Linear Harmonic Analysis of Free-Piston Stirling Engines

摘要

The equations that govern the behavior of free-piston Stirling engines are nonlinear differential equations. Traditional solution methods have been time-stepping integrations that can be plagued by numerical instabilities and can use large amounts of computer time. Closed-form analytical solutions are possible if the working gas behaves isothermally or if the nonlinear terms in the governing equations are replaced with accurate approximations. An almost closed-form solution method, called the linear harmonic analysis (LHA), has been developed for free-piston Stirling engine applications by representing all of the periodic variables with harmonic functions. The solution method accounts for the important thermodynamic losses that are coupled together in free-piston engines, yet it is efficient enough for optimization studies. The LHA method was compared with a standard numerical integration method to verify its mathematical accuracy. The LHA and numerical predictions for a sample free-piston Stirling engine configuration differed by <5% for all important parameters. Sensitivity studies using the LHA method have also shown that the thermodynamic loss assumptions used in an analysis can have a significant impact on the predicted dynamic behavior of a free-piston Stirling engine. (ERA citation 11:038163)