Effect of synthetic jet control on the sound radiated from a circular cylinder in the laminar regime

In this article, we focus on the effect of active control via synthetic jets (SJs) on sound generated by a two-dimensional circular cylinder using the acoustic analogy method. The cylinder is immersed in the uniform upstream flow, where the corresponding Reynolds number is 100 and the Mach number is 0.1. A pair of SJs is deployed near the cylinder’s separation point issuing periodically varying forcing, with different combinations of forcing frequency and phase difference. The lattice Boltzmann method (LBM) is coupled with the multi-direct forcing immersed boundary method to solve the near-field flow dynamics. The mechanism of the sound generation lies in that pressure pluses are induced by the periodic vortex shedding from the cylinder’s surface, i.e., dipoles. In cases with active flow control, extra monopoles are generated by the unsteady flowrate resulted from the SJs' periodic blow/suction. Interactions between monopoles and dipoles are confirmed to have big impacts on the acoustic field. The acoustic analogy method is used for various cases with a wide range of control parameters, because it has a considerably lower computational cost than the direct simulation method. Taking into account the effect of the monopole, the acoustic analogy method is developed for solving two-dimensional sound field by substituting the Green’s function. Results indicate that the primary lockon and the secondary lock-on occurs in the specified control parameters. Frequencies of vortex shedding are related to the SJs’ frequency, deviating the unforced frequency. Due to the noise induced by flow, the frequency and phase difference of the SJs also have significant impacts on sound field. The far-field noise is enlarged although the SJs reduce drag, due to the induced extra monopole, as well as the strengthened hydrodynamic fluctuation. Further increasing SJs’ frequency or decreasing the phase differences will enlarge the far-field noise and make the directivity transformed from dipole to monopole, since the SJs’ selfnoise is stronger. Moreover, it is found that the acoustic power increases by approximately 4-18dB compared with the unforced circular cylinder and the drag dipole is strengthened in all combinations of control parameters. This study deepens the understanding of the effect of SJs on sound field, while providing a reference for future researches on control strategies of suppressing noise generated from bluff bodies.