基于弱可压缩方法的水中声流的数值分析

Numerical Analysis of Acoustic Streaming in Water Based on Weak Compressible Method

为研究水中的非线性声波传播问题,主要开展了基于弱可压缩方程的理论分析及水中声波动及声流模拟工作。首先,采用正压流体的密度与压力函数,结合黏性流体动力学方程,对方程组采用特征变量的波动分析,证明了该方程能描述水中的涡旋和声波传递。然后,结合时空守恒元解元算法求解该方程组;并对一些典型气动声学问题进行了计算和对比研究。通过计算分析了二维顶盖半圆腔驱动流,计算结果与其他研究结论进行对比分析,证实了该方法可以准确模拟出流体的黏性;通过对平面声波在不同黏性流体中传播进行了数值模拟,声波衰减趋势与理论解完全一致。最后,通过对Rayleigh声流问题进行非定常数值模拟,得到的模拟结果与其他研究学者结论完全一致。这说明,采用二维弱可压缩方程组及时空守恒元解元方法,能够模拟水中的声波传播及耗散过程。

To study nonlinear sound wave propagation in water,the theoretical analysis based on weak compressible equations,and the simulation of underwater sound fluctuations and acoustic streaming were carried out.Firstly,based on the density and pressure functions of the positive pressure fluid,the weakly compressible equations were derived with viscous effect.By characteristic analysis of these equations,it was proved that these equation could simulate the vortex and sound waves in water.Then,space-time conservation element and solution element method were used to solve the equations.Some typical aeroacoustics problems were calculated and compared.The2 D driving flow of semicircle cavity were calculated.Compared with other research conclusions,it was proved that the method can accurately simulate the viscosity of the fluid.By numerically simulating the propagation of planar sound waves in different viscous fluids,the attenuation of sound wave trend was completely consistent with the theoretical solution.Finally,the unsteady numerical simulation of Rayleigh acoustic flow was carried out,and the simulation results were exactly the same as those of other researchers.This showed that the 2-D weak compressible equations and the space-time conservation element and solution element method could simulate the sound wave propagation and dissipation in water.