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Asymptotic study of linear instability in a viscoelastic pipe flow

Published online by Cambridge University Press:  31 January 2022

Ming Dong Open the ORCID record for Ming Dong [Opens in a new window]  and
Mengqi Zhang Open the ORCID record for Mengqi Zhang [Opens in a new window]
Ming Dong*
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Mengqi Zhang*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore
*
†Email addresses for correspondence: dongming@imech.ac.cn, mpezmq@nus.edu.sg
†Email addresses for correspondence: dongming@imech.ac.cn, mpezmq@nus.edu.sg
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Abstract

It is recently found that viscoelastic pipe flows can be linearly unstable, leading to the possibility of a supercritical transition route, in contrast to Newtonian pipe flows. Such an instability is referred to as the centre mode, which was studied numerically by Chaudhary et al. (J. Fluid Mech., vol. 908, 2021, p. A11) based on an Oldroyd-B model. In this paper, we are interested in expanding the parameter space investigated and exploring the asymptotic scalings related to this centre instability in the Oldroyd-B viscoelastic pipe flow. It is found from the asymptotic analysis that the centre mode exhibits a three-layered asymptotic structure in the radial direction, a wall layer, a main layer and a central layer, which are driven by pure viscosity, axial and/or radial pressure gradient, and a combined effect of viscosity and elasticity, respectively. Depending on the relations of the control parameters, two regimes, the long-wavelength and short-wavelength centre instabilities, emerge, for which the central-layer thicknesses are of different orders of magnitude. Our large-Reynolds-number asymptotic predictions are compared to the numerical solutions of the original eigenvalue system, and favourable agreement is achieved, especially when the parameters approach their individual limits. In addition to revealing the dominant factors and their balances, the asymptotic analysis describes the instability system by reducing the number of control parameters, and furthermore explaining the collapse of the numerical results for different re-scalings.

JFM classification

Non-Newtonian Flows: Viscoelasticity Non-Newtonian Flows: Polymers Instability: Shear-flow instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 935 , 25 March 2022 , A28
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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