The Method of Continuous Distribution of Singularities to Treat the Stokes Flow of the Arbitrary Oblate Axisymmetrical Body

Zhu Min; Wu Wang-yi

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1985 > 6(10): 859-871

Zhu Min, Wu Wang-yi. The Method of Continuous Distribution of Singularities to Treat the Stokes Flow of the Arbitrary Oblate Axisymmetrical Body[J]. Applied Mathematics and Mechanics, 1985, 6(10): 859-871.

Citation:

PDF( 762 KB)

The Method of Continuous Distribution of Singularities to Treat the Stokes Flow of the Arbitrary Oblate Axisymmetrical Body

Zhu Min,
Wu Wang-yi

Department of Mechanics, Peking University, Beijing

Received Date: 1984-11-26
Publish Date: 1985-10-15

Abstract

Abstract

This paper deals with the Stokes flow of the arbitrary oblate axisymmetrical body by means of constant density and quadratic distribution function approximation for the method of continuous distribution of singularities. The Sampson spherical infinite series arc chosen as fundamental singularities. The convergence, accuracy and range of application of both two approximations are examined by the unbounded Stokes flow past the oblate spheroid. It is demonstrated that the drag factor and pressure distribution both conform with the exact solution very well. Besides, the properties, accuracy and the range of application are getting belter with the improving of the approximation of the distribution function. As an example of the arbitrary oblate axisymmetrical bodies, the Stokes flow of the oblate Cassini oval are calculated by these two methods and the results are convergent and consistent. Finally, with the quadratic distribution approximation the red blood cell, which has physiologic meaning, is considered and for the first time the(orresponding drag factor and pressure distribution on the surface of the cell are obtained.

FullText(HTML)

References(12)

References

[1]	Chwang,A.T.and T.Y.T.Wu,Hydromechanics of low Reynolds number flow,Part 2,Singularity method for Stokes flows,J.Fluid Mech.,67(1975),787-815.
[2]	Gluckman,M.J,S.Weinbaum and R.Pfeffer,Axisymmetric slow viscous flow past an arbitrary convex body of revolution,J.Fluid Mech.,55(1972),677-709.
[3]	Youngren,G.K.and A.Acrivos,Stokes flow past a particle of arbitrary shape:A numerical method of solution,J.Fluid Mech.,69(1975),377-403.
[4]	Weinbaum,S.,Lectures on Mathematics in the Life Sciences(1981),114.
[5]	Smith,A.M.O.and J.L.Hess,Prog.Aero.Sci.(1966),8.
[6]	吴望一,解任意形伏非细长长轴对称体Stokes流动的一种新方法,中国科学,A辑,2(1984).
[7]	吴望一、王少华,Stokes流动中连续奇点线分布法的分段抛物近似.力学学报,5(1984).
[8]	吴望一、何青,蠕动流中连续奇点线分布法的分段线性近似,应用数学和力学,5,6(1984),793-800.
[9]	吴望一、朱敏,解任意形状扁轴对称体的环形奇点分布法.(待发表)
[10]	Sampson,R.A.,On Stokes current-function.Phil.Tran.R.Soc.A,182(1891),449.
[11]	Happel,J.and H.Brenner,Low Reynolds Number Hydrodynamics,Prentice-Hall(1965).
[12]	Fung,Y.C.,Biomechanics,Springer-Verlag,New York Inc.(1981).