Optimization of Endwall Contours of a Turbine Blade Row Using an Adjoint Method

This paper presents the application of a viscous adjoint method in the optimization of a low-aspect-ratio turbine blade through spanwise restaggering and endwall contouring. A generalized wall-function method is implemented in a Navier-Stokes flow solver coupled with Menter’s SST k-ω turbulence model to simulate secondary flow with reduced requirements on grid density. Entropy production through the blade row combined with a flow turning constraint is used as the objective function in the optimization. With the viscous adjoint method, the complete gradient information needed for optimization can be obtained by solving the governing flow equations and their corresponding adjoint equations only once, regardless of the number of design parameters. The endwall profiles are contoured alone in the first design case, while it is combined with spanwise restaggering in the second design case. The results demonstrate that it is feasible to reduce flow loss through the blade redesign while maintaining the same mass-averaged flow turning by using the viscous adjoint optimization method. The performance of the redesigned blade is calculated and compared at off-design conditions.