Derivation and numerical case study of a one-dimensional, compressible-flow model of a novel free-piston Stirling engine

摘要

Free-piston Stirling engines have in recent years attracted renewed interest worldwide for uses specifically relating to micro-combined heat and power generation. To aid prospective engine researchers with the modelling and analysis of such engines, this paper presents the derivation and numerical simulation of an exemplary, single-acting free-piston Stirling engine. A transient third-order theoretical model was derived from first principles, by discretising the working fluid and the regenerator metal-mesh into one-dimensional arrays of finite-sized control volumes. The working fluid transport equations and the non-linearised dynamic equations of the displacer and power piston were solved sequentially using a fully-explicit, transient numerical scheme with first-order upwind differencing. To demonstrate the usefulness of this model, sample simulation results are presented as a case study to the anticipated operation of a novel, 100 W engine prototype. Thereafter, a sensitivity study was conducted in which the power piston load, hot-end temperature and charge pressure was varied. From the sensitivity study, it is recommended that a control system be developed and implemented so as to ensure the steady oscillatory motion of both displacer and piston without collisions occurring.