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

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 combinat...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 44; no. 10; pp. 2498 - 2507
Main Authors Schuster, Eugenio, Luo, Lixiang, Krstić, Miroslav
Format Journal Article
LanguageEnglish
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
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2008.02.018