Appendix gap losses in Stirling engines – review of recent findings

Abstract

The appendix gap loss in Stirling cycle machines is generated by the annular gap around the thermally insulating, thin-walled dome typically attached to a piston or displacer plunging into the hot cylinder volume of an engine or the cold volume of a cryocooler. It was considered to be of minor importance for decades. Thus, simplified analytical models were considered sufficiently accurate for its description, until numerical simulations and experimental results gave rise to a more detailed analysis revealing that, neglecting entrance and end effects, the flow is typically laminar, but unsteady. Subsequently, an enhanced analytical model accounting for fluidic and thermal inertia effects as well as the volumetric displacement by the seal was developed. Compared to the previous ones, this model predicts a shift of the optimum width to smaller values, a higher minimum overall loss and furthermore, an option to decrease the loss by reducing the effective seal diameter. This could be experimentally confirmed as well as the unsteady gas temperature profiles predicted by this model. Subsequently, both theoretically and experimentally founded correlations for the radial and axial energy transport in the gap were derived and implemented in a differential simulation of the gap within a third order code.