On multiphase turbulence models for collisional fluid–particle flows

Fox, Rodney O.

doi:10.1017/jfm.2014.21

Cited by 180 publications

(218 citation statements)

References 74 publications

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“…Consequently, if we decompose the fluid fluctuating energy in two components, one of them induced by large scale collective motion and the other one due to small scale fluid-particle wake turbulence (also referred to in the literature as pseudo-turbulent kinetic energy), E f = E f + δE f , the second component would be far greater than the first one. Note that a rigorous formulation of the energy decomposition is reviewed in Fox (2014) . The strong coupling seems to be intrinsic to liquid fluidization whereas the opposite is true in gas fluidization, which is essentially related to difference in particle inertia.…”

Section: Particle and Fluid Velocity Variancementioning

confidence: 99%

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Particle resolved direct numerical simulation of a liquid–solid fluidized bed: Comparison with experimental data

Özel

Motta

Abbas

et al. 2017

International Journal of Multiphase Flow

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao. (10), respectively. In this paper, we compare the statistical quantities computed from numerical results with the experimental data obtained with 3-D trajectography and High Frequency PIV. Fluidization law predicted by the numerical simulations is in very good agreement with the experimental curve and the main features of trajectories and Lagrangian velocity signal of the particles are well reproduced by the simulations. The evolution of particle and flow velocity variances as a function of bed solid volume fraction is also well captured by the simulations. In particular, the numerical simulations predict the right level of anisotropy of the dispersed phase fluctuations and its independence of bed solid volume fraction. They also confirm the high value of the ratio between the fluid and the particle phase fluctuating kinetic energy. A quick analysis suggests that the fluid velocity fluctuations are mainly driven by fluid-particle wake interactions (pseudo-turbulence) whereas the particle velocity fluctuations derive essentially from the large scale flow motion (recirculation). Lagrangian autocorrelation function of particle fluctuating velocity exhibits large-scale oscillations, which are not observed in the corresponding experimental curves, a difference probably due to a statistical averaging effect. Evolution as a function of the bed solid volume fraction and the collision frequency based upon transverse component of particle kinetic energy correctly matches the experimental trend and is well fitted by a theoretical expression derived from Kinetic Theory of Granular Flows.

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Section: Particle and Fluid Velocity Variancementioning

confidence: 99%

“…17 ). Février et al (2005) and Fox (2014) who suggested that the total particle velocity fluctuations can be decomposed in large and small scale fluctuations E p = E p + δE p . The first part contains particle large scale motion represented by the streamlines of Fig.…”

Section: Particle Fluctuation Time Scalesmentioning

confidence: 99%

Particle resolved direct numerical simulation of a liquid–solid fluidized bed: Comparison with experimental data

Özel

Motta

Abbas

et al. 2017

International Journal of Multiphase Flow

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“…In an effort towards developing a macroscopic multiphase turbulence model, Fox (2014) recently derived the exact Reynolds-averaged (RA) equations for collisional fluid-particle flows. Through phase-space integration, the collisional Boltzmann equation was replaced by a set of macroscale moment equations.…”

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confidence: 99%

“…Unlike in most previous derivations of turbulence models for moderately dense granular flows, a clear distinction was made between the granular temperature, which appears in the kinetic theory (KT) constitutive relations, and the particle-phase turbulent kinetic energy k p , which appears in the turbulent transport coefficients. The derivation by Fox (2014) is completely general and can be applied to any kinetic-based model for the disperse phase, including weakly and non-collisional flows, and leads to new insights about multiphase turbulence. For example, in addition to the classical production by mean shear, the transport equation for the fluid-phase turbulent kinetic energy k f contains an additional production term due to the mean velocity difference between the particle and fluid phases.…”

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confidence: 99%

On fluid–particle dynamics in fully developed cluster-induced turbulence

2015

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At sufficient mass loading and in the presence of a mean body force (e.g. gravity), an initially random distribution of particles may organize into dense clusters as a result of momentum coupling with the carrier phase. In statistically stationary flows, fluctuations in particle concentration can generate and sustain fluid-phase turbulence, which we refer to as cluster-induced turbulence (CIT). This work aims to explore such flows in order to better understand the fundamental modelling aspects related to multiphase turbulence, including the mechanisms responsible for generating volume-fraction fluctuations, how energy is transferred between the phases, and how the cluster size distribution scales with various flow parameters. To this end, a complete description of the two-phase flow is presented in terms of the exact Reynolds-average (RA) equations, and the relevant unclosed terms that are retained in the context of homogeneous gravity-driven flows are investigated numerically. An Eulerian-Lagrangian computational strategy is used to simulate fully developed CIT for a range of Reynolds numbers, where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. The adaptive filtering technique recently introduced in our previous work (Capecelatro et al., J. Fluid Mech., vol. 747, 2014, R2) is used to evaluate the Lagrangian data as Eulerian fields that are consistent with the terms appearing in the RA equations. Results from gravity-driven CIT show that momentum coupling between the two phases leads to significant differences from the behaviour observed in very dilute systems with one-way coupling. In particular, entrainment of the fluid phase by clusters results in an increased mean particle velocity that generates a drag production term for fluid-phase turbulent kinetic energy that is highly anisotropic. Moreover, owing to the compressibility of the particle phase, the uncorrelated components of the particle-phase velocity statistics are highly non-Gaussian, as opposed to systems with one-way coupling, where, in the homogeneous limit, all of the velocity statistics are nearly Gaussian. We also observe that the particle pressure tensor is highly anisotropic, and thus additional transport equations for the separate contributions † Email address for correspondence: jsc359@cornell.edu On fluid-particle dynamics in cluster-induced turbulence 579 to the pressure tensor (as opposed to a single transport equation for the granular temperature) are necessary in formulating a predictive multiphase turbulence model.

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“…Clustering of particles is also found in simulations where the feedback from the particles to the flow is included, see, e.g., refs. [33,34]. In those cases, gravity may also play an important role, i.e., horizontal and vertical pipes may show different clustering phenomena, see e.g., refs.…”

Section: Discussionmentioning

confidence: 99%

Turbophoresis in forced inhomogeneous turbulence

Mitra

Haugen

2018

Eur. Phys. J. Plus

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Abstract. We show, by direct numerical simulations, that heavy inertial particles (characterized by Stokes number St) in inhomogeneously forced statistically stationary isothermal turbulent flows cluster at the minima of mean-square turbulent velocity. Two turbulent transport processes, turbophoresis and turbulent diffusion together determine the spatial distribution of the particles. If the turbulent diffusivity is assumed to scale with turbulent root-mean-square velocity, as is the case for homogeneous turbulence, the turbophoretic coefficient can be calculated. Indeed, for the above assumption, the non-dimensional product of the turbophoretic coefficient and the rms velocity is shown to increase with St for small St, reach a maxima for St ≈ 10 and decrease as ∼ St −0.33 for large St.

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On multiphase turbulence models for collisional fluid–particle flows

Cited by 180 publications

References 74 publications

Particle resolved direct numerical simulation of a liquid–solid fluidized bed: Comparison with experimental data

Particle resolved direct numerical simulation of a liquid–solid fluidized bed: Comparison with experimental data

On fluid–particle dynamics in fully developed cluster-induced turbulence

Turbophoresis in forced inhomogeneous turbulence

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