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Numerical Simulations of laminar-turbulent transition in particle-laden channel flow
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: 0000-0002-9172-6311
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)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: urn:nbn:se:kth:diva-42706OAI: oai:DiVA.org:kth-42706DiVA: diva2:447476
Note
QC 20111013Available from: 2011-10-13 Created: 2011-10-12 Last updated: 2011-10-13Bibliographically 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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