Stirling Thermodynamics using Phasor Notation

Abstract

Phasor mathematics is used to develop the isothermal Stirling cycle and extended to the ideal adiabatic Stirling cycle. The results are developed for piston – piston (alpha) machines and displacer – piston (beta and gamma) machines. The effect of non-ideal regeneration is handled by defining a regenerator effectiveness ratio. The importance of the amplitude pressure ratio (pressure amplitude to the mean pressure) is developed and shown to be a useful parameter when evaluating the effect of dead volume or when applying simple cycle analyses. The analysis is developed for both power producing and cooling engines. The utility of these analyses is discussed with respect to calibrated results of real machines.