MHD Channel Flow Control in 2D: Mixing Enhancement by Boundary Feedback
E. Schuster, L. Luo, M. Krstic
Automatica 44 (2008) 2498-2507
Abstract
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A nonlinear Lyapunov-based boundary feedback control law is proposed for mixing enhancement in a 2D magnetohydrodynamic
(MHD) channel flow, also known as Hartmann flow, which is electrically conducting, incompressible, and subject to an external
transverse magnetic field. The MHD model is a combination of the Navier-Stokes PDE and the Magnetic Induction PDE,
which is derived from the Maxwell equations. Pressure sensors, magnetic field sensors, and micro-jets embedded into the walls
of the flow domain are employed for mixing enhancement feedback. The proposed control law, designed using passivity ideas,
is optimal in the sense that it maximizes a measure related to mixing (which incorporates stretching and folding of material
elements), while at the same time minimizing the control and sensing efforts. A DNS code is developed, based on a hybrid
Fourier pseudospectral-finite difference discretization and the fractional step technique, to numerically assess the controller.