An Analytical Oscillating-Flow Thermal Analysis of the Heat Exchangers and Regenerator in Stirling Machines

A closed form-expression for the effectiveness of the heat exchangers and regenerator of a Stirling cycle machine is given. This result may be used in a simple way in order to evaluate their effect on the machine performance. The proposed method, indeed, allows the actual cycle gas temperatures in the heater and cooler to be obtained readily, once the geometry of the heater, cooler and regenerator is known and some quantities characterizing the engine dynamics (strokes, frequency and phase angle of the moving elements) and its heat-exchange processes (inlet temperatures of the heating and cooling fluids, and their volumetric flow rates) are measured. Thus, an immediate indication about the effectiveness of the heat exchangers and regenerator as well as about the machine thermal efficiency may be obtained. The availability of a closed-form expression for the heater, regenerator and cooler effectiveness is useful especially for those engines, like the free-piston Stirling engines, whose design requires the application of analytically based optimization criteria.