Optimizing an acoustic liner by automatic differentiation of a compressible flow solver

Abstract

The attenuation power of an acoustic liner is optimized by unsteady compressible flow simulations that model the presence of the liner with a time-domain impedance boundary condition (TDIBC). Two test cases are considered: a one-dimensional impedance tube and a two-dimensional grazing incidence tube. The impact of the liner on the pressure field is tuned through various TDIBC parameters imposed at the boundary where the liner surface is located. Automatic differentiation of the direct numerical simulation (DNS) code yields the gradients of the time-integrated pressure perturbations with respect to the TDIBC parameters. The gradients are subsequently used in an iterative process that minimizes the perturbations at a given location. In both test cases considered, TDIBC parameters are found which are more effective at attenuating perturbation frequencies other than those the initial TDIBC is designed to cancel. Finally, a sensitivity analysis reveals the importance of the choice of the initial TDIBC parameters for finding optimized settings. Our results pave the way to a wider application of the presented procedure in more complex problems with bulk flow motion and larger perturbation amplitudes.