Turbulent acoustic streaming with large Reynolds number and its effects on the thermal conduction and mixing

声流是由声波非线性效应引起的平均质量流。紊流声流可以增强容器内物料的热传导、混合和搅拌。由于对大雷诺数声流的物理特性缺乏充分的认识，阻碍了此类技术的发展。本文从理论上和数值上研究了封闭管内由大振幅谐振气体振荡引起的大雷诺数声流。理论分析的方法是基于奇异摄动。数值方法是一种高分辨率迎风TVD格式和一种标准MAC方法。主要结果可以概括如下：(1)我们研究了一维振荡，这在我们的问题中是最重要的。我们已经证明，调幅发生在初始瞬态，并且气体中的温度是由于冲击波产生的热量而提高的。(2)声流的流线受到激波的扭曲。(3)大规模数值模拟证实了涡旋加倍分岔的存在。(4)我们用数值方法证明了二维盒子中声流稳态解的分岔会产生一对稳态解，这对稳态解失去了原解的对称性。分岔后的流运动是箱体内的大规模循环运动。这意味着具有大雷诺数的声流可能对容器中材料的热传导、混合和搅拌有用。

Acoustic streaming is a mean mass flow induced by the nonlinear effect of acoustic waves. It has been expected that turbulent acoustic streaming can enhance the thermal conduction, mixing, and stirring of materials in vessels. The lack of a full understanding of the physical characters of acoustic streaming with large Reynolds number prevents the development of such technologies. In the present study, we have theoretically and numerically investigated acoustic streaming with large Reynolds number induced by large amplitude resonant gas oscillations in a closed tube. The method of theoretical analysis is based on the singular perturbation. The numerical methods are a high-resolution upwind TVD scheme and a standard MAC method.The main results can be summarized as follows:(1) We have examined the one-dimensional oscillations, which is of the most fundamental importance in our problem. We have shown that the amplitude modulation occurs in an initial transient state, and that the temperature in the gas is raised by the heat production due to the shock waves.(2) The streamlines of acoustic streaming are distorted by the shock waves.(3) A vortex doubling bifurcation has been demonstrated by a large scale numerical simulation.(4) We have numerically shown that a bifurcation of steady state solution of acoustic streaming in a 2-dimensional box creates a pair of steady state solutions, which lose the symmetry of the original solution. The streaming motion after the bifurcation is a large scale circulatory motion in the box. This means that acoustic streaming with large Reynolds number may be useful for thermal conduction, mixing, and stirring of materials in vessels.