Research PaperNumerical model for Stirling cycle machines including a differential simulation of the appendix gap

•The essentials of a 1-dimensional regenerative cycle simulation code are revealed.•An extension by a differential model of the appendix gap is introduced.•Simulated appendix gap losses are very sensitive to the heat transfer assumptions.•The new model includes interactions between the losses and the wall temperatures.

One-dimensional differential models are an important tool for the design optimization of Stirling engines and other regenerative machines, since they require far less computing time than multi-dimensional CFD-models and are yet capable of describing the various loss mechanisms including their mutual interdependencies. So far, the so-called appendix gap losses - thermal losses caused by the annular gap around the insulating dome, which is typically attached to pistons or displacers exposed to elevated or cryogenic temperatures - have usually not been directly included in differential models, because available estimates based on simplified analytical models only predicted a moderate magnitude of these. Instead, these estimates were therefore simply superimposed on the numerical results. However, recent findings indicate that these losses have thus been underestimated, since the analytical models are based on partially questionable assumptions. To investigate their actual magnitude, an existing one-dimensional differential simulation code, which is capable of modelling various regenerative cycles by selection of the required components from a library, was extended by another cylinder component that includes a differential model of the appendix gap. This contribution presents and discusses the results obtained by this extended simulation code in comparison to the predictions by a simplified and a more enhanced analytical model. It turns out that the numerical results are highly dependent on the modelling of both axial convection and the radial heat exchange between the gas and the walls, and that the unsteady flow and temperature profiles in the gap presumably need to be considered here by enhanced approaches - possibly based on complex numbers. Furthermore, an introductory overview of the simulation code is given, particularly focusing on the model structure, the basic assumptions and limitations of applicability, the discretization technique as well as the formulation and the solution of the differential equation system.