Optimum Heat Conductance Distribution for Power Optimization of a Regenerated Closed Brayton Cycle

Abstract

In this paper, the power output of the cycle is taken as objective for performance optimization of an irreversible regenerated closed Brayton cycle coupled to constant-temperature thermal energy reservoirs in the viewpoint of finite time thermodynamics (FTT) or entropy generation minimization (EGM). The analytical formulae about the relations between power output and pressure ratio are derived with the heat resistance losses in the hot-and cold-side heat exchangers and the regenerator, the irreversible compression and expansion losses in the compressor and turbine, and the pressure drop loss in the piping. The maximum power output optimization is performed by searching the optimum heat conductance distribution corresponding to the optimum power output among the hot-and cold-side heat exchangers and the regenerator for the fixed total heat exchanger inventory. The influence of some design parameters, including the temperature ratio of the heat reservoirs, the total heat exchanger inventory, the efficiencies of the compressor and the turbine, and the pressure recovery coefficient, on the optimum heat conductance distribution and the maximum power output are provided. The power plant design with optimization leads to smaller size including the compressor, turbine, and the hot-and cold-side heat exchangers and the regenerator.

Differences and relations of objectives, constraints, and decision parameters in the optimization of individual heat exchangers and thermal systems

“…The optimal heat capacity rates of each fluid for the least areas of each heat exchanger can also be obtained through solving such equations as the system constraints, eqs. (14)- (16), and the partial differentials of Π A,i , eqs. (a9)-(a13), respectively.…”

“…Solving these equations together with the system constraints, eqs. (14)- (16), gives the optimal heat capacity rates of each fluid and heat transfer areas of each heat exchanger for the least total entropy generation rate. …”

“…Solving the equations including the system constraints, eqs. (14)- (16), and the partial differentials, eqs. (a14)-(a20), gives the allocation of the total heat capacity rate for the least entropy generation of a single heat exchanger.…”

“…(20), with the inherent overall relations, eqs. (14)- (16), and a given total capacity rate, as constraints. The partial differentials of the Lagrange function, Π Sg,t , with respect to C h,i , C c,i and A i provides another optimization equations, eqs.…”

“…As a consequence, scholars make great efforts on thermal system optimization, for instance, Chen et al [16] optimized the heat conductance distribution to search the optimum power output of a regenerated closed Brayton cycle, and Zhao and Chen [17] explored the optimal thermal conductances versus various system requirements and boundary conditions of a refrigeration system. In this aspect, the entropy generation-based optimization objectives are also widely employed.…”