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

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.