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.

中文翻译：

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优化斯特林循环低温冷却器的活塞路径

理想的斯特林循环为理想表示的斯特林循环机器的活塞路径提供了清晰的控制策略。然而，对于非平衡斯特林循环机器，旨在模拟理想循环的四个冲程的活塞路径不一定会产生最佳性能。在这篇文章中，我们提出了一个问题：什么是警察- 特定非平衡斯特林低温冷却器的最佳活塞路径？为此，我们考虑了一个省力的斯特林制冷机模型，该模型由一组耦合的常微分方程组成，并考虑了几种损失现象。对于该模型和示例性参数集，活塞路径优化是通过基于最优控制理论的间接迭代梯度方法完成的。针对工作空间的两种不同体积约束重复优化：一种表示 alpha-Stirling 配置，另一种表示 beta-Stirling 配置。与谐波活塞路径相比，最佳活塞路径可显着改善警察约 88 % 用于 alpha-Stirling 和 ca。最大 117 % 的 beta-Stirling-警察工作频率。此外——即使优化是为了最大限度地执行警察——冷却能力随着更大的比率而增加。