Unsteady force on a spherical bubble at finite Reynolds number with small fluctuations in the free‐stream velocity
Unsteady force on a spherical bubble at finite Reynolds number with small fluctuations in the free‐stream velocity
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DOI：
10.1063/1.858501
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发表时间：
1992
影响因子：
4.6
通讯作者：
R. Mei;J. Klausner
中科院分区：
文献类型：
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作者：
R. Mei;J. Klausner
在雷诺数为0.1 ~ 200的条件下，考虑了自由流速度波动较小的静止球形气泡的非定常流动。利用有限差分法和基于波动幅值较小的正则扰动格式，得到了定常分量和非定常分量的Navier-Stokes方程的解。在有限雷诺数条件下，研究了非定常阻力与波动频率的关系。结果表明，准稳态阻力可以用稳态阻力系数和瞬时速度表示。数值结果表明，低频非定常力ω随ω线性增加，而不是随ω1/2线性增加，这是由Stokes方程的蠕变流解引起的。发现在有限雷诺数下的附加质量力与爬行流和势流相同。在有限Re的历史力被识别和仔细地评估。当ω较小时，历史力的虚分量随ω线性增加，当ω变大时，虚分量随ω - 1/2衰减。这意味着历史力在时域上的记忆比非定常Stokes方程的解所预测的要短得多。数值计算结果表明，在低频率下，即使在大雷诺数下，涡度的粘性扩散和流场加速度共同作用的历史力也是有限的。
Unsteady flow over a stationary spherical bubble with small fluctuations in the free‐stream velocity is considered for Reynolds number ranging from 0.1 to 200. Solutions to the Navier–Stokes equations of both steady and unsteady components are obtained using a finite‐difference method and a regular perturbation scheme based on the amplitude of the fluctuations being small. The dependence of the unsteady drag on the frequency of the fluctuations is examined at finite Reynolds number. It is shown that the quasisteady drag can be represented by using the steady‐state drag coefficient and the instantaneous velocity. Numerical results indicate that the unsteady force at low frequency, ω, increases linearly with ω rather than increasing linearly with ω1/2, which results from the creeping flow solution of the Stokes equation. The added‐mass force at finite Reynolds number is found to be the same as in creeping flow and potential flow. The history force at finite Re is identified and carefully evaluated. The imaginary component of the history force increases linearly with ω when ω is small and decays as ω−1/2 as ω becomes large. The implication is that the history force has a much shorter memory in the time domain than predicted by the solution of the unsteady Stokes equation. Numerical results suggest that the history force, which is due to the combination of the viscous diffusion of the vorticity and the acceleration of the flow field, at low frequency is finite even at large Reynolds number.