Simulation of solid—liquid flows in a vertical pipe by a collision model

Asakura, Kuniomi; Asari, Tetsuhiro; Nakajima, Ikutaro

doi:10.1016/s0032-5910(97)03294-4

Cited by 20 publications

(18 citation statements)

References 3 publications

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“…Singh et al [13] proposed another repulsive force model which allows the particles to come arbitrarily close and even slightly to overlap each other. In addition to using the concept of repulsive forces to construct collision models, there are also other ways to form such models, for example, conservation collision models which are based on the conservation of linear momentum and kinetic energy [14], lubrication collision models [15] and stochastic collision models [16] which are based on physical properties of the particles, as well as semi-experiential collision models [17], etc. In this paper, following those models proposed by Glowinski, Joseph, Singh and coauthors, we describe a new repulsive force model which cannot only prevent the particles from getting too close to each other, it can also deal with the case of particle overlapping when numerical simulations bring the particles very close or even overlapping due to unavoidable numerical truncation errors.…”

Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method

Wan

Turek

2005

Numerical Methods in Fluids

150

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SUMMARYDirect numerical simulation techniques for particulate ow by the ÿctitious boundary method (FBM) are presented. The ow is computed by a multigrid ÿnite element solver and the solid particles are allowed to move freely through the computational mesh which can be chosen independently from the particles of arbitrary shape, size and number. The interaction between the uid and the particles is taken into account by the FBM in which an explicit volume based calculation for the hydrodynamic forces is integrated. A new collision model based on papers by Glowinski, Joseph, Singh and coauthors is examined to handle particle-particle and particle-wall interactions. Numerical tests show that the present method provides a very e cient approach to directly simulate particulate ows with many particles.

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Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method

Wan

Turek

2005

Numerical Methods in Fluids

150

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“…The Lagrangian coupling method was employed and Table I summarizes the parameter settings for the sand (Asakura et al, 1997). The Lagrangian coupling method was employed and Table I summarizes the parameter settings for the sand (Asakura et al, 1997).…”

Section: Mathematical Model and Simulation Methodsmentioning

confidence: 99%

Influence of Dentation Angle of Labyrinth Channel of Drip Emitters on Hydraulic and Anti‐Clogging Performance

Liu

et al. 2018

Irrigation and Drainage

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The geometric parameters of labyrinth channels play an important role in the hydraulic and anti‐clogging performance of drip emitters. In this study, the flow fields, individual representative sands and sand groups in the labyrinth channel of emitters, with dentation angles of 90°, 60°, 45° and 30°, were firstly simulated using a computational fluid dynamics discrete element method (CFD–DEM) of coupling. Particle tracking velocimetry (PTV) was used to trace individual representative sands. The numerical results were verified with clear water hydraulic performance tests and muddy water anti‐clogging performance tests. The results suggest that the discharge coefficient and flow exponent declined when the dentation angle of the labyrinth channel was reduced. A large number of sand groups were observed to enter the vortex areas and move in a circular manner. The time it took for particles to pass through the labyrinth channel lengthened when the velocity decreased and as a result, the probability of emitter clogging increased. Therefore, by using a recommended angle range of 90° to 60° and a combined higher hydraulic performance level, emitters were less likely to clog. It was a novel approach to adopt a CFD–DEM coupling method to conduct numerical analysis of individual sand particles and sand groups in the investigation of emitter anti‐clogging issues. The findings will increase the design efficiency of flow channels and will save human and material resources. © 2018 John Wiley & Sons, Ltd.

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“…The lift force acting on spherical particles in shear flow is in opposite direction to the flow and it is expressed (Arnold et al, 1989) as (5.87) where C L is the lift coefficient that depends on particle Reynolds number (Asakura et al, 1997) and C L ϭ 0.25 for dilute suspension flows including spherical particles. The term (ٌ ϫ V Ϫ c ) in the equation is the liquid flow vorticity due to rotational motion of particles and is proportional to the lift force.…”

Section: Averaged Interfacial Forcesmentioning

confidence: 99%

Modeling the Flow of Settling Suspensions

2008

Solid-Liquid Two Phase Flow

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Flow of settling particles differs substantially from the flow of nonsettling particles in three basic aspects: need for averaging, flow pattern formation, and extension of the concept of interface. Since the particles tend to settle during transport through the pipe, different packing densities exist in the radial direction of the pipe in horizontal flow. Averaging techniques have to be developed to be able to use Navier-Stokes equations to model the flow behavior. Variation of compaction densities of the particles in the radial direction causes the formation of different flow behaviors of particles to arise within the same cross-sectional area. The segregation of particles into different sections necessitates an extension of the concept of the interface. Along with the solid-liquid interfaces on the surface of the particles, interfaces also exist between layers of different compactions in the pipe. The variations in these interfaces should also be taken into account in the momentum balance equation. The mathematical methods and models used in describing two-phase flow will be taken up in this chapter. BASIC CONCEPTS IN MODELING OF TWO-PHASE FLOWWhatever the flow pattern that exists in solid-liquid two-phase flow an interface between the solid particles and the liquid is always present. Besides the phase interface between the solids and the liquid, another type of interface is defined between layers of a flowing suspension with different compaction levels.There are two main approaches used in flow models, the Lagrangian and Eulerian approaches. These approaches are initially explained for a single-phase (fluid) flow and then for homogeneous solid-liquid suspension flow. Eulerian and Lagrangian approaches for single-phase flowIn the Eulerian approach, a control volume is fixed in space (constant x, y, and z) through which the fluid flows. However, the control volume moves with the fluid in the Lagrangian approach with a velocity equal to that of the fluid stream V.The difference in the Eulerian and Lagrangian approaches can best be illustrated with the continuity equation. The continuity equation in Eulerian form is derived by using a 291

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Simulation of solid—liquid flows in a vertical pipe by a collision model

Cited by 20 publications

References 3 publications

Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method

Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method

Influence of Dentation Angle of Labyrinth Channel of Drip Emitters on Hydraulic and Anti‐Clogging Performance

Modeling the Flow of Settling Suspensions

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