An application of the finite difference-based lattice Boltzmann model to simulating flow-induced noise

This paper presents a novel approach to simulate aerodynamically generated sounds by modifying the finite difference-based lattice BGK compressible fluid model for the purpose of speeding up the calculation and also stabilizing the numerical scheme. With the model, aerodynamic sounds generated by a uniform flow around a two-dimensional circular cylinder at Re = 150 are simulated. The third-order-accurate up-wind scheme is used for the spatial derivatives, and the second-order-accurate Runge-Kutta method is applied for the time marching. The results show that we successively capture very small acoustic pressure fluctuations, with the same frequency of the Karman vortex street, much smaller than the whole pressure fluctuation around a circular cylinder. The propagation velocity of the acoustic waves shows that the points of peak pressure are biased upstream owing to the Doppler effect in the uniform flow. For the downstream, on the other hand, it is faster. It is also apparent that the amplitude of sound pressure is proportional to r(-1/2), r being the distance from the centre of the circular cylinder. Moreover, the edgetone generated by a two-dimensional jet impinging on a wedge to predict the frequency characteristics of the discrete oscillations of a jet-edge feedback cycle is investigated. The jet is chosen long enough to guarantee the parabolic velocity profile of the jet at the outlet, and the edge is of an angle of alpha = 23 degrees. At a stand-off distance w, the edge is inserted along the centreline of the jet, and a sinuous instability wave with real frequency is assumed to be created in the vicinity of the nozzle exit and to propagate towards the downstream. We have succeeded in capturing small pressure fluctuations resulting from periodic oscillation of jet around the edge. Copyright (c) 2006 John Wiley & Sons, Ltd.