Studies on three-temperature, three-cylinder Stirling cycle machine (accuracy of vector analysis)

A simple vector analysis method aimed to quickly determine the performance of complicated multi-cylinder Stirling cycle machines such as the Vuilleumier cycle machine was introduced by the authors in 1992. It has proven to be a very simple graphical method for the design and analysis of future complicated Stirling cycle machines. In this method, it is assumed that all volume variations and pressure changes are sinusoidal. Actually, all volume fluctuations can be assumed to be sinusoidal without large errors, but pressure fluctuation deviates from sinusoidal assumptions, because pressure is a reciprocal of the total sinusoidal volume fluctuation. The pressure value estimated by this vector analysis method is compared to the exact calculation and the error is calculated and discussed. It is known that the error depends on the pressure ratio and the dead volume ratio, and the error is less than 10% in many cases. The features and details of a newly made experimental, small, pressurized (6 MPa) three-temperature (hot, cold and middle temperature), three-cylinder Stirling cycle machine are described. This machine was basically designed by this vector analysis method. This machine can work as a cooler and/or a heat pump, by adjusting the phase angle of the hot cylinder and depending upon whether motor power and/or heat input is supplied. Rotating vector analysis was performed on a free piston or a pulse tube machine (Storch, 1988), but this report gives new convenient methods for complicated Stirling cycle systems