三维斯托克斯流动在扁球坐标系中的基本解及其应用

庄宏; 严宗毅; 吴望一

三维斯托克斯流动在扁球坐标系中的基本解及其应用

1.
北京大学力学与工程科学系, 北京 100871;
2.
4837-267-605,Pharmaceutical Sciences, Pharmacia Corporation, 301 Henrietta Street,Kalamazoo, Michigan, USA

基金项目: 国家自然科学基金项目资助(86030028;38970244)

详细信息

作者简介:
庄宏(1965- ),男,河南南阳人,北京大学理学硕士,美国犹他大学理学博士,研究员,在药剂学与生物医学方面发表专业论文多篇.

中图分类号: O357.2
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- 被引次数: 0
出版历程
- 收稿日期: 2000-05-18
- 修回日期: 2001-10-15
- 刊出日期: 2002-05-15

The Three-Dimensional Fundamental Solution to Stokes Flow in the Oblato Spheroidal Coordinates With Applications to Multiple Spheroid Problems

1.
Faculty of Traffic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P R China;
2.
Department of Civil Engineering, The University of Hong Kong, Pokfulam Road

摘要

摘要: 通过把Lamb基本解中的调和函数转换为扁球坐标系下的表达式,这项研究成功地得到了一个新的Stokes流动三维基本解.此基本解可用于解决任意多个扁椭球处于任意位置和方向时的流动问题.应用最小二乘法,三维流动问题中常遇到的收敛性差的困难在此得以完全克服.结果表明该方法具有准确度高,收敛性好和计算量小的特点.由于扁球可用于模拟从圆盘到圆球的多种物体形状,此基本解被用于系统地分析了各种几何因素对两个扁球所受力和力矩的影响.为了显示此方法的通用性,该基本解还用于研究了两例三个扁球的问题.
- Stokes流动 /
- 基本解 /
- 三维 /
- 扁椭球 /
- 多极子配置 /
- 最小二乘法 /
- 低雷诺数 /
- 多体问题
Abstract: A new three-dimensional fundamental solution to the Stokes flow was proposed by transforming the solid harmonic functions in Lamb.s solution into expressions in terms of the oblate spheroidal coordinates.These fundamental solutions are advantageous in treating flows past an arbitrary number of arbitrarily positioned and oriented oblate spheroids.The least squares technique was adopted herein so that the convergence difficulties often encountered in solving three-dimensional problems were completely avoided.The examples demonstrate that present approach is highly accurate,consistently stable and computationally effecient.The oblate spheroid may be used to model a variety of particle shapes between a circular disk and a sphere.For the first time,the effect of various geometric factors on the forces and torques exerted on two oblate spheroids were systematically studied by using the proposed fundamental solutions.The generality of this approach was illustrated by two problems of three spheroids.
- Stokes flow /
- fundamental solution /
- three-dimension /
- oblate spheroid /
- multipole collocation /
- least squares method /
- low Reynolds number /
- multiple particle

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参考文献(16)

[1]	Weinbaum S,Ganatos P,YAN Zong-yi.Numerical multipole and boundary integral equation techniques in Stokes flow[J].Ann Rev Fluid Mech,1990,22:275-316.
[2]	Gluckman M J,Pfeffer R,Weinbaum S.A new technique for treating multiparticle slow viscous flow:axisymmetric flow past spheres and spheroids[J].J Fluid Mech,1971,50(4):705-740.
[3]	Guckman M J,Weinbaum S,Pfeffer R.Axisymmetric slow viscous flow past an arbitrary convex body of revolution[J].J Fluid Mech,1972,55(4):677-709.
[4]	Ganatos P,Pfeffer R,Weinbaum S.A numerical-solution technique for three-dimensional Stokes flows,with application to the motion of strongly interacting spheres in a plane[J].J Fluid Mech,1978,84(1):79-111.
[5]	YAN Zong-yi,Weinbaum S,Ganatos P,et al.The three-dimensional hydrodynamic interaction of a finite sphere with a circular orifice at low Reynolds number[J].J Fluid Mech,1987,174:39-68.
[6]	Hassonjee Q,Ganatos P,Pfeffer R.A strong-interaction theory for the motion of arbitrary three-dimensional clusters of spherical particles at low Reynolds number[J].J Fluid Mech,1988,197:1-37.
[7]	Leichtberg S,Peffer R,Weinbaum S.Stokes flow past finite coaxial clusters of spheres in a circular cylinder[J].Int J Multiphase Flow,1976,3(2):147-169.
[8]	Ganatos P,Weinbaum S,Pfeffer R.A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries.Part 1.Perpendicular motion[J].J Fluid Mech,1980,99(4):739-753.
[9]	Ganatos P,Pfeffer R,Weinbaum S.A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries.Part 2.Parallel motion[J].J Fluid Mech,1980,99(4):755-783.
[10]	Dagan Z,Weinbaum S,Pfeffer R.General theory for the creeping motion of a finite sphere along the axis of a circular orifice[J].J Fluid Mech,1982,117:143-170.
[11]	Yoon B J,Kim S.A boundary collocation method for the motion of two spheroids in Stokes flow:hydrodynamic and colloidal interactions[J].Int J Multiphase Flow,1990,16(4):639-649.
[12]	Hsu R,Ganatos P.The motion of a rigid body in viscous fluid boundary by a plane wall[J].J Fluid Mech,1989,207:29-72.
[13]	是长春,王为国,吴望一.圆球沿无限长锥形管道运动时的轴对称蠕流[J].北京大学学报(自然科学版),1988,24(1):85-94.
[14]	Lamb H.Hydrodynamics[M].6th edn.New York:Dover,1945.
[15]	Happel J,Brenner H.Low Reynolds Number Hydrodynamics[M].2nd edn.The Hague:Martinus Noordhoff Publishers,1973.
[16]	Goldman A J,Cox R G,Brenner H.The slow motion of two identical arbitrarily oriented spheres through a viscous fluid[J].Chem Eng Sci,1966,21(12):1151-1170.