Theoretically and experimentally founded simulation of the appendix gap in regenerative machines

Sauer, Jan; Kuehl, Hans-Detlev

doi:10.1016/j.applthermaleng.2019.114530

Cited by 5 publications

(11 citation statements)

References 32 publications

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“…Fig. 13: Results for the dependency of the appendix gap loss on the gap width obtained by numerical simulation using complex transport equations and three empirical approaches in comparison to those obtained by the two specified analytical models [29] Furthermore, Fig. 13 provides an explanation for the deviating slopes of the curves in the limiting case of vanishing gap widths, which could already be observed in Fig.…”

Section: Numerical Simulation and Optimization Of The Appendix Gapmentioning

confidence: 82%

“…Because of these open issues and since neither a satisfactory theoretical nor a sufficient experimental validation of the aforementioned modelling approaches for the heat transfer was available, this issue was investigated in more detail by Sauer and Kühl [29]. To describe the heat transfer, they tentatively applied correlations based on the complex Nusselt number concept, which had previously been derived by Pfeiffer on the basis of the aforementioned unsteady analytical model for the flow and temperature profiles in the gap [30].…”

Section: Numerical Simulation and Optimization Of The Appendix Gapmentioning

confidence: 99%

“…The result is therefore found to consist of three components, one of which is constant, whereas the others are periodic functions of 𝜔𝜔𝜔𝜔 or 2𝜔𝜔𝜔𝜔 , respectively. To describe their corresponding phase shifts by complex constants, three different complex temperature ratios 𝝉𝝉 𝟏𝟏 , 𝝉𝝉 𝟐𝟐 and 𝝉𝝉 𝟑𝟑 must be introduced, which are complex functions of Γ , 𝜃𝜃 𝑢𝑢 and 𝑃𝑃𝑅𝑅 𝜔𝜔 [29]. Implementing these in the third order model, a theoretically founded reference model for the transport phenomena in the gap, which is supported by the experimental results presented in chapter 3, was created.…”

Section: Numerical Simulation and Optimization Of The Appendix Gapmentioning

confidence: 99%

“…Fig.12: Dependency of the various loss mechanisms in the appendix gap on the gap width according to the discussed analytical models in comparison to the results of numerical simulations using three different approaches for the modelling of the heat transfer[29] 𝐻𝐻 ̇= 𝜋𝜋 𝑑𝑑 𝐶𝐶 𝜌𝜌 𝑐𝑐 𝑝𝑝 � 𝑢𝑢(𝑦𝑦)[𝑇𝑇(𝑦𝑦) − 𝑇𝑇 0 ] 𝑑𝑑𝑦𝑦 ℎ 0…”

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confidence: 99%

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Appendix gap losses in Stirling engines – review of recent findings

Kühl

Sauer

2021

E3S Web Conf.

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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.

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Section: Numerical Simulation and Optimization Of The Appendix Gapmentioning

confidence: 82%

Section: Numerical Simulation and Optimization Of The Appendix Gapmentioning

confidence: 99%

Section: Numerical Simulation and Optimization Of The Appendix Gapmentioning

confidence: 99%

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confidence: 99%

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Appendix gap losses in Stirling engines – review of recent findings

Kühl

Sauer

2021

E3S Web Conf.

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“…The simulation accuracy of the program kpsim has been demonstrated repeatedly, inter alia for the considered experimental machine 38,40,52 . However, the modification of the simulation code must also be validated.…”

Section: Numerical Simulation and Optimizationmentioning

confidence: 94%

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

Sauer

Kühl

2021

Intl J of Energy Research

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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.

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