ISBN 978-3-8439-2548-8

978-3-8439-2548-8, Reihe Thermodynamik

Jens Pfeiffer
Unsteady Analytical Model for Appendix Gap Losses in Stirling Cycle Machines (Band 19)

162 Seiten, Dissertation Technische Universität Dortmund (2015), Softcover, A5

Zusammenfassung / Abstract

Stirling cycle machines applied in decentralized energy conversion imply a significant potential for the reduction of greenhouse gases. For their design, high-accuracy models are needed. In this work, it is shown that previously existing models for the thermal losses, which are caused by an annular gap between the displacer and the cylinder in such machines, are insufficient. These losses, referred to as appendix gap losses, amount up to 10 % of the heat input to a heat engine. Besides heat conduction, two loss mechanisms can be identified, which have an opposite dependency on the clearance between displacer and cylinder wall, the appendix gap width. The shuttle heat transfer, which is caused by the oscillating displacer wall along the axial cylinder temperature gradient, is decreased by a larger gap width, whereas the net enthalpy flow by the cyclic in- and outflow of gas in the gap is increased. This leads to a specific optimum gap width for each machine. The existing modeling approaches can be differentiated in closed-form expressions, which can be solved analytically, and in differential approaches, which have to be solved numerically. The former are based on too gross simplifying assumptions and are partly error-prone. The latter are imprecise due to the inaccurate modeling of the heat transfer between gas and walls. Based on the prevailing laminar flow in the gap, analytical solutions for the unsteady oscillating flow and the gas temperature profile are derived directly from the conservations laws. Herewith, a new analytical model is developed, which requires fewer simplifying assumptions compared to the existing models. Furthermore, the dependency of the loss mechanisms on the axial gap position is investigated, and herewith, the curved temperature profile along the cylinder obtained in previous differential simulations can be confirmed. In consequence, the common assumption of a linear temperature profile becomes obsolete. The losses predicted by the model are of higher magnitude, which allows an improved modeling accuracy of existing experimental data. The optimum gap width is shifted to smaller values and an investigation of optimization potentials shows that the losses can be decreased remarkably with an alternative seal design. Finally, an easy applicable closed-form expression is derived for the optimum gap width, which allows an improved design of cylinder systems in Stirling cycle machines in future.