Interaction of a slender vortex with a rigid sphere: Dynamics and far-field sound
Interaction of a slender vortex with a rigid sphere: Dynamics and far-field sound
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细长涡旋与刚性球体的相互作用：动力学和远场声音
DOI：
10.1121/1.421081
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
R. Klein
中科院分区：
文献类型：
--
作者：
O. Knio;L. Ting;R. Klein
采用跟踪涡丝中心线运动的涡元方案分析了细长涡丝与静止刚性球之间的相互作用。细丝速度表示为自诱导速度和由于球的存在而产生的势速度之和。自诱导速度的数值估计使用线Biot-Savart积分仔细desingularized，以反映正确的渐近行为的核心涡度分布拉伸和粘性扩散的影响下。同时，从最近导出的公式，表示为一个线积分沿着的图像的细丝中心线在球与规则的权重函数的潜在速度的评估。从定常球外非定常涡流的远场特性出发，导出了声远场的计算公式。结果表明，细长涡丝与球的相互作用产生了偶极子和四极子。
Interactions between a slender vortex filament and a stationary rigid sphere are analyzed using a vortex element scheme which tracks the motion of the filament centerline. The filament velocity is expressed as the sum of a self-induced velocity and potential velocity due to the presence of the sphere. The self-induced velocity is estimated numerically using a line Biot–Savart integral which is carefully desingularized so as to reflect the correct asymptotic behavior of the core vorticity distribution under the influence of stretching and viscous diffusion. Meanwhile, the potential velocity is evaluated from a recently derived formula, which expresses it as a line integral along the image of the filament centerline in the sphere with regular weight functions. From the far-field behavior of an unsteady vortical flow outside a stationary sphere, formulas for the acoustic far field are obtained. It is shown that the interaction between the slender vortex filament and the sphere generates dipoles and quadrupol...