Optimizing the Piston Paths of Stirling Cycle Cryocoolers

Abstract The ideal Stirling cycle provides a clear control strategy for the piston paths of ideal representations of Stirling cycle machines. For non-equilibrium Stirling cycle machines however, piston paths aiming to emulate the ideal cycle’s four strokes will not necessarily yield best performance. In this contribution, we ask the question: What are the COP-optimal piston paths for specific non-equilibrium Stirling cryocoolers? To this end, we consider a low-effort Stirling cryocooler model that consists of a set of coupled ordinary differential equations and takes several loss phenomena into account. For this model and an exemplary parameter set, piston path optimizations are done with an indirect iterative gradient method based on optimal control theory. The optimizations are repeated for two different kinds of volume constraints for the working spaces: one representing an alpha-Stirling configuration, the other a beta-Stirling configuration. Compared to harmonic piston paths, the optimal piston paths lead to significant improvements in COP of ca. 88 % for the alpha-Stirling and ca. 117 % for the beta-Stirling at the maximum-COP operational frequency. Additionally—and even though the optimizations were performed for maximum COP—cooling power was increased with even lager ratios.