,.' Heat Transfer in Refrigerator Condensers and Evaporators D. M. Admiraal and C. W. Bullard ACRCTR-48 August 1993 For additional information: Air Conditioning and Refrigeration Center University of Illinois Mechanical & Industrial Engineering Dept. 1206 West Green Street Urbana, IL 61801 Prepared as part ofACRC Project 12 Analysis ofRefrigerator-Freezer Systems (217) 333-3115 C. W. Bullard, Principal Investigator The Air Conditioning and Refrigeration Center was founded in 1988 with a grant from the estate of Richard W. Kritzer, the founder of Peerless of America Inc. A State of Illinois Technology Challenge Grant helped build the laboratory facilities. The ACRC receives continuing support from the Richard W. Kritzer Endowment and the National Science Foundation. Thefollowing organizations have also become sponsors of the Center. Acustar Division of Chrysler Allied-Signal, Inc. Amana Refrigeration, Inc. Brazeway, Inc. Carrier Corporation Caterpillar, Inc. E. I. du Pont de Nemours & Co. Electric Power Research Institute Ford Motor Company Frigidaire Company General Electric Company Harrison Division of GM ICI Americas, Inc. Modine Manufacturing Co. Peerless of America, Inc. Environmental Protection Agency U. S. Army CERL Whirlpool Corporation For additional information: Air Conditioning & Refrigeration Center Mechanical & Industrial Engineering Dept. University ofIllinois 1206 West Green Street Urbana IL 61801 2173333115 Table of Contents Page List of Tables ............................................................................................................................. v List of Figures ........................................................................................................................... vi Nomenclature .......................................................................................................................... vii Chapter 1. Introduction ........................................................................................................................ 1 1.1 Purpose ......................................................................................................................... 1 1.2 Development of the variable conductance model ..................................................... 2 1.3 Heat transfer correlations .......................................................................................... 3 1.3.1 Two-phase correlations .................................................................................. 3 1.3.2 Single-phase correlations ............................................................................... 6 2. Evaporator Model ............................................................................................................ 9 2.1 The two zone model ..................................................................................................... 9 2.2 The one zone model ................................................................................................... 16 2.3 Comparison with constant conductance models .................................................... 18 2.4 Summary .................................................................................................................... 19 3. Condenser Model ............................................................................................................ 20 3.1 Air-side complexities ................................................................................................. 20 3.2 Recirculation fraction ............................................................................................... 21 3.3 Volumetric air flow rate and leak fraction ............................................................. 23 3.4 Condenser inlet air temperature ............................................................................. 23 3.5 Governing equations ................................................................................................. 26 3.6 Summary .................................................................................................................... 31 4. Conclusions and Suggestions for Future Research ............................................ 33 4.1 Conclusions ................................................................................................................ 33 4.2 Suggestions for future research ............................................................................... 35 References ................................................................................................................................. 37 Appendix A. Objective Functions for Parameter Estimation ................................................... 38 B. Evaporator and Condenser Geometric Complexities ........................................ 42 B.l Evaporator ................................................................................................................ 42 B.2 Condenser .................................................................................................................. 43 C. Split Fraction and Volumetric Air Flow Rate in the Evaporator ................. 45 D. Possible Improvements In Condenser Performance .......................................... 49 D.l Improving air flow ................................................................................................... 49 D.2 Eliminating recirculation ......................................................................................... 50 111 E. Calculation of Refrigerant Mass Flow Rate .......................................................... 52 F. Comparison of Measured and Calculated Data .................................................. 56 IV List of Tables ThWe ~~ 2.1 Results of evaporator model ............................................................................................. 14 2.2 Calculation of air split fraction and volumetric flow rate ................................................. 15 2.3 Two-zone constant conductance results ............................................................................ 18 3.1 Recirculation fraction ........................................................................................................ 22 3.2 Summary of condenser results .......................................................................................... 29 C.1 Independent calculation of air split fraction and volume flow rate .................................. 47 C.2 Simultaneous calculation of air split fraction and volume flow rate ................................ 48 v List of Figures mpre ~~ 1.1 Comparison of BoPierre and ChatolWattelet heat transfer coefficients ....................... 5 2.1 Evaporator heat exchanger geometry ............................................................................ 9 2.2 Comparison of calculated and measured evaporator loads for data set I .................... 12 2.3 Comparison of calculated and measured evaporator loads for data set 11 ................... 12 2.4 Heat load confidence interval vs. volumetric air flow rate ......................................... 13 2.5 Air flow through refrigerator compartment ................................................................ 15 2.6 Comparison of ChatolW attelet and BoPierre parameter estimation ........................... 17 3.1 Condenser heat exchanger geometry .......................................................................... 20 3.2 Comparison of calculated and measured values of grille inlet temperature ............... 22 3.3 Front view of condenser air inlet ................................................................................ 24 3.4 Condenser inlet air temperature distribution ............................................................... 24 3.5 Average air inlet temperatures .................................................................................... 25 3.6 Comparison of calculated and measured condenser loads .......................................... 30 4.1 Contributions to overall heat transfer resistance ......................................................... 35 C.1 Air mixture control volume ......................................................................................... 45 E.1 Data set I refrigerant mass flow measurements .......................................................... 53 E.2 Data set II refrigerant mass flow measurements ......................................................... 54 F.1 Evaporator exit temperature comparison, data set 1.. .................................................. 56 F.2 Evaporator exit temperature comparison, data set II .................................................. 56 F.3 Single-zone evaporator load comparison, data set II .................................................. 57 F.4 Condenser load comparison, Reeves (1992) ............................................................... 57 F.5 Condenser load comparison, data set I.. ...................................................................... 58 F.6 Condenser load comparison, data set II ...................................................................... 58 vi Nomenclature A area [ft2] C heat capacity (rbcp) [Btu/(h·oP)] cp specific heat [Btu/(lbm·op)] D internal tube diameter eft] f fraction G mass flux [lbm/(h·ft2)] g acceleration of gravity [ft/s2] h heat transfer coefficient [Btu/(h·ft2.oP)] hfg heat of vaporization [Btu/lbm] J mechanical equivalent of heat [778.3 ft·lbf/Btu] k thermal conductivity [Btu/(h·ft·oP)] L length of tube eft] Ih mass flow rate [lbm/h] Q