Optimization of the Appendix Gap Design in Stirling Cycle Machines

Abstract

This contribution presents a new optimization procedure for the design of the appendix gap in Stirling engines. This is of special interest, since the thermal losses associated with the appendix gap, an annular gap around the displacer in the cylinder system, may amount to as much as 10 percent of the heat input to a Stirling engine. Furthermore, recent experimental investigations and an extensive literature review revealed that the accuracy of the existing models for these losses and the derived design rules for the appendix gap are insufficient. The optimization procedure presented here is based on a recently developed and published, more detailed analytical model. In order to generally analyze any optimization potentials, this model is first subject to numerical optimizations. The choice of the correct gap width implies the major optimization potential, but there are additional options, e. g. by axial variation of the gap width. By choosing a conical design with an expansion towards the open end, the loss can be reduced by more than 10 percent. Furthermore, the gap loss can be reduced by a modification of the seal design, reducing the volumetric displacement and the almost isothermal buffer volume at the bottom end of the gap. If the gap width is minimized here, whereas a larger width is admitted in the remaining section, a constant gap width is acceptable. Finally, an analytical, easily applicable closed-form solution for the optimum gap width and the corresponding overall gap loss has been derived and validated.