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Stability analysis of channel flow laden with small particles.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
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 [en]
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: urn:nbn:se:kth:diva-42271ISBN: 978-91-7501-100-4 (print)OAI: oai:DiVA.org:kth-42271DiVA: diva2:446176
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
List of papers
1. Modal and non-modal stability of particle-laden channel flow
Open this publication in new window or tab >>Modal and non-modal stability of particle-laden channel flow
2011 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 23, no 6, 064110- p.Article in journal (Refereed) Published
Abstract [en]

Modal and non-modal linear stability analysis of channel flow with a dilute particle suspension is presented where particles are assumed to be solid, spherical, and heavy. The two-way coupling between particle and fluid flow is therefore modeled by the Stokes drag only. The results are presented as function of the particle relaxation time and mass fraction. First, we consider exponentially growing perturbations and extend previous findings showing the potential for a significant increase of the critical Reynolds number. The largest stabilization is observed when the ratio between the particle relaxation time and the oscillation period of the wave is of order one. By examining the energy budget, we show that this stabilization is due to the increase of the dissipation caused by the Stokes drag. The observed stabilization has led to the hypothesis that dusty flows can be more stable. However, transition to turbulence is most often subcritical in canonical shear flows where non-modal growth mechanisms are responsible for the initial growth of external disturbances. The non-modal analysis of the particle-laden flow, presented here for the first time, reveals that the transient energy growth is, surprisingly, increased by the presence of particles, in proportion to the particle mass fraction. The generation of streamwise streaks via the lift-up mechanism is still the dominant disturbance-growth mechanism in the particle laden flow; the length scales of the most dangerous disturbances are unaffected, while the initial disturbance growth can be delayed. These results are explained in terms of a dimensionless parameter relating the particle relaxation time to the time scale of the instability. The presence of a dilute solid phase therefore may not always work as a flow-control strategy for maintaining the flow as laminar. Despite the stabilizing effect on modal instabilities, non-modal mechanisms are still strong in internal flows seeded with heavy particles. Our results indicate that the initial stages of transition in dilute suspensions of small particles are similar to the stages in a single phase flow.

Keyword
channel flow, drag, flow instability, flow simulation, laminar to turbulent transitions, modal analysis, shear flow, suspensions, two-phase flow
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-37171 (URN)10.1063/1.3599696 (DOI)000292333300028 ()2-s2.0-79959919722 (Scopus ID)
Funder
Swedish e‐Science Research Center
Available from: 2011-08-02 Created: 2011-08-02 Last updated: 2017-12-08Bibliographically approved
2. Modal and non-modal stability analysis of a channel flow seeded with light particles
Open this publication in new window or tab >>Modal and non-modal stability analysis of a channel flow seeded with light particles
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.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-42708 (URN)
Note
QS 20120316Available from: 2011-10-13 Created: 2011-10-12 Last updated: 2017-12-08Bibliographically approved
3. Numerical Simulations of laminar-turbulent transition in particle-laden channel flow
Open this publication in new window or tab >>Numerical Simulations of laminar-turbulent transition in particle-laden channel flow
2011 (English)Report (Other academic)
Abstract [en]

Direct Numerical Simulation of a particle-laden channel flow is performed, with particles assumed solid, spherical and heavy. Two-way coupling between fluidand particles is modeled with Stokes drag. The equations describing the fluid flow are solved with an Eulerian mesh and those describing particles are solved in a Lagrangian frame. The numerical code is validated with results from linear optimal growth from previous studies; the optimal growth of streamwise vortices resulting in streamwise streaks is still the most efficient mechanism for disturbance amplification at subcritical conditions as for the case of a single phase fluid.

We consider transition initiated by two initial disturbances well-known in literature, streamwise vortices and oblique waves. The threshold energy for transition is computed for both cases. It is observed that streamwise vortices in combination with an oblique wave as additional initial disturbance, result ina small increase of threshold energy compared to a clean fluid. In addition, the time at which transition occurs clearly increases for disturbances of equal initial energy. The threshold energy in the case of the so-called oblique scenario, increases by a factor about 4 in the presence of particles. The results are explained by considering the reduced amplification of oblique modes in the presence of particles.

The results from these two classical scenarios indicate that, although stability analysis shows hardly any effect on optimal growth, particles do influence secondary instabilities and streak breakdown, thus the non-linear stages of transition, in two different ways. The presence of particles introduced threedimensional, streamwise-dependent modulations, especially at low concentrations, that may trigger and enhance secondary instabilities of streamwiseindependent streaks. On the other hand, particles decrease the amplitude ofoblique modes thus delaying transition initiated by their nonlinear interactions as in the oblique scenario.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. 15 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-42706 (URN)
Note
QC 20111013Available from: 2011-10-13 Created: 2011-10-12 Last updated: 2011-10-13Bibliographically approved

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