A technique for calculating the efficiency and power of Stirling machines is presented. This technique is based on the First Law of Thermodynamics for processes with Finite speed and the Direct Method for closed systems, In order to apply the Direct Method to Stirling Cycles, a new and novel PV Px diagram is presented that shows the effects of pressure losses due to friction, finite speed and throttling processes in the regenerator of the Stirling engine. The method used for the analysis of this irreversible cycle with finite speed involves the direct integration of equations based on the first law for processed, with finite speed to obtain the cycle efficiency and power directly, This technique is termed the Direct Method. The results predicted by this analysis are in good agreement with the actual engine performance data of 12 different Stirling engines, over a range Of Output from economy to maximum power. This provides a solid verification that this analysis. based on the Direct Method, can accurately predict actual Stirling engine performance. particularly with regard to efficiency and output power. In addition to the powerful predictive capabilities of the Direct Method. the new PV Px diagram for the Stirling cycle is both an effective and an intuitive tool for explaining the operation and design of Stirling machines. Copyright (C), 2002 John Wiley Sons. Ltd.

Les cycles des machines a froid et pompes a chaleur de Stirling sont etudies en tenant compte de la vitesse finie des processus. L'approche est basee sur une nouvelle methode d'optimisation des processus et cycles a vitesse finie. Elle est appelee la Methode Directe d'etude et evaluation des irreversibilites. Dans ce cadre le premier principe de la Thermodynamique pour des processus a vitesse finie est applique a chaque transformation du cycle inverse de Stirling. Les performances de ces cycles sont evaluees en prenant en compte les irreversibilites internes generees par la vitesse finie, notamment (1) les pertes de pression dues au laminage du gaz dans le regenerateur, (2) les pertes de pression dues a la vitesse finie du piston, (3) les pertes de pression dues aux frottements interne et mecanique et (4) l'irreversibilite due a la regeneration imparfaite de la chaleur dans le regenerateur.

A new and novel diagram for the Stirling cycle that uses PV / Px coordinates is presented. This diagram is used in conjunction with the First Law of Thermodynamics for processes with finite speed [2-10] and with the Direct Method [10-15] to determine the pressure losses that occur in a Stirling machine operating at real or finite speed. Once these losses have been determined, the power and efficiency of the Stirling engine may be readily calculated. These analytical results have been compared to experimental performance data for a variety of operating Stirling engines [16-20]. Excellent agreement has been obtained between the experimental data and the analytic prediction. In addition to the powerful predictive capabilities of the analysis, the now PV / Px diagram for the Stirling cycle that is presented provides an intuitive tool that would be a very useful aid in explaining the operation and design of Stirling machines to others.