圆管Poiseuille流动中平均速度的一种修正剖面及其稳定性研究
A Kind of Distortion of Mean Velocity Profile in Pipe Poiseuille Flow and Its Stability Behaviour
-
摘要: 本文给出了圆管Poiseuille流动中Hagen-Poiseuille速度剖面的一种修正剖面.这种剖面可看作是轴对称扰动各谐波分量非线性相互作用对平均流影响的一般体现.通过对这种速度剖面的稳定性研究,本文首次得到轴对称扰动造成失稳的结果,提出了Hagen-Poiseuille流动一种新的产生失稳的可能途径.Abstract: This paper presents a kind of distortion of Hagen-Poiseuille velocity profile in pipe Poiseuilleflow. This distortion can be regarded as a general expression of the influence on the mean flow by nonlinear interaction of various components of axisymmetric perturbations. Through the investigation of the stability behaviour of this velocity profile, this paper obtains unstable result induced by axisymmetric perturbations for the first time, and thus presents a new possible approach which leads to instability of Hagen-Poiseuille flow.
-
[1] Lin,C.C.,On the stability of two-dimensional parallel flows,Quart.Appl.Math.,3(1945),117-142,218-234,277-301. [2] Reynolds,W.C.and M.C.Potter,Finite-amplitude instability of paralle shear flows,J.F.M.,27(1967),465. [3] Zhou,H.,On the nonlinear theory of stability of plane Poiseuille flow in the subcritical range,Proc.R.Soc.,London,A 381(1982),407-418. [4] Sexl,T.,Zur stabilittfrage der Poiseuilleschen und Couetteschen strmung,Ann.Phys.,83(1927),835;84(1927),807. [5] Synge,J.L.,Hydrodynamic stability,Semicentennial Publ.Am.Math.Soc.,2(1983),227. [6] Pekeris,C.L.,Stability of the laminar flow through a straight pipe of circular cross-section to infinitesimal disturbances which are symmetrical about the axis of the pipe,Proc.U.S.Nat.Acad.Sci.,34(1948),285. [7] Gill,A.E.,On the behaviour of small disturbances to Poiseuille flow in a circular pipe J.F.M.,21(1965),145-172. [8] Davey,A.and P.G.Drazin,The stability of Poiseuille flow in a pipe,J.F.M.,36(1969),209-218. [9] Salwen,H.and C.E.Grosch,The stability of Poiseuile flow in a pipe of circular cross-section,J.F.M.,54(1972),93. [10] LesSen,M.,S.G.Sadler and T.Y.Liu,Stability of pipe Poiseuille flow,Phys.Fluids.,11(1968),1404-1409. [11] Gary,V.K.and W.T.Rouleau,Linear spatial stability of pipe Poiseuille flow,J.F,M.,54(1972),113. [12] Munakata,Ken-iti,The stability of Poiseuille flow in a circular pipe,J.Phys.Soc.,Jan.,52(1983),2004-2015. [13] Tatsumi,Tomomasa,Stability of the laminar inlet-flow prior to the formation of Poiseuille regime,J.Phys.Soc.,Jap.,7(1952),489-502. [14] Leite,R.J.,An experimental investigation of the stability of Poiseuille flow,J.F.M.,5(1969)81. [15] Davey,A.and H.P.F.Nguyen,Finite-amplitude stability of pipe flow,J.F.M.,45(1971),701-720. [16] Itoh,N.,Nonlinear stability of parallel flows with subcritical Reynolds number,Part 2,Stability of pipe Poiseuille flow to finite axisymmetric disturbances,J.F.M.,82(1977),469-479. [17] Davey,A.,On Itoh's finite amplitude stability theory for pipe flow,J.F.M.,86.(1978)695-703. [18] Patera,A.T.and S.A.Orszag,Finite-amplitude stability of axisymmetric pipe flow,J.F.M.,112(1981),467-474. [19] Stuart,J.T.,On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows,Ⅰ.The basic behaviour in plane Poiseuille flow,J.F.M.,9(1960),353-370. [20] Watson,J.,On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows,Ⅱ.the development of a solution for plane Poiseuille flow and for plane Couette flow,J.F.M.,9(1960),371-389. [21] 赵耕夫,圆管Poiseuille流轴对称有限扰动稳定性研究,第三届全国流体力学学术会议,中国力学学会,长沙〔1985). [22] Gill,A.E.,A mechanism for instability of plane Couette flow and of Poiseuille flow in a pipe,J.F.M.21(1962),503-511. [23] Thomas,L.H.,The stability of plane Poiseuille flow,Phys.Rev.,91(1953),780. [24] Orszag,S.A.,Accurate solution of the Orr-Sommerfeld stability equation,J.F.M.,50(1971),689-703.
点击查看大图
计量
- 文章访问数: 1836
- HTML全文浏览量: 63
- PDF下载量: 546
- 被引次数: 0