An Effective Model for the Simulation of Transpiration Cooling

doi:10.1007/s42967-023-00304-7

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (4): 2064-2092.doi: 10.1007/s42967-023-00304-7

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An Effective Model for the Simulation of Transpiration Cooling

Siegfried Müller, Michael Rom

Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

收稿日期:2023-04-06 修回日期:2023-08-03 接受日期:2023-08-03 发布日期:2024-12-20
通讯作者: Michael Rom,E-mail:rom@igpm.rwth-aachen.de;Siegfried Müller,E-mail:mueller@igpm.rwth-aachen.de E-mail:rom@igpm.rwth-aachen.de;mueller@igpm.rwth-aachen.de
基金资助:
Open Access funding enabled and organized by Projekt DEAL.Financial support has been provided by the German Research Foundation (Deutsche Forschungsgemeinschaft-DFG) in the framework of the Sonderforschungsbereich Transregio 40.

An Effective Model for the Simulation of Transpiration Cooling

Siegfried Müller, Michael Rom

Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

Received:2023-04-06 Revised:2023-08-03 Accepted:2023-08-03 Published:2024-12-20
Contact: Michael Rom,E-mail:rom@igpm.rwth-aachen.de;Siegfried Müller,E-mail:mueller@igpm.rwth-aachen.de E-mail:rom@igpm.rwth-aachen.de;mueller@igpm.rwth-aachen.de
Supported by:
This work greatly benefited from feedback by anonymous reviewers. HH, SWF, and SO were partially funded by AFOSR MURI FA9550-18-502, ONR N00014-18-1-2527, N00014-18-20-1-2093, N00014-20-1-2787. HH was also supported by the NSF Graduate Research Fellowship under Grant No. DGE-1650604.

摘要/Abstract

摘要： Transpiration cooling is numerically investigated, where a cooling gas is injected through a carbon composite material into a hot gas channel. To account for microscale effects at the injection interface, an effective problem is derived. Here, effects induced by microscale structures on macroscale variables, e.g., cooling efficiency, are taken into account without resolving the microscale structures. For this purpose, effective boundary conditions at the interface between hot gas and porous medium flow are derived using an upscaling strategy. Numerical simulations in 2D with effective boundary conditions are compared to uniform and non-uniform injection. The computations confirm that the effective model provides a more efficient and accurate approximation of the cooling efficiency than the uniform injection.

关键词: Transpiration cooling, Darcy-Forchheimer flow, Multiscale modeling, Effective boundary conditions

Abstract: Transpiration cooling is numerically investigated, where a cooling gas is injected through a carbon composite material into a hot gas channel. To account for microscale effects at the injection interface, an effective problem is derived. Here, effects induced by microscale structures on macroscale variables, e.g., cooling efficiency, are taken into account without resolving the microscale structures. For this purpose, effective boundary conditions at the interface between hot gas and porous medium flow are derived using an upscaling strategy. Numerical simulations in 2D with effective boundary conditions are compared to uniform and non-uniform injection. The computations confirm that the effective model provides a more efficient and accurate approximation of the cooling efficiency than the uniform injection.

Key words: Transpiration cooling, Darcy-Forchheimer flow, Multiscale modeling, Effective boundary conditions

Siegfried Müller, Michael Rom. An Effective Model for the Simulation of Transpiration Cooling[J]. Communications on Applied Mathematics and Computation, 2024, 6(4): 2064-2092.

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An Effective Model for the Simulation of Transpiration Cooling

An Effective Model for the Simulation of Transpiration Cooling

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