Mixing Enhancement by Boundary Feedback Control in 2D MHD Channel Flow: A Numerical Study
E. Schuster, L. Luo
AIAA Fluid Dynamics Meeting
San Francisco, California, June 2006
Abstract
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A direct numerical simulation (DNS) code has been developed, based on
a hybrid Fourier pseudospectral-finite difference discretization
scheme and the fractional step technique, to simu- late a
two-dimensional (2D) magnetohydrodynamic (MHD) channel flow, also
known as Hartmann flow. This flow is characterized by an electrically
conducting, incompressible fluid moving between parallel plates in the
presence of an externally imposed transverse magnetic field. The
system is described by the MHD equations, a combination of the
Navier-Stokes equation and the Magnetic Induction equation, which is
derived from the Maxwell equations. The laminarization effect of the
imposed magnetic field is studied numerically. In addition, a
nonlinear, Lyapunov-based, boundary feedback control law designed for
mixing enhancement is numerically tested. Pressure sensors, magnetic
field sensors, and micro-jets embedded into the walls of the flow
domain are considered in this work to implement a feedback control law
that maximizes a measure related to mixing (which incorporates
stretching and folding of material elements), and minimizes the
control and sensing efforts.