半无穷长圆管内的低雷诺数入口流

吴望一; R. 斯加拉克

半无穷长圆管内的低雷诺数入口流

吴望一¹,
R. 斯加拉克²

1.
北京大学力学系;
2.
美国哥伦比亚大学土木工程和工程力学系

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出版历程
- 收稿日期: 1983-01-18
- 刊出日期: 1983-12-15

The Creeping Motion in the Entry Region of a Semi-Infinite Circular Cylindrical Tube

Wu Wang-yi¹,
Richard Skalak²

1.
Department of Mechanics, Peking University, Beijing;
2.
Department of Civil Engineering and Engineering Mechanics, Bioengineering Institute, Columbia University, New York

摘要

摘要: 1969年Lew及Fung^[1]计算了圆管内的低雷诸数入口流.1982年Dagan等人^[2]得到了有限长圆柱形孔道内蠕动流的级数解.[1]中所得的数值解实质上代表有限长圆管内的低雷诺数入口流,因为一般解中的富氏积分已用富氏级数代替.本文直接计算富氏积分,更精确地求出了真正的半无穷长圆管内Stokes入口流的速度分布,压力分布以及流函数,与此对应的入口段长度为圆管半径的1.2倍,接近于Lew及Fung得到的结果1.3倍.此外,本文还研究了配置法的收敛性,证明了此法在入口流问题中具有很好的收敛性,因此可以在其他类似的问题中采用.

Abstract: In 1969, Lew and Fung^[1] considered the inlet flow into a semi-infinite circular cyfinder at low Reynolds mumber Dagan, et al.^[2] in 19$Z obtained a series solution for the creeping motion through a pore of finite length directly The numerical results oblained in[1]also describe the entrance flow in tube of a finite length, because the Fourier integrals in the general solutions are replaced by Fourier series.In the present paper, the Fourier integrals are evaluated numerically and the velocity, pressure distribution and the stream function in the entry region of a semi-infinite circular cylindrical tube for a uniform entry velocity are obtained more preciselp.The corresponding inlet length which is equal to (1,2) times the radius of the tube is close to the factor (1.3) suggested hyLew and Fung.^[1] The collucation technique applied in the present paper is shown to converge rapidly and it should be useful in other similar problems.

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参考文献(9)

[1]	Lew, H.S and Y, C, Fung, J.Biomechamcs, 2(1969).105-119.
[2]	Dagan, Z.,S.Weinbaum and R, Pfeffer, J,Fluid Mech.,115(1982),502-523.
[3]	Goldstein, S, (ed),Modern Developments in Fluid Mechanics,1(1938),299-311.
[4]	Rosenhead, L.(ed.), Laminar Boundary Layers, Oxford University Press, London,(1963).
[5]	Schlichting, H.,Boundary Layer Theory, 4th Edition, McGraw-Hill, New York(1962).168.
[6]	Gluckman, M, J.,S, Weinbaum and R, Pfeffer, J.Fluid 147ech,55 (1972).677-709.
[7]	Stimson, M, and O,B.Jeffery, Proc, Roy.Soc.,A11]1, 110(1926).
[8]	Rabinowitz, P and G, weiss, MTAG, 13(1959).285-293.
[9]	Happel, J.and H, Brenner, Low Reynolds Number Hydrodynamics, 2nd Edition,Noordhoff International Publishing, Leyden, (1973).