Buoyancy-driven motion of a gas bubble through viscous liquid in a round tube
Buoyancy-driven motion of a gas bubble through viscous liquid in a round tube
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气泡通过圆管中粘性液体的浮力驱动运动
DOI：
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发表时间：
2008
影响因子：
3.7
通讯作者：
James Q. Feng
中科院分区：
文献类型：
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作者：
James Q. Feng
采用边界拟合网格的伽辽金有限元法求解非线性Navier-Stokes方程，计算了粘性液体在圆管内因浮力驱动而相对于气泡的稳态轴对称流动。当气泡相对于管尺寸较小时（例如，气泡的体积等效半径小于管半径R的四分之一），气泡表现出与在扩展液体中运动的气泡相似的行为，如果毛细数不是太小，则随着雷诺数（Re）的增加而发展成球帽形状。当气泡体积等效半径大于管半径时，可以观察到长泡（也称为泰勒泡）的特征，特别是当表面张力效应相对较弱时（例如韦伯数We大于1）。在大多数情况下，弗劳德数Fr的计算值与从长气泡的实验数据中得出的相关公式吻合得很好，甚至对于体积等效半径为管半径四分之三的（短）气泡也是如此。计算得到的长气泡表面轮廓均为长尾状，但通过调整Re和We的参数值可以得到不同的尾形。在较大的韦伯数下（例如We=10），气泡尾部形成一个凹形轮廓，在小Re处形成一个气体“杯”，在大Re处形成一个边缘急剧弯曲的“裙”。当We≤1时，气泡尾部轮廓呈圆形，局部曲率不大，但在较大re时可能出现微凹尾。韦伯数较小时，特别是体积<3πR3的气泡，通常在管壁附近出现不均匀的环形膜，说明表面张力效应可能起复杂的作用。然而，对于体积等效半径大于管半径的气泡，Fr的计算值通常与气泡长度无关。当气泡长度达到约2.5管半径时，其前缘半径值与体积大得多的长气泡基本相同。对沿气泡表面的牵引力z分量分布的研究揭示了长气泡以与气泡体积无关的终端速度上升的基本机制。
The steady axisymmetric flow of viscous liquid relative to a gas bubble due to its buoyancy-driven motion in a round tube is computed by solving the nonlinear Navier–Stokes equations using a Galerkin finite-element method with a boundary-fitted mesh. When the bubble is relatively small compared with the tube size (e.g. the volume-equivalent radius of the bubble is less than a quarter of the tube radius R), the bubble exhibits similar behaviour to one moving in an extended liquid, developing a spherical-cap shape with increasing Reynolds number (Re) if the capillary number is not too small. The long-bubble (also known as a Taylor bubble) characteristics can be observed with bubbles of volume-equivalent radius greater than the tube radius, especially when the surface tension effect is relatively weak (e.g. for Weber number We greater than unity). The computed values of Froude number Fr for most cases agree well with the correlation formulae derived from experimental data for long bubbles, and even with (short) bubbles of volume-equivalent radius three-quarters of the tube radius. All of the computed surface profiles of long bubbles exhibit a prolate-like nose shape, yet various tail shapes can be obtained by adjusting the parameter values of Re and We. At large Weber number (e.g. We=10), the bubble tail forms a concave profile with a gas ‘cup’ developed at small Re and a ‘skirt’ at large Re with sharply curved rims. For We≤1, the bubble tail profile appears rounded without large local curvatures, although a slightly concave tail may develop at large Re. non-uniform annular film adjacent to the tube wall is commonly observed when Weber number is small, especially for bubbles of volume <3πR3, suggesting that the surface tension effect can play a complicated role. Nonetheless the computed value of Fr is found to be generally independent of the bubble length for bubbles of volume-equivalent radius greater than the tube radius. If the bubble length reaches about 2.5 tube radii, the value of its frontal radius becomes basically the same as that for long bubbles of much larger volume. An examination of the distribution of the z-component of traction along the bubble surface reveals the basic mechanism for long bubbles rising at a terminal velocity that is independent of bubble volume.