1. Introduction
The Stirling engine, invented in 1816, running according to a
reversible closed cycle knew a practical use as a reliable and sure engine,
during almost one century before being supplanted by the
spark-ignition engine. Nowadays, the Stirling machines are in commercial
use only as heat pump, used mainly for cryogenic cooling
and air liquefaction. As an engine, the Stirling remains a field of
numerous researches and development works. Recent experimental
realizations demonstrate power densities as well as noteworthy effi-
ciencies [1]. One of the most promising applications of the Stirling
cycle is the free piston Stirling engine (FPSE) configuration [2–4].
The optimal design of FPSEs is a difficult task. Indeed, no
mechanical linkage fixes the strokes and phase angle for the moving
elements. Hence, a global dynamic analysis is required to predict
the periodic steady operation. Due to the complexity of this
analysis, the isothermal assumption is usually adopted. Hence,
the pressure as a function of the piston and displacer positions
can be expressed in an analytical way. Linearization methods are
then used to obtain the performances of the engine [5–8]. However,
these models do not take into account the thermal losses of
the engine which lead to erroneous predictions of the performances.
Therefore, there is a need for an accurate analytical thermodynamic
isothermal model which can be used in accordance
with the dynamical analysis of the FPSE for preliminary design
purpose.