Experimental Investigation of Displacer Seal Geometry Effects in Stirling Cycle Machines

Abstract

This contribution deals with an experimental investigation of the optimization potential of Stirling engines and similar regenerative machines by an enhanced design of the cylinder liner and the seal. The latter is mounted at the bottom end of the gap surrounding pistons and displacers that separate cylinder volumes at different temperature levels. The thermal loss associated with this gap may amount to more than 10% of the heat input into these machines. Mostly, its design is reduced to an estimation of the optimum width by analytical models, which usually do not account for further relevant optimization parameters, such as a step in the cylinder wall. However, a recently developed, enhanced analytical model predicts that this loss may be significantly reduced by such a step. In this work, this design was realized and investigated experimentally according to this prediction by modification of the cylinder liner and the seal of an extensively tested laboratory-scale machine. The results confirm that such a design actually reduces the thermal loss substantially, presumably by reducing the cyclic mass flows through the open end of the gap. Additionally, it even improves the net power output due to a reduced volumetric displacement by the piston or displacer, resulting in smaller flow losses and thermal regenerator losses, whereas the pressure amplitude remains virtually unchanged, contrary to initial expectations. This has led to the remarkable conclusion that the design of most Stirling engines is possibly suboptimal in this respect and may be improved a posteriori by a minor modification; i.e., a reduction of the effective displacer seal diameter.

Appendix gap losses in Stirling engines – review of recent findings

“…10. The slight increase of the former may be additionally explained by the reduction of the flow losses, which could be experimentally confirmed [25]. On the other hand, the hot and the warm heat flows are reduced by the smaller volumetric displacement resulting in lower indicated amounts of heat as visualized by the p,V-loop areas in Fig.…”

“…Fig. 9 exemplarily shows the p,V plots and the wall temperature profiles obtained in Stirling mode under nominal operating conditions as specified in [25]. Surprisingly, it turns out that the pressure amplitude is almost unchanged despite the reduced displacer stroke volume.…”

“…Despite the deviations, it can thus be concluded that the presented analytical model provides the closest approximation of the actual, evidently very complex situation in the appendix gap that is currently available. To additionally verify the aforementioned optimization result concerning the seal design obtained by Pfeiffer and Kühl on the basis of this analytical model, i.e., the recommendation to reduce the gap width as far as possible, the experimental machine was modified once again by reducing the outer diameter of the seal and the displacer base as far as possible and by inserting a new cylinder liner with an accordingly reduced inner diameter [25]. It was not possible to realize a value of zero for the gap width ratio, but the minimum value 𝑟𝑟 ℎ = 0.21 is very close to the actual, numerically obtained optimum according to Pfeiffer and Kühl [18].…”

“…Fig. 8: Illustration of the modification of the seal design as realized by Sauer and Kühl [25] Considering that the actual volumetric displacement is decreased by this modification, a reduced specific power of the cycle had to be accepted as a side effect, since the closed-cycle p,V-integrals designating the indicated work and heat exchange of the cycle, respectively, are accordingly diminished by the reduction of the stroke volumes next to the displacer and furthermore, by a decreased amplitude of the pressure due to the lower thermal compression.…”

“…Fig. 11: Comparison of the gas volume displaced by the seal in the appendix gap for 𝑟𝑟 ℎ = 1 , 𝑟𝑟 ℎ = 0.5 and 𝑟𝑟 ℎ = 0 with special regard to thermal compression and dead volume effects [25] Evidently, the observed performance improvements are not only caused by the anticipated reduction of appendix gap loss, which -by the way -could not be directly measured, but only be confirmed indirectly by a comparison of the cyclic gas temperature measurements indicating a reduced mass flow amplitude in the gap and thus a lower enthalpy loss in case of 𝑟𝑟 ℎ = 0.21 . Instead, these improvements are also caused by a series of positive feedback effects involving other cycle components as well as their interaction, which can of course not be described by separate analytical models of the appendix gap and of other components, but only by numerical simulation of the entire cycle including all major loss mechanisms and their interactions, and therefore also including a differential model of the appendix gap.…”