Magnetohydrodynamik drag reduction and efficiency

Two cases are considered in order to study possible drag reductions due to the action of electromagnetic forces.
1. A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations and Poisson electric potential equation are solved at a Reynolds number Re=3000 and 6000, based on the laminar centreline velocity V0 and channel half-width d. The tau-collocation spectral method developed by J. Kim. et al. is used. The Crank-Nikolson method for the viscous and a third-order Runge-Kutta method for the nonlinear term and the Lorentz force are applied. The resolution was 64x65x64 in the streamwise, wall-normal and spanwise directions. For an electromagnetic actuator consisting basically of a spanwise oscillating force, we analysed the drag reduction and its efficiency for various load number. It is shown that a load number of order one leads to a significant increase of the efficiency in comparison to the standard case of high small load number.

2. For the flow around a sphere we found an internal alternating electromagnetic field source which leads to a strong drag reduction. The analysis is done in the Stokes approximation analytically and then at Reynolds number Re ~ 300 numerically using a pseudospectral code. A simple gradient-type optimisation was applied in order to tailor the magnetic field source for the purpose of a reduced drag. We considered the simplified case (decoupling of fluid flow and electromagnetic fields) of large load numbers, with the drawback that the strong drag reductions obtained are certainly inefficient from the energetical point of view.