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The influence of inertia on the rotational dynamics of spheroidal particles suspended in shear flow
KTH, School of Engineering Sciences (SCI), Mechanics. (Research group of Fredrik Lundell)ORCID iD: 0000-0002-2346-7063
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Dispersed particle flows occur in many industrial, biological and geophysical applications. The knowledge of how these flow behave can for example lead to improved material processes, better predictions of vascular diseases or more accurate climate models. These particle flows have certain properties that depend on single particle motion in fluid flows and especially how they are distributed both in terms of spatial position and, if they are non-spherical, in terms of orientation. Much is already known about the motion of perfectly spherical particles. For non-spherical particles, apart from their translation, it is important to know the the rotational motion due to local velocity gradients. Such studies have usually been restricted by the assumption that particles are extremely small compared to fluid length scales. In this limit, both inertia of the particle and inertia of the fluid can be neglected for the particle motion. This thesis gives a complete picture of how a spheroidal particle (a particle described by a rotation of an ellipse around one of its principal axes) behave in a linear shear flow when including both fluid and particle inertia, using numerical simulations. It is observed that this very simple problem possess very interesting dynamical behavior with different stable rotational states appearing as a competition between the two types of inertia. The effect of particle inertia leads to a rotation where the mass of the particle is concentrated as far away from the rotational axis as possible, i.e.\ a rotation around the minor axis. Typically, the effect of fluid inertia is instead that it tries to force the particle in a rotation where the streamlines of the flow remain as straight as possible. The first effect of fluid inertia is thus the opposite of particle inertia and instead leads to a particle rotation around the major axis. Depending on rotational state, the particles also affect the apparent viscosity of the particle dispersion. The different transitions and bifurcations between rotational states are characterized in terms of non-linear dynamics, which reveal that the particle motion probably can be described by some reduced model. The results in this theses provides fundamental knowledge and is necessary to understand flows containing non-spherical particles.

Abstract [sv]

Flöden med dispergerade partiklar påträffas i många industriella, biologiska och geofysiska tillämpningar. Kunskap om hur dessa flöden beter sig kan bl.a. leda till förbättrade materialprocesser, bättre förutsägelser om hjärt- och kärlsjukdomar eller mer noggranna väderprognoser. Dessa flödens egenskaper beror på hur enskilda partiklar rör sig i en fluid och speciellt hur de är fördelade både i termer av position och, om de är icke-sfäriska, i termer av orientering. Mycket är redan känt om rörelsen av perfekt sfäriska partiklar. För icke-sfäriska partiklar är det inte bara translationen som är av intresse utan det är även viktigt att veta hur partiklarna roterar till följd av lokala hastighetsgradienter. Sådana studier har tidigare varit begränsade av antagandet att partiklarna är extremt små jämfört med fluidens typiska längdskalor. I denna gräns kan både partikelns och fluidens tröghet antas försumbar. Den här avhandlingen ger en komplett bild av hur en sfäroidisk partikel (en partikel som beskrivs av en rotation av en ellips runt en av dess huvudaxlar) beter sig i ett linjärt skjuvflöde när tröghetseffekter inkluderas. Resultaten har erhållits genom numeriska simuleringar. Det visar sig att detta enkla problem är väldigt rikt på olika dynamiska beteenden med flera stabila rotationstillstånd som uppstår tilll följd av både partikel- och fluidtröghet. Inverkan av partikeltröghet leder till en rotation där massan av partikeln är koncentrerad så långt ifrån rotationsaxeln som möjligt, d.v.s. en rotation runt lillaxeln. Den typiska inverkan av fluidtröghet är istället att fluiden försöker påtvinga partikeln en rotation där strömlinjer förblir så raka som möjligt. Primärt leder detta till att partikeln istället roterar runt storaxeln. Beroende på rotationstillstånd, så har partikeln även olika inverkan på den märkbara viskositeten av partikeldispersionen. De olika övergångarna och bifurkationerna mellan rotationstillstånd är karaktäriserade i termer av icke-linjär dynamik, vilket visar på att partikelrörelserna förmodligen kan beskrivas med en reducerad modell. Resultaten i denna avhandling är därför fundamental kunskap och ett nödvändigt steg mot att förstå beteendet av flöden med dispergerade, icke-sfäriska partiklar.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , x, 86 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2014:11
Keyword [en]
Fluid mechanics, dispersed particle flows, inertia, non-spherical particles, non-linear dynamics
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-143663ISBN: 978-91-7595-093-8 (print)OAI: oai:DiVA.org:kth-143663DiVA: diva2:708152
Presentation
2014-04-24, D3, Lindstedtsvägen 5, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20140328

