AIAA-2002-3224

American Institute of Aeronautics and Astronautics

1

EXPERIMENTAL STUDY OF LAMINAR FILM CONDENSATION ON BANK OF HORIZONTAL TUBES WITH STEFAN NUMBER GREATER THAN UNITY

R. K. Sharma* and R. L. Mahajan

Department of Mechanical Engineering University of Colorado

Boulder, CO80309-0427

Abstract

In this paper, we report steady state experimental data for laminar condensation heat transfer on bank of smooth horizontal tubes for fluids with Stefan number greater than unity. The condensation experiments were carried out in saturated vapor of FC5311 on 9.5 mm, 12.7 mm, 15.88 mm and 22.2 mm diameter copper tubes for spacing-to-diameter ratios (s/D) ranging from 2 to 12. Experimental heat transfer coefficients were calculated for each tube based on the sensible heat gain of the cooling water. A comparison with the past analytical predictions of the ratio of heat transfer from the top tube to that from the lower tubes in a bank of tubes reveals two major differences. First, Chen’s correlation over-predicts heat transfer rates from the lower tubes. Second, our data indicate that the heat transfer rate from the lower tubes is a strong function of s/D. Assumptions made in Chen’s analysis are critically examined and the discrepancy is explained in terms of non-validity of those assumptions and ignoring of the different hydrodynamics that arise for different vertical spacing between the tubes. The condensate and the momentum gain by the jets issuing from the upper tubes are different for different s/D ratios. For low spacing-to-diameter ratio (s/D=6) tube banks, condensation heat transfer from the lower tubes deteriorates due to the formation of a finite condensate film on the top of these tubes. For high spacing-to-diameter ratio (s/D>6) tube banks, however, momentum gain between tubes leads to instability of condensate jets thereby enhancing the condensation heat transfer on the lower tubes. Finally, heat transfer correlations are formulated to predict condensation heat transfer for tube banks with different spacing-to-diameter ratios.

Introduction

In the last couple of decades, a new family of Fluorinert fluids with high Stefan numbers

)( fghTCpS ∆= has gained prominence due to its

application in various industries. Condensation soldering for electronic assemblies1-5 is one such example. It involves immersing articles with pre-deposited solder in a body of saturated Fluorinert fluid vapor. The hot vapors condense on the relatively colder solder, release latent heat; melt the solder which then forms the required bond. Commercially available fluids,

like FC-70, FC-5311 and Galden LS-230, used in condensation soldering have Stefan numbers ( fghTCpS ∆= ) greater than unity, upto 3.5.

The correlations used in the design of a bank of tubes in the cooling coil of the condensation soldering equipment involved are generally those developed for fluids with S less than unity. The initial experimental data by Wenger and Mahajan3 suggested that these correlations may be conservative. While Chen6,7 has analyzed laminar film condensation over a bank of tubes, no experimental study, to-date, has been reported in literature on this topic. Of particular interest is an assessment of the accuracy of Chen’s analysis and a study of the effect of the spacing between the tubes on the heat transfer rates.

Nomenclature

Cp Specific heat, (J/(kg.K) D Characteristic dimension, m d Diameter of the condensate column (or jet) Gr Grashoff number ( )23

lgD ν= g Acceleration due to gravity, (m/s2) hfg Latent heat of vaporization (kJ/kg) J Momentum parameter, S/Pr, Chen (1961) L Length of specimen or tube, (m) m& Condensate flow rate, (kg/s) Nu Nusselt number, ( )lkhD= Pr Prandtl number, ( )kCpµ= T Temperature, K s Center-to-center spacing between tubes S Stefan or Jakob number fgp hTC ∆= k Thermal conductivity, (W/m. K) h Heat transfer coefficient (W/m2.K)

Q& Heat flux, (W/m2) Rej jet (or column) Reynolds number ( )lUd ν= U Velocity of the condensate We Weber number ( )ldU σρ 2=

Z Ohnesorge number ( )( )2/1/ lll dσρµ= Greek: µ Dynamic viscosity, (Pa.s) ν Kinematic viscosity, (m2/s) ρ Density, (kg/m3) σ Surface tension, (N/m) θ,φ Angle of convection region

