The objective of this paper is to apply numerical method to simulate the single bubble dynamics under the acoustic standing waves, which is an extensive research of our previous work (Ma et al. Ultrason. Sonochem., vol. 42, 2018, pp. 619-630). The Navier-Stokes equation, which considers the acoustic radiation force caused by acoustic standing wave, is used to capture the transient shape variation, pressure fluctuation, and the direction of the bubble motion, especially for the case of the bubble near the rigid boundary. Several normalized parameters, such as acoustic pressure amplitude, acoustic wave number, and bubble size, are investigated in temporal and spatial scales to actively influence the direction of the liquid jet caused by bubble collapse. The numerical results show that due to the strong interaction with the acoustic standing wave, the bubble loses the spherical shape and generates a high-speed liquid jet. It worth noting that a significantly high pressure and velocity peak is respectively founded at the boundary wall, which is caused by the toroidal bubble collapse. Furthermore, in the standing wave field, single bubble would have distinctly different behaviors with the change of its resonance radius size. The high-speed liquid jet is always directed towards the node of an acoustic standing wave when the radius of bubble is larger than the resonance size, while the liquid jet is directed to the antinode when the radius of bubble is much smaller than the resonance size, closely with the primary Bjerknes force. Finally, the investigation shows that the single bubble will collapse much earlier during the deformation process with the increase of the normalized pressure amplitude.

本文的目的是应用数值方法来模拟声驻波下的单个气泡动力学，这是对我们先前工作的广泛研究（Ma等人，Ultrason.Sonochem。，卷。》，2018年第42卷，第619-630页）。Navier-Stokes方程考虑了声驻波引起的声辐射力，用于捕获瞬态形状变化，压力波动和气泡运动的方向，特别是对于气泡在刚性边界附近的情况。在时间和空间尺度上研究了几个归一化参数，例如声压幅度，声波数和气泡大小，以积极影响由气泡破裂引起的液体射流的方向。数值结果表明，由于与声驻波的强相互作用，气泡失去了球形，并产生了高速液体射流。值得注意的是，在边界壁处分别建立了一个很高的压力峰和速度峰，这是由环形气泡破裂引起的。此外，在驻波场中，单个气泡会随着其共振半径大小的变化而具有明显不同的行为。当气泡的半径大于共振大小时，高速液体射流总是指向声驻波的节点，而当气泡的半径小于共振大小时，高速液体射流指向波腹。 ，与主要的Bjerknes部队保持紧密联系。最后，研究表明，随着归一化压力幅值的增加，单个气泡在变形过程中会更早地坍塌。当气泡的半径大于共振大小时，高速液体射流总是指向声驻波的节点，而当气泡的半径小于共振大小时，高速液体射流指向波腹。 ，与主要的Bjerknes部队保持紧密联系。最后，研究表明，随着归一化压力幅值的增加，单个气泡在变形过程中会更早地坍塌。当气泡的半径大于共振大小时，高速液体射流总是指向声驻波的节点，而当气泡的半径小于共振大小时，高速液体射流指向波腹。 ，与主要的Bjerknes部队保持紧密联系。最后，研究表明，随着归一化压力幅值的增加，单个气泡在变形过程中会更早地坍塌。