Pore Scale Study On Simulation Of Sound Propagation In Porous Media By Lattice Boltzmann Method

Sound propagation in porous materials has gained more and more attention due to its wide applications in many fields of science and engineering. Through a better theoretical understanding of acoustic propagation in complex porous media, underwater noise can be controlled effectively. While, most of research started from a macroscopic perspective rather than from microscopic point of view. In this paper, Multi-Relaxation-Time lattice Boltzmann method, a kind of mesoscopic method, is used to simulate the propagation of sound in porous media at pore scale to explore the relation between porous structural parameter (porosity, tortuosity, particle size) or characteristic of acoustic wave (frequency) with transmission coefficients of acoustic waves. In our paper, tortuosity of flow path in the porous medium, a characteristic of material transport in porous media, is estimated from an indirect way through the ordinary molecular diffusion which is simulated by lattice Boltzmann method as well. Numerical results show that the relations between tortuosity and porosity are related with the shape and the distribution of particles. Finally, with these direct simulations, we investigate numerically the effects of the length, tortuosity, porosity, particle sizes of porous samples and angular frequency of plane waves on the transmission coefficients in porous media, respectively. It can be found that tortuosity, particle sizes and length of porous media play important roles in the transmission coefficients while the sound waves passing through the porous media. And the effect of porosity can be included in which of tortuosity because of the relationships between tortuosity and porosity. We can obtain an equation, Tc= exp[-(C · A(T)L+B(T))], where Tc is the transmission coefficient which is equal to the ratio of the amplitudes of sound pressure after passing through porous media, Pout, to the amplitudes of the incident waves, A. C is the coefficient related to the particle sizes, A(T) and B(T) are the equations related with tortuosity. And we find that the transmission coefficient, Tc, will reach the upper limit when the angular frequency of plane waves decrease gradually. The limit is equal to the transmission coefficient when Pin is fixed.