Available from: 2014-03-28 Created: 2014-03-26 Last updated: 2014-03-28Bibliographically approved
List of papers
1. Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow
Open this publication in new window or tab >>Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow
2014 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 738, 563-590 p.Article in journal (Refereed) Published
Abstract [en]

The basic dynamics of a prolate spheroidal particle suspended in shear flow is studied using lattice Boltzmann simulations. The spheroid motion is determined by the particle Reynolds number (Re-p) and Stokes number (St), estimating the effects of fluid and particle inertia, respectively, compared with viscous forces on the particle. The particle Reynolds number is defined by Re-p = 4Ga(2)/nu, where G is the shear rate, a is the length of the spheroid major semi-axis and nu is the kinematic viscosity. The Stokes number is defined as St = alpha . Re-p, where alpha is the solid-to-fluid density ratio. Here, a neutrally buoyant prolate spheroidal particle (St = Re-p) of aspect ratio (major axis/minor axis) r(p) = 4 is considered. The long-term rotational motion for different initial orientations and Re-p is explained by the dominant inertial effect on the particle. The transitions between rotational states are subsequently studied in detail in terms of nonlinear dynamics. Fluid inertia is seen to cause several bifurcations typical for a nonlinear system with odd symmetry around a double zero eigenvalue. Particle inertia gives rise to centrifugal forces which drives the particle to rotate with the symmetry axis in the flow-gradient plane (tumbling). At high Re-p, the motion is constrained to this planar motion regardless of initial orientation. At a certain critical Reynolds number, Re-p = Re-c, a motionless (steady) state is created through an infinite-period saddle-node bifurcation and consequently the tumbling period near the transition is scaled as vertical bar Re-p - Re-c vertical bar(-1/2). Analyses in this paper show that if a transition from tumbling to steady state occurs at Re-p = Re-c, then any parameter beta (e. g. confinement or particle spacing) that influences the value of Re-c, such that Re-p = Re-c as beta = beta(c), will lead to a period that scales as vertical bar beta - beta c vertical bar(-1/2) and is independent of particle shape or any geometric aspect ratio in the flow.

Keyword
complex fluids, multiphase and particle-laden flows, nonlinear dynamical systems
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-140130 (URN)10.1017/jfm.2013.599 (DOI)000328486400024 ()2-s2.0-84910138134 (Scopus ID)
Note

QC 20140121

Available from: 2014-01-21 Created: 2014-01-17 Last updated: 2017-12-06Bibliographically approved
2. The dynamical states of a prolate spheroidal particle suspended in shear flow as a consequence of particle and fluid inertia
Open this publication in new window or tab >>The dynamical states of a prolate spheroidal particle suspended in shear flow as a consequence of particle and fluid inertia
2015 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 771, 115-158 p.Article in journal (Refereed) Published
Abstract [en]

