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.

2D and 3D thermoelastic phenomena in double wall transpiration cooling systems for gas turbine blades and hypersonic flight

“…For critical engine hot stage components, such as conventional turbine rotor blades, the major importance of thermal stresses over mechanical (centrifugal/inertial) stresses [25][26][27] and aerodynamic bending (gas bending) stresses has been shown [4,22,28]. However, information for non-conventional double wall configurations is limited to the reports by Murray et al [4], Elmukashfi et al [29] and the recent work by the authors [20].…”

“…The study identified that significant thermal stresses mainly arise by a temperature gradient through the thickness of the outer wall as well as by the average temperature difference between the two walls which are mechanically coupled by the pedestals. The latter was studied in more depth by Elmukashfi et al [29] who derived both FE and plate theory solutions for 2D and axisymmetric flat double wall geometric idealisations, that described the nature of the thermal stress field as a function of geometry. The sensitivity of thermal stresses as a function of primary geometric features, temperature field perturbations as well as heat transfer, coolant flow constants i.e.…”

Multiscale analysis of thermomechanical stresses in double wall transpiration cooling systems for gas turbine blades

“…The merit of the approach is that it allows for a rapid evaluation of the film effectiveness and blade external temperature distributions as well as of the coolant mass flow consumption. Elmukashfi et al [32] explored the thermoelastic stress field in simple double wall elements, including the effect of cooling parameters, i.e. Re and Biot number, and perturbations of the temperature field, on peak stresses.…”

“…In contrast to the aerothermal aspects of DWTC, systematic studies of the mechanical performance is limited to a few recent studies [12,[32][33][34], mainly conducted by the authors. These studies indicate that DWTC systems can experience severe thermal stresses [34] as significant stress concentration factors (SCF) occur at holes and pedestals [12].…”

Influence of Spanwise and Streamwise Film Hole Spacing on Adiabatic Film Effectiveness for Effusion-Cooled Gas Turbine Blades

“…However, metal effectiveness and mechanical stresses should be considered for a better understanding of the overall consequences on more engine-like designs. This is an area of research investigated by Elmukashfi et al [21], and something that the authors of this study look to expand upon.…”