Preliminary results from a numerical study on the appendix gap losses in a Stirling engine

Analytical expressions for the losses in the displacer clearance gap, a.k.a. the appendix gap, have been refined during the last decades. But most real life Stirling engines violate the assumptions behind these expressions and hence the expressions may not be applicable. In this study the gap has been included directly into a one dimensional Stirling engine model. Practical aspects of the method, such as handling the moving wall in the gap while achieving an energy conserving model formulation and handling discontinuous derivatives in the equations, are discussed. A study on the convergence of the spatial discretisation in the gap showed that a relatively coarse discretisation was adequate for studying the appendix gap losses and showed significant variations in the axial wall temperature gradients along the gap. A parameter study on the size of the displacer clearance gap was performed with different algorithms for computing the heat transfer in the gap. The results showed higher losses for small gap sizes but smaller losses for large gap sizes when compared to analytical expressions for the appendix gap losses. The appendix gap losses were found to influence both the heat intake and work output of the engine.