Control of mixing by boundary feedback in 2D channel flow. (English) Zbl 1055.93039
The problem of enhancing mixing by means of boundary feedback control in 2D channel flow is considered. This is done by first designing feedback control strategies for the stabilization of the parabolic equilibrium flow, then applying this feedback with the sign of the input reversed.
The result is enhanced instability of the parabolic equilibrium flow, which leads rapidly to highly complex flow patterns. Simulations of the deformation of dye blobs positioned in the flow indicate (qualitatively) that effective mixing is obtained for small control effort as compared with the nominal (uncontrolled) flow.
A mixedness measure \(P_\varepsilon\) is constructed to quantify the mixing observed, and is shown to be significantly enhanced by the application of the destabilizing control feedback.
The result is enhanced instability of the parabolic equilibrium flow, which leads rapidly to highly complex flow patterns. Simulations of the deformation of dye blobs positioned in the flow indicate (qualitatively) that effective mixing is obtained for small control effort as compared with the nominal (uncontrolled) flow.
A mixedness measure \(P_\varepsilon\) is constructed to quantify the mixing observed, and is shown to be significantly enhanced by the application of the destabilizing control feedback.
Reviewer: Zbigniew Dżygadło (Warszawa)
MSC:
| 93C20 | Control/observation systems governed by partial differential equations |
| 76D55 | Flow control and optimization for incompressible viscous fluids |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93D15 | Stabilization of systems by feedback |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
boundary feedback control; channel flow; complex flow patterns; parabolic equilibrium flow; Lyapunov stability; mixing control; control of fluid flowsReferences:
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