An Effective Model for the Simulation of Transpiration Cooling

Siegfried Müller, Michael Rom

Communications on Applied Mathematics and Computation ›› 2023, Vol. 6 ›› Issue (4) : 2064-2092. DOI: 10.1007/s42967-023-00304-7
Original Paper

An Effective Model for the Simulation of Transpiration Cooling

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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.

Keywords

Transpiration cooling / Darcy-Forchheimer flow / Multiscale modeling / Effective boundary conditions

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Siegfried Müller, Michael Rom. An Effective Model for the Simulation of Transpiration Cooling. Communications on Applied Mathematics and Computation, 2023, 6(4): 2064‒2092 https://doi.org/10.1007/s42967-023-00304-7

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Funding
Deutsche Forschungsgemeinschaft; RWTH Aachen University (3131)

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