Mathematical modeling of a general heat-dynamics active network for free piston Stirling engines

Abstract

This research focuses on the modeling of free piston Stirling engines (FPSEs) from the perspective of heat-dynamics using network theory. The active attribute of Stirling regenerator and the differences between Stirling and thermoacoustic devices are stressed. General network transmission equations of Stirling components are derived, and two-port active network models in distributed form are developed for four typical FPSEs constructions. With intrinsic attribute of FPSEs being considered, nonlinear network parameters are treated to balance the accuracy and practicability of the model. The frequency equation is derived for startup analysis of FPSEs. The verification and comparisons are made between the present model and experiments as well as existing network models from open literature. Results indicate that the present network model is with the mean prediction error of 2.71% for oscillation frequency and 8.5% for brake power, compared to eight sets of experimental data from NASA RE-1000 prototype. Meanwhile, the mean prediction error is improved by 11.6% for oscillation frequency and 6.5% for brake power, compared to the existing network model from open literature. This general heat-dynamics active network model in distributed form can provide a design guideline and analytical tool with satisfactory accuracy for the development of new FPSE prototypes.