FORCED- CONVECTION CONDENSATION INSIDE TUBES Donald P. Traviss Anton B. Baron Warren M. Rohsenow Report No. DSR 72591-74 American Society of Heating, Refrigeration and Air Conditioning Engineers Contract No. ASHRAE RP63 Engineering Projects Laboratory Department of Mechanical Engineering 4J Massachusetts Institute of Technology Cambridge, Massachusetts 02139 July 1, 1971 ENGINEERING PROJECTS LABORATORY J4 3NGINEERING PROJECTS LABORATOR 4GINEERING PROJECTS LABORATO' ~!INEERING PROJECTS LABORAT' NEERING PROJECTS LABORA EERING PROJECTS LABOR ERING PROJECTS LABO' RING PROJECTS LAB' TNG PROJECTS LAB IG PROJECTS LAB PROJECTS L PROJECTF ROJEC- OJEr TT/ Technical Report No. 72591-74 FORCED-CONVECTION CONDENSATION INSIDE TUBES by Donald P. Traviss Anton B. Baron Warren M. Rohsenow Sponsored by: Technical Committee 1.3 American Society of Heating, Refrigeration, and Air Conditioning Engineers Contract No: ASHRAE RP63 DSR Project No: 72591-74 July 1, 1971 Heat Transfer Laboratory Mechanical Engineering Department Massachusetts Institute of Technology Massachusetts Avenue, Cambridge, 02139 110u mw FORCED-CONVECTION CONDENSATION INSIDE TUBES by Donald P. Traviss Anton G. Baron Warren M. Rohsenow Massachusetts Institute of Technology ABSTRACT High vapor velocity condensation inside a tube was studied analy- tically. The von Karman universal velocity distribution was applied to the condensate flow, pressure drops were calculated using the Lockhart- Martinelli method, and heat transfer coefficients were calculated from the momentum and heat transfer analogy. Subsequently, the analysis was reduced to an accurate, but simplified form, to facilitate calculations. Experimental data for refrigerants R-12 and R-22 condensing in a 0.315 in. I. D. tube were obtained for mass fluxes from 1.2 x 105 to 11.3 x 105 lbm/hr-ft 2, qualities from 0.02 to 0.96, and saturation tem- peratures from 75 to 140*F. On the basis of the data and analysis, a simplified non-dimensional presentation of the results evolved. The agreement between the majority of the data and the analysis was within + 15 percent. INN fl, Acknowledgement The authors are grateful to ASHRAE Technical Committee TC 1.3 for support of this work. MININ111111", Table of Contents Abstract. . . . . . . . . . . . . . . . . .. . Acknowledgment . . . . . . Table of Contents. . . . . Nomenclature.. . . . . . . Introduction . . . . . . . Experiment . . . . . . . . General Description of Test Facility. . . . . . . Test Procedure. . . . Data Reduction. . . . Analysis. . . . . . . . . . Calculation Procedure for Analytical Results. Results. . . . . . . . . . . . . Conclusions. . . . . . . . . . . . - - - . References . . . . . . . . . . . . . . . . . Figures. . . . . . . . . . Experimental Apparatus Graph of B vs.6+ . Graph of M vs. 6+ cri t Graph of F vs. Re . 2 Baker Flow Regime Map Comparison of AnalysiE and Heat Transfer Data .. Comparison of AnalysiE and Pressure Gradient Data Appendix 1. Tables of Data . . Appendix 2......... List of Relevant Variables for Computer Program . Computer Program for Calculating Analytical Results . . . . . . 101 Nomenclature A cross sectional area ft2 a axial acceleration due to external force ft/hr2 B buoyancy modulus c specific heat BTU/lbm-0F D tube inside diameter ft E ratio of eddy conductivity to eddy viscosity F defined in Eq. (16) lbf/ft 2-ft 0 F defined in Eq. (28a,b,c) 2 Fr Froude number G mass velocity lbm/ft -hr 2 g0 constant: 4.17 x 108 lbm-ft/lbf-hr h local heat transfer coefficient BTU/hr-ft - F z havg average heat transfer coefficient BTU/hr-ft 2-o F h fg latent heat of vaporization BTU/lbm K thermal conductivity BTU/ft-hr-0 F L total length of condensation ft M defined in Eq. (25) Nu Nusselt number dP/dz pressure gradient lbf/ft 2-ft Pr Prandtl number q/A heat flux BTU/hr-f t2 Re Reynolds number S perimeter ft T temperature 0F IM'. AT difference between vapor and wall temperatures *F U mean velocity ft/hr uT friction velocity as defined in Eq. (21) ft/hr v local axial velocity ft/hr W mass flow rate lbm/hr x quality Xtt Lockhart-Martinelli parameter defined in Eq. (6) y radial distance from the wall ft z axial distance from condenser inlet ft a void fraction a ratio of interface velocity to average liquid velocity 6 thickness of the condensate film ft S h eddy conductivity Sm eddy