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Published in: Meccanica 4/2014

01-04-2014

Linear stability of particle laden flows: the influence of added mass, fluid acceleration and Basset history force

Authors: Joy Klinkenberg, H. C. de Lange, Luca Brandt

Published in: Meccanica | Issue 4/2014

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Abstract

Both modal and non-modal linear stability analysis of a channel flow laden with particles is presented. The particles are assumed spherical and solid and their presence modelled using two-way coupling, with Stokes drag, added mass and fluid acceleration as coupling terms. When the particles considered have a density ratio of order one, all three terms become important. To account for the volume and mass of the particles, a modified Reynolds number is defined. Particles lighter than the fluid decrease the critical Reynolds number for modal stability, whereas heavier particles may increase the critical Reynolds number. Most effect is found when the Stokes number defined with the instability time scale is of order one. Non-modal analysis shows that the generation of streamwise streaks is the most dominant disturbance-growth mechanism also in flows laden with particles: the transient growth of the total system is enhanced proportionally to the particle mass fraction, as observed previously in flows laden with heavy particles. When studying the fluid disturbance energy alone, the optimal growth hardly changes. We also show that the Basset history force has a negligible effect on stability. The inclusion of the extra interaction terms does not show any large modifications of the subcritical instabilities in wall-bounded shear flows.

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Appendix
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Metadata
Title
Linear stability of particle laden flows: the influence of added mass, fluid acceleration and Basset history force
Authors
Joy Klinkenberg
H. C. de Lange
Luca Brandt
Publication date
01-04-2014
Publisher
Springer Netherlands
Published in
Meccanica / Issue 4/2014
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-013-9828-2

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