Separation control based on turbulence transition around a two-dimensional hump at different Reynolds numbers

Separation and reattachment around a two-dimensional hump controlled by a two-dimensional periodic excitations induced by a dielectric barrier discharge plasma actuator are investigated at Reynolds numbers of 4000 and 16, 000 based on the freestream velocity and the hump height. A two-dimensional excitation is adopted in the present study for promoting two-dimensional instability in the shear layer and a resulting laminar-turbulent transition. Note that the most effective frequency for reattachment is fh(=f*u∞*/h*)=0.20 among the presently considered cases at both Reynolds numbers, which is close to the reference value previously reported for the flow around a backward-facing step (Hasan, 1992).This frequency is the highest among the frequencies that provide sufficient time for the vortex scale to become the hump height. In addition, the momentum balance around the hump is examined by decomposing the averaged momentum equations. The velocity fluctuation terms are found to be considerable in size: they increase around the separation position under periodic excitation control. These terms are balanced with other terms: the gradient of the velocity fluctuation in the streamwise direction is comparable to the sum of convection terms of the time-averaged velocity and that in the wall-normal direction is comparable to the pressure gradient in the wall-normal direction. The control performance for reattachment is correlated with these velocity fluctuation effects. There is a possibility that the excitation control enforces reattachment by increasing turbulence fluctuation and modifying the momentum transfer balance.