On the stability of boundary layer flows controlled by Lorentz forces


On the stability of boundary layer flows controlled by Lorentz forces

Albrecht, T.; Mutschke, G.; Grundmann, R.

We investigate numerically the transition to turbulence in a flat-plate boundary layer controlled by electromagnetic forces. The fluid considered is incompressible, Newtonian and low conductive. Similar to boundary layer suction, when applying a steady, wall-parallel, and streamwise orientated Lorentz force as suggested by Gailitis and Lielausis [1] in the early 1960s, the Blasius velocity profile is transformed to an exponential one gaining a critical Reynolds number which is increased by two orders of magnitude.

Two and three dimensional direct numerical simulation (DNS) of both linear and nonlinear stages of the transition process were performed, as well as a linear stability analysis (LSA) of the intermediate velocity profiles. DNS and also LSA results confirm the expected increased stability of the controlled flow. Depending on Lorentz force strength transition to turbulence is delayed or even stopped by either damping primary instability, or, in the nonlinear case, by suppressing the emerge of Omega-vortices which usually preceeds the breakdown to turbulence. Surprisingly, both DNS and LSA results suggest interesting linear stability characteristics of the intermediate velocity profiles.

In DNS (Re based on inflow displacement thickness is 360), to initiate transition, small amplitude disturbances are introduced near the inflow boundary, forming Tollmien-Schlichting waves (TSW) which grow and decay in uncontrolled case corresponging to linear stability theory. When applying a Lorentz force, all investigated TSW are damped. The decay rate is maximum in a region near the onset of control and decreases as the velocity profile evolves towards the exponential shape. This observation could suggest that in the intermediate region there are profiles more stable than the exponential one, although we are aware that from these decay rates one cannot conclude directly the stability of a velocity profile, notably its critical Reynolds number. However, our assumption is confirmed by LSA results where critical Reynolds numbers of intermediate profiles are found to be larger than for the exponential profile.

References:

1. A. Gailitis, O. Lielausis , „On a possibility to reduce the hydrodynamic resistance of a plate in an electrolyte,“ Applied Magnetohydrodynamics, Reports of the Physics Institute Riga, v. 12, p. 143-146, 1961

Keywords: boundary layer; flow stability; flow control; magneto-hydrodynamics

  • Lecture (Conference)
    7th World Congress on Computational Mechanics, 16.-22.07.2006, Los Angeles, California, United States

Permalink: https://www.hzdr.de/publications/Publ-8276
Publ.-Id: 8276