A new second order thermal model for accurate simulation of the transient and steady–state response of beta-type Stirling engines based on time-varying calculation of thermal losses

Abstract

A novel numerical second order transient thermal model for beta-type Stirling engines (TTMS) was developed taking into account the transient heat transfer between the engine cylinder walls and pistons and the working gas in the expansion and compression space in order to determine the total power output and thermal efficiency with higher accuracy. The time-dependent energy equilibriums were formulated by including the transient thermal response of the cylinder walls and pistons until steady state operation was achieved. In addition, the transient response of the heat exchangers (cooler, regenerator and heater) was developed in order to determine more accurately the enthalpy of the working gas that enters or exits each compartment of the engine. The solution of the governing differential equations at each time step can be achieved with the implementation of a conventional fixed point algorithm. Various loss mechanisms were incorporated in order to increase the accuracy of the developed model. The TTMS was applied to the GPU-3 Stirling engine and the thermal response of the engine was calculated. The steady state results were compared to both experimental results and other numerical second order models in the literature which showed that TTMS can predict the thermal efficiency and the power output of the engine with an improved accuracy of as high as 65% and 62% respectively compared to the more advanced second order models published in the literature. The information of the transient response of the engine will be valuable for automotive and other energy applications in the industry.