MHD channel flow control in 2D: Mixing enhancement by boundary feedback

• Published in: Automatica (Oxford) Vol. 44; no. 10; pp. 2498 - 2507
• Main Authors: Schuster, Eugenio, Luo, Lixiang, Krstić, Miroslav
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2008; Elsevier
• Subjects: Active mixing enhancement; Distributed parameter systems; Exact sciences and technology; Flow control; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Magnetohydrodynamics and electrohydrodynamics; MHD flow control; Nonlinear boundary control; Physics; Active mixing enhancement; MHD flow control; Nonlinear boundary control; Distributed parameter systems; Magnetohydrodynamics; Mixing; Control system analysis; Magnetometers; Pipe flow; Control program; Non linear control; Control synthesis; Maxwell equations; Passivity; Discretization; Feedback; Flow control; Boundary control; Modelling; Pressure sensors; Spectral method; Electromagnetism; Fractional step method; Electrical conduction; Non linear effect; Navier-Stokes equations; Lyapunov function; Lyapunov methods; Finite difference method
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2008.02.018

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.