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Flow instability and transitions in Taylor–Couette flow of a semidilute non-colloidal suspension

Published online by Cambridge University Press:  06 April 2021

Changwoo Kang Open the ORCID record for Changwoo Kang [Opens in a new window]  and
Parisa Mirbod Open the ORCID record for Parisa Mirbod [Opens in a new window]
Changwoo Kang
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W. Taylor Street, Chicago, IL60607, USA Department of Mechanical Engineering, Jeonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do54896, Republic of Korea
Parisa Mirbod*
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W. Taylor Street, Chicago, IL60607, USA
*
† Email address for correspondence: [email protected]
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Abstract

Flow of a semidilute neutrally buoyant and non-colloidal suspension is numerically studied in the Taylor–Couette geometry where the inner cylinder is rotating and the outer one is stationary. We consider a suspension with bulk particle volume fraction ${\phi _b} = 0.1$, the radius ratio $(\eta = {r_i}/{r_o} = 0.877)$ and two particle size ratios $\mathrm{\epsilon }\,( = \; d\textrm{/}a) = 60,\;200$, where d is the gap width ($= {r_o} - {r_i}$) between cylinders, a is the suspended particles’ radius and $r_i$ and $r_o$ are the inner and outer radii of the cylinder, respectively. Numerical simulations are conducted using the suspension balance model (SBM) and rheological constitutive laws. We predict the critical Reynolds number in which counter-rotating vortices arise in the annulus. It turns out that the primary instability appears through a supercritical bifurcation. For the suspension of $\mathrm{\epsilon } = 200$, the circular Couette flow (CCF) transitions via Taylor vortex flow (TVF) to wavy vortex flow (WVF). Additional flow states of non-axisymmetric vortices, namely spiral vortex flow (SVF) and wavy spiral vortex flow (WSVF) are observed between CCF and WVF for the suspension of $\mathrm{\epsilon } = 60$; thus, the transitions occur following the sequence of CCF → SVF → WSVF → WVF. Furthermore, we estimate the friction and torque coefficients of the suspension. Suspended particles substantially enhance the torque on the inner cylinder, and the axial travelling wave of spiral vortices reduces the friction and torque coefficients. However, the coefficients are practically the same in the WVF regime where particles are almost uniformly distributed in the annulus by the axial oscillating flow.

JFM classification

Flow Control: Instability control Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A12
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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