长波在弯曲管道中的传播——Ⅰ变截面弯管中长波传播的基本分析

顾圣士; 方光熊

长波在弯曲管道中的传播——Ⅰ变截面弯管中长波传播的基本分析

上海交通大学应用数学系

计量
- 文章访问数: 1673
- HTML全文浏览量: 95
- PDF下载量: 489
- 被引次数: 0
出版历程
- 收稿日期: 1982-03-20
- 刊出日期: 1983-02-15

Propagation of a Long Wave in a Curved Duct(Ⅰ) Basic Analysis of Long Wave Propagation in a Curved Duct with Variable Cross Section

Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai

摘要

摘要: 本文研究长波在三维变截面弯管中的传播问题.通过建立正交曲线坐标系,以波数k和管道横截面的特征半径a的乘积ka作为小参数,对波动方程进行无量纲处理,用正则摄动法,把三维的Helmholtz方程化为二维的Laplace(或Poisson)方程和一维的Webster方程.并分析了管道的几何参数(横截面面积、管道中心线的曲率和挠度)对复速度势渐近展开的各阶项的影响.文中指出,横截面面积的变化首先影响浙近解的零阶项.在横截面的形状具有某种对称性时,管道中心线的曲率首先影响渐近解的二阶项,而挠度首先影响渐近解的三阶项.最后,给出了长波在弯曲圆管中传播的实例.

Abstract: The propagation of a long wave in a three-dimensional curved duct with variable cross section is studied in this paper. It is shown that a three-dimensional Helmholtz equation can be decomposed into a two-dimensional Laplace (or Poisson) equation and a one-dimensional Webster equation by the curvilinear orthogonal coordinate system,non-dimensionization of reduced wave equation and regular perturbation with small parameter ka,where k is the wave number and a is the characteristic radius of the duct. The influences of the duct's geometric parameters (thearea variation of the cross section,the curvature and torsion of the central line) on the asymptotic expansion of the solution are analysed. It is concluded that the effects of the variation of the cross sectional area first appear in the first term of the asymptotic expansion,and when the cross section shape has certain symmetric properties,the effects of the curvature and torsion of the central line first appear in the third and the fourth terms,respectively. An example of long wave propagation in a curved circular duct is also given at the end of this paper.

HTML全文

参考文献(7)

[1]	Helmholtz,H.,Theorie der Luftschwingungen in Rohren mit offenen Enden.Crelle's J.Reine Angewandete Math.Bd.57,(1860),1-72.
[2]	Rayleigh,Lord,Theory of Sound,Dover,New York,Vol.2,(1945).196-201,487-491.
[3]	Lesser,M.B.and J.A.Lewis,Applications of matched asymptotic expansion mathods to acoustics.I.The Webster Hohn equation and the stepped duct,J.Acoust.Soc.Am.51,(1972),1664-1669.
[4]	Lesser,M.B.and J.A.Lewis,Applications of matched asymptotic expansion methods to acoustics II.The openended duct,J.Acoust.Soc.Am.52,(1972),1406-1410.
[5]	Ting Lu(丁汝) and Joseph B.Keller,Radiation from the open end of a cylindrical or conical pipe and scattering from the end of a rod or slab,J.Acoust.Soc.Am.Vol.61,No.6,(1977),1438-1444.
[6]	Ting Lu(丁汝),Studies in the motion and decay of vortices in Aircraft wake Turbulence and its Detection,edited by J.H.Olsen,A.Goldburg and M.Rogers,Plenum Press,N.Y.(1971),11-40.
[7]	Nayfen Ali Hasan,Perturbation Methods,John Wiley and Sons.Inc.(1973).