Optimization of the phase angle in ideal Stirling engines using the concept of `tidal´ and `ancillary´ domains

In a parallel publication (Finkelstein, 1996), a new analysis of the ideal loss-less Stirling cycle machine was presented based upon the concept of overlapping `tidal´ and `ancillary´ domains. This has led to the definition of the following two dimensionless parameters: the `specific performance´ for the unified measure of output for engines, refrigerators and heat pumps, and the `tidal compression ratio´, which is akin to the compression ratio in internal combustion machines and uniquely defines the operational characteristics of any Stirling cycle machine. An analysis to replace the alternative traditional Schmidt equation was presented and a new expression for the general performance of practical Stirling engines was derived from first principles. An analytical optimization of the volumes of the three internal heat exchangers was also included. In this present paper, which is an extension of the above analysis, these new equations for the performance are utilized for an analytical optimization of the phase angles. It is shown that the optimum phase lead of the expansion space and the optimum phase lag of the compression space for an ideal isothermal machine is precisely π/4 for all possible machines. This is independent of the previous conclusion that the pressure vector should have a zero phase lag or lead