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Modal and non-modal stability analysis of a channel flow seeded with light particles
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-4346-4732
2011 (English)In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390Article in journal (Other academic) Submitted
Abstract [en]

Both modal and non-modal stability analysis of a channel flow laden with light particles is presented. The particles are assumed spherical and solid and their presence modeled using two-way coupling, with Stokes drag, added mass and fluid acceleration as coupling terms. The Stokes drag is a function of particle relaxation time and mass fraction, while added mass and fluid acceleration are a function of mass fraction and density ratio. When the particles considered have a density ratio of order one, all three terms are important. Modal analysis shows a decrease in critical Reynolds number proportional to the mass fraction for all particle relaxation times at a density ratio of one. Lighter particles decrease the critical Reynolds number further, whereas heavier particles might increase the critical Reynolds number. Most effect is found when the stability Stokes number is of order one. Non-modal analysis shows that the transient growth of the total system is enhanced in proportion to the particle mass fraction, as observed in flows laden with heavy particles. The generation of streamwise streaks is still the most dominant disturbance-growth mechanism in particle laden flows with light particles. Thus, the presence of particles may not work to delay the transition.

Place, publisher, year, edition, pages
2011.
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-42708OAI: oai:DiVA.org:kth-42708DiVA: diva2:447482
Note
QS 20120316Available from: 2011-10-13 Created: 2011-10-12 Last updated: 2017-12-08Bibliographically approved
In thesis
1. Stability analysis of channel flow laden with small particles.
Open this publication in new window or tab >>Stability analysis of channel flow laden with small particles.
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with the stability of particle laden flows. Both modal and non-modal linear analyses have been performed on two-way coupled particleladen flows, where particles are considered spherical, solid and either heavy or light. When heavy particles are considered, only Stokes drag is used as interaction term. Light particles cannot be modeled with Stokes drag alone, therefore added mass and fluid acceleration are used as additional interaction forces.

The modal analysis investigates the asymptotic behavior of disturbances on a base flow, in this thesis a pressure-driven plane channel flow. A critical Reynolds number is found for particle laden flows: heavy particles increase the critical Reynolds number compared to a clean fluid, when particles are not too small or too large. Neutrally buoyant particles, on the other hand, have no influence on the critical Reynolds number.

Non-modal analysis investigates the transient growth of disturbances, before the subsequent exponential behavior takes over. We investigate the kinetic energy growth of a disturbance, which can grow two to three orders of magnitude for clean fluid channel flows. This transient growth is usually the phenomenon that causes transition to turbulence: the energy can grow such that secondary instabilities and turbulence occurs. The total kinetic energy of a flow increases when particles are added to the flow as a function of the particle mass fraction. But instead of only investigating the total energy growth, the non-modal analysis is expanded such that we can differentiate between fluid and particle energy growth. When only the fluid is considered in a particle-laden flow, the transient growth is equal to the transient growth of a clean fluid. Besides thes Stokes drag, added mass and fluid acceleration, this thesis also discusses the influence of the Basset history term. This term is often neglected in stability analyses due to its arguably weak effect, but also due to difficulties in implementation. To implement the term correctly, the history of the particle has to be known. To overcome this and obtain a tractable problem, the square root in the history term is approximated by an exponential. It is found that the history force as a small effect on the transient growth.

Finally, Direct numerical simulations are performed for flows with heavy particles to investigate the influence of particles on secondary instabilities. The threshold energy for two routes to turbulence is considered to investigate whether the threshold energy changes when particles are included. We show that particles influence secondary instabilities and particles may delay transition.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. v, 30 p.
Series
Trita-MEK, ISSN 0348-467X ; 2011:10
Keyword
Transition, modal analysis, non-modal analysis, Direct Numerical Simulations, multi-phase flow, heavy particles, light particles, particle-laden
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-42271 (URN)978-91-7501-100-4 (ISBN)
Presentation
2011-10-07, Sal M2, Brinellvägen 64, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Funder
Swedish e‐Science Research Center
Note
QC 20111013Available from: 2011-10-13 Created: 2011-10-06 Last updated: 2012-05-24Bibliographically approved

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