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arXiv 2011.12513physics.flu-dyn
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振动刚性球周围声边界层的解析解

Analytical solution for an acoustic boundary layer around an oscillating rigid sphere

Evert Klaseboer, Qiang Sun, Derek Y. C. Chan

摘要:

流体动力学中的解析解可用于阐明复杂流动的物理特性,并可用作数值模型的测试用例。在这项工作中,我们提出的声学边界层,在可压缩流体中执行小振幅谐波直线运动的刚性球周围的发展的解析解。描述主流的数学框架与线性弹性固体中的波传播的数学框架相同,不同之处在于波数出现复数而不是实值。该解在特殊的极限条件下恢复到著名的经典解:薄边界层极限条件下的势流解、大球半径极限条件下的振荡平板解和无限声速不可压缩极限条件下的Stokes流解。作为分析结果,得到了稳态的二阶声流流动。该流动由雷诺应力张量驱动,该雷诺应力张量产生于围绕这样的刚性球体的轴对称一阶主流。这些结果是用对球的小振幅振荡有效的非线性纳维-斯托克斯方程线性化得到的。流动流服从时均Stokes方程,其体积力由Nyborg模型给出,其中上述可压缩牛顿流体中的主流用于估计时均体积力。数值结果,探索不同的制度的复杂的横向和纵波数的主要流动的特点。

英文摘要:

Analytical solutions in fluid dynamics can be used to elucidate the physics of complex flows and to serve as test cases for numerical models. In this work, we present the analytical solution for the acoustic boundary layer that develops around a rigid sphere executing small amplitude harmonic rectilinear motion in a compressible fluid. The mathematical framework that describes the primary flow is identical to that of wave propagation in linearly elastic solids, the difference being the appearance of complex instead of real valued wave numbers. The solution reverts to well-known classical solutions in special limits: the potential flow solution in the thin boundary layer limit, the oscillatory flat plate solution in the limit of large sphere radius and the Stokes flow solutions in the incompressible limit of infinite sound speed. As a companion analytical result, the steady second order acoustic streaming flow is obtained. This streaming flow is driven by the Reynolds stress tensor that arises from the axisymmetric first order primary flow around such a rigid sphere. These results are obtained with a linearization of the non-linear Navier-Stokes equations valid for small amplitude oscillations of the sphere. The streaming flow obeys a time-averaged Stokes equation with a body force given by the Nyborg model in which the above mentioned primary flow in a compressible Newtonian fluid is used to estimate the time-averaged body force. Numerical results are presented to explore different regimes of the complex transverse and longitudinal wave numbers that characterize the primary flow.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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