The objective of the present numerical study is to increase mixing in turbulent flow
behind a backward-facing step using a systematic feedback control method. Spatially
and temporally varying blowing and suction with zero-net mass flow rate are provided
at the step edge, based on the sensing of the spanwise distribution of the wall pressure
fluctuations at a downstream location. The cost functional to be increased is the
root-mean-square spanwise pressure-gradient fluctuations at the sensing location, which
may be associated with mixing behind the backward-facing step. Given the cost
functional, the actuation at the step edge is determined through the suboptimal
feedback control procedure of Choi et al. (1993). Large-eddy simulations of turbulent
flow are conducted at a Reynolds number of 5100 based on the step height and
free-stream velocity. The results of suboptimal feedback controls are compared with
those of non-feedback single-frequency actuations. In case of the suboptimal control,
velocity and vorticity fluctuations substantially increase downstream of the
backward-facing step as well as in the recirculation zone. As a result, the reattachment length
is significantly reduced, as compared to those of uncontrolled flow and flow with
single-frequency actuations. A simple open-loop control method is devised from the
suboptimal feedback control result, producing nearly the same mixing enhancement
as the feedback control.