# Séminaire de Mécanique d'Orsay

## Le 17 octobre 2024 à 14h00 - Salle de conférences du LIMSI Bât. 507

### Shape Optimisation Under Stochastic Perturbations and Turbulence Stabilisation Using Ensemble Variation

## Yacine Bengana

Department of Aeronautics, Imperial College

We explore the optimisation of flow control strategies using an ensemble-variation (EnVar) method, applied to both shape optimisation and turbulence stabilisation. First, we investigate the optimisation of a two-dimensional cylinder shape to minimise mean drag at Reynolds number ($Re=100$), with random noise introduced through an Ornstein-Uhlenbeck process added to the free-stream velocity. The noise significantly impacts the instantaneous drag; however, the optimal shape, constrained to a constant cross-sectional area and constructed using Fourier coefficients, is found to be a robust oval. This shape achieves a total drag reduction of $23.5%$, notably diminishing the pressure drag component related to vortex shedding, although the viscous drag from the cylinder surface increases slightly.
Building on this framework, we are currently investigating the amplitude dependence of the optimal mean distortion in turbulent channel flow. In parallel, recent experimental and computational studies have demonstrated that flattening the mean velocity profile is an effective strategy for stabilising turbulence in pipe flow (Kühnen et al., 2018, Nat. Phys.). However, a follow-up study employing an adjoint-based optimisation approach found that reducing the mean shear near the wall might be more effective than merely flattening the mean velocity, particularly at higher forcing amplitudes (Marensi et al., 2020, J. Fluid Mech.). This ensemble variation optimisation approach enables us to explore regimes of relatively small-amplitude mean distortion that were previously inaccessible. By applying a streamwise-localised linear damping force, we optimise its wall-normal profile to effectively mitigate turbulence effects. At low forcing amplitudes, the optimal damping is concentrated near the half-channel height, aligning with findings from Kühnen et al. (2018). However, as the amplitude increases, the optimal damping coefficient profile shifts toward the near-wall region, resulting in a distinctive 'M' shape, which reveals complex physical mechanisms in the stabilisation of turbulence.

Accès Salle de conférences du LIMSI Bât. 507