Closed-loop control of unsteadiness over a rounded backward-facing step
- 12 June 2012
- journal article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 703, 326-362
- https://doi.org/10.1017/jfm.2012.223
Abstract
The two-dimensional, incompressible flow over a rounded backward-facing step at Reynolds number $\mathit{Re}= 600$ is characterized by a detachment of the flow close to the step followed by a recirculation zone. Even though the flow is globally stable, perturbations are amplified as they are convected along the shear layer, and the presence of upstream random noise renders the flow unsteady, leading to a broadband spectrum of excited frequencies. This paper is aimed at suppressing this unsteadiness using a controller that converts a shear-stress measurement taken from a wall-mounted sensor into a control law that is supplied to an actuator. A comprehensive study of various components of closed-loop control design – covering sensor placement, choice and influence of the cost functional, accuracy of the reduced-order model, compensator stability and performance – shows that successful control of this flow requires a judicious balance between estimation speed and estimation accuracy, and between stability limits and performance requirements. The inherent amplification behaviour of the flow can be reduced by an order of magnitude if the above-mentioned constraints are observed. In particular, to achieve superior controller performance, the estimation sensor should be placed upstream near the actuator to ensure sufficient estimation speed. Also, if high-performance compensators are sought, a very accurate reduced-order model is required, especially for the dynamics between the actuator and the estimation sensor; otherwise, very minute errors even at low energies and high frequencies may render the large-scale compensated linearized simulation unstable. Finally, coupling the linear compensator to nonlinear simulations shows a gradual deterioration in control performance as the amplitude of the noise increases.
This publication has 23 references indexed in Scilit:
- Transition delay using control theoryPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2011
- Control of a separated boundary layer: reduced-order modeling using global modes revisitedTheoretical and Computational Fluid Dynamics, 2010
- Closed-loop control of an open cavity flow using reduced-order modelsJournal of Fluid Mechanics, 2009
- Convective instability and transient growth in flow over a backward-facing stepJournal of Fluid Mechanics, 2008
- Modeling of transitional channel flow using balanced proper orthogonal decompositionPhysics of Fluids, 2008
- A Linear Systems Approach to Flow ControlAnnual Review of Fluid Mechanics, 2007
- Control of turbulent boundary layersPhysics of Fluids, 2003
- Optimal and robust control and estimation of linear paths to transitionJournal of Fluid Mechanics, 1998
- The effect of flow oscillations on cavity dragJournal of Fluid Mechanics, 1987
- Guaranteed margins for LQG regulatorsIEEE Transactions on Automatic Control, 1978