Effect of Using Different Equations of State in the Analysis of Rotary Displacer Stirling Engine

Abstract

The ideal gas equation of state is defined for a theoretical gas composed of molecules that have perfect elastic collisions and no intermolecular interchange forces. However, it has been widely reported that such an ideal model may not be a realistic representation under certain circumstances, in particular when the compressibility factor (Z) is not close to unity, and the consideration of other equations of state (real models) is imperative. This study investigates the effect of using different equations of state, namely, the van der Waals, Redlich-Kwong, and Peng-Robinson equations, in the ideal isothermal analysis of a rotary displacer Stirling engine with the most commonly used gases, helium and air. The results are obtained numerically considering two major SE applications (cryocooling and distributed power generation) and two sets of operating conditions, and plotted in the form of Pressure-Volume diagrams. The amount of work per cycle based on the ideal gas model is taken as reference to compare the results from other models. The data show that at low pressure or high temperature conditions (corresponding to low density), the ideal gas equation is suitable for both gases, and using different models has no significant impact in the overall analysis. Additionally, while the use of ideal gas model is rather practical and fast, implementation of other models necessitate intensive computational processes.