Profiled End Wall Design Using an Adjoint Navier–Stokes Solver

A methodology to minimize blade secondary losses by modifying turbine end walls is presented. The optimization is addressed using a gradient-based method, where the computation of the gradient is performed using an adjoint code and the secondary kinetic energy is used as a cost function. The adjoint code is implemented on the basis of the discrete formulation of a parallel multigrid unstructured mesh Navier–Stokes solver. The results of the optimization of two end walls of a low-pressure turbine row are shown.