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

J. Klinkenberg, H.C. Lange, de, L. Brandt

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

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.
LanguageEnglish
Pages811-827
Number of pages17
JournalMeccanica
Volume49
Issue number4
DOIs
StatePublished - 2014

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histories
Reynolds number
Fluids
fluids
Linear stability analysis
Channel flow
Shear flow
Drag
disturbances
particle mass
channel flow
shear flow
drag
inclusions
interactions
energy

Cite this

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title = "Linear stability of particle laden flows : the influence of added mass, fluid acceleration and Basset history force",
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.",
author = "J. Klinkenberg and {Lange, de}, H.C. and L. Brandt",
year = "2014",
doi = "10.1007/s11012-013-9828-2",
language = "English",
volume = "49",
pages = "811--827",
journal = "Meccanica",
issn = "0025-6455",
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}

Linear stability of particle laden flows : the influence of added mass, fluid acceleration and Basset history force. / Klinkenberg, J.; Lange, de, H.C.; Brandt, L.

In: Meccanica, Vol. 49, No. 4, 2014, p. 811-827.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Linear stability of particle laden flows : the influence of added mass, fluid acceleration and Basset history force

AU - Klinkenberg,J.

AU - Lange, de,H.C.

AU - Brandt,L.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

U2 - 10.1007/s11012-013-9828-2

DO - 10.1007/s11012-013-9828-2

M3 - Article

VL - 49

SP - 811

EP - 827

JO - Meccanica

T2 - Meccanica

JF - Meccanica

SN - 0025-6455

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