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Global stability analysis of complex fluids
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
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 [en]
non-Newtonian flow, Carreau model, Oldroyd-B model, FENE-P model, modal analysis, nonmodal analysis, sensitivity analysis
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-139405ISBN: 978-91-7501-958-1 (print)OAI: oai:DiVA.org:kth-139405DiVA: diva2:686892
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
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

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