On the efficiency of MHD drag reduction

Permanent magnets and high electric current densities are often used to achieve reasonable Lorentz forces for a magnetohydrodynamic flow control. This choice, however, usually leads to a low energetic efficiency for the flow control of seawater. We present results of direct numerical simulations of turbulent channel flow [1] drag reduction using electromagnetic forces. The Lorentz force is created by a permanent magnetic field and an electric current from electrodes placed on the bottom wall. The Reynolds number Re, the magnetic interaction parameter N and the load factor k are the control parameters of the problem.
In the first case we used a spanwise oscillating force. The efficiency is the ratio between saved and used power [2]. We found that the efficiency at the load factor k = 4 is about 100 times larger than at k = 1000.
In the second case a streamwise Lorentz force [3] was used. The flow is accelerated near the bottom and the thrust force applied to the bottom wall is directed against the mean flow. The energetic efficiency is the ratio between the mechanical power necessary to move the flat plate with a given velocity and the used electric power. The efficiency is more than 0.9 at k = 0.8.
The main result is that a significant efficiency improvement is possible if load factors k in the order of 1 are used.
References:
1. R.D. Moser, J. Kim and Nagi N. Mansour, "Direct numerical simulation of turbulent channel flow up to Ret = 590," Phys. Fluids, v. 11, no. 4, p. 943-945, 1999.
2. T.W. Berger, J. Kim, C. Lee and L. Lim, "Turbulent boundary layer control utilizing the Lorentz force," Phys. Fluids, v. 12, no. 3, p. 631-649, 2000.
3. A. Gailitis and O. Lielausis, "On the possibility of drag reduction of a flat plate in an electrolyte," Applied Magnetohydrodynamics, Rep. of the Phys. Inst., AN Latv. SSR, v. 12, p. 143-146, (in Russ.), 1961.