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Stability of fluids with shear-dependent viscosity in the lid-driven cavity
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-4346-4732
2012 (English)In: Journal of Non-Newtonian Fluid Mechanics, ISSN 0377-0257, E-ISSN 1873-2631, Vol. 173-174, 49-61 p.Article in journal (Refereed) Published
Abstract [en]

The classical problem of the lid-driven cavity extended infinitely in the spanwise direction is considered for non-Newtonian shear-thinning and shear-thickening fluids, where the viscosity is modeled by the Carreau model. Linear stability is used to determine the critical Reynolds number at which the two-dimensional base-flow becomes unstable to three-dimensional spanwise-periodic disturbances. We consider a square cavity, characterized by steady unstable modes, and a shallow cavity of aspect ratio 0.25, where oscillating modes are the first to become unstable for Newtonian fluids. In both cases, the critical Reynolds number first decreases with decreasing power-index n (from shear-thickening to shear-thinning fluids) and then increase again for highly pseudoplastic fluids. In the latter case, this is explained by the thinner boundary layers at the cavity walls and less intense vorticity inside the domain. Interestingly, oscillating modes are found at critical conditions for shear-thickening fluids in a square cavity while the shallow cavity supports a new instability of lower frequency for large enough shear-thinning. Analysis of kinetic energy budgets and structural sensitivity are employed to investigate the physical mechanisms behind the instability.

Place, publisher, year, edition, pages
2012. Vol. 173-174, 49-61 p.
Keyword [en]
Linear stability, Non-Newtonian fluids, Lid-driven cavity, Sensitivity
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-96449DOI: 10.1016/j.jnnfm.2012.02.004ISI: 000303943800006Scopus ID: 2-s2.0-84858742078OAI: oai:DiVA.org:kth-96449DiVA: diva2:530900
Funder
Swedish e‐Science Research Center
Note

QC 20120605

Available from: 2012-06-05 Created: 2012-06-04 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Global stability analysis of complex fluids
Open this publication in new window or tab >>Global stability analysis of complex fluids
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The main focus of this work is on the non-Newtonian effects on the inertial instabilities in shear flows. Both inelastic (Carreau) and elastic models (Oldroyd-B and FENE-P) have been employed to examine the main features of the non-Newtonian fluids; shear-thinning, shear-thickening and elasticity. Several classical configurations have been considered; flow past a circular cylinder, in a lid-driven cavity and in a channel. We have used a wide range of tools for linear stability analysis, modal, non-modal, energy and sensitivity analysis, to determine the instability mechanisms of the non-Newtonian flows and compare them with those of the Newtonian flows. Direct numerical simulations have been also used to prove the results obtained by the linear stability analysis.

Significant modifications/alterations in the instability of the different flows have been observed under the action of the non-Newtonian effects. In general, shear-thinning/shear-thickening effects destabilize/stabilize the flow around the cylinder and in a lid driven cavity. Viscoelastic effects both stabilize and destabilize the channel flow depending on the ratio between the viscoelastic and flow time scales. The instability mechanism is just slightly modified in the cylinder flow whereas new instability mechanisms arise in the lid-driven cavity flow. We observe that the non-Newtonian effect can alter the inertial flow at both baseflow and perturbation level (e.g. Carreau fluid past a cylinder or in a lid driven cavity) or it may just affect the perturbations (e.g. Oldroyd-B fluid in channel). In all the flow cases studied, the modifications in the instability dynamics are shown to be strongly connected to the contribution of the different terms in the perturbation kinetic energy budget.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. viii, 26 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2013:20
Keyword
non-Newtonian flow, Carreau model, Oldroyd-B model, FENE-P model, modal analysis, nonmodal analysis, sensitivity analysis
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-139405 (URN)978-91-7501-958-1 (ISBN)
Presentation
2013-12-13, Q2, Osquldasväg 10, Stockholm, 10:15
Opponent
Supervisors
Note

QC 20140113

Available from: 2014-01-13 Created: 2014-01-13 Last updated: 2014-01-13Bibliographically approved
2. Stability analysis and inertial regimes in complex  flows
Open this publication in new window or tab >>Stability analysis and inertial regimes in complex  flows
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this work we rst study the non-Newtonian effects on the inertial instabilities in shear flows and second the inertial suspensions of finite size rigid particles by means of numerical simulations.

In the first part, both inelastic (Carreau) and elastic models (Oldroyd-B and FENE-P) have been employed to examine the main features of the non-Newtonian fluids in several congurations; flow past a circular cylinder, in a lid-driven cavity and in a channel. In the framework of the linear stability analysis, modal, non-modal, energy and sensitivity analysis are used to determine the instability mechanisms of the non-Newtonian flows. Signicant modifications/alterations in the instability of the different flows have been observed under the action of the non-Newtonian effects. In general, shear-thinning/shear-thickening effects destabilize/stabilize the flow around the cylinder and in a lid driven cavity. Viscoelastic effects both stabilize and destabilize the channel flow depending on the ratio between the viscoelastic and flow time scales. The instability mechanism is just slightly modied in the cylinder flow whereas new instability mechanisms arise in the lid-driven cavity flow.

In the second part, we employ Direct Numerical Simulation together with an Immersed Boundary Method to simulate the inertial suspensions of rigid spherical neutrally buoyant particles in a channel. A wide range of the bulk Reynolds numbers, 500<Re<5000, and particle volume fractions, 0<\Phi<3, is studied while fixing the ratio between the channel height to particle diameter, 2h/d = 10. Three different inertial regimes are identied by studying the stress budget of two-phase flow. These regimes are laminar, turbulent and inertial shear-thickening where the contribution of the viscous, Reynolds and particle stress to transfer the momentum across the channel is the strongest respectively. In the inertial shear-thickening regime we observe a signicant enhancement in the wall shear stress attributed to an increment in particle stress and not the Reynolds stress. Examining the particle dynamics, particle distribution, dispersion, relative velocities and collision kernel, confirms the existence of the three regimes. We further study the transition and turbulence in the dilute regime of finite size particulate channel flow. We show that the turbulence can sustain in the domain at Reynolds numbers lower than the one of the unladen flow due to the disturbances induced by particles.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. x, 60 p.
Series
TRITA-MEK, ISSN 0348-467X
Keyword
non-Newtonian flow, global stability analysis, inertial suspensions, particle dynamics
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-177850 (URN)978-91-7595-782-1 (ISBN)
Public defence
2015-12-18, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20151127

Available from: 2015-11-27 Created: 2015-11-27 Last updated: 2015-11-27Bibliographically approved

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