.4

0.6500.5928.9

0.6710.6217.5

0.4960.42015.4

0.5370.47511.5

0.5560.5245.7

0.6200.5727.8

0.659

0.6077.9I0.710

0.6626.7

Table 9. Comparisons between experimental results and those calculatedusing the proposed correlation for 90 % gasoline 10 % ethanol


Experimental


0.513

0.5051.6

0.532

0.5727.5

0.5590.5885.2

0.568

0.5893.7

0.579

0.63710.0

0.596

0.67813.7

0.599

0.52911.7

0.607

0.5538.9

0.618

0.6140.6

0.629

0.6645.6

0.636

0.71412.20.688

0.7458.3


using the proposed correlation for 85 % gasoline 15 % ethanol


Experimental


0.493

0.39819.30.526

0.42619.10.695

0.46718.80.668

0.54916.40.692

0.57919.40.781

0.62923.80.543

0.41425.00.615

0.46121.90.699

0.51516.90.747

0.58117.10.793

0.61918.3

25



Experimental


0.454

0.39812.2

0.531

0.45614.2

0.586

0.50513.8

0.665

0.56914.5

0.707

0.61313.2

0.743

0.65611.8

0.542

0.46314.6

0.579

0.49215.1

0.629

0.54613.3

0.697

0.62011.1

0.732

0.64511.9

0.768

0.67911.6



Experimental


0.507

0.45011.3

0.561

0.50310.3

0.629

0.54912.7

0.756

0.63615.9

0.811

0.66917.5

0.844

0.71415.4

0.510

0.45910.0

0.639

0.53715.9

0.684

0.59912.4

0.758

0.66012.2

0.819

0.72013.3

0.889

0.75914.7

26

Slngle~ ~"bbIY- Iphase IU9_-t--liquid

slug - annular

Figure 1. Flow Regimes in Forced-Convective Boiling

Temperature andchart re.corders

c:::::>

Heater II

Thermocouplelocations

WaHmeter--Variable voltagetransformer

Figure 2. Schematic of the Experimental Apparatus

27

90I ---J).

n6n0"

pou

70 u 600tV"

\.. 50;:) .- ,~I(j ••••• •\.. -•4.' a.E

~30

20l

o Wall sur face temperature• Mixture temparature10'0

102030405060708090100

Pe'rcen ll~n~th of t~be

Figure 3. Tube wall and liquid temperature variations

28

104N.J

101 10

Slug - annular

• Wa terA R. 22o R12-R 22 MixturesD Gasoline-Ethanol

~1:<\lf~~ii103 PeSo 104

Figure 4. Two-phase Heat Transfer Correlation Results

•

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on the generalized correlation equation of two...

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