*Hewlett-Packard Co. Laboratories 1501 Page Mill Road, ms 1183 Palo Alto, CA 94304

8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference24-26 June 2002, St. Louis, Missouri

AIAA 2002-3224

Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

AIAA-2002-3224

American Institute of Aeronautics and Astronautics

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Γ Condensate flow rate per unit length Subscript l liquid/condensate v vapor n number of tubes o outer chen using Chen7 correlation bottom based on bottom tube top based on top tube

Literature Review

The classical analysis of film condensation heat transfer on vertical flat surfaces and horizontal tubes is due to Nusselt8. Assuming a linear temperature profile, neglecting inertia, convection, and vapor shear, the local heat transfer rate, Nux , was derived as :

( )( )

4/13

4

−

−=

wsatl

fgglx TTk

xghNu

ν

ρρ (1)

Several researchers have extended and modified the analysis since then. Rohsenow9 used integral analysis to obtain a correction for sensible heat effects during condensation and showed that replacing hfg in Eq. (1) by h’

fg takes care of the correction where

( )Shh fgfg 68.01' += for 0<S<1 (2) and S is the Stefan or Jakob number.

Sparrow and Gregg10 showed for the first time that laminar film condensation on a vertical plate could be treated within the framework of boundary-layer approximation. Using similarity transformations to solve the boundary-layer equations, they showed that, except for low Prandtl number fluids, Rohsenow’s approximate analysis was quite adequate. Inclusion of inertia terms had little effect on heat transfer for fluids with Prandtl numbers greater than unity. At low Prandtl numbers, however, the effect of inertia was significant with the results departing from Nusselt predictions as the Stefan number ( )fghTCpS ∆= increased.

Koh et al.11 applied the boundary layer treatment to include shear forces at the vapor-liquid interface. For all Prandtl numbers, effect of interfacial shear on heat transfer was negligible as long as the Stefan number was low. However, at high Stefan numbers, it caused a substantial reduction in heat transfer in low Prandtl number fluids. Subsequent analytical research by Rose12 has shown that, the vapor shear effect is a function of momentum parameter ( )PrSJ = . An assumption of infinite condensation rate was made in this analysis.

Using similarity transformation formulation and assuming vanishing vapor velocity at the vapor-liquid interface, Sparrow and Greg13 presented a boundary layer analysis of condensation on single horizontal tube. Chen6 carried out an analytical study of laminar film

condensation on a single tube including the inertia effects and assuming that the vapor was stationary outside the vapor boundary layer. In a companion paper, Chen7 extended the single tube analysis to multiple tubes and examined the effect of condensation between tubes within the framework of boundary-layer theory. It was shown that other than splashing and non-uniform spilling, condensation and momentum gain between tubes may be the reason for the higher than predicted experimental heat transfer coefficients from lower tubes14,15. The analytical results were presented in an approximate formula in the following form:

( )[ ]4/1

4/11 15.095.01

02.068.0112.01

−+++

−+=SJJSJS

nSnhh

Nu

n

(3)

In the absence of inertia effects, 0=J , and Chen’s7 solution (Eq. (3)) reduces to Nusselt-Rohsenow correction (Eq. (2)).

Based on a systematic study of condensation heat transfer, Kutateladze et al. 16,17 have provided extensive experimental data and analyses of film condensation on smooth horizontal tube banks for refrigerants R12 and R21. For single tubes, Kutateladze and Gogonin16 concluded that condensation heat transfer coefficients were close to Nusselt predictions only for We ( )[ ]( )2/1σρρ vlgD −= values greater than 10. Conducting experiments with identical tubes at s/D = 2 and 5, Kutateladze et al.17 concluded that the influence of free-fall speed of condensate on condensation heat transfer was negligible. By varying condensate flow rates by changing the cooling water temperatures; condensation experiments were carried out on banks composed of 3, 6, 10 and 45mm diameter tubes. Although, heat transfer coefficients from individual tubes in a bank were not calculated, the authors visually observed that intensity of the tube heat transfer depended on the hydrodynamics of condensate flow on each tube.

