Polytropic Exponents for Common Refrigerants

Analysis of compression mechanisms requires a prediction of the pressure during the compression and expansion processes. A common model is the polytropic process, PV = constant. This paper presents a method for determining the best polytropic exponent to use and suggests values for some common refrigerants used in the air conditioning and refrigeration industry. INTRODUCTION When a gas undergoes a reversible process, the process frequently takes place in such a manner that a plot of log P vs. log V is a straight line. For such a process PV = constant. This is called a polytropic process. It can be shown that for an ideal gas with constant specific heats undergoing a reversible adiabatic (i.e. isentropic) process, n is equal to the ratio of specific heats, Cp/Cv. Though technically a formidable list of requirements, this turns out to be an excellent model for the compression and expansion of a refrigerant in the cylinder of a compressor. Though rigorous models based on accurate thermodynamic equations of state are certainly available, the simple polytropic process is adequate for determining forces and moments on compressor parts. Any inaccuracy introduced by using this model will be small considering the uncertainty in predicting the actual operating conditions that the compressor will eventually experience in the field. Specific heats Cp and Cv of real refrigerants vary with temperature and pressure. Some refrigerants have specific heats that vary more than others. This is not only a violation of the constant specific heat requirement it makes it ambiguous as to which temperature and pressure to use. This suggests the need for some form of regression or averaging method. The recommendation below is based on the idea that one of the most important predictions from a compressor mechanism simulation is the input power requirement. It is proposed that the polytropic exponent n be chosen such that the average shaft input power of the simplified PV model match one using an accurate equation of state for a representative compression cycle. Specifically, the cycle chosen is the ideal isentropic compressor operating at the ARI rating conditions for which this refrigerant is most commonly used. MATHEMATICAL MODELS The Ideal PV diagram for PV = constant Work done at the moving boundary for the compression process, going from state 1 (start of compression) to state 2 (start of discharge) is given by