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Stability analysis and inertial regimes in complex  flows
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
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 [en]
non-Newtonian flow, global stability analysis, inertial suspensions, particle dynamics
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-177850ISBN: 978-91-7595-782-1 (print)OAI: oai:DiVA.org:kth-177850DiVA: diva2:874531
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
List of papers
1. First instability of the flow of shear-thinning and shear-thickening fluids past a circular cylinder
Open this publication in new window or tab >>First instability of the flow of shear-thinning and shear-thickening fluids past a circular cylinder
2012 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 701, 201-227 p.Article in journal (Refereed) Published
Abstract [en]

The first bifurcation and the instability mechanisms of shear-thinning and shear-thickening fluids flowing past a circular cylinder are studied using linear theory and numerical simulations. Structural sensitivity analysis based on the idea of a 'wavemaker' is performed to identify the core of the instability. The shear-dependent viscosity is modelled by the Carreau model where the rheological parameters, i.e. the power-index and the material time constant, are chosen in the range 0.4 <= n <= 1.75 and 0.1 <= lambda <= 100. We show how shear-thinning/shear-thickening effects destabilize/stabilize the flow dramatically when scaling the problem with the reference zero-shear-rate viscosity. These variations are explained by modifications of the steady base flow due to the shear-dependent viscosity; the instability mechanisms are only slightly changed. The characteristics of the base flow, drag coefficient and size of recirculation bubble are presented to assess shear-thinning effects. We demonstrate that at critical conditions the local Reynolds number in the core of the instability is around 50 as for Newtonian fluids. The perturbation kinetic energy budget is also considered to examine the physical mechanism of the instability.

Keyword
instability, non-Newtonian flows, wakes
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-98714 (URN)10.1017/jfm.2012.151 (DOI)000304914400007 ()2-s2.0-84864262728 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20120703

Available from: 2012-07-03 Created: 2012-07-02 Last updated: 2017-12-07Bibliographically approved
2. Stability of fluids with shear-dependent viscosity in the lid-driven cavity
Open this publication in new window or tab >>Stability of fluids with shear-dependent viscosity in the lid-driven cavity
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.

Keyword
Linear stability, Non-Newtonian fluids, Lid-driven cavity, Sensitivity
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-96449 (URN)10.1016/j.jnnfm.2012.02.004 (DOI)000303943800006 ()2-s2.0-84858742078 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20120605

Available from: 2012-06-05 Created: 2012-06-04 Last updated: 2017-12-07Bibliographically approved
3. Linear stability analysis of channel flow of viscoelastic Oldroyd-B and FENE-P fluids
Open this publication in new window or tab >>Linear stability analysis of channel flow of viscoelastic Oldroyd-B and FENE-P fluids
2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 737, 249-279 p.Article in journal (Refereed) Published
Abstract [en]

We study the modal and non-modal linear instability of inertia-dominated channel flow of viscoelastic fluids modelled by the Oldroyd-B and FENE-P closures. The effects of polymer viscosity and relaxation time are considered for both fluids, with the additional parameter of the maximum possible extension for the FENE-P. We find that the parameter explaining the effect of the polymer on the instability is the ratio between the polymer relaxation time and the characteristic instability time scale (the frequency of a modal wave and the time over which the disturbance grows in the non-modal case). Destabilization of both modal and non-modal instability is observed when the polymer relaxation time is shorter than the instability time scale, whereas the flow is more stable in the opposite case. Analysis of the kinetic energy budget reveals that in both regimes the production of perturbation kinetic energy due to the work of the Reynolds stress against the mean shear is responsible for the observed effects where polymers act to alter the correlation between the streamwise and wall-normal velocity fluctuations. In the subcritical regime, the non-modal amplification of streamwise elongated structures is still the most dangerous disturbance-growth mechanism in the flow and this is slightly enhanced by the presence of polymers. However, viscoelastic effects are found to have a stabilizing effect on the amplification of oblique modes.

