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Numerical study of viscoelastic upstream instability

Published online by Cambridge University Press:  17 March 2023

Sai Peng ,
Tingting Tang ,
Jianhui Li Open the ORCID record for Jianhui Li [Opens in a new window] ,
Mengqi Zhang Open the ORCID record for Mengqi Zhang [Opens in a new window]  and
Peng Yu Open the ORCID record for Peng Yu [Opens in a new window]
Sai Peng
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
Tingting Tang
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
Jianhui Li
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Guangxi Academy of Science, Nanning 530007, PR China
Mengqi Zhang
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575, Singapore
Peng Yu*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen 518055, PR China Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, PR China
*
† Email address for correspondence: yup6@sustech.edu.cn
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Abstract

In this work, we report numerical results on the flow instability and bifurcation of a viscoelastic fluid in the upstream region of a cylinder in a confined narrow channel. Two-dimensional direct numerical simulations based on the FENE-P model (the finite-extensible nonlinear elastic model with the Peterlin closure) are conducted with numerical stabilization techniques. Our results show that the macroscopic viscoelastic constitutive relation can capture the viscoelastic upstream instability reported in previous experiments for low-Reynolds-number flows. The numerical simulations reveal that the non-dimensional recirculation length (LD) is affected by the cylinder blockage ratio (BR), the Weissenberg number (Wi), the viscosity ratio (β) and the maximum polymer extension (L). Close to the onset of upstream recirculation, LD with Wi satisfy Landau-type quartic potential under certain parameter space. The bifurcation may exhibit subcritical behaviour depending on the values of L2 and β. The parameters β and L2 have nonlinear influence on the upstream recirculation length. This work contributes to our theoretical understanding of this new instability mechanism in viscoelastic wake flows.

JFM classification

Non-Newtonian Flows: Viscoelasticity Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 959 , 25 March 2023 , A16
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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