Most of the studies of condensation heat transfer discussed above are for relatively small sensible heat effects for fluids with Stefan numbers less than unity. Applications such as condensation soldering for electronic assemblies and thermal curing of underfill epoxies have motivated the study of condensation of high Stefan number fluids. The only experimental study to-date, dealing specifically with fluids with Stefan number greater than unity is due to Mahajan et al.18. Conducting laminar film condensation experiments on copper spheres with Fluorinert fluid FC-70, it was shown that for these large Prandtl number (Pr=323 @ T=25oC) and high Stefan number fluids (S=3.5), the Nusselt-Rohsenow equations (1) and (2), are accurate predictors. The heat transfer rates were calculated based on quasi-steady temperature response of the spheres. The deviations from theoretical values was 10% lower at higher values of S and 35% lower at lower S. This

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was attributed to non-condensable components whose fraction became increasingly larger as surface temperature approached saturation temperature. Sharma and Mahajan19 studied the condensation of FC5311 on finite horizontal cylinders and vertical cylinders. The contribution from condensation on ends of horizontal cylinders and top of vertical cylinders was included.

Although the above reported studies of Mahajan et al.18 and of Sharma and Mahajan19 have broken some ground in providing experimental data for high Stefan number fluids, there are no reported experimental studies of condensation of such fluids on preferred condenser geometries like a bank of tubes. The analysis of Chen7 suggests that the conventional condensation heat transfer correlation for a bank of tubes20 can be in significant error for such fluids. Careful experimental data is needed to validate Chen’s analysis and to develop correlations. The present study was undertaken to fill this gap.

Experiment

The experimental apparatus, as shown in Fig. 1, consists of a 305mmx305mmx458mm vessel made from a 4mm thick stainless steel sheet fitted with a 1.5kW immersion heater at the bottom and 6mm OD cooling water coils at the top. The 1.5 kW immersion heater was supplemented by two 1.5 kW plug-in immersion heaters operating at 208V. The additional heating capacity maintained a region of pure saturated vapor up to 350mm high above the liquid level in the vessel. Viton gaskets with temperature ratings above 215oC were used to seal the vessel openings provided for the plug-in heaters. The electric immersion heaters were used to boil the liquid while the water-cooled coils at the top were used to condense the vapor. Since this vapor is ~27 times heavier than air, a stable stratified saturated vapor region can be maintained in steady state between the cooling coils and the top of the boiling liquid. Power input to the heaters was controlled using a variac. A thermocouple probe was positioned inside the jar during the experiment to record saturation temperature of the vapor.

Three holes, each 25mm in diameter and 55mm apart, were plasma-cut at identical locations on opposite walls of the vessel. Assuming a 50mm liquid level to cover the immersion heaters, the lowest hole was cut about 150mm from the bottom of the vessel. The instrumented cooling tubes were inserted through these holes. The tubes are held in position by brass compression fittings, retrofitted with neoprene O-rings, both at the entry and exit of the chamber. The O-rings help in providing an airtight seal between the fitting and the tube. Care was taken while positioning the tube to ensure that it was horizontal. Square openings of 150mm side were plasma-cut on opposite walls facing the instrumented tubes to visualize the condensation process. The openings were provided with borosilicate glass

covers to seal off the vapors and provide a clear view of the condensation process.

The instrumented tube was made out of a medium thickness copper tube with an OD of 22mm. Constantan wires, 40 SWG, were positioned inside the tube through 1.6mm ID holes drilled at prospective thermocouple locations. These holes were sealed with lead-free silver solder thus forming a junction between the constantan wire and copper tube. The cleaned tube was tested for leakage with pressurized water. The free ends of the constantan wires were routed outside through the tube and connected to a data acquisition system. A 40 SWG copper wire was soldered on the outside of the tube and connected to the data acquisition system thus completing the junction for the wall thermocouples. The outer surface of the instrumented tube was carefully cleaned with emery paper and wiped with acetone to remove oxides and oil. Cooling water inlet and outlet temperatures were measured by inserting, 1.6mm diameter, T-type thermocouple probes, perpendicularly, up to the centerline of the copper tube at the entry and exit locations of the vessel. The choice of thermocouple probe was based on the range of temperatures measured and the required sensitivity. Neoprene gaskets, 2mm thick and 5mm in diameter, were glued on to the thermocouple by CrazyGlue™ adhesive to maintain a predetermined projection length inside the tube. To prevent leakage of cooling water, the thermocouple entry locations were sealed with RTV Silicone sealant. The residual vapor cooling system consisted of a set of 6mm OD cooling coils located just below the lid of the vessel. Both the instrumented tube and cooling coils were housed in the stainless steel vessel. To reduce the thermal stress on the sight glasses, the heater power was ramped using a proportional, integral and differential (PID) controller and a solid-state relay (SSR) with feedback from the temperature of the liquid pool.

