Constrained Shape Optimization of Airfoil Cascades Using a Navier-Stokes Solver and a Genetic/SQP Algorithm

Abstract

The objective in this aerodynamic shape design effort is to minimize total pressure loss across the two-dimensional linear airfoil cascade row while satisfying a number of constraints. They included fixed axial chord, total torque, inlet and exit flow angles, and blade cross-section area, while maintaining thickness distribution greater than a minimum specified value. The aerodynamic shape optimization can be performed by using any available flow-field analysis code. For the analysis of the performance of intermediate cascade shapes we used an unstructured grid based compressible Navier-Stokes flow-field analysis code with k-e turbulence model. A robust genetic optimization algorithm was used for optimization and a constrained sequential quadratic programming was used enforcement of certain constraints. The airfoil geometry was parameterized using conic section parameters and B-splines thus keeping the number of geometric design variables to a minimum while achieving a high degree of geometric flexibility and robustness. Significant reductions of the total pressure loss were achieved using this constrained method for a supersonic exit flow axial turbine cascade.