Analysis of Unsteady Gas Temperature Measurements in the Appendix Gap of a Stirling Engine

2019

Energies

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.

Section: Seal Design Modification In the Convertible Laboratory-scale Machinementioning

confidence: 99%

Section: Seal Design Modification In the Convertible Laboratory-scale Machinementioning

confidence: 99%

Section: Gas Temperaturesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 2 more Smart Citations

Experimental Investigation of Displacer Seal Geometry Effects in Stirling Cycle Machines

2019

Energies

“…Considering that the hydrodynamic entry length in laminar flow may extend to more than 50 times the hydraulic diameter, this assumption will probably apply to a small section around the center of the gap only, if at all. So, Sauer and Kühl performed experimental investigations to verify the predictions by the analytical model [20,21]. For this purpose, an experimental machine was used, the design of which had been downsized to laboratory scale by application of similarity-based scaling rules [22].…”

Section: Experimental Investigation Of the Appendix Gap Lossmentioning

confidence: 99%

Appendix gap losses in Stirling engines – review of recent findings

2021

E3S Web Conf.

Self Cite

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.

Performance improvements in Stirling cycle machines by a modified appendix gap geometry

Intl J of Energy Research

2021

Self Cite

Summary In this contribution, the optimization potential of the seal geometry in Stirling machines is explored both numerically and analytically, leading to a significant reduction of the related losses which are often referred to as appendix gap losses. These are induced by the narrow gap between the displacer and the cylinder and have mostly been underestimated so far. A recent experimental investigation revealed large optimization potentials by reduction of the seal and cylinder wall diameter near the seal, resulting in reduced appendix gap losses and further indirect positive effects. In this work, these experimental findings could be reproduced by a one‐dimensional differential simulation model at a fully satisfyingaccuracy. Furthermore, these investigations reveal that the optimum geometry is largely machine‐dependent. To provide an easily applicable design rule for this optimum geometry, a refined analytical model for the mass flow at the top of the gap is derived, which is based on a phasor analysis and a linearized mass balance that also accounts for changes in the spatial mean gas temperature in the gap. The optimum design predicted by this model is very close to numerical optimization results and sufficiently accurate under practical aspects. Furthermore, this model contributes to a better theoretical understanding of the loss mechanisms in the gap.