Keyword
instability, non-Newtonian flows
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-139290 (URN)10.1017/jfm.2013.572 (DOI)000327799800015 ()
Funder
Swedish e‐Science Research Center
Note

QC 20140108

Available from: 2014-01-08 Created: 2014-01-08 Last updated: 2017-12-06Bibliographically approved
4. The planar X-junction flow: stability analysis and control
Open this publication in new window or tab >>The planar X-junction flow: stability analysis and control
Show others...
2014 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 753, 1-28 p.Article in journal (Refereed) Published
Abstract [en]

The bifurcations and control of the flow in a planar X-junction are studied via linear stability analysis and direct numerical simulations. This study reveals the instability mechanisms in a symmetric channel junction and shows how these can be stabilized or destabilized by boundary modification. We observe two bifurcations as the Reynolds number increases. They both scale with the inlet speed of the two side channels and are almost independent of the inlet speed of the main channel. Equivalently, both bifurcations appear when the recirculation zones reach a critical length. A two-dimensional stationary global mode becomes unstable first, changing the flow from a steady symmetric state to a steady asymmetric state via a pitchfork bifurcation. The core of this instability, whether defined by the structural sensitivity or by the disturbance energy production, is at the edges of the recirculation bubbles, which are located symmetrically along the walls of the downstream channel. The energy analysis shows that the first bifurcation is due to a lift-up mechanism. We develop an adjustable control strategy for the first bifurcation with distributed suction or blowing at the walls. The linearly optimal wall-normal velocity distribution is computed through a sensitivity analysis and is shown to delay the first bifurcation from Re = 82.5 to Re = 150. This stabilizing effect arises because blowing at the walls weakens the wall-normal gradient of the streamwise velocity around the recirculation zone and hinders the lift-up. At the second bifurcation, a three-dimensional stationary global mode with a spanwise wavenumber of order unity becomes unstable around the asymmetric steady state. Nonlinear three-dimensional simulations at the second bifurcation display transition to a nonlinear cycle involving growth of a three-dimensional steady structure, time-periodic secondary instability and nonlinear breakdown restoring a two-dimensional flow. Finally, we show that the sensitivity to wall suction at the second bifurcation is as large as it is at the first bifurcation, providing a possible mechanism for destabilization.

Keyword
flow control, instability, wakes/jets
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-139407 (URN)10.1017/jfm.2014.364 (DOI)000341118600002 ()2-s2.0-84904425092 (Scopus ID)
Funder
EU, European Research Council, ALORS 2590620
Note

QC 20141007. Updated from submitted to published. Correction in: Journal of Fluid Mechanics, vol. 753, page: 560, WoS: 000341118600023

Available from: 2014-01-13 Created: 2014-01-13 Last updated: 2017-12-06Bibliographically approved
5. Laminar, Turbulent, and Inertial Shear-Thickening Regimes in Channel Flow of Neutrally Buoyant Particle Suspensions
Open this publication in new window or tab >>Laminar, Turbulent, and Inertial Shear-Thickening Regimes in Channel Flow of Neutrally Buoyant Particle Suspensions
2014 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 113, no 25, 254502- p.Article in journal (Refereed) Published
Abstract [en]

The aim of this Letter is to characterize the flow regimes of suspensions of finite-size rigid particles in a viscous fluid at finite inertia. We explore the system behavior as a function of the particle volume fraction and the Reynolds number (the ratio of flow and particle inertia to viscous forces). Unlike single-phase flows, where a clear distinction exists between the laminar and the turbulent states, three different regimes can be identified in the presence of a particulate phase, with smooth transitions between them. At low volume fractions, the flow becomes turbulent when increasing the Reynolds number, transitioning from the laminar regime dominated by viscous forces to the turbulent regime characterized by enhanced momentum transport by turbulent eddies. At larger volume fractions, we identify a new regime characterized by an even larger increase of the wall friction. The wall friction increases with the Reynolds number (inertial effects) while the turbulent transport is weakly affected, as in a state of intense inertial shear thickening. This state may prevent the transition to a fully turbulent regime at arbitrary high speed of the flow.

