Cooling Load Density Optimization of an Irreversible Simple Brayton Refrigerator

Abstract

The performance optimization of an irreversible simple Brayton refrigerator coupled to constant-temperature heat reservoirs is carried out by taking the cooling load density, i.e., the ratio of cooling load to the maximum specific volume in the cycle, as the optimization objective using finite-time thermodynamics (FTT) or entropy generation minimization (EGM) in this paper. The analytical formulae about the relations between cooling load density and pressure ratio, as well as between coefficient of performance (COP) and pressure ratio are derived with the heat resistance losses in the hot- and cold-side heat exchangers, and the irreversible compression and expansion losses in the compressor and expander. The influences of the effectiveness of the heat exchangers, the temperature ratio of the reservoirs, and the efficiencies of the compressor and expander on the cooling load density versus COP are provided by numerical examples. The cooling load density optimization is performed by searching the optimum pressure ratio of the compressor, and searching the optimum distribution of heat conductance of the hot- and cold-side heat exchangers for the fixed total heat exchanger inventory. The influences of some design parameters, including the effectiveness of the heat exchangers between the working fluid and heat reservoirs, the efficiencies of compressor and expander, the temperature ratio of heat reservoirs, on the maximum cooling load density, the optimum heat conductance distribution and the optimum pressure ratio are provided by numerical examples. The refrigeration plant design with optimization leads to a smaller size including the compressor, expander, and the hot- and cold-side heat exchangers.