Unsteady Adjoint Method for Aeroacoustic Propeller Optimization

Abstract

The development of an adjoint method for design optimization of a propeller in an unsteady flow field is presented. The methodology follows the continuous-discrete approach, where the adjoint equations are formulated in a continuous form and afterwards discretized in the same way as the flow equations are discretized. The time-dependent flow and adjoint equations are solved respectively to determine the aeroacoustics performance and gradients of the functionals. The aerodynamic characteristics are obtained using NLR’s CFD solver ENSOLV, while the acoustic characteristics are calculated using the Ffowcs Williams and Hawkings equation. Two aspects are highlighted, namely the development and verification of (i) the unsteady adjoint solver and (ii) the adjoint phase-lagged boundary condition. Computational results are presented for test cases ranging from an academic single airfoil to an industrially relevant propeller configuration.