Numerical prediction of acoustic sounds occurring by the flow around a circular cylinder

Acoustic sounds generated by uniform flow around a two-dimensional circular cylinder at Re=150 are simulated by applying the finite difference lattice Boltzmann method. A third-order-accurate up-wind scheme is used for the spartial derivatives. A second-order-accurate Runge-Kutta scheme is also used for time marching. Very small acoustic pressure fluctuation, with same frequency as that of Karman vortex street, is compared with pressure fluctuation around a circular cylinder. The propagation velocity of acoustic sound shows that acoustic approaching the upstream, due to the Doppler effect in uniform flow, slowly propagates. For the downstream, on the other hand, it quickly propagates. It is also apparent that the size of sound pressure is proportional to the central distance γ-1/2 of the circular cylinder