Generalized stability theory of polydisperse particle-laden flows. Part1. Channel flow
We present a generalized hydrodynamic stability theory for interacting particles in polydisperse particle-laden flows. The addition of dispersed particulate matter to a clean flow can either stabilize or destabilize the flow, depending on the particles' relaxation time-scale relative to the car...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
19.04.2022
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Subjects | |
Online Access | Get full text |
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Summary: | We present a generalized hydrodynamic stability theory for interacting
particles in polydisperse particle-laden flows. The addition of dispersed
particulate matter to a clean flow can either stabilize or destabilize the
flow, depending on the particles' relaxation time-scale relative to the carrier
flow time scales and the particle loading. To study the effects of
polydispersity and particle interactions on the hydrodynamic stability of shear
flows, we propose a new mathematical framework by combining a linear stability
analysis and a discrete Eulerian sectional formulation to describe the flow and
the dispersed particulate matter. In this formulation, multiple momentum and
transport equations are written for each size-section of the dispersed phase,
where interphase and inter-particle mass and momentum transfer are modelled as
source terms in the governing equations. A new modal linear stability framework
is derived by linearizing the coupled equations. Using this approach,
particle-flow interactions, such as polydispersity, droplet vaporization,
condensation, and coalescence, may be modelled. The method is validated with
linear stability analyses of clean and monodisperse particle-laden flows. We
show that the stability characteristics of a channel flow laden with particles
drastically change due to polydispersity. While relatively large monodisperse
particles tend to stabilize the flow, adding a second size section of a very
small mass fraction of low-to-moderate Stokes number particles may
significantly increase the growth rates, and for high-Reynolds numbers may
destabilize flows that might have been regarded as linearly stable in the
monodisperse case. These findings may apply to a vast number of fluid mechanics
applications involving particle-laden flows such as atmospheric flows,
environmental flows, medical applications, propulsion, and energy systems. |
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DOI: | 10.48550/arxiv.2204.08959 |