Chaotic sensitivity analysis of noise at chevron nozzle exits

The computation of sensitivities of turbulent fluid flows to input parameter perturbations is important for gradient-based multi-disciplinary design optimization, uncertainty quantification, mesh adaptation and so on. Since linearized perturbation equations are unstable in chaotic systems, conventional adjoint sensitivity analysis methods that are successful with steady RANS solutions, fail in the case of high-fidelity chaotic numerical simulations such as LES. At present, some potential candidates for sensitivity computation in chaotic systems are shadowing-based and ensemble-based methods. Ensemble-based methods exhibit poor rate of convergence and are hence impractical for eddy-resolving simulations; Shadowing-based methods are not guaranteed to converge since the computed shadowing trajectories may be rare trajectories that do not correspond to the average dynamics of the fluid system. We propose an alternative called Space-Split-Sensitivity (S3) computation that provably converges to the mean response of a chaotic system to parameter perturbations. We demonstrate that the new algorithm enables optimization of chevron nozzle geometry to reduce the noise produced by jet engines.