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Local Evaporative Heat Transfer Coefficient in Turbulent Free-Falling Liquid Films

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Local Evaporative Heat Transfer Coefficient in Turbulent Free-Falling Liquid Films ht. J. Hear Mass Transfer. Vol. 31, No. 4, pp. 731-742, 1988 0017-9310/88$3.00+0.00 Printed in Great Britain 0 1988 Pergamon Press plc Local evaporative heat transfer coefficient in turbulent free-falling liquid films J. A. SHMERLERt and I. MUDAWWAR Boiling and Two-phase Flow Laboratory, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, U.S.A. (Received 4 June 1987 and infinalform 19 August 1987) Abstract-Evaporative heating of a free-falling turbulent liquid film has been investigated experimentally and numerically. The tilm exhibited a long thermal development length persisting up to more than one half of the 781 mm long heated test section. The increased length of the development region is attributed to the formation of a boundary layer at the film interface. This boundary layer was predicted numerically and observed in temperature measurements within the film. The heat transfer coefficients are averaged over the lower section of the tube and correlated as a function of the Reynolds and Prandtl numbers. Numerical predictions are made for the development region and for fully developed heat transfer coefficients using three different eddy diffusivity models. Comparison with experimental data reveals that two of these models are fairly successful in predicting the extent of the thermal development region and the time-averaged evaporative heat transfer coefficient; yet the data indicate the need for development of a new model which accurately accounts for local and spatial wave-induced variations of film thickness. 1. INTRODUCTION a similar approach with the addition of new gas absorption data and the effects of concurrent vapor THE CHARACTERISTICS of free-falling evaporating films flow. Seban and Faghri [12] looked at several model- are of importance in many aspects of thermal engin- ing schemes in an attempt to predict Chun and eering and chemical processes. While a need has been Seban’s data and new data collected on essentially the shown for an improved understanding of falling film same apparatus as Chun’s [17]. They concluded that transport processes, the amount of heat transfer data the best predictions are made using Limberg’s [9] remains limited as shown by the summary of exper- model near the wall, modified with the interface damp- imental investigations in Table 1. ing function of Mills and Chung. Although their The study by Chun and Seban [2] is the most often model predicts the data reasonably well, a physical sighted reference on evaporative heating of falling inconsistency occurs as there is a discontinuity films. They presented correlations for heat transfer between the two functions. Mudawwar and El-Masri coefficients in the wavy laminar and the turbulent [ 151presented an eddy diffusivity function which com- regimes as functions of the Reynolds and Prandtl bines the Van Driest damping function and the exper- numbers. They also found a correlation for the tran- imental turbulence data of Ueda et al. [ 181 to produce sition Reynolds number as a function of Prandtl num- an eddy diffusivity profile that is continuous over the ber. Fujita and Ueda [3] presented evaporation data entire film thickness. at a pressure of 1 atm. Their data followed the trends All of the turbulence models are semi-empirical, but shown by Chun and Seban but were an average of are based on a very limited data base. The present 10% higher. study provides a new data base by obtaining heat While the experimental work is limited, many eddy transfer coefficients over a wide range of Reynolds diffusivity models have been developed specifically for and Prandtl numbers. A test section 78 1 mm long was predicting heat transfer coefficients for falling films used to determine heat transfer coefficients during [4-151. The majority of these models use a modified thermal development and in the fully developed Van Driest function near the wall and a damping regime, and to determine the behavior of the tem- function to model the turbulent activity at the film perature profile across the film thickness. A numerical interface. Mills and Chung [8] presented a model that study was also performed to determine how well the uses a modified Van Driest function and a heat-mass available turbulence models predict the new data. transfer analogy with the gas absorption results of Lamourelle and Sandal1 [ 161 to model the eddy diffu- sivity near the film interface. Hubbard et al. [l l] used 2. EXPERIMENTAL SYSTEM The experimental apparatus was the same as that described in ref. [19]. The test section shown in Fig. 1 t Current address : AT&T Bell Laboratories, Liberty Cor- was 25.4 mm in diameter and consisted of a 300 mm ners, NJ 07060, U.S.A. long porous plastic film distributor, a 757 mm long 731 732 J. A. SHMERLER and I. MUDAWWAR NOMENCLATURE acceleration due to gravity u* friction velocity, J(r,/p) heat transfer coefficient for evaporative u + dimensionless film velocity, u/u* heating, q,l(T,- T,,,) X longitudinal position from the entrance to dimensionless heat transfer coefficient, the heated section (M 2’3)/(kg”3) Y distance from the solid wall k thermal conductivity Y+ dimensionless distance from the solid wall, Ka Kapitza number, (p’g)/(pa’) yu*/v. L length of the heated section Pr Prandtl number Pr, turbulent Prandtl number, E,,,/E,, 4 local heat flux Greek symbols 4w wall heat flux thermal diffusivity Re Reynolds number, 4l?