After benchmarking experiments with single tube, steady state experiments were carried out in double tube configurations on 9.5mm, 12.7mm, 15.9mm and 22.2mm OD commercial copper tubes. The double tube configuration experiments provided tube spacing to diameter ratios (s/D) ranging from 2 to 12. Experiments in three tube configurations were conducted with 9.5mm, 12.7mm and 15.9mm OD commercial copper tubes with s/D values ranging from 2 to 6. Twisted strips of Teflon were inserted inside the instrumented tubes as turbulators to provide adequate mixing of hot and cold fluid streams. Low conductivity of Teflon prevented any significant conduction loss from the wall. The uncertainty in the temperature and flow measurements was ~0.5oC and 10ml/sec, respectively.

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American Institute of Aeronautics and Astronautics

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Analysis

Temperature measurements at the inlet and outlet of each instrumented tube were used to calculate the heat transferred on each tube during condensation.

( )outin TTCpmQ −= & (4) The average wall temperature of each cooling tube, in turn, was obtained from the arithmetic mean of the wall thermocouple measurements at each location around the tube.

∑∑=ii

wi

w iTT (5)

Knowing Q and Tw , the averaged condensation heat transfer coefficient, ho ,on each tube could be easily calculated using the direct method.

( )[ ]wsatoo TTAQh −= / (6) where Ao is the outer surface area of the cooling tube and Tsat is the vapor saturation temperature. The condensate flow rate was evaluated from the condensation heat transfer coefficient in the following manner.

( )( )fgl

wsato

hDTTh

µπ−

=Γ (7)

Based on condensate flow rates, liquid Reynolds number ( )lµΓ= 4 was calculated and compared with Kutateladze’s16 condition to verify the formation of condensate jets. The next important step in analyzing the heat transfer phenomena is to determine the stability of the jets issuing from the bottom of the top tube. To this end one needs to determine the balance between the condensate inertia and the surface tension, as characterized by Weber number and jet Reynolds number, respectively.

lll dUWe σρ 2= (8)

lj Ud ν=Re (9) where d is the diameter of the jet and U is the velocity of the jet. The condensate jet becomes unstable if the gas-based Weber number Weg ( )lv dU σρ 2= exceeds the critical Weber number shown below: ( ) 9.041.32.1 ZWe

crg += (10)

This relationship was based on estimation of jet break-up length from results obtained by Sterling and Sleicher21. In Eq. (10) Z is the Ohnesorge number Z defined in terms of liquid Weber number and jet Reynolds number as follows:

( ) 2/12/1 Re σρµ dWeZ lljl == (11) Results

To benchmark our set up, we first present our condensation heat transfer results for a single tube. The data for the 2-tube and 3-tube bank configurations are discussed in the subsequent section and compared with the past analytical relations. Discrepancies between the

two are noted and new formulations are presented to correlate the experimental data. Experimental results for a single tube:

Steady state experiments were carried out on single tubes and compared with analytical results7,22. The ratio of local and average temperature difference, ∆T/(∆T)m, based on the measured vapor and wall temperatures at different circumferential locations followed a cosine distribution around the circumference23. The average condensation heat transfer coefficients also matched Chen’s7 results for single tubes, after appropriate viscosity correction18. An excellent match was observed when single tube results were compared with quasi-steady condensation results on high-aspect ratio horizontal cylinders20. Results for multiple tube configurations:

