An Adjoint Approach for Rapid Coupled Aerodynamic and Aeroacoustic Optimisation of Aerofoils

This work presents a gradient-based framework for aerofoil shape optimisation targeting turbulent boundary layer trailing-edge (TBL-TE) noise reduction under fixed operating conditions. A two-dimensional viscous panel method is coupled with a semi-empirical wall-pressure spectrum (WPS) model and Amiet’s trailing-edge noise formulation to enable rapid aeroacoustic prediction. A discrete-adjoint code is developed to efficiently compute design gradients, allowing gradient-based optimisation utilising a hierarchical shape deformation approach. The approach is demonstrated by applying it to the noise reduction of a NACA 0012 subject to aerodynamic performance constraints. Optimised shapes are found that have substantial reductions in overall sound pressure level (OASPL), driven primarily by delayed transition and reductions in boundary layer thickness. To assess the validity of using low-fidelity simulation methods in the optimisation framework, the optimised shapes are evaluated using high-fidelity Lattice Boltzmann Method (LBM) simulations. The low-fidelity simulations show good agreement in OASPL to the LBM simulations for the baseline NACA 0012 aerofoil, but deviate when noise-optimised shapes are simulated, showing a difference of up to 9dB. It is found that these differences are primarily attributable to under-prediction of boundary layer displacement thickness, which strongly influences low-frequency wall-pressure spectra and subsequent far-field noise.