Power density optimisation of an irreversible variable-temperature heat reservoir closed intercooled regenerated Brayton cycle

SYNOPSIS In this paper, power density, defined as the ratio of power output to maximum specific volume in the cycle, is analysed and optimised for an irreversible closed intercooled regenerated Brayton cycle coupled to variable-temperature heat reservoirs, according to the theory of finite-time thermodynamics. The analytical formulae for dimensionless power density and efficiency, as functions of the total pressure ratio, the inter-cooling pressure ratio, the component (i.e. regenerator, intercooler, and hot- and cold-side heat exchangers) effectivenesses, the compressor and turbine efficiencies, the thermal capacity rates of the working fluid and the heat reservoirs, the pressure recovery coefficients, the heat reservoir inlet temperature ratio, and the inlet temperature ratio of cooling fluid in the intercooler and the cold-side heat reservoir, are derived. The optimum dimensionless power density is obtained by optimising the intercooling pressure ratio. The maximum dimensionless power density is obtained by identifying the optimum heat conductance distributions between the hot- and cold-side heat exchangers for a fixed total heat exchanger inventory and fixed heat conductance distributions of the regenerator and the intercooler, and by identifying the optimum intercooling pressure ratio. When the optimisation is performed with respect to the total pressure ratio of the cycle, the maximum dimensionless power density can be maximised again, and a double maximum power density and corresponding optimum total pressure ratio are obtained. Further, as the optimisation is performed with respect to the thermal capacitance rate matching between the working fluid and the heat reservoir, the double-maximum power density is maximised again and a thrice-maximum power density is obtained. The effects of the heat reservoir inlet temperature ratio, the inlet temperature ratio of cooling fluid in the intercooler and the cold-side heat reservoir, the efficiencies of the compressors and the turbine, and the total heat exchanger inventory on the maximum power density and the corresponding efficiency, optimum intercooling pressure ratio, and optimum heat conductance distributions between the hot- and cold-side heat exchangers, the twice-maximum power density and the corresponding efficiency and optimum total pressure ratio, as well as the thrice-maximum power density are analysed by numerical examples. In the analysis, the heat resistance losses in the four heat exchangers, the irreversible compression and expansion losses in the compressors and the turbine, the pressure drop loss in the piping, and the effects of finite thermal capacity rate of the three heat reservoirs are taken into account.