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

Keywords: MHD flow control Nonlinear boundary control Active mixing enhancement Distributed parameter systems a b s t r a c t 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. Recent years have been marked by dramatic advances in active flow control (see Aamo and Krstic (2002) and the references therein), which, if implemented through micro-electro-mechanical sensors and actuators, can become effective in reducing drag and separation over aircraft wings, eliminating in-stabilities in various sections of jet engines (inlet, compressor rotating stall, combustion thermoacoustic oscillations, etc.), reducing jet noise, reducing thermal signature of jet exhaust through actively controlled mixing, and steering the overall vehicle. Up until now active feedback flow control developments have had little impact on electrically conducting fluids moving in electromagnetic fields. Active feedback control in electrically conducting flows, implemented through micro-electro-mechanical or micro-electromagnetic actuators and sensors, can be used to optimally achieve the desired level of stability (when suppression of turbulence is desired) or instability (when enhancement of mixing is desired). As a result, a small amount of active control applied to magnetohydrodynamic (MHD) flows, magnetogasdynamic (MGD) flows, and plasma flows can dramatically change their equilibrium profiles and stability (turbulent fluctuation) properties. These changes influence heat transfer, hydrodynamic drag, pressure drop, and the pumping power required to drive the fluid. Prior work in the area of active control of electrically-conducting-fluid flows focuses mainly on electro-magneto-hydro-dynamic (EMHD) flow control for hydrodynamic drag reduction, through turbulence control, in weak electrically conducting fluids such as saltwater. Traditionally two types of actuator designs have been used: one type generates a Lorentz field parallel to the wall in …