A hybrid algorithm for far-field noise minimization

A general unsteady adjoint formulation is applied to a hybrid acoustic prediction algorithm to provide an efficient far-field noise minimization algorithm. Two-dimensional unsteady Navier–Stokes (NS) computations for calculating the properties of acoustic sources are combined with the Ffowcs Williams and Hawkings (FW–H) wave propagation formulation to calculate the resulting far-field noise. Two different time-marching methods, namely an implicit multi-stage and an implicit multi-step method, are used for time discretization. The hybrid NS/FW–H solver is verified by comparison to an analytical solution and a Navier–Stokes solution. A discrete-adjoint Newton–Krylov algorithm is used to enable gradient-based shape optimization to minimize far-field noise computed using the hybrid solver. Objective functions considered include remote inverse shape designs for verification as well as the far-field pressure fluctuations for a blunt trailing edge airfoil in an unsteady turbulent flow environment. The examples presented demonstrate that the combination of a discrete-adjoint Newton–Krylov algorithm with a hybrid NS/FW–H far-field noise prediction method can be an efficient design tool for reducing aerodynamically generated noise.