二维流面上的流动问题的速度图方法

李开泰; 史峰

doi:10.3879/j.issn.1000-0887.2010.03.009

二维流面上的流动问题的速度图方法

doi: 10.3879/j.issn.1000-0887.2010.03.009

李开泰,
史峰

西安交通大学理学院,西安 710049

基金项目: 国家自然科学基金资助项目(10971165;10771167;10926080)

详细信息

作者简介:
李开泰(1937- ),男,福建人,教授,博士生导师(联系人.Tel:+86-29-82669051;Fax:+86-29-83237910;E-mail:ktli@mai.lxjtu.edu.cn).

中图分类号: O183;O175;O35
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- 被引次数: 0
出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-02-02
- 刊出日期: 2010-03-15

Hodograph Method of Flow on Two-Dimensional Manifold

College of Science, Xi'an Jiaotong University, Xi'an 710049, P. R. China

摘要

摘要: 对于一些特殊的流动,尤其是平面上的位势流动,速度图方法有其显著的优点．对于理想流体来说,流面总是存在的,在流面上,流动的速度向量总是在其切空间里．通过引入流函数和势函数,采用张量分析作为工具,给出了二维曲流面上位势流动的速度图方法,得到了流函数满足的速度图方程,为一些特殊的流动问题提供了一类分析方法．并且,对于得到的二维速度图方程,得到了相应的特征方程和特征根,从而可以对方程的类型进行分类．最后,给出了一些特殊流动的实例．
- 速度图方法 /
- 位势流 /
- 流面 /
- 流函数 /
- 位势函数
Abstract: For some special flow, especially the potential flow in the plane, there are obvious advantages using the tool of hodograph method. For the realistic flow, there exists stream surface, namely, two-dmi ensionalmanifold, on which the velocity vector of the flow liesits tangent space. By in troducing the stream function and potential function, the hodograph method for potential flow on a surface was established with the help of tensor analysis, which provided a kind of analysis method. For the derived hodograph equation, the characteristic equation and its characteristic roots were also derived, from which the type of the hodograph equation of the second order can be classified. Moreover, some examples for special surfaces were given.
- hodograph method /
- potential flow /
- stream surface /
- stream function /
- potential function

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参考文献(9)

[1]	Cherry T M. Flow of a compressible fluid about a cylinder[J].Proceedings of the Royal Society of London,Series A: Mathematical and Physical Sciences,1947, 192(1028): 45-79. doi: 10.1098/rspa.1947.0138
[2]	von Krmn T.Compressibility effects in aerodynamics[J].Journal of the Aeronautical Sciences,1941, 8(9): 337-356.
[3]	Tsien H S. Two-dimensional subsonic flow of compressible fluids[J].Journal of the Aeronautical Sciences,1939, 6(10): 399-407.
[4]	Li K T,Huang A X.Mathematical aspect of the stream-function equations of compressible turbomachinery flows and their finite element approximation using optimal control[J].Computer Methods in Applied Mechanics and Engineering,1983, 41(2): 175-194. doi: 10.1016/0045-7825(83)90005-1
[5]	李开泰,黄艾香.张量分析及其应用[M].北京:科学出版社, 2000.
[6]	Li K T,Huang A X,Zhang W L.A dimension split method for the 3-D compressible Navier-Stokes equations in turbomachine[J].Communications in Numerical Methods in Engineering,2002, 18(1): 1-14.
[7]	Li K T,Su J,Huang A X.Geometrical design of blade’s surface and boundary control of Navier-Stokes equations[J].Academic Journal of Xi′an Jiaotong University,2007, 19(1): 1-6.
[8]	Il′in A A.The Navier-Stokes and Euler equations on two-dimensional closed manifolds[J].Mathematics of USSR Sbornik,1991, 69(2): 559-579. doi: 10.1070/SM1991v069n02ABEH002116
[9]	Wu C H.A General Theory of Three-Dimensional Flow in Subsonic and Supersonic Turbo-maohines of Axial,Radial and Mixed-Flow Types[R]. NACA TN2604, 1952.