Using Eq. (6), the averaged condensation heat transfer coefficients for the top and bottom tubes, htop and hbottom respectively, were calculated from the experimental data for both the two-tube and three-tube banks. These are plotted in Figs. 2 and 3 as hbottom/htop vs Stefan number. For comparison, Chen’s7 correlation is also shown on these plots. We first note that for both the 2-tube and 3-tube bank arrangements, Chen’s correlation over-predicts the ratio. Recalling that the heat transfer rate from the top tube matches with the analytical predictions for a single tube, the implication is that the experimental heat transfer rate from the bottom tube (s) is (are) lower than predicted by Chen’s correlation. Secondly, the data clearly indicates the dependence of the heat transfer rate from the lower tubes on s/D. For the two-tube bank, the experimental ratio is over 75% lower than Chen’s correlation for low s/D (2<s/D<6) and by more than 20% for high s/D (6<s/D<12). For the three-tube bank, the results show a similar trend although the effect of s/D seems to be less pronounced.

The experiments differ from Chen’s assumption in the following ways. (1) Our visual observations, discussed in the next section, indicate that the condensate flow from the upper tubes is in the form of columns instead of a continuous film assumed in Chen’s analysis. (2) The film thickness at the stagnation point of the lower tube is finite unlike the zero-thickness assumption by Chen (3) Chen’s analysis does not consider the instabilities that affect the condensate film. (4). The effect of spacing between tubes is not considered in that analysis.

Flow Visualizations

High-speed motion pictures were taken of the condensate flow from the tubes. Figure 4 shows the view of condensate columns draining from the bottom of the top tube. The clear indication is that the condensate runs off as columns (or jets). It was also observed that these condensate columns undergo a

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American Institute of Aeronautics and Astronautics

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constant process of birth, growth and coalescence. Further, the condensate flow from the lower tube was much more wavy. At higher condensate flow rates, there was an increase in the frequency of column formation and the tendency of the columns to combine and form a continuous film. Figure 5 shows the close-up view of condensate columns draining from the bottom of the lower tube. Note, the waviness in the condensate columns created by interaction between the vapor and falling condensate. The general view of condensation process on a two-tube bank is shown in Fig. 6.

The spacing between the columns measured by these high-speed recordings was found to be of the order of 5-6 mm. This is very close to the Taylor

wavelength25 ( ){ }gll ρσπ 22= of 6.5mm. The suggestion is that the formation of columns is governed by the growth of instability waves at the liquid-vapor interface.

Figure 7 presents photograph of the condensate column for a high tube spacing configuration (s/D ~ 8) clearly revealing the locations where the column hits the film on the lower tube. The condensate film at these locations is disturbed by splashing and intermittent formation of craters. Note the wavy profile of the condensate layer at the top of the tube. In comparison to the dark smooth images of columns in Fig. 4, the columns in Fig. 7 appear to have broken up into a train of droplets, before falling on the lower tube.

Model Development

To develop a model for the observed condensation phenomena, the visual observations discussed above were augmented by measurements of temperature of the condensate column leaving the top tube. The temperature was found to be close to the saturation temperature. This result showed that the sub-cooled condensate quickly warmed up and arrived at the lower tubes at saturation temperature.

Figure 8 presents a physical model of the condensate falling onto a horizontal tube in the bank. The falling condensate, being at saturation temperature creates a region (of arc-length xs) on the tube surface where heat is transferred to the cooling water by pure convection. Due to the absence of temperature gradient at the vapor- liquid interface, condensation heat transfer does not occur in this region. As the condensate close to the tube wall cools by convection heat transfer to the cooling water, a thermal boundary layer develops in the condensate film on the tube. The onset of condensation heat transfer occurs after a certain angle φ or arc-length xs, when the thermal boundary layer thickness equals the film thickness 26. The angle φ is given by Rogers26.

( ) 3/13/11 RePr385.0 −= GrP φ (12)

where ( ) ( )∫= θθφ dSinP 3/1 . The Nusselt number in

this region is given by ( ) φφφ QGrNu l

9/19/13/1 RePr969.0 −= (13) where Q(φ) is a function of P(φ) 16 and Nuφ is defined in terms of gravitational-viscous length scale. Calculation of angle φ for all the lower tubes revealed a value close to 170o for three-tube bank and 110o for two-tube bank. This indicates that condensation on the bottom tube can only occur at the lower surface. However, condensation heat transfer at the lower surface of the tube is negligible due to high condensate film thickness in that region. As a result it is reasonable to expect that heat transfer primarily occurs at the top surface and is governed by convection in the film (see Eq. (13)).

