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Rheological measurements and transition to turbulence for moderate Reynolds number inertial suspensions

Published online by Cambridge University Press:  31 May 2024

Yichuan Song  and
Melany L. Hunt Open the ORCID record for Melany L. Hunt [Opens in a new window]
Yichuan Song
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Melany L. Hunt*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: hunt@caltech.edu
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Abstract

Particulate flows at moderate particle Reynolds numbers are important in critical engineering and geological applications. This experimental study explores neutrally buoyant suspensions in an outer-rotating coaxial rheometer for solid fractions, $\phi$, from 0.1 to 0.5, and particle Reynolds number, $Re$, from 0.5 to 800, covering laminar, transitional and turbulent regimes; $Re$ is defined in terms of the square of the particle diameter and the shear rate. For $0.1 < \phi < 0.4$ and $0.5 < Re <10$, the direct torque measurements normalised by the laminar flow torque, $M/M_{lam}$, are independent of $Re$, but depend on $\phi$. For the same range of $\phi$ and for $10< Re<100$, the normalised torques depend on both $\phi$ and $Re$, and show an increasing dependence on $Re$. As $Re$ increases, the flow transitions to turbulence. Small particles delay the turbulent transition for $\phi \leqslant 0.3$, while large particles augment the transition. A modified Reynolds number, $Re^\prime$, that depends linearly on the particle diameter and the maximum velocity, $U_{o}$, is introduced for both laminar and turbulent flows and shows a better correlation of the results as compared with $Re$. For $\phi = 50\,\%$, the normalised torque minus the torque at zero rotational speed is nearly independent of $Re^\prime$. Rheological models based on $Re^\prime$ and the Krieger–Dougherty relative viscosity are proposed in the laminar regime for $10< Re^\prime <500$; in the turbulent regime, a correlation is proposed in terms of $Re^\prime$ and $\phi$ for $1000< Re^\prime < 6000$.

JFM classification

Complex Fluids: Suspensions Multiphase and Particle-laden Flows: Particle/fluid flow

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 988 , 10 June 2024 , A19
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© The Author(s), 2024. Published by Cambridge University Press

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