viscosity P absolute viscosity lbm/ft-hr V kinematic viscosity ft 2/hr p density lbm/ft3 T shear stress lbf/ft2 SUBSCRIPTS e exit f friction g gravity k liquid v vapor z local value 0 wall 6 INTRODUCTION When saturated vapor flows in a tube that is cooled by an exterior fluid, some of the vapor condenses on the tube wall and forms a liquid film. Condensation inside tubes occurs in many applications, particu- larly in refrigeration condensers. The main resistance to heat transfer for refrigerants and other low-conductivity fluids is the resistance to conduction through the condensate film. The analysis of Nusselt [1] outlined the basic approach to this problem. At low flow rates and velocities, a laminar condensate film forms on the tube wall; and for a horizontal tube, the liquid accumulates at the bottom. Experimental data for this situation are in good agreement with the results [2], [3], and [4]. A turbulent condensate film evolves at higher flow rates. This problem has been studied by several investigators (for instance: Akers [5], Chen [6], Soliman [7], and Patel [8], and the resulting correlations have usually relied on empirical methods. Carpenter and Colburn [9] derived a semi-empirical equation of limited application. Rohsenow et al. [10] obtained the heat transfer coefficient for a liquid film on a vertical flat plate by using the momentum and heat transfer analogy. Later papers [11], [12], and [131 employed the same approach. More recent developments by Bae et al. [14] and Kosky and Staub [15] employed variations of the Lockhart-Martinelli pressure drop model. In ideal annular flow, the condensate forms a film of uniform thickness on the tube wall and the vapor flows in the interior core. In practice, this pattern may be modified by waves, entrainment, and stratification. However, these effects are hard to predict or 11016 analyze, and annular flow is usually assumed to exist in the para- metric range of interest. Since the vapor core is very turbulent, radial temperature gradients are neglected. In addition, the tem- peratures in the vapor core and at the liquid-vapor interface are assumed to be equal to the saturation temperature. Axial heat con- duction and subcooling of the liquid film are also neglected. In the present paper, the momentum and heat transfer analogy is applied to the annular model using the von Karman universal velocity distribution to describe the liquid film. This seems to be the most accurate method for describing the condensate flow and heat transfer. An order of magnitude analysis and non-dimensionalization of this theory result in a simple formulation for the local heat transfer coefficient. The analysis is compared to experimental data and the results are used to obtain a general design equation for forced- convection condensation. 8 EXPERIMENT General Description of Test Facility The basic apparatus is shown schematically in Fig. 1. It consisted of a closed-loop refrigerant flow circuit driven by a mechanical-sealed rotor pump. An electrically heated boiler generated vapor which passed through a flow meter and into the test section. An aftercondenser downstream from the test section condensed any remaining vapor and en- sured liquid refrigerant at the pump inlet. The pump was connected to a by-pass loop, and a valve in the by-pass loop was used to regulate the flow rate and pressure in the test section. The return line from the boiler incorporated a filtering-drying element and a commercial sight glass and moisture indicator. Front and rear views of the experi- mental apparatus are shown in Fig. 2. The test section was a tube-in-tube heat exchanger: the re- frigerant flowed through the inner tube and the water flowed counter- currently in the annulus or jacket. The inner tube was a commercial 3/8 in. 0. D. (0.315 in. I. D.), continuous copper tube 16 1/2 ft. long and extended 2 ft upstream from the test section. Seven brass rings, each incorporating a pressure tap, were soldered to the inner tube at 29 in intervals. These split the annulus length- wise into six sections. Heat transfer and pressure drop measurements were made in each of these sections. Adjoining sections of the water jacket were connected in series by flexible hoses to ensure mixing. Two differential thermocouples were located at the inlet and outlet of