2D Viscous Aerodynamic Shape Design Optimization for Turbine Blades Based on Adjoint Method Available to Purchase

Since the adjoint method can perform the quick and exact sensitivity analysis and save large computational resources, it has been the highlight in aerodynamic shape design optimization field. The purpose of this work was to extend the adjoint method into turbomachinery applications for viscous and compressible flow and to improve the aerodynamic performance. Being considered as the cost function, the minimization of entropy generation rate was applied to the direct design. The adjoint boundary conditions of the corresponding cost function were derived in detail, by using non-slip boundary condition on the blade wall and neglecting the viscous effect on the cascade inlet and outlet. Numerical techniques used in CFD were employed here to solve the adjoint linear Partial Difference Equations (PDEs). With the solved adjoint variables, final expression of the cost function gradient with respect to the design variables was formulated. Combined with quasi-Newton algorithm, the aerodynamic design approach for turbine blades was presented, which was independent of the Navier-Stokes (N-S) solver being used. Finally, to validate the present optimization algorithm, an aerodynamic design case of transonic turbomachinery blade was performed and analyzed.