Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres

Tenneti, Sudheer; Garg, Rahul; Subramaniam, Shankar

doi:10.1016/j.ijmultiphaseflow.2011.05.010

Cited by 377 publications

(355 citation statements)

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“…The computational domain size was 24 × 14 × 8 and the centre of the particle was put at position x 1 = 8, x 2 = 7 and x 3 = 1. The flow was simulated for two resolutions; the coarsest one was given by N r = 4, N θ = 24, N φ = 48, N 1 = 88, N 2 = 68 and As a fourth validation, the pressure and viscous parts of the drag force on a sphere in the flow past a structured array of spheres were computed and compared to results obtained by Tenneti et al (2011). These authors used an immersed boundary method (second-order accurate direct forcing embedded into a pseudo-spectral computation; the same method was recently used by Mehrabadi et al (2015)).…”

Section: Results Of Test Casesmentioning

confidence: 99%

“…It is remarked that many variants of immersed boundary methods exist and have been validated for flows past multiple particles -see also, for example, Uhlmann (2005), Mark & van Wachem (2008) and Breugem (2012). In the test presented by Tenneti et al (2011), a face-centred cubic (FCC) array of particles was used with a particle volume fraction α = 0.2. To simulate this case with the present method, four particles were placed in the FCC pattern in a cubic periodic domain of length (10π/3) 1/3 .…”

Section: Results Of Test Casesmentioning

confidence: 99%

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Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Vreman

2016

J. Fluid Mech.

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A statistically stationary homogeneous isotropic turbulent flow modified by 64 small fixed non-Stokesian spherical particles is considered. The particle diameter is approximately twice the Kolmogorov length scale, while the particle volume fraction is 0.001. The Taylor Reynolds number of the corresponding unladen flow is 32. The particle-laden flow has been obtained by a direct numerical simulation based on a discretization of the incompressible Navier-Stokes equations on 64 spherical grids overset on a Cartesian grid. The global (space-and time-averaged) turbulence kinetic energy is attenuated by approximately 9 %, which is less than expected. The turbulence dissipation rate on the surfaces of the particles is enhanced by two orders of magnitude. More than 5 % of the total dissipation occurs in only 0.1 % of the flow domain. The budget of the turbulence kinetic energy has been computed, as a function of the distance to the nearest particle centre. The budget illustrates how energy relatively far away from particles is transported towards the surfaces of the particles, where it is dissipated by the (locally enhanced) turbulence dissipation rate. The energy flux towards the particles is dominated by turbulent transport relatively far away from particles, by viscous diffusion very close to the particles, and by pressure diffusion in a significant region in between. The skewness and flatness factors of the pressure, velocity and velocity gradient have also been computed. The global flatness factor of the longitudinal velocity gradient, which characterizes the intermittency of small scales, is enhanced by a factor of six. In addition, several point-particle simulations based on the Schiller-Naumann drag correlation have been performed. A posteriori tests of the point-particle simulations, comparisons in which the particle-resolved results are regarded as the standard, show that, in this case, the point-particle model captures both the turbulence attenuation and the fraction of the turbulence dissipation rate due to particles reasonably well, provided the (arbitrary) size of the fluid volume over which each particle force is distributed is suitably chosen.

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Section: Results Of Test Casesmentioning

confidence: 99%

Section: Results Of Test Casesmentioning

confidence: 99%

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Vreman

2016

J. Fluid Mech.

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“…In such cases, the fluid flow time scales are much shorter than the time scales over which particle configurations change so that one can view drag as the result of the gas flowing through static (and random) assemblies of particles. Nowadays fully resolved simulations of fluid flow through assemblies of static particles are standard routine [19][20][21][22] and a great many correlations have been proposed based on such simulations. As shown by [23], the situation for liquid-solid systems that have low to intermediate Stokes numbers is very different.…”

Section: Modelling Assumptions and Proceduresmentioning

confidence: 99%

Assessing Eulerian–Lagrangian simulations of dense solid-liquid suspensions settling under gravity

