Numerical model for Stirling cycle machines including a differential simulation of the appendix gap

Sauer, Jan; Kuehl, Hans-Detlev

doi:10.1016/j.applthermaleng.2016.09.176

Cited by 22 publications

(10 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The so-called appendix gap loss, a severely design-dependent and significant thermal loss that may easily amount to more than 10% of the heat input to Stirling engines or Vuilleumier heat pumps, is associated with the annular gap surrounding pistons and displacers. Usually, it is either evaluated using separate analytical models for the two major underlying mechanisms, the so-called shuttle-loss [15,16] and the so-called enthalpy loss [17,18], or by numerical simulation [19][20][21][22][23][24]. Particularly in the case of free piston machines featuring close tolerance seals rather than sliding seals, leakage losses need to be considered additionally [25].…”

Section: Introductionmentioning

confidence: 99%

Experimental Investigation of Displacer Seal Geometry Effects in Stirling Cycle Machines

Sauer

Kühl

2019

Energies

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Experimental Investigation of Displacer Seal Geometry Effects in Stirling Cycle Machines

Sauer

Kühl

2019

Energies

View full text Add to dashboard Cite

show abstract

“…To further analyze the appendix gap loss numerically and in particular, to reproduce the aforementioned experimental results, Sauer and Kühl extended an existing third order model for regenerative cycles by a differential simulation of the appendix gap [28]. Because of its modular structure, it may be used to simulate any operating mode of the aforementioned convertible experimental machine, and it features a faster computational speed than the model by Andersen, though at the cost of a simplified handling of the momentum equation.…”

Section: Numerical Simulation and Optimization Of The Appendix Gapmentioning

confidence: 99%

Appendix gap losses in Stirling engines – review of recent findings

Kühl

Sauer

2021

E3S Web Conf.

Self Cite

View full text Add to dashboard 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.

show abstract

“…However, all these studies used simple geometries to derive closed formulas for the shuttle and enthalpy pumping losses. Recently, Sauer and Kuehl [28] pointed out the importance of coupling the differential equations of the appendix gap to the main differential equations of the whole engine. This can achieve more accurate estimation for these losses compared with the analytical models which are based on partially questionable assumptions and simple geometries.…”

Section: Shuttle Heat Transfer and Enthalpy Pumping Lossesmentioning

confidence: 99%

Energy and Exergy Analyses of Stirling Engine using CFD Approach

Ghafour

Mikhael

Ghandour

2020

ARFMTS

View full text Add to dashboard Cite

A comprehensive characterization of the GPU-3 Stirling engine losses with the aid of the CFD approach is presented. Firstly, a detailed description of the losses-related phenomena along with the method of calculating each type of loss are addressed. Secondly, an energy analysis of the engine is carried out in order to specify the impact of each type of losses on the performance. Finally, the design effectivity of each component of the engine is investigated using an exergy analysis. The results reveal that the hysteresis loss occurs mainly within the working spaces due to the flow jetting during the first part of the expansion strokes. Additionally, the pressure difference between the working spaces is the main driver for the flow leakage through the appendix gap. The exposure of the displacer top wall to the jet of hot gas flowing into the expansion space during expansion stroke essentially increases the shuttle heat loss. A new definition for the regenerator effectiveness is presented to assess the quality of the heat storage and recovery processes. The energy analysis shows that regenerator thermal loss and pumping power represent the largest part of the engine losses by about 9.2% and 7.5% of the heat input, respectively. The exergy losses within regenerator and cold space are the highest values among the components, consequently, they need to be redesigned.

show abstract

Numerical model for Stirling cycle machines including a differential simulation of the appendix gap

Cited by 22 publications

References 17 publications

Experimental Investigation of Displacer Seal Geometry Effects in Stirling Cycle Machines

Experimental Investigation of Displacer Seal Geometry Effects in Stirling Cycle Machines

Appendix gap losses in Stirling engines – review of recent findings

Energy and Exergy Analyses of Stirling Engine using CFD Approach

Contact Info

Product

Resources

About