External acoustic control of the laminar vortex shedding past a bluff body

This paper deals with the active control of the compressible flow past a bluff-body by means of external acoustic sources. We successfully suppress the transition leading to the von-Karman vortex street. The derived adjoint-based framework allows the determination of the corresponding acoustic sources for generic bluff-body shapes. In particular, we determine the optimal spatial position for the control, i.e. where the acoustic source is most efficient, and the associated temporal signal. For the proposed example, a two-dimensional cylindrical body, the resulting acoustic actuation is anti-symmetric and harmonic. We found that the limits of our control approach are related to the limits of linear acoustics. The methodology and the results proposed in this paper can be used to design a control strategy coupled with a continuation procedure able to obtain the unstable solutions beyond the critical threshold.