An instability mechanism for particulate pipe flow

Anthony Rouquier; Alban Potherat; Chris Pringle

doi:10.1017/jfm.2019.264

An instability mechanism for particulate pipe flow

Anthony Rouquier, Alban Potherat, Chris Pringle

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Abstract

We present a linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles, two-way coupled to the fluid velocity field via Stokes drag (Saffman, J.A Fluid Mech., vol.A 13 (01), 1962, pp.A 120-128). We extend previous analysis in a channel (Klinkenberg etA al., Phys. Fluids, vol.A 23 (6), 2011, 064110) to allow for the initial distribution of particles to be inhomogeneous in a similar manner to Boronin (Fluid Dyn., vol.A 47 (3), 2012, pp.A 351-363) and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability offering an alternative route to turbulence within this problem.

Original language	English
Pages (from-to)	247-265
Number of pages	19
Journal	Journal of Fluid Mechanics
Volume	870
Early online date	8 May 2019
DOIs	https://doi.org/10.1017/jfm.2019.264
Publication status	Published - 10 Jul 2019

Bibliographical note

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

Particulate flow
shear flow
instability
Key wordsparticle/fluid flow

ASJC Scopus subject areas

Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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10.1017/jfm.2019.264

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title = "An instability mechanism for particulate pipe flow",

abstract = "We present a linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles, two-way coupled to the fluid velocity field via Stokes drag (Saffman, J.A Fluid Mech., vol.A 13 (01), 1962, pp.A 120-128). We extend previous analysis in a channel (Klinkenberg etA al., Phys. Fluids, vol.A 23 (6), 2011, 064110) to allow for the initial distribution of particles to be inhomogeneous in a similar manner to Boronin (Fluid Dyn., vol.A 47 (3), 2012, pp.A 351-363) and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability offering an alternative route to turbulence within this problem.",

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author = "Anthony Rouquier and Alban Potherat and Chris Pringle",

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AU - Potherat, Alban

AU - Pringle, Chris

N1 - Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

PY - 2019/7/10

Y1 - 2019/7/10

N2 - We present a linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles, two-way coupled to the fluid velocity field via Stokes drag (Saffman, J.A Fluid Mech., vol.A 13 (01), 1962, pp.A 120-128). We extend previous analysis in a channel (Klinkenberg etA al., Phys. Fluids, vol.A 23 (6), 2011, 064110) to allow for the initial distribution of particles to be inhomogeneous in a similar manner to Boronin (Fluid Dyn., vol.A 47 (3), 2012, pp.A 351-363) and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability offering an alternative route to turbulence within this problem.

AB - We present a linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles, two-way coupled to the fluid velocity field via Stokes drag (Saffman, J.A Fluid Mech., vol.A 13 (01), 1962, pp.A 120-128). We extend previous analysis in a channel (Klinkenberg etA al., Phys. Fluids, vol.A 23 (6), 2011, 064110) to allow for the initial distribution of particles to be inhomogeneous in a similar manner to Boronin (Fluid Dyn., vol.A 47 (3), 2012, pp.A 351-363) and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability offering an alternative route to turbulence within this problem.

KW - Particulate flow

KW - shear flow

KW - instability

KW - Key wordsparticle/fluid flow

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DO - 10.1017/jfm.2019.264

M3 - Article

SN - 0022-1120

VL - 870

SP - 247

EP - 265

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -

An instability mechanism for particulate pipe flow

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Chris Pringle

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An instability mechanism for particulate pipe flow

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Chris Pringle

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