Optimal control of circular cylinder wakes using long control horizons

Abstract

The classical problem of suppressing vortex shedding in the wake of a circular cylinder by using body rotation is revisited in an adjoint-based optimal control framework. The cylinder's unsteady and fully unconstrained rotation rate is optimized at Reynolds numbers between 75 and 200 and over horizons that are longer than in previous studies, where they are typically of the order of a vortex shedding period or shorter. In the best configuration, the drag is reduced by 19%, the vortex shedding is effectively suppressed, and this low drag state is maintained with minimal cylinder rotation after transients. Unlike open-loop control, the optimal control is shown to maintain a specific phase relationship between the actuation and the shedding in order to stabilize the wake. A comparison is also given between the performance of optimizations for different Reynolds numbers, cost functions, and horizon lengths. It is shown that the long horizons used are necessary in order to stabilize the vortex shedding efficiently.

Model Predictive Control of a Separated Flow around a Circular Cylinder at a Low Reynolds Number

“…One consists of deviation from an ideal unseparated flow and the other includes viscous dissipation energy. The objective functions employed in [9] evaluate physical quantities on the surface of the cylinder, whereas our objective functions evaluate them within the spatial domain.…”

“…MPC has been applied to fluid flows such as thermal fluid [6], a turbulent flow [7], a heated turbulent flow [8], and a flow with vortex shedding around a 2D cylinder [9]. Control targets are internal flows in [6]- [8] and external flows in [9] and this paper. Generally, a considerable attention should be paid to treatment of the outer boundary conditions for external flows.…”

“…Generally, a considerable attention should be paid to treatment of the outer boundary conditions for external flows. The decisive difference from [9] is the control input. In [9], the flow around a cylinder is controlled by rotating the cylinder itself.…”

“…The decisive difference from [9] is the control input. In [9], the flow around a cylinder is controlled by rotating the cylinder itself.…”

Feedback control of unstable flows: a direct modelling approach using the Eigensystem Realisation Algorithm

“…This approach can also be used as an off-line adjoint-based optimisation technique if applied to the full (potentially nonlinear) Navier-Stokes equations (e.g. Bewley, Moin & Temam 2001;Protas & Styczek 2002;Joe et al 2010;Flinois & Colonius 2015). In this case, the results are useful for revealing effective control mechanisms, which can for instance be exploited using intuition-based controllers (e.g.…”