An implicit and explicit BEM sensitivity approach for thermo-structural optimization

A computer-automated shape optimization methodology has been developed for the purpose of providing internal cooling systems designers the ability to optimize the internal cooling configuration, geometry and heat transfer enhancements for greater cooling efficiency and more durable turbine airfoils. The methodology presents the theory and practical programming requirements for coupling existing computer design and analysis tools together into a new and powerful design system. The goal of this paper is to demonstrate the computational advantages of using implicit sensitivity with the boundary element method (BEM) within this system over other more brute force methods. For this research, BEM algorithms for nonlinear heat conduction and thermo-elasticity were developed and coupled to an unstructured finite volume CFD code for the hot gas flow and a quasi-one-dimensional thermo-fluid system for the analysis of the internal coolant network. These computational tools were controlled by a constrained hybrid optimization algorithm to provide aerodynamic, thermal and internal fluid flow analyses on modified designs. The coolant supply total pressure, turbine inlet temperature, coolant wall thickness, thickness of ribs, rib positions, rib orientations, pin fin diameters and trip strip heights were incorporated into the set of optimization design variables. In order to improve performance, sensitivity gradients of the objective and constraint functions with respect to the geometric and heat transfer enhancement design variables were obtained using implicit differentiation of the boundary element system of equations. A three-to-one improvement in the optimization convergence rate and greater gradient accuracy were obtained for the two-dimensional thermal optimization problems. An order of magnitude larger computing time reduction was realized for three-dimensional thermal optimizations at the expense of additional memory, and another order of magnitude is expected for thermo-elastic optimization problems. Examples include studies of the accuracy of the design sensitivities with respect to forward and central finite differences, and validation of the optimization process using a symmetric cooled configuration. q 2003 Published by Elsevier Science Ltd.