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Homogenization of the fluid flow and heat transfer in transpiration cooled multi-layer plates. (English) Zbl 1107.76382

Summary: To predict the aerothermal behavior of transpiration cooled plates, a multi-scale approach based on the homogenization method of periodic material structures is developed. This method allows one to calculate effective equivalent thermophysical properties either for each layer or for the multi-layer of superalloy, bondcoat and TBC. A general formulation is developed here for the fluid flow through a porous media which is able to deduce as equivalent macroscopic behavior either a Darcy law with a constant permeability or a more general Fochheimer law with a permeability function of the mean velocity. Effective Darcy permeabilities are calculated by solving special Stokes flow problems on a unit cell. Finally, effective conductivities and permeabilities are determined for different configurations of cylindrical and shaped transpiration cooling channels.

MSC:

76M50 Homogenization applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
76D99 Incompressible viscous fluids
80M40 Homogenization for problems in thermodynamics and heat transfer

Software:

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References:

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