Lattice Boltzmann modeling of backward-facing step flow controlled by a synthetic jet

This article investigates the effect of a synthetic jet (SJ) on the flow over a backward-facing step (BFS) in the weakly turbulent flow regime using the lattice Boltzmann method. The SJ operates with various momentum coefficients Cμand forcing frequencies fjet*. As Cμincreases, the reattachment length decreases, whereas increasing fjet*causes the reattachment length at first decrease and then increase. A minimum reattachment length appears at Cμ= 0.3125, fjet*= 1.6, corresponding to a 40% reduction compared with the uncontrolled case. Two mechanisms for the mediated flow are found: (1) A suitable control frequency leads to a lock-on state that prompts vertical momentum transfer and laminarizes the flow near the separation point, (2) Regular vortices emerge after wall reattachment in controlled cases. Fast Fourier and wavelet transform of the velocity near the separation point reveal that the monitored frequency becomes locked-on when fjet*> 1.6, making the flow quasi-periodic and dramatically reducing the reattachment length. Turbulent kinetic energy spectra indicate that the monitored frequencies are dominated by the forcing frequency and that active control laminarizes the local flow. Proper orthogonal decomposition is used to extract coherent structures at multiple scales. In the dominant mode, reattaching wake vortices are regulated by active control. In the second mode, irregular wake vortices emerge after fjet*= 2, which attenuates the SJ forcing and increases the reattachment length. This study provides insights on typical flows past a BFS and will shed more light on the design of closed-loop control strategies for separation flows.