National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-159118 (URN)10.1103/PhysRevLett.113.254502 (DOI)000346673900003 ()2-s2.0-84919752869 (Scopus ID)
Funder
EU, European Research Council, ERC-2013-CoG-616186Swedish Research Council
Note

QC 20150128

Available from: 2015-01-28 Created: 2015-01-22 Last updated: 2017-12-05Bibliographically approved
6. Channel flow of rigid sphere suspensions: Particle dynamics in the inertial regime
Open this publication in new window or tab >>Channel flow of rigid sphere suspensions: Particle dynamics in the inertial regime
2016 (English)In: International Journal of Multiphase Flow, ISSN 0301-9322, E-ISSN 1879-3533, Vol. 78, 12-24 p.Article in journal (Refereed) Published
Abstract [en]

We consider suspensions of neutrally-buoyant finite-size rigid spherical particles in channel flow and investigate the relation between the particle dynamics and the mean bulk behavior of the mixture for Reynolds numbers 500 ≤ Re ≤ 5000 and particle volume fraction 0 ≤ Φ ≤ 0.3, via fully resolved numerical simulations. Analysis of the momentum balance reveals the existence of three different regimes: laminar, turbulent and inertial shear-thickening depending on which of the stress terms, viscous, Reynolds or particle stress, is the major responsible for the momentum transfer across the channel. We show that both Reynolds and particle stress dominated flows fall into the Bagnoldian inertial regime and that the Bagnold number can predict the bulk behavior although this is due to two distinct physical mechanisms. A turbulent flow is characterized by larger particle dispersion and a more uniform particle distribution, whereas the particulate-dominated flows is associated with a significant particle migration towards the channel center where the flow is smooth laminar-like and dispersion low. Interestingly, the collision kernel shows similar values in the different regimes, although the relative particle velocity and clustering clearly vary with inertia and particle concentration.

Place, publisher, year, edition, pages
Elsevier, 2016
Keyword
IMMERSED BOUNDARY METHOD, PRESSURE-DRIVEN FLOW, LINEAR SHEAR FLOWS, POISEUILLE FLOW, CONCENTRATED SUSPENSIONS, NUMERICAL SIMULATIONS, SELF-DIFFUSION, MIGRATION, STRESS, LIFT
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-177849 (URN)10.1016/j.ijmultiphaseflow.2015.09.008 (DOI)000367771300002 ()2-s2.0-84944810937 (Scopus ID)
Funder
EU, European Research Council, ERC-2013-CoG-616186Swedish Research Council, VR 2011-5354Swedish Research Council, 2014-5001
Note

QC 20152227. QC 20160203

Available from: 2015-11-27 Created: 2015-11-27 Last updated: 2017-12-01Bibliographically approved
7. Transition and self-sustained turbulence in dilute suspensions of finite-size particles
Open this publication in new window or tab >>Transition and self-sustained turbulence in dilute suspensions of finite-size particles
2015 (English)In: Theoretical and Applied Mechanics Letters, ISSN 2095-0349, Vol. 5, 121-125 p.Article in journal (Refereed) Published
Abstract [en]

We study the transition to turbulence of channel flow of finite-size particle suspensions at low volume fraction, i.e., Φ ≈ 0.001. The critical Reynolds number above which turbulence is sustained reduces to Re ≈ 1675, in the presence of few particles, independently of the initial condition, a value lower than that of the corresponding single-phase flow, i.e., Re ≈ 1775. In the dilute suspension, the initial arrangement of the particles is important to trigger the transition at a fixed Reynolds number and particle volume fraction. As in single phase flows, streamwise elongated disturbances are initially induced in the flow. If particles can induce oblique disturbances with high enough energy within a certain time, the streaks breakdown, flow experiences the transition to turbulence and the particle trajectories become chaotic. Otherwise, the streaks decay in time and the particles immigrate towards the channel core in a laminar flow. 

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-177847 (URN)10.1016/j.taml.2015.04.004 (DOI)2-s2.0-84944751845 (Scopus ID)
Note

QC 20151127

Available from: 2015-11-27 Created: 2015-11-27 Last updated: 2017-12-01Bibliographically approved

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