Equation (13) gives lower tube Nusselt number a dependence of D-1/4. It is well known that Nusselt number for condensation on a single tube varies as D3/4 (Eq. (1)). Therefore the ratio of heat transfer coefficients of the bottom and top tubes is given by

1−∝ Dh

h

top

bottom (14)

Figure 9 shows the plot of heat transfer coefficient ratios against the spacing-to-diameter ratio (s/D). Due to limitations of the experimental setup, the spacing between tubes for the s/D values 2 to 6 were identical. For these spacing-to-diameter ratios, the heat transfer coefficient ratio for two-tube banks and three-tube banks increases as the spacing-to-diameter ratio increases. This is consistent with Eq. (14). The linear dependence is reflected in the equations shown in Fig. 9. Unlike in the two-tube case, the bottom tube in the three-tube bank is inundated with condensate from two tubes. The resulting constants of proportionality of three-tube and two-tube banks are, therefore, different.

The dependence in Eq. (14), however, does not hold good for s/D greater than 6. At higher spacing-to-diameter ratios, the condensate flow falling on the bottom tube is no longer laminar and break-up of condensate columns, aided by Rayleigh instabilities, sets in27. To understand this phenomenon, the experimental vapor-based Weber numbers were calculated at the top of bottom tube and compared with the critical values obtained from Eq. (10). The plot in Fig. 10 compares experimental Weg with the (Weg)cr for different spacing-to-diameter ratios. Weg values for two-tube bank with s/D less than 6 are below the criterion, indicating laminar condensate flow between the tubes. Weg values for two-tube bank with s/D more than 6 are above the criterion and signify liquid breakup in the condensate column before it reaches the top of bottom tube.

Going back to Fig. 9, we note that for the high s/D (>6) the ratio of heat transfer coefficients is higher at lower s/D values and appears to decrease as the s/D

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values increase. This is not unexpected since increase in s/D values indicates a smaller departure from (Weg)cr

(see Fig.10) , decreasing the intensity of instability and, subsequent, liquid breakup. For very large spacing, s, the heat transfer coefficient ratio should reduce to unity representing a case when tubes are so far apart that condensate from the top tube does not affect condensation on the bottom tube. As shown in the equation on Fig. 9, heat transfer coefficient ratios follow an inverse power relation with s/D, implying an asymptotic value of unity as the s/D becomes very large. A comparison of Figs 9 and 10 for these large s/D (>6) cases also suggests a Weber number dependence for heat transfer ratios, warranting further investigation.

Similar considerations arise for the three-tube configuration with low s/D. Figure 10 shows that the Weg values are less than the high spacing two-tube configuration but higher than those for the low spacing two-tube configuration. Although the spacing between tubes is small, the condensation on the middle tube increases the condensate flow and hence, inertia of the liquid jet.

Summary

An in-depth experimental study of condensation of fluids bank of horizontal tubes with high Stefan number has been presented. Condensation experiments were carried out on tube banks with tube spacing-to-diameter ratios (s/D) ranging from 2 to 12. Heat transfer coefficients were calculated for condensation in two-tube and three-tube banks. The comparison of ratio of heat transfer coefficients for the bottom and top tube of each configuration with Chen’s correlation revealed differences between the two. Chen’s correlation over-predicted heat transfer from bottom tubes by 75% for low s/D and by 20% for high s/D ratios, in case of two-tube bank. For the three-tube bank, the experimental results were lower than predictions by 75%.

