Eur. Phys. J. B 19, 607-622 (2001)
https://doi.org/10.1007/s100510170306

Asymptotic analysis of wall modes in a flexible tube revisited

Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India

Corresponding author: ^a kumaran@chemeng.iisc.ernet.in

Received: 12 June 2000
Revised: 8 November 2000
Published online: 15 February 2001

Abstract

The stability of wall modes in fluid flow through a flexible tube of radius R surrounded by a viscoelastic material in the region R < r < H R is analysed using a combination of asymptotic and numerical methods. The fluid is Newtonian, while the flexible wall is modelled as an incompressible viscoelastic solid. In the limit of high Reynolds number (Re), the vorticity of the wall modes is confined to a region of thickness in the fluid near the wall of the tube. Previous numerical studies on the stability of Hagen-Poiseuille flow in a flexible tube to axisymmetric disturbances have shown that the flow could be unstable in the limit of high Re, while previous high Reynolds number asymptotic analyses have revealed only stable modes. To resolve this discrepancy, the present work re-examines the asymptotic analysis of wall modes in a flexible tube using a new set of scaling assumptions. It is shown that wall modes in Hagen-Poiseuille flow in a flexible tube are indeed unstable in the limit of high Re in the scaling regime . Here Σ is a nondimensional parameter characterising the elasticity of the wall, and , where ρ and η are the density and viscosity of the fluid, and G is the shear modulus of the wall medium. The results from the present asymptotic analysis are in excellent agreement with the previous numerical results. Importantly, the present work shows that the different types of unstable modes at high Reynolds number reported in previous numerical studies are qualitatively the same: they all belong to the class of unstable wall modes predicted in this paper.