Homogenization of the thermal properties of transpiration cooled multi-layer plates

To predict the aerothermal behaviour of transpiration cooled plates, a multi-scale approach based on the homogenization method of periodic material structures is presented. This method allows to calculate effective equivalent thermophysical properties either for each layer or for the multi-layer of superalloy, bondcoat and thermal barrier coating. Its variational formulation and finite element discretization are then presented. From the 3-D conjugate flow and heat transfer analysis, the stationary state is extracted and transferred to the micro-scale unit cell discretized by finite elements. The effect of the different cooling designs on the effective orthotropic conductivities are then discussed. Finally, the influence of the FE discretization and the position of unit cell on these effective thermal properties is investigated. (C) 2002 Elsevier Science B.V. All rights reserved.