N-S方程的拟序扰动序列与改善的渐近展开匹配法

李大鸣; 张红萍; 高永祥

N-S方程的拟序扰动序列与改善的渐近展开匹配法

1.
天津大学, 建筑工程学院, 天津, 300072;
2.
天津大学, 机械工程学院, 天津, 300072

基金项目: 国家自然科学基金资助项目(29676030)

详细信息

作者简介:
李大鸣(1957- ),男,河北人,副教授,博士.

中图分类号: O29;TB126
计量
- 文章访问数: 2686
- HTML全文浏览量: 130
- PDF下载量: 525
- 被引次数: 0
出版历程
- 收稿日期: 2001-04-10
- 修回日期: 2002-04-01
- 刊出日期: 2002-08-15

Series Perturbations Approximate Solutions to N-S Equations and Modification to Asymptotic Expansion Matched Method

1.
School of Civil Engineering, Tianjin University, Tianjin 300072, P.R.China;
2.
School of Machinery Engineering, Tianjin University, Tianjin 300072, P.R.China

摘要

摘要: 提出了以拟序扰动序列逼近N-S方程定解问题渐近解的一种方法。对N-S方程及其边界条件的渐近拟序扰动序列解进行了讨论,并应用此方法对球坐标系中的圆球绕流进行求解,改善了渐近展开匹配方法,使匹配函数更容易确定。改善后的阻力曲线与实测资料相比在雷诺数小于等于4×10⁴以前完全吻合。
- 渐近展开匹配法 /
- 拟序扰动 /
- N-S方程 /
- 圆球绕流
Abstract: A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted.Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted.By the ameliorative asymptotic expansion matched method,the matched functions are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
- asymptotic expansion matched method /
- series perturbation /
- N-S equation /
- viscous fluid flow past a sphere

HTML全文

参考文献(16)

[1]	钱伟长. 奇异摄动理论及其在力学中的应用[M].北京:科学出版社,1981,111-119.
[2]	谢定裕. 渐近方法——在流体力学中的应用[M]. 北京:友谊出版公司,1983,26-43.
[3]	Nayfeh A H. Perturbation Methods[M]. New York: Wiley, 1973,23-31.
[4]	Van Dyke M. Perturbation Methods in Fluid Mechanics[M]. New York: Academic Press Inc, 1964, 9-20.
[5]	Kaplun S. Low Reynolds number flow past a circular cylinder[J]. J Math Mech,1957,6(3):595-603.
[6]	Stokes G G. On the effect of the internal friction of fluids on the motion of pendulums[J]. Trans Camb Phil Soc, 1851,9(2):8-106.
[7]	Oseen C W. Ueber die Stokes'sche formel, und uber eine verwandte aufgabe in der hydrodynamik[J]. Ark Math Astronom Fys,1910,6(29):154-160.
[8]	Chester W. On Oseen's approximation[J]. J Fluid Mech, 1962,13(3):557-569.
[9]	易家训. 流体力学[M]. 章克本,张涤明,陈启强,等译. 北京:高等教育出版社,1982,262-277.
[10]	Whitehead A N. Second approximations to viscous fluid motion[J]. Quart J Pure Appl Math,1889,23(1):143-152.
[11]	Goldstein S. The steady flow of viscous fluid past a fixed spherical obstacle at small Reynolds numbers[J]. Proc Roy Soc Ser A, 1929,123(1):225-235.
[12]	Kaplun S, Lagerstrom P A. Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers[J]. J Math Mech,1957,6(3):585-593.
[13]	Proudman I, Pearson J R A. Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder[J]. J Fluid Mech, 1957,2(2):237-262.
[14]	Chester W,Breach D R. On the flow past a sphere at low Reynolds numbers[J]. J Fluid Mech, 1969,37(4):751-760.
[15]	Taneda S. Studies on wake vortices (Ⅲ): Experimental investigation of the wake behind a sphere at low Reynolds numbers[J]. Rep Res Inst Appl Mech Kyushu Univ, 1956,4(1):99-105.
[16]	Maxworthy T. Accurate measurements of sphere drag at low Reynolds numbers[J]. J Fluid Mech,1965,23(2):369-372.