The ratio of heat transfer coefficients for two-tube banks with 2<s/D<6 increased linearly with s/D. The heat transfer phenomenon for low spacing-to-diameter ratios (2<s/D<6) was explained using a physical model based on existence of a finite film thickness at the stagnation point of the bottom tube. Heat transfer coefficient ratios for high spacing configuration were about 30% higher than that of low spacing tube bank. The enhancement of heat transfer phenomenon was explained using the criterion for onset of Rayleigh instabilities in the condensate column. Heat transfer coefficient ratios for three tubes also showed a linear variation with s/D values between 2 and 6. The constant of proportionality was higher due to higher condensate flow rate and incipient waviness in the film. These results will provide basis for improved condenser design for high Stefan number fluids.

References

[1] Chu, T. Y., Mollendorf, J. C. and Pfahl, R. C. Jr, 1974, “Soldering using condensation heat transfer”, Proc. Tech. Prog., NEPCON West, Anaheim, CA.

[2] Pfahl, R. C., Jr., Mollendorf, J. C. and Chu, T. Y., 1975, “Condensation Soldering”, Welding Journal, Vol. 54, No. 1, p. 22.

[3] Wenger, G. M. and Mahajan, R. L., Sept. 1979a, “Condensation Soldering Technology-Part I: Condensation soldering fluids and heat transfer”, Insulation/Circuits, p 131.

[4] Wenger, G. M. and Mahajan, R. L., Oct. 1979b, “Condensation Soldering Technology-Part II: Equipment and Production”, Insulation/Circuits, p 133.

[5] Wenger, G. M. and Mahajan, R. L., Oct. 1979c, “Condensation Soldering Technology-Part III: Installation and Application”, Insulation/Circuits, p 135

[6] Chen, M. M., Feb 1961, “An analytical study of laminar film condensation: Part 1-Flat Plates”, ASME J. Heat Transfer, Vol. 83, pp48-54.

[7] Chen, M. M., Feb 1961, “An analytical study of laminar film condensation: Part 2-Single and Multiple Horizontal Tubes”, ASME J. Heat Transfer, Vol. 83, pp55-60

[8] Nusselt, W., 1916, “Die Oberflachenkondensation des Wasserdampfers”, Teil I, II, Z. VDI, Vol. 27, pp541

[9] Rohsenow, W. M., Nov 1956, “Heat transfer and temperature distribution in laminar film condensation”, Trans. ASME, Vol. 78, p1645-1648

[10] Sparrow, E. M. and Gregg, J. L., 1959a, “A boundary treatment of laminar film condensation”, ASME J. Heat Transfer, Vol. 81, pp13-18

[11] Koh, J. C. Y., 1961, “An integral treatment of two-phase boundary layer in film condensation”, ASME J. Heat Transfer, Vol, pp359-362

[12] Rose, J.W., Feb 1998, “Condensation heat transfer fundamentals”, Trans. IchemE, Vol. 76, Part A, pp143-152.

[13] Sparrow, E. M. and Gregg, J. L., 1959b, “Laminar condensation heat transfer on a horizontal cylinder”, ASME J. Heat Transfer, pp291-296

[14] Short, B. E. and Brown, H. E.,1951, “Condensation of vapors on vertical bank of horizontal tubes”, Gen. Disc. Heat Transfer, pp27-31.

[15] Young, F. L. and Wohlenberg, W. J., Nov 1942, “Condensation of saturated Freon-12 vapor on a bank of Horizontal Tubes”, Trans. ASME, pp787-794

[16] Kutateladze, S. S., 1982, “Semi-Empirical theory of film condensation of pure vapors”, Intl. J. Heat Mass Transfer, Vol. 25, No. 5, pp653-660

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[17] Kutateladze, S. S., Gogonin, I. I., Sosunov, V. I., 1985, “The influence of condensate flow rate on heat transfer in film condensation of stationary vapor on horizontal tube banks”, Int. J. Heat Mass Transfer, Vol. 28, No. 5, pp1011-1018

[18] Mahajan, R. L., Chu, T. Y. and Dickinson, D. A., May 1991, “An experimental study of laminar film condensation with Stefan number greater than unity”, ASME J. Heat Transfer, Vol. 113, pp472-478.

