Homogenization of the fluid flow and heat transfer in transpiration cooled multi-layer plates

Abstract

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.