The objective of 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 flowfield analysis code. For the analysis of the performance of intermediate cascade shapes, we used an unstructured-grid-based compressible Navier-Stokes flowfield analysis code with a k-ε turbulence model. A robust genetic optimization algorithm was used for optimization, and a constrained sequential quadratic programming was used for 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.
