Shape optimisation for a stochastic two-dimensional cylinder wake using ensemble variation*

This talk concerns the optimisation of a two-dimensional cylinder shape to minimise the mean drag in the presence of random noise at Reynolds number Re=100. The noise is provided by the Ornstein-Uhlenbeck process added to the free stream inlet velocity. Because of the added mass effect, the noise introduces large fluctuations to the instantaneous drag. The optimisation problem is solved using an ensemble-variation method (EnVar). To keep the same internal cylinder space, we constrain the cylinder cross-section area to be a constant value. The cylinder shape is built with Fourier coefficients. We also added a penalty term to avoid non-smooth cylinder surfaces. The optimal shape that minimises the mean drag is found to be close to an oval, the rear side of which is a little blunter than the front. Moreover, it is shown that this oval shape is robust to the noise level because the stochastic oscillations do not significantly alter the cylinder wake mean flow. We observed that the optimisation process significantly reduces the pressure drag component related to the vortex shedding. However, the viscous drag originating from the cylinder surface is marginally increased by 3.5%. Finally, the total drag is decreased by 23.5%.