Institute of Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland.
J Acoust Soc Am. 2011 Jun;129(6):3490-501. doi: 10.1121/1.3589247.
In this paper, theoretical calculations as well as numerical simulations are performed for the time-averaged acoustic force and torque on a rigid cylinder of arbitrary size in a fluid with low viscosity, i.e., the acoustic boundary layer is thin compared to the cylinder radius. An exact analytical solution and its approximation are proposed in the form of an infinite series including Bessel functions. These solutions can be evaluated easily by a mathematical software package such as mathematica and matlab. Three types of incident waves, plane traveling wave, plane standing wave, and dual orthogonal standing waves, are investigated in detail. It is found that for a small particle, the viscous effects for an incident standing wave may be neglected but those for an incident traveling wave are notable. A nonzero viscous torque is experienced by the rigid cylinder when subjected to dual orthogonal standing waves with a phase shift even when the cylinder is located at equilibrium positions without imposed acoustic forces. Furthermore, numerical simulations are carried out based on the FVM algorithm to verify the proposed theoretical formulas. The theoretical results and the numerical ones agree with each other very well in all the cases considered.
本文针对低粘度流体中任意尺寸刚性圆柱所受的时均声波力和力矩进行了理论计算和数值模拟，即与圆柱半径相比，声边界层较薄。本文提出了一种精确的解析解及其近似解，其形式为包含贝塞尔函数的无穷级数。这些解可以通过数学软件包（如 mathematica 和 matlab）轻松评估。详细研究了三种类型的入射波，即平面行波、平面驻波和双正交驻波。研究发现，对于小粒子，入射驻波的粘性效应可以忽略不计，但入射行波的粘性效应则不可忽略。当刚性圆柱处于没有施加声力的平衡位置时，即使受到双正交驻波的相位移动，也会经历非零的粘性扭矩。此外，还基于有限体积法（FVM）算法进行了数值模拟，以验证所提出的理论公式。在所有考虑的情况下，理论结果与数值结果非常吻合。
