Hybrid Perturbation-Galerkin Solution of the Flow in a Circular Cross-Section Tube With Constriction

SHEN Xin-rong; GAO Qi; ZHANG Ben-zhao; ZHANG Jin-suo

Volume 25 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(2): 197-205

SHEN Xin-rong, GAO Qi, ZHANG Ben-zhao, ZHANG Jin-suo. Hybrid Perturbation-Galerkin Solution of the Flow in a Circular Cross-Section Tube With Constriction[J]. Applied Mathematics and Mechanics, 2004, 25(2): 197-205.

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Hybrid Perturbation-Galerkin Solution of the Flow in a Circular Cross-Section Tube With Constriction

Department of Mechanics, Zhejiang University, Hangzhou 310027, P. R. China

Received Date: 2001-11-13
Rev Recd Date: 2003-09-30
Publish Date: 2004-02-15

Abstract

Abstract

Using hybrid perturbatin-Galerkin technique,a crcular cross-section tube model with sinu-soidal wall is studied.This technique can remove the limitation of small parameters for perturbation and the difficulty of selecting good coordinate functions about Galerkin technique.The effects caused by the boundary conditions and the Reynolds number on the flow were discussed.The position of the separate and reattachment points was obtained.The tendency of the variation about the shear stress on the wall and friction factor along the axis direction were also analyzed.The results at a small parameter have good agreements with the perturbation ones.
- hybrid perturbation-Galerkin technique,
- circular cross-section tube with constriction,
- blood flow

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References

[1]	Waters S L,Pedley T J.Oscillatory flow in a tube of time-dependent curvature-Patr 1:Perturbation to flow in a stationary curved tube[J].J Fluid Mech,1999,383:327—352. doi: 10.1017/S0022112099004085
[2]	Young D F.Effect of a time dependent stenosis on flow through a tube[J].J Eng Industry， Trans ASME,1968,90:248—252. doi: 10.1115/1.3604621
[3]	Lee J S,Fung Y C.Flow in locally constricted tube at low Reynolds numbers[J].J Appl Mech,Trans ASME,1969,37:9—16.
[4]	Young D F,Tasi F Y.Flow characteristics in models of arterial stenosis Ⅰ-steady flow[J].J Biomech,1973,6:395—410. doi: 10.1016/0021-9290(73)90099-7
[5]	Young D F,Tasi F Y.Flow characteristics in models of arterial stenosis Ⅱ-unsteady flow[J].Ibid,1973,6:411—425.
[6]	Daly B J.A numerical study of pulsatile flow through stenosed canine femoral arteries[J].J Biomech,1976,9:465—475. doi: 10.1016/0021-9290(76)90090-7
[7]	Chow J C F,Soda K.Laminar flow in tubes with constriction[J].Phys Fluids,1972,15:1700—1708. doi: 10.1063/1.1693765
[8]	McDonald D A.On steady flow through modeled vascular stenosis[J].J Biomech,1979,12:13—20. doi: 10.1016/0021-9290(79)90004-6
[9]	Deshpande M D.Steady laminar and trubulent flow through vascular stenosis models[D].Ph D Dissertation. Georgia Institute of Technology,1977.
[10]	Morgan B E,Young D F.An integral method for the analysis of flow in arterial stenosis[J].Bull Math Biol,1974,36:39—53.
[11]	Young D F.The fluid mechanics of arterial stenosis[J].J Biomech Eng,Trans ASME,1979,101:157—175. doi: 10.1115/1.3426241
[12]	Ahmed K N,Chad D B.Hybrid perturbation/Bubnow-Galerkin technique for nonlinear thermal analysis[J].AIAA Journal,1984,22(2):287—294. doi: 10.2514/3.8381
[13]	Joseph C F C,Kunihisea S.Laminar flow in tubes with constriction[J].The Physics of Fluids,1972,15(10):1700—1706. doi: 10.1063/1.1693765
[14]	Padmanabhan N,Decanathan R.Mathematical model of an arterial stenosis,allowing for tethering[J].Medical & Biological Engineering & Computing,1981,19:385—390.
[15]	Padmanbhan N,Jayaraman G.Flow in a curved tube with constriction—an application to the arterial system[J].Medical & Biological Engineering & Computing,1985,25:208—215.
[16]	XUE Lei,TANG Jin-chun,SUN Bing-nan.Galerkin solutions of laminar flow in Helical elliptical pipes[J].Acta Mchanica Sinica,1998,30(6):648—655.