Closed-form expressions are sought which will allow the rapid and accurate calculation of pressure variation, flow velocities, and flow friction losses in crank-driven Stirling cycle machines. The compression and expansion spaces of the Stirling machine are assumed to be isothermal and their volumes are assumed to vary sinusoidally. It is further assumed that the cyclic pressure variation of the working fluid and the flow velocities within the passages of the machine can be represented by sinusoids. Closed-form expressions are deduced for the amplitude and phase of these variations. Using the expressions so deduced, formulae are derived for frictional losses in the three heat exchangers, taking into account the variation in mass flow rate over the cycle and the difference in amplitude of mass flow between the two ends of the regenerator. By comparing these expressions with calculations based on the assumption of an average flow rate over the cycle, it is shown that the latter method leads to flow losses being underestimated by more than 50 percent. It is recommended that the formulae deduced here be used for first-stage design work.

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