/p F mass flow rate per unit film width T local temperature 6 film thickness r,, inlet temperature 6 + dimensionless film thickness, Gu*/v T, mean temperature Eh eddy heat diffusivity TS interface temperature s, eddy momentum diffusivity T sat saturation temperature p dynamic viscosity TW wall temperature V kinematic viscosity T+ dimensionless temperature, P liquid density ~y*(Tw- Wqw d surface tension u local velocity component in the flow Z local shear stress direction 7, wall shear stress. 1 Table 1. Experimental studies on evaporative heating of falling films Author Struve [l] Chun and Seban [2] Fujita and Ueda [3] Present study Injection method nozzle sintered tube sintered tube (152 mm) porous plastic (300 mm) Tube diameter 32 mm o.d. 28.6 mm o.d. 16 mm o.d. 25.4 mm o.d. 26 mm i.d. 28.4 mm id. 14 mm i.d. 24.6 mm id. Adiabatic length 0 317.5 mm 250 mm copper rod 757 mm Heated length 1250 mm 292 mm 6OOand 1OOOmm 781 mm Heating method steam condensation electrical resistance electrical resistance electrical resistance Test fluid Rll water water water Reynolds number x7cL8800 320-21000 700-9100 500&37 500 Prandtl number 4.12 1.77-5.7 1.8-2.0 1.75-5.4 adiabatic hydrodynamic development section made volumetric heat generation within the stainless steel of G-10 fiberglass based phenolic plastic, and heated tube. Reference [19] describes the apparatus and ther- length of 781 mm. The latter was a polished stainless mocouple locations in detail. The saturation temp- steel tube with a wall thickness of 0.41 mm through erature was both measured and calculated from the which a high d.c. current was passed to produce a chamber pressure, determined from measurements constant wall flux. made with a high accuracy pressure transducer. Heat transfer coefficients were determined from the All tests were performed using deionized water difference between the wall temperature and the satu- which was deaerated before introduction into the ration temperature. Pairs of thermocouples 180” apart experimental apparatus. A vacuum pump removed at 17 locations along the heated length measured the noncondensible gases from the system to give pure inside wall temperature. The pairs were unequally saturated conditions within the flow loop. After spaced with the thermocouples grouped closer to- charging the system and achieving equilibrium pres- gether at the top of the heated length to monitor ther- sure and temperature conditions, fluid was circulated mal boundary layer development. The outside wall at the maximum flow rate to give the greatest film temperature was calculated from these measure- thickness. The selected operating conditions were ments by performing a control volume energy balance achieved through the control of the chamber pressure assuming an adiabatic inner surface and uniform and inlet temperature of the fluid. The temperature Local evaporative heat transfer coefficient in turbulent free-falling liquid films 733 r-- FIG. 1. Schematic diagram of the fluid delivery system. was controlled through a heat exchanger located upstream of the test chamber. The pressure was main- AL tained at a level equal to the saturation value by con- q 37620 Pr = 1.75 0 31220 trolling the condensation rate of the generated vapor, 0.5 which was achieved by adjusting the amount of cool- t A 23060 0 17460 ant passing through the condensing heat exchanger. 0.4 l At high power levels, where a large amount of vapor ‘k was generated, a vacuum pump supplemented the 0.3 condenser. During the tests, the power level was kept below the wall heat flux necessary for the onset of nucleate boiling (ONB). This value was determined from a manipulation of a correlation for ONB presented in ref. 1201using the correlation for the evaporation heat 0 0.2 0.4 0.6 0.0 1.0 transfer coefficient presented by Chun and Seban [2]. x/L The wall heat flux was always kept at least 25% below FIG. 2. Variation of the evaporative heat transfer coefficient the value determined to produce boiling incipience. with distance along the heated section for Pr = 1.75. Temperature measurements along the heated length were recorded upon reaching steady-state conditions. New test conditions were achieved by decreasing the between 1.75 and 5.42.
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