[19] Sharma, R. K. and Mahajan, R. L., Oct 2000, “Experimental study of laminar film condensation on horizontal and vertical cylinders with Stefan number greater than unity”, 8th Brazilian Conference on Thermal Engineering and Sciences, Porto Alegre

[20] Incropera, F. P. and Dewitt, D. P., 1990, “Fundamentals of heat and mass transfer”, Wiley

[21] Sterling, A. M. and Sleicher, C. A., 1975, “The instability of capillary jets”, J. Fluid Mech., Vol. 68, Part 3, pp477-495

[23] Memory, S. B. and Rose, J. W., 1991, “Free convection laminar film condensation on a horizontal tube with variable wall temperature”, Intl. J. Heat Mass Transfer, Vol. 34, pp2775-2778.

[24] Sharma, R.K., 2001, “Transport Phenomena in two-phase flows during condensation of special fluids and non-azeotropic fluid mixtures”, PhD Thesis, University of Colorado, Boulder

[25] Yung, D., Lorenz, J. J., Ganic, E. N., 1980, “ Vapor/Liquid interaction and Entrainment in falling film evaporators”, ASME J. Heat Transfer, Vol. 102, pp20-25

[26] Rogers, J.T., 1981, “Laminar falling film flow and heat transfer characteristics on horizontal tubes”, Can. J. Chem. Eng., Vol. 59, pp213-221

[27] Lin, S. P. and Reitz, R. D., 1998, “Drop and spray formation from a liquid jet”, Annu. Rev. Fluid Mech., Vol. 30, pp85-10

COOLING COILS

SIGHT GLASS

IMMERSION HEATERS

INSTRUMENTED TUBE

COOLING WATER (IN/OUT)

Figure 1. Schematic for Condensation experiments on Bank of Tubes

WALL THERMOCOUPLES

STAINLESS STEEL VESSEL

VAPOR THERMOCOUPLE

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0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5 4S

h bot

tom

/hto

p

s / D = 4 . 3 1; D = 12 . 7 m ms / D = 8 . 6 2 ; D = 12 .7 m m

s / D = 5 . 7 5 ; D = 9 . 5 2 m ms / D =11.5 ; D = 9 . 5 2 m mC h e n 's P re dic tio n n=2s / D = 3 . 4 5 , D = 15 .8 7 5 m m

s / D = 6 . 8 8 , D = 15 .8 7 5 m m

Figure 2. Comparison of ratio of experimental heat transfer coefficients for bank of two tubes with Chen’s 7 predictions

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5 4

S

hbot

tom

/hto

p

C h e n 's Pre diction n =3

s/D=5.75, D=9.52m m , n=3s/D=3.45, D=15.875m m

s/D=4.31, D=12.7m m

Figure 3. Comparison of ratio of experimental heat transfer coefficients for bank of three tubes with Chen’s 7 predictions

Coalesce

Birth

Figure 4. View of the condensate columns draining from the bottom of top tube

AIAA-2002-3224

American Institute of Aeronautics and Astronautics

9

Figure 5. View of the condensate inundation from the lower tube

Note the ripples in the condensate columns

Figure 6. Condensate flow from a bank of two horizontal tubes

Figure 7. Condensate flow on to bottom tube for high spacing-to-diameter ratio tube bank

AIAA-2002-3224

American Institute of Aeronautics and Astronautics

10

Tw

R

x

Tsat

φ δ

δh

Figure 8. Simplified flow of condensate in a bank of tubes

Ratio = 0.1368(s/D) + 0.265

Ratio= 0.0508(s/D) + 1.0261

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10 12 14s/D

hbot

tom

/hto

p

2 tubes 2<s/D<62 tubes 6<s/D<12

3 tubes, 2<s/D<6

Figure 9. Variation of ratio of heat transfer coefficients with spacing-to-diameter ratios

Ratio=1+2.36(s/D)-1.0

AIAA-2002-3224

American Institute of Aeronautics and Astronautics

11

Figure 10. Comparison of experimental and calculated Weber numbers, based on maximum jet break-up length

0

0.5

1

1.5

2

2.5

3

0 5 10 15

Spacing-to-Diameter Ratio (s/D)

Vap

or-b

ased

Web

er N

umbe

r (W

ev )

Two Tubes (s /D<6)Three TubesTwo Tubes (s /D>6)

Rayleigh Break-up Criterion (We cr)