Numerical simulation of concentration interface in stratified suspension: Continuum–particle transition

Yamamoto, Yasufumi; Hisataka, Fumiya; Harada, Shusaku

doi:10.1016/j.ijmultiphaseflow.2015.03.007

Cited by 19 publications

(16 citation statements)

References 32 publications

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“…Whilst the condition on the particle coupling is given by the Stokes number (St < 1), there is also a condition on the particle volume fraction to take in account. Harada et al (2013) and Yamamoto et al (2015) derived a dimensionless number in order to characterise the transition between fluid-like and particle-like settling. Although this number is only valid for narrow channel configurations, which are considerably different from ours, it highlights the fact that the particle size, volume fraction and characteristic length scale of the flow are critical parameters to define the validity of the continuum assumption.…”

Section: Model Caveatsmentioning

confidence: 99%

“…Further studies of settling-driven gravitational instabilities have taken theoretical approaches, such as using linear stability analyses to predict the growth rate and characteristic wavelengths of the instability at very early stages (Burns and Meiburg, 2012;Yu et al, 2013;Alsinan et al, 2017). Moreover, various numerical models simulating settling-driven gravitational instability have also been developed (Jacobs et al, 2013;Burns and Meiburg, 2014;Yamamoto et al, 2015;Chou and Shao, 2016;Keck et al, 2021). Most numerical approaches to this problem have used continuumphase models, where the coupling between particles and fluid is strong enough to describe them as a single-phase (Burns and Meiburg, 2014;Yu et al, 2014;Chou and Shao, 2016).…”

Section: Introductionmentioning

confidence: 99%

“…However, for large particle diameters and small particle volume fractions, collective behaviour no longer occurs and the continuum-phase method cannot be applied. In this case, there is a need to explicitly model particle motion, taking the drag force into consideration (Yamamoto et al, 2015;Chou and Shao, 2016). This paper presents an innovative method to implement a continuum model by coupling the Lattice Boltzmann Method (LBM) with a low-diffusivity finite difference (FD) scheme.…”

Section: Introductionmentioning

confidence: 99%

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Modelling Settling-Driven Gravitational Instabilities at the Base of Volcanic Clouds Using the Lattice Boltzmann Method

et al. 2021

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Field observations and laboratory experiments have shown that ash sedimentation can be significantly affected by collective settling mechanisms that promote premature ash deposition, with important implications for dispersal and associated impacts. Among these mechanisms, settling-driven gravitational instabilities result from the formation of a gravitationally-unstable particle boundary layer (PBL) that grows between volcanic ash clouds and the underlying atmosphere. The PBL destabilises once it reaches a critical thickness characterised by a dimensionless Grashof number, triggering the formation of rapid, downward-moving ash fingers that remain poorly characterised. We simulate this process by coupling a Lattice Boltzmann model, which solves the Navier-Stokes equations for the fluid phase, with a Weighted Essentially Non Oscillatory (WENO) finite difference scheme which solves the advection-diffusion-settling equation describing particle transport. Since the physical problem is advection dominated, the use of the WENO scheme reduces numerical diffusivity and ensures accurate tracking of the temporal evolution of the interface between the layers. We have validated the new model by showing that the simulated early-time growth rate of the instability is in very good agreement with that predicted by linear stability analysis, whilst the modelled late-stage behaviour also successfully reproduces quantitative results from published laboratory experiments. The results show that the model is capable of reproducing both the growth of the unstable PBL and the non-linear dependence of the fingers’ vertical velocity on both the initial particle concentration and the particle diameter. Our validated model is used to expand the parameter space explored experimentally and provides key insights into field studies. Our simulations reveal that the critical Grashof number for the instability is about ten times larger than expected by analogy with thermal convection. Moreover, as in the experiments, we found that instabilities do not develop above a given particle threshold. Finally, we quantify the evolution of the mass of particles deposited at the base of the numerical domain and demonstrate that the accumulation rate increases with time, while it is expected to be constant if particles settle individually. This suggests that real-time measurements of sedimentation rate from volcanic clouds may be able to distinguish finger sedimentation from individual particle settling.

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Section: Model Caveatsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling Settling-Driven Gravitational Instabilities at the Base of Volcanic Clouds Using the Lattice Boltzmann Method

et al. 2021

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“…As in previous studies [7,22,24], we employed Lagrangian tracking of individual particles with two-way coupling using a point-force model. We could ignore particle inertia by assuming that the particle response time was much shorter than the liquid flow timescale, and thus the Stokes number was much smaller than unity.…”

Section: System and Simulationmentioning

confidence: 99%

Macroscopic and microscopic hydrodynamic mixing of stratified suspensions

et al. 2021

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We conducted numerical experiments to investigate the mixing of stratified suspensions containing different types of particles. We used a point-force two-way coupling method. We studied the mixing behavior of stratified suspensions and we discovered two types of mixing: microscopic (individual-particle-level) and macroscopic (vessel-scale) collective mixing. In addition, we examined the vertical mixing speed of the stratified suspension. We used a simple theoretical model to analyze the fingering settling velocity. Then we introduced a nondimensional number representing the difference in collectivities of the upper and lower suspensions while accounting for particle terminal velocities. We discovered that the proposed nondimensional parameter has a negative sign that distinguishes the mixing form of only microscopic individual-particle-level mixing and a positive value that predicts the speed of macroscopic collective mixing of stratified suspensions.

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“…The settling of a stratified suspension in a simple flow channel also shows complicated behaviors depending on the suspension conditions [7][8][9][10][11]. At large particle diameter and low concentration, suspended particles settle individually (particle-like settling) at terminal velocity.…”

Section: Introductionmentioning

confidence: 99%

Scale-independent model of gravitational settling of particulate suspension in a fractal channel

Kurose

Ishizawa

Soriano

et al. 2019

Chemical Engineering Science

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Gravitational settling of solid particles into a fractal-shaped channel was investigated experimentally and theoretically. Previous studies have reported that the settling behavior of particles in liquid-filled channels depends strongly on particle properties and suspension conditions. At small particle size and high concentration, particles settle collectively like an immiscible fluid with respect to the surrounding one. In this study, we examined the gravitational dispersion behavior of solid particles in a three-dimensional fractal-shaped channel under various collective conditions.The experimental results showed that the settling behavior varies with the collectivity of suspended particles. In the case of high collectivity conditions, settling velocity is enhanced by a density-driven instability, which depends not only on the physical properties of the particles and fluid but also on channel geometry. We developed a model of temporal change in the volumetric occupancy ratio in a suspended region. This model describes the invasion of particles into a fractal channel. Our model comprises only the fractal characteristics of the channel, such as a homothetic ratio and a bifurcation number. Consequently, This model could provide a rough prediction of the gravity-induced invasion behavior of particles into any fractal-shaped channel.

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Numerical simulation of concentration interface in stratified suspension: Continuum–particle transition

Cited by 19 publications

References 32 publications

Modelling Settling-Driven Gravitational Instabilities at the Base of Volcanic Clouds Using the Lattice Boltzmann Method

Modelling Settling-Driven Gravitational Instabilities at the Base of Volcanic Clouds Using the Lattice Boltzmann Method

Macroscopic and microscopic hydrodynamic mixing of stratified suspensions

Scale-independent model of gravitational settling of particulate suspension in a fractal channel

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