The Discrete Adjoint of a Turbomachinery RANS Solver

Since adjoint flow solvers allow for the computation of sensitivities of global flow parameters under geometric variations in an amount of time which is nearly independent of the number of geometric parameters, automatic shape optimization can be accelerated considerably by the use of an adjoint solver. In this article, a systematic approach for the development of an exact discrete adjoint of a turbomachinery flow solver is described. By using finite differences to differentiate the numerical fluxes, the problems associated with automatic and hand differentiation are circumvented. Moreover, a general treatment of the adjoint numerical boundary conditions is presented. As a result, an exact adjoint boundary condition for the conservative mixing planes is obtained. In combination with nonreflecting boundary conditions the latter are crucial for accurate flow simulations in turbomachinery. The adjoint is validated on the basis of a transonic compressor stage.Copyright © 2009 by ASME