The Harmonic Adjoint Approach to Unsteady Turbomachinery Design

This paper demonstrates how the worksum output produced by the linear harmonic ow analysis can be obtained by an adjoint harmonic analysis which, under certain conditions, is a more ecient alternative to the usual linear approach. The adjoint approach has been developed for aeronautical optimal design by Jameson [10, 11]. At each optimisation step, a single adjoint ow calculation determines the sensitivity of a steady-state functional (e.g. lift or drag) to a large number of geometric design parameters. The same idea is applied in this paper in the context of linear unsteady ow analysis, to compute the worksum values corresponding to any input unsteady ow perturbations, whereas the usual approach would require a separate linear unsteady ow calculation for each set of input