Analysis of the Thermomechanical Stresses in Double-Wall Effusion Cooled Systems

Abstract

In this study, thermal stresses in a double-wall cooling system are analyzed. We consider an infinite flat double-wall geometry and assume that it can be represented by an axisymmetric unit cell, wherein the thermal loadings and deformation at the boundaries are determined by periodicity conditions. A thermal model is initially developed to obtain the thermal fields using a combination of empirical correlations and computational fluid dynamics (CFD) analysis. The thermal fields are then analyzed such that both the first-order and higher order approximations are determined. A theoretical solution is derived assuming that the temperature gradient takes place only across the outer skin using the first-order approximations. The solution yields an equibiaxial stress state in the skins, which are driven by the thermal curvature of the outer skin. To investigate other geometrical features and higher order approximations, a finite element model is used to solve Fourier’s law of heat conduction and mechanical equilibrium equations. The numerical and theoretical results are found to be in excellent agreement. We determine that the increase of distance between pedestals reduces the stresses. Furthermore, the stress concentration factor at the fillet increases with the increase of both the radius and pedestal diameter and the decrease of the skin thickness. Increasing the number of film holes limits stresses to the external surface of the outer skin. The increase of the Reynolds number in the impingement hole increases the Biot number in the outer skin, which increases the stresses. The higher order approximations of the heat transfer coefficients play a minor role.