Impact of collisional versus viscous dissipation on flow instabilities in gas–solid systems

Yin, Xiaolong; Zenk, John R.; Mitrano, Peter; Hrenya, Christine M.

doi:10.1017/jfm.2013.268

Cited by 24 publications

(25 citation statements)

References 31 publications

(32 reference statements)

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“…It is reasonable to expect that direct numerical simulations (DNS) 28 and CFD-DEM simulations 29,30 , which resolve the particle-scale dynamics, should be chaotic as elastic 31 and inelastic 32 hard-sphere MD simulations are known be chaotic, even in the absence of clustering. For continuum predictions, however, the picture is not so clear.…”

Section: Introductionmentioning

confidence: 99%

Are continuum predictions of clustering chaotic?

Fullmer

Hrenya

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Gas-solid multiphase flows are prone to develop an instability known as clustering.Two-fluid models, which treat the particulate phase as a continuum, are known to reproduce the qualitative features of this instability, producing highly-dynamic, spatiotemporal patterns. However, it is unknown whether such simulations are truly aperiodic or a type of complex periodic behavior. By showing that the system possesses a sensitive dependence on initial conditions and a positive largest Lyapunov exponent, λ 1 ≈ 1/τ , we provide a tentative answer: continuum predictions of clustering are chaotic. We further demonstrate that the chaotic behavior is dimensionally dependent, a conclusion which unifies previous results and strongly suggests that the chaotic behavior is not a result of the fundamental kinematic instability, but of the secondary (inherently multidimensional) instability.a) E-mail: william.fullmer@colorado.edu b) Corresponding Author, E-mail: hrenya@colorado.edu 1 Granular matter is a collection of discrete, interacting solid particles which, like classic (molecular) matter, can be generally classified into one of three states 1 : i) under static conditions granular heaps or piles can sustain gravity-induced stress and behave like a solid 2 ; ii) dense granular flows characterized by enduring and multi-particle contacts behave similarly to a fluid 3 ; and iii) rapid granular flows characterized by instantaneous contacts described as a granular gas 4 . However, it is worth noting that all three granular states are only superficially similar to their molecular counterparts due to the dissipative nature of particle-particle contacts (inelasticity, friction, etc.) 1,4 . In industrial operations, rapid (collision-dominated) granular flows are often encountered in devices in which the particles are fluidized by a gas 5 ; such gas-solid flows are the focus of this work. Rapid gas-solid flows are prone to an instability termed clustering in which particles tend to form spatially inhomogeneous patterns of high and low concentrations 6 . Continuum or two-fluid models have long been known to be able to predict the qualitative nature of the clustering instability 7 and more recent quantitative assessments have also shown promising results 8-10 However,it is yet unknown whether or not such predictions are chaotic. We take a first step in answering this question by simulating fluidization in an unbounded domain and calculating a positive largest Lyapunov exponent, thereby indicating that continuum predictions of clustering are in fact chaotic. Further, we show that chaotic behavior may be reduced to periodic behavior by constraining the dimensionality of the system.

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Section: Introductionmentioning

confidence: 99%

Are continuum predictions of clustering chaotic?

Fullmer

Hrenya

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In the presence of a carrier phase, viscous damping by the fluid results in clustering of non-dissipative particles (Wylie & Koch 2000). In a recent study, Yin et al (2013) compared the relative contributions of these instabilities in dissipative gas-solid systems. One of the most widely investigated mechanisms is preferential concentration of particles by coherent vortical structures, first realized numerically by Eaton & Fessler (1994).…”

Section: Introductionmentioning

confidence: 99%

Numerical study of collisional particle dynamics in cluster-induced turbulence

2014

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We present a computational study of cluster-induced turbulence (CIT), where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. A separation of length scales must be established when evaluating the particle dynamics in order to distinguish between the continuous mesoscopic velocity field and the uncorrelated particle motion. To accomplish this, an adaptive spatial filter is employed on the Lagrangian data with an averaging volume that varies with the local particle-phase volume fraction. This filtering approach ensures sufficient particle sample sizes in order to obtain meaningful statistics while remaining small enough to avoid capturing variations in the mesoscopic particle field. Two-point spatial correlations are computed to assess the validity of the filter in extracting meaningful statistics. The method is used to investigate, for the first time, the properties of a statistically stationary gravity-driven particle-laden flow, where particle-particle and fluid-particle interactions control the multiphase dynamics. Results from fully developed CIT show a strong correlation between the local volume fraction and the granular temperature, with maximum values located at the upstream boundary of clusters (i.e. where maximum compressibility of the particle velocity field exists), while negligible particle agitation is observed within clusters.

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“…Recent work has also compared the relative contributions of these mechanisms in gas-solid flows of inelastic particles (Yin et al 2013). Many prior fundamental studies (Hopkins & Louge 1991;Brito & Ernst 1998;Luding & Herrmann 1999;Li & Kuipers 2003;Conway & Glasser 2004;Rice & Hrenya 2009) of clustering rely on molecular dynamics (MD) simulations.…”

Section: Introductionmentioning

confidence: 99%

Kinetic-theory predictions of clustering instabilities in granular flows: beyond the small-Knudsen-number regime

et al. 2013

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In this work we quantitatively assess, via instabilities, a Navier-Stokes-order (smallKnudsen-number) continuum model based on the kinetic theory analogy and applied to inelastic spheres in a homogeneous cooling system. Dissipative collisions are known to give rise to instabilities, namely velocity vortices and particle clusters, for sufficiently large domains. We compare predictions for the critical length scales required for particle clustering obtained from transient simulations using the continuum model with molecular dynamics (MD) simulations. The agreement between continuum simulations and MD simulations is excellent, particularly given the presence of well-developed velocity vortices at the onset of clustering. More specifically, spatial mapping of the local velocity-field Knudsen numbers (Kn u ) at the time of cluster detection reveals Kn u 1 due to the presence of large velocity gradients associated with vortices. Although kinetic-theory-based continuum models are based on a smallKn (i.e. small-gradient) assumption, our findings suggest that, similar to molecular gases, Navier-Stokes-order (small-Kn) theories are surprisingly accurate outside their expected range of validity.

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Impact of collisional versus viscous dissipation on flow instabilities in gas–solid systems

Cited by 24 publications

References 31 publications

Are continuum predictions of clustering chaotic?

Are continuum predictions of clustering chaotic?

Numerical study of collisional particle dynamics in cluster-induced turbulence

Kinetic-theory predictions of clustering instabilities in granular flows: beyond the small-Knudsen-number regime

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