The lift force on a spherical bubble in a viscous linear shear flow
The lift force on a spherical bubble in a viscous linear shear flow
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DOI：
10.1017/s0022112098001621
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发表时间：
1998-08
影响因子：
3.7
通讯作者：
D. Legendre;J. Magnaudet
中科院分区：
文献类型：
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作者：
D. Legendre;J. Magnaudet
通过求解Navier-Stokes方程，数值研究了粘性线性剪切流中球形气泡定常运动的三维绕流。气泡表面被假定为是干净的，使外部流服从零剪切应力条件，不会引起任何旋转的气泡。本研究的主要目标是提供气泡所经历的升力的完整描述，以及在很大范围的雷诺数（0.1[les ]Re[les ]500，Re基于气泡直径）和剪切速率（0[les ]Sr[les ]1，Sr是气泡速度差与相对速度之间的比率）范围内产生该力的机制。为此目的的流场的结构，雷诺数的影响上流向涡量场和切向速度的分布在气泡的表面首先详细研究。它示出，后者的分布中起着核心作用的升力的生产是显着依赖于粘性效应。关于升力系数的数值结果显示在低雷诺数和高雷诺数下非常不同的行为。这两个渐近制度揭示了气泡表面产生的涡量和未扰动流中包含的涡量各自所起的作用。在低雷诺数下，升力系数强烈地依赖于雷诺数和剪切速率。相反，对于中等到高雷诺数，这些依赖性被发现是非常弱的。在低雷诺数和高雷诺数极限下，升力系数的数值与现有的渐近结果吻合得很好。这些渐近解的有效性的范围指定通过改变问题的特征参数和检查相应的升力系数的演变。数值结果也被用于获得经验关联有用的实际计算在有限的雷诺数。然后检查升力的瞬态行为。研究发现，从无扰流开始，由于涡量场需要有限的时间才能达到其稳定分布，即使在雷诺数很高的情况下，升力的值在短时间内也不同于其稳定值。这一发现证实了在无粘剪切流的升力系数的初始值的分析推导。最后，在高雷诺数下的升力和阻力系数随剪切速率的演变进行了具体的调查。发现当剪切速率变大，即Sr=O（1）时，升力系数出现一个小的但一致的减小，而阻力系数则出现一个非常显著的增大，这主要是由压力分布的改变引起的。上面的一些结果用来说明，众所周知的附加质量系数和升力系数之间的相等关系只在弱剪切和近定常流的极限情况下才成立。
The three-dimensional flow around a spherical bubble moving steadily in a viscous linear shear flow is studied numerically by solving the full Navier–Stokes equations. The bubble surface is assumed to be clean so that the outer flow obeys a zero-shear-stress condition and does not induce any rotation of the bubble. The main goal of the present study is to provide a complete description of the lift force experienced by the bubble and of the mechanisms responsible for this force over a wide range of Reynolds number (0.1[les ]Re[les ]500, Re being based on the bubble diameter) and shear rate (0[les ]Sr[les ]1, Sr being the ratio between the velocity difference across the bubble and the relative velocity). For that purpose the structure of the flow field, the influence of the Reynolds number on the streamwise vorticity field and the distribution of the tangential velocities at the surface of the bubble are first studied in detail. It is shown that the latter distribution which plays a central role in the production of the lift force is dramatically dependent on viscous effects. The numerical results concerning the lift coefficient reveal very different behaviours at low and high Reynolds numbers. These two asymptotic regimes shed light on the respective roles played by the vorticity produced at the bubble surface and by that contained in the undisturbed flow. At low Reynolds number it is found that the lift coefficient depends strongly on both the Reynolds number and the shear rate. In contrast, for moderate to high Reynolds numbers these dependences are found to be very weak. The numerical values obtained for the lift coefficient agree very well with available asymptotic results in the low- and high-Reynolds-number limits. The range of validity of these asymptotic solutions is specified by varying the characteristic parameters of the problem and examining the corresponding evolution of the lift coefficient. The numerical results are also used for obtaining empirical correlations useful for practical calculations at finite Reynolds number. The transient behaviour of the lift force is then examined. It is found that, starting from the undisturbed flow, the value of the lift force at short time differs from its steady value, even when the Reynolds number is high, because the vorticity field needs a finite time to reach its steady distribution. This finding is confirmed by an analytical derivation of the initial value of the lift coefficient in an inviscid shear flow. Finally, a specific investigation of the evolution of the lift and drag coefficients with the shear rate at high Reynolds number is carried out. It is found that when the shear rate becomes large, i.e. Sr=O(1), a small but consistent decrease of the lift coefficient occurs while a very significant increase of the drag coefficient, essentially produced by the modifications of the pressure distribution, is observed. Some of the foregoing results are used to show that the well-known equality between the added mass coefficient and the lift coefficient holds only in the limit of weak shears and nearly steady flows.