Optimum Refrigerating Efficiency and Exergy Index of a Two-Stage Refrigeration Cycle

This paper presents results of an optimization study for a two-stage vapor compression refrigeration cycle based on the refrigerating efficiency and exergy index. Traditional two-stage refrigeration cycle studies have focused on the first law performance, while those studies dealing with the second law have primarily been limited to performance analysis as opposed to performance optimization. Results of this study indicate that the use of the common approximation of the geometric mean to find the optimum interstage pressure leads to nearly optimum results for the refrigerating efficiency, with maximum error in the neighborhood of 5%. However, the error associated with using this approximation to find the optimum exergy index is too large, approaching 15%. Second law optimization revealed that the optimum data curves themselves have maxima for each set of conditions tested. There are a series of conditions that lead to the conclusion that, for a given system, there is an optimum set of conditions that lead to the lowest amount of exergy destruction for that system. Polynomial equations have been fitted to the resultant optimum data for the refrigerating efficiency and exergy index. These equations allow for the reproduction of optimum points based on high- and low-pressure compressor efficiencies and condenser and evaporator pressures.