A new one-dimensional model of free-piston Stirling engine based on quasi-steady flow approximation and simi-implicit numerical method

Abstract

Free-piston Stirling engine is a widely used device for thermal-to-electric conversion especially in aerospace applications. A dynamic model for free-piston Stirling engine is established in this paper for the purpose of modeling the free-piston Stirling engine more accurately and understanding its operation characteristics. This paper proposes a new one-dimension numerical model with quasi-steady flow approximation for free-piston Stirling engine with linear alternator, which can be categorized as third-order theoretical model for Stirling engine. The corresponding simi-implicit discretizationmethod is presented. In order to accurately obtain the thermal efficiency of the Stirling machine, various energy loss mechanisms are taken into consideration. A beta type free-piston Stirling engine, Component Test Power Convertor, is studied to demonstrate the correctness and accuracy of the numerical model established in this paper. The dynamic steady-state anticipated operation condition is simulated first. Then, the sensitivity analysis is carried out in which the effect of load resistance, heater temperature and cooler temperature, and charged pressure on the system operation parameter is studied. The predicted system parameters including frequency, displacer and piston amplitude, output power, and alternator output voltage and current agrees well with the designed value. Under the dynamic steady operation condition, the simulated indicated power is 15.51 kW and the electric power is 13.12 kW. The relative deviation between the predicted electric power and the measured output electric power of 12.78 kW is 2.66 %. The corresponding indicated efficiency and thermal-to-electric efficiency is 25.06 % and 21.20 % respectively. The amplitude of displacer and piston is 13.96 mm and 13.69 mm for this condition. Compared with the experimental data at different piston amplitude, the derivation of predicted engine parameters is within 10 %. The comparison with experimental results proves the accuracy of the proposed model in this paper. Compared with the previous model based on the adiabatic thermodynamic model, the third-order model presented in this paper shows higher accuracy on system parameter prediction for free-piston Stirling engine.