A Simple Approach to Calculate the Regenerator Effectiveness in Stirling Machines

In this paper a closed-form solution for the regenerator effectiveness of a Stirling machine is given. This result may be used in a simple way in order to evaluate its effect on the machine performance. The proposed method, indeed, allows an immediate indication about the effectiveness value to be obtained, thus avoiding complex numerical simulation techniques, once the regenerator geometry is known and some quantities characterizing the engine dynamics (strokes, frequency and phase angle of the moving elements) and thermodynamics (higher and lower cycle temperatures) have been measured experimentally. The developed procedure cannot be considered as alternative to more sophisticated methods giving an accurate prediction of the regenerator performance. However, the availability of a closed-form expression for the regenerator effectiveness is useful especially for those engines, like the free-piston Stirling engines, whose design requires the application of analytically based optimization criteria.