Derksen

2018

Computers & Fluids

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We study dense solid-liquid suspensions through numerical simulations. The liquid flow is solved by the lattice-Boltzmann method on a fixed (Eulerian), cubic, uniform grid. Spherical solid particles are tracked through that grid. Our main interest is in cases where the grid spacing and the particle diameter have the same order of magnitude (Critical issues then are the mapping operations that relate properties on the grid and properties of the particles, e.g. the local solids volume fraction seen by a particle, or the distribution of solid-to-liquid hydrodynamic forces over grid points adjacent to a particle.For assessing the mapping operations we compare results for particles settling under gravity in fully periodic, three-dimensional domains of simulations with ( )

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“…Fully resolved simulations of flow through fixed arrangements of spherical particles have allowed for parametrization of the effective drag coefficient for a wide range of Θ p and Re p , and recently several relationships for C d (Re p , Θ p ) have been proposed (see Tang et al (2015) for a recent review). For this work, the correlation of Tenneti, Garg & Subramaniam (2011) is chosen because (i) it is valid up to Re p = 300 and (ii) it has been developed as a correction to the dilute limit, C d (Re p , 0), rather than the low-Reynolds-number limit, C d (0, Θ p ). This attribute allows particle shape effects to be more easily incorporated into the drag law by, for example, specifying the C d (Re p , 0) relationship for angular natural sand particles (Fredsøe & Deigaard 1992) rather than the typical relation for smooth spherical particles (Schiller & Naumann 1935).…”

Section: Hydrodynamic Forcesmentioning

confidence: 99%

Particle based modelling and simulation of natural sand dynamics in the wave bottom boundary layer

Finn

Apte

2016

J. Fluid Mech.

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Sand transport and morphological change occur in the wave bottom boundary layer due to sand particle interactions with an oscillatory flow and granular interactions between particles. Although these interactions depend strongly on the characteristics of the particle population, i.e. size and shape, little is known about how natural sand particles behave under oscillatory conditions and how variations in particle size influence transport behaviour. To enable this to be studied numerically, an Euler-Lagrange point-particle model is developed which can capture the individual and collective dynamics of subaqueous natural sand grains. Special treatments for particle collision, friction and hydrodynamic interactions are included to take into account the wide size and shape variations in natural sands. The model is used to simulate sand particle dynamics in two asymmetric oscillatory flow conditions corresponding to the vortex ripple experiments of Van der Werf et al. (J. Geophys. Res., vol. 112, 2007, F02012) and the sheet-flow experiments of O'Donoghue & Wright (Coast. Engng, vol. 50, 2004, pp. 117-138). A comparison of the phase resolved velocity and concentration fields shows overall excellent agreement between simulation and experiments. The particle based datasets are used to investigate the spatio-temporal dynamics of the particle-size distribution and the influence of three-dimensional vortical features on particle entrainment and suspension processes. For the first time, it is demonstrated that even for the relatively well-sorted medium-size sands considered here, the characteristics of the local grain size population exhibit significant space-time variation. Both conditions demonstrate a distinct coarse-over-fine armouring at the bed surface during low-velocity phases, which restricts the vertical mobility of finer fractions in the bed, and also results in strong pickup events involving disproportionately coarse fractions. The near-bed layer composition is seen to be very dynamic in the sheet-flow condition, while it remains coarse through most of the cycle in the vortex ripple condition. Particles in suspension spend more time sampling the upward directed parts of these flows, especially the smaller fractions, which delays particle settling and enhances the vertical size sorting of grains in suspension. For the submillimetre grain sizes considered, most † Email address for correspondence: J.Finn@liv.ac.uk

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Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres

Cited by 377 publications

References 60 publications

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

Assessing Eulerian–Lagrangian simulations of dense solid-liquid suspensions settling under gravity

Particle based modelling and simulation of natural sand dynamics in the wave bottom boundary layer

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