摘要
在考虑界面张力的条件下，用边界层方法通过把液体粘性对无粘势流的影响化为修改势流在自由面上边界条件的办法，导出了数值模拟二维气泡在粘性液体中上升和变形的边界积分方法．势流计算采用Ｌａｇｒａｎｇｅ坐标，粘性修正采用Ｅｕｌｅｒ坐标．边界层近似的误差为δ的三次方量阶（即Ｒｅ的负二分之三次方量阶）．数值模拟结果显示，在大气泡（大Ｒｅｙｎｏｌｄｓ数）情形，粘性的影响很小．随着气泡尺寸的减小，表面张力和粘性的影响都增强，但与表面张力相比。
Under the consideration of surface tension the boundary integral method for
numerical simulation of a two dimensional bubble rising and distorting in a viscous liquid is
derived by use of the boundary layer approximation where the effects of the liquid viscosity on
the inviscid potential flow are reduced to the modifications of boundary conditions of the
potential flow on the free surface. The potential flow computations and the viscous
modifications are conducted in the frames of Lagramge coordinates and Euler coordinates
respectively.The order of error of the boundary layer approximation is O(δ 3)=ORe -32 . The
numerical simulation results show that for large bubble (high Reynolds number) cases the
effects of viscosity are small. When the size of the bubble reduces the effects of surface
tension and viscosity increase but compared with the former the latter is in a secondary
position.
出处
《复旦学报（自然科学版）》
CAS
CSCD
北大核心
1999年第2期146-152,共7页
Journal of Fudan University：Natural Science
基金
上海市教育发展基金
复旦大学青年基金
关键词
气泡
数值模拟
粘性液体
E-L法
上升运动
two dimensional bubble
surface tension
liquid viscosity
boundary layer
boundary integral method