The rotational motion of a prolate spheroidal particle suspended in shear flow is studied by a lattice Boltzmann method with external boundary forcing (LB-EBF). It has previously been shown that the case of a single neutrally buoyant particle is a surprisingly rich dynamical system that exhibits several bifurcations between rotational states due to inertial effects. It was observed that the rotational states were associated with either fluid inertia effects or particle inertia effects, which are always in competition. The effects of fluid inertia are characterized by the particle Reynolds number Rep=4Ga2/ν, where G is the shear rate, a is the length of the particle major semi-axis and ν is the kinematic viscosity. Particle inertia is associated with the Stokes number St=α· Rep, where alpha is the solid-to-fluid density ratio. Previously, the neutrally buoyant case (St=Rep) was studied extensively. However, little is known about how these results are affected when St≢Rep, and how the aspect ratio rp (major axis/minor axis) influences the competition between fluid and particle inertia in the absence of gravity. This work gives a full description of how prolate spheroidal particles in the range 2≤ rp≤ 6 behave depending on the chosen St and Rep. Furthermore, consequences for the rheology of a dilute suspension containing such particles are discussed. Finally, grid resolution close to the particle is shown to affect the quantitative results considerably. It is suggested that this resolution is a major cause of quantitative discrepancies between different studies. Thus, the results of this work and previous direct numerical simulations of this problem should be regarded as qualitative descriptions of the physics involved, and more refined methods must be used to quantitatively pinpoint the transitions between rotational states.

Keyword
bifurcation, complex fluids, multiphase and particle-laden flows
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:kth:diva-143775 (URN)10.1017/jfm.2015.127 (DOI)000355985900009 ()2-s2.0-84928476779 (Scopus ID)
Funder
Knut and Alice Wallenberg FoundationÅForsk (Ångpanneföreningen's Foundation for Research and Development)
Note

QC 20150609. Updated from manuscript to article in journal.

Available from: 2014-03-28 Created: 2014-03-28 Last updated: 2017-12-05Bibliographically approved
3. Effect of fluid and particle inertia on the rotation of an oblate spheroidal particle suspended in linear shear flow
Open this publication in new window or tab >>Effect of fluid and particle inertia on the rotation of an oblate spheroidal particle suspended in linear shear flow
2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 91, no 5, 053017Article in journal (Refereed) Published
Abstract [en]

This work describes the inertial effects on the rotational behavior of an oblate spheroidal particle confined between two parallel opposite moving walls, which generate a linear shear flow. Numerical results are obtained using the lattice Boltzmann method with an external boundary force. The rotation of the particle depends on the particle Reynolds number, Rep = Gd-2 nu(-1) (G is the shear rate, d is the particle diameter,. is the kinematic viscosity), and the Stokes number, St = alpha Re-p (a is the solid-to-fluid density ratio), which are dimensionless quantities connected to fluid and particle inertia, respectively. The results show that two inertial effects give rise to different stable rotational states. For a neutrally buoyant particle (St = Re-p) at low Re-p, particle inertia was found to dominate, eventually leading to a rotation about the particle's symmetry axis. The symmetry axis is in this case parallel to the vorticity direction; a rotational state called log-rolling. At high Re-p, fluid inertia will dominate and the particle will remain in a steady state, where the particle symmetry axis is perpendicular to the vorticity direction and has a constant angle phi(c) to the flow direction. The sequence of transitions between these dynamical states were found to be dependent on density ratio alpha, particle aspect ratio r(p), and domain size. More specifically, the present study reveals that an inclined rolling state (particle rotates around its symmetry axis, which is not aligned in the vorticity direction) appears through a pitchfork bifurcation due to the influence of periodic boundary conditions when simulated in a small domain. Furthermore, it is also found that a tumbling motion, where the particle symmetry axis rotates in the flow-gradient plane, can be a stable motion for particles with high r(p) and low alpha.

Keyword
Lattice-Boltzmann Method, Ellipsoidal Particles, Molecular Dimensions, Viscous-Fluid, Couette Flows, Suspensions, Motion, Dynamics
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-143776 (URN)10.1103/PhysRevE.91.053017 (DOI)000354927700010 ()2-s2.0-84930668697 (Scopus ID)
Funder
ÅForsk (Ångpanneföreningen's Foundation for Research and Development)
Note

QC 20150616. Updated from manuscript to article in journal.

Available from: 2014-03-28 Created: 2014-03-28 Last updated: 2017-12-05Bibliographically approved

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