Thermodynamic Design of Stirling Cycle Machines

Abstract

When local, instantaneous departures from ideal reversible behaviour are evaluated in terms of the entropy generation rate, the differential equations describing the unsteady processes in the Stirling cycle machine give way to steady flow forms. A simple multiplication by T_o gives immediately the local, instantaneous rate of loss of available work. The paper exploits this fact to obtain, from an ideal model of the flow processes, the indicated cycle work of the real (irreversible) cycle. The result is of the form:

{(geometric parameters), τγ, N_RE, N_PR, N_F, … (dimensionless groups in order of diminishing influence)}

where τ, N_RE, N_F etc. are dimensionless groups of the operating parameters, engine speed, p_ref, T_e, T_c etc. and γ is the specific heat ratio of the working fluid, which is shown to be the only fluid property that independently influences Z.

The approach is an alternative to the time consuming solution of the defining differential equations and provides a convenient design tool which has long been lacking in this area. The only assumption additional to those invoked in conventional computer modelling of the Stirling cycle is that actual gas processes do not depart excessively from those predicted by the ideal model of the flow—for example from those provided by the so-called ‘adiabatic’ cycle model.