Adjoint-Based Flow Sensitivity Analyis Using Arbitrary Control Surfaces

This article describes how to extend the dsicrete adjoint method to functionals that are evaluated on arbitrary rotational control surfaces that intersect the flow domain at a position specified by the user, e.g. the pressure loss coefficient of a single blade in a multi-stage configuration. The definition and implementation of the mixed-out states on such surfaces is revisited. The calculation of the corresponding right-hand sides in the adjoint system is explained. These techniques can be used to specify functionals that quantify the deviation of the radial distribution of the flow angles, relative mass flow, etc. from a given target distribution. Sensitivity studies using the conventional approach, i.e. by means of finite differences of many steady solutions, are compared to results based on the adjoint method. The applications demonstrate that the agreement between adjoint and conventional sensitivity predictions is excellent, if the exact definition of the surface functionals is taken into account.