Shape optimisation for a stochastic two-dimensional cylinder wake using ensemble variation
Author(s)
Lorente-Macias, Javier
Bengana, Yacine
Hwang, Yongyun
Type
Journal Article
Abstract
In the present study, the shape of a two-dimensional cylinder is optimised to minimise the mean drag in laminar unsteady flow under a noisy environment. A small inline stochastic oscillation in the free-stream velocity, which follows the Ornstein–Uhlenbeck process, is considered for the noise. The small noise is found to yield a large random fluctuation in instantaneous drag of the cylinder due to the effect of added mass. Subject to the strong random fluctuation of drag, the shape optimisation is performed using an ensemble-variation-based method (EnVar), as the conventional adjoint-based optimisation is not applicable to such a flow environment with unknown free-stream noise. The optimised cylinder geometry is found to be a nearly-symmetric slender oval at a low Reynolds number. As the Reynolds number is increased, two optimal shapes emerge: one is identical to the oval obtained at the low Reynolds number, and the other is an asymmetric oval, the rear side of which is more slender than the front side, reminiscent of an aerofoil. Despite the large random fluctuation in the instantaneous drag, the optimal cylinder shapes obtained for different levels of the upstream noise are found to be almost identical. It is shown that the robust nature of the optimal cylinder shape originates from the limited influence of the small upstream noise on the mean flow properties of the cylinder wake. Finally, the optimised cylinder primarily reduces the pressure component of the drag, associated mainly with vortex shedding in the wake, and this is achieved by marginally increasing the viscous drag through the shape change.
Date Issued
2023-03-25
Date Acceptance
2023-02-06
Citation
Journal of Fluid Mechanics, 2023, 959, pp.1-20
ISSN
0022-1120
Publisher
Cambridge University Press
Start Page
1
End Page
20
Journal / Book Title
Journal of Fluid Mechanics
Volume
959
Copyright Statement
Copyright © 2023 Cambridge University Press. This article has been published in a revised form in Journal of Fluid Mechanics [https://doi.org/10.1017/jfm.2023.122]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works.
Identifier
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/shape-optimisation-for-a-stochastic-twodimensional-cylinder-wake-using-ensemble-variation/4A636EDA0BE8632E310956C957AD4727
Publication Status
Published
Article Number
A7
Date Publish Online
2023-03-16