Heating load density optimization of an irreversible simple Brayton cycle heat pump coupled to counter-flow heat exchangers

This paper presents a theoretical investigation on the finite time thermodynamic performance for an irreversible Brayton cycle heat pump (BCHP) coupled to counter-flow heat exchangers. The heating load density, i.e. the ratio of heating load to the maximum specific volume in the cycle, is taken as the optimization objective. Relations between heating load density and pressure ratio and between COP (coefficient of performance) and pressure ratio for BCHP in which the irreversibilities of heat resistance losses in the hot and cold-side heat exchangers and non-isentropic losses in the compression and expansion processes are derived. The analytical expression obtained for the cycle performance enabled its optimization through addressing the effects of mechanical and thermal inefficiencies of all components comprising the cycle. The influences of the temperature ratio of the reservoirs, the efficiencies of the compressor and expander and the effectiveness of the heat exchangers on the heating load density are provided. The cycle performance optimizations are performed by searching the optimum distribution of heat conductance of the hot- and cold-side heat exchangers for the fixed total heat exchanger inventory and the optimum heat capacity rate matching between the working fluid and the heat reservoirs. The BCHP design with heat loading density optimization leads to a smaller size of all equipments comprising the heat pump.