New second-order polytropic numerical model for Stirling cycle heat pump

Any machine design needs an understanding of the procedures that determine the operating principles and governing equations of the system. This understanding is necessary to investigate the behavior of the system and to draw an estimate of performance. In this paper, a new second-order numerical model was developed to predict the performance of the Stirling cycle heat pump. The governing differential equation of the Stirling heat pump has been developed by coupling the effect of polytropic heat transfer, shuttle heat loss, and mass leakage to buffer space and into the two working spaces. The proposed numerical modeling is simulated using MATLAB software. The model has been experimentally validated by converting the existing FEMTO-60 engine into a heat pump. In addition, this model is validated by changing the governing equation in an engine model accordingly. The newly developed numerical model predicted performance COP of 0.9, 1.2, and 1.6 with a relative error of 1.1 %, 9.0 %, and 14.3 % at frequencies of 12.1 Hz, 9.7 Hz, and 7.3 Hz, respectively, for nitrogen gas at a working pressure of 17.5 bar.