气泡和液滴在上升或下降时大变形的数值模拟

The NumericaI Simulation of Large Deformation of Bubbles and Drops During Their Rlsing or Descending

本文在考虑界面张力的条件下用涡片方法导出了二维无粘气泡和液滴在另一种静止无粘流体中上升或下降时运动和变形的支配方程，提出了求解支配方程的数值方法，并在数值模拟的例子中研究了空气泡和煤油滴在水中上升时及水滴在煤油中下降时的变形规律，研究了数值模拟中界面张力对界面形状的影响。气泡上升的数值模拟结果与相应的试验结果基本一致。数值模拟结果表明本方法可正确模拟气泡和液滴在上升或下降过程中的大变形，直到界面发生间断为止。通过数值模拟发现，对于尺寸较小的气泡，忽略界面张力的数值模拟结果与实际情形相差很远；即使是对尺寸较大的气泡，忽略界面张力的数值模拟结果也与实际不符。数值模拟结果还表明，为了进一步提高气泡和液滴大变形阶段数值模拟结果的精度，应在方法中考虑流体粘性的影响。

ln this paper the governing equations for the motion and deformation of a 2-D bubble and drop of an inviscid fluid rising or descend-ing in otherwise inviscid fluid are,with the consideration of surface-tension,derived by the vortex sheet method,the numerical method for-solving the governing equations are proposed and the deformations of air bubbles and kerosene drops rising in water and the deformatios of water drops descending in kerosene are studied in the numerical simulation examples.The numerical simulation results of the bubbles are in good agreemnet with the corresponding experimental results by WaIters and Davidson.The numerical simulation results show that the method propos～ed in this paper can simulate properly the large deformations of bub-bles and drops during their rising or descending untiI the stage of occur-ance of the interfacial discontinuities.It is found from the numerical simulations that when the surface-tension is neglected the numerical simulation results for small bubbles are far different from the actual situations.Even for large bubbles the numerical simulation results without consideration of surface-tension are also inconsistent with the actual situations.The numerical simulation results also show that in order to enhance further the accuracy of numerical simulation results for bubbles and drops in their large deformation stage it is necessary in the method to take the fltid viscosities into consideration.