Numerical investigation of transition control in low conductive fluids

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 alinear stability analysis (LSA) of the calculated intermediate velocity profiles. DNS and preliminary LSA results confirm the expected increased stability of the controlled flow. Depending on Lorentz force strength transition to turbulence is delayed or even stopped. Suprisingly, both DNS and LSA results suggest interesting stability characteristics of the intermediate velocity profiles.

In DNS, to initiate transition, small amplitude disturbances are introduced by means of an oscillating body force within a small region near the inflow boundary, forming Tollmien-Schlichting waves (TSW) which grow and decay in uncontrolled case corresponging to linear stability theory. When applying Lorentz force, TSW of all investigated frequencies 0.4 <= F+ <= 3.75 are damped within the computational domain extending over 900 times the inflow displacement thickness d1i. Reynolds number, based on d1i, is 360. The decay rate based on the maximum rms value in wall-normal direction of the streamwise velocity component, is maximum in a region near the onset of control and decreases as the velocity profile approaches the exponential state. 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 preliminary LSA results where critical Reynolds numbers of intermediate profiles are found to be larger than for the exponential profile.

By three dimensional DNS we show that transition to turbulence can be stopped even in it's late stage. While the evolution of Lambda vorticies from former two dimensional TSW remains almost unchanged, the emerge of Omega vorticies is supressed with increasing Lorentz force strength, thus relaminarizing the flow.

[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, Vol. 12, pp. 143-146, 1961