Single Particle Settling Research Articles

A fully-resolved LBM-LES-DEM numerical scheme for adhesive and cohesive particle-laden turbulent flows in three dimensions

Adhesive and cohesive particle-laden turbulent flows play a crucial role in numerous natural and industrial processes. Herein, a fully-resolved LBM-LES-DEM numerical scheme is developed for a better understanding of these flows in three dimensions. This numerical scheme is four-way coupling, where the adhesive and cohesive forces, such as van der Waals force, capillary force and viscous force, are embedded into DEM to simulate adhesive and cohesive particle-particle interactions, and the MRT-D3Q19 LBM is combined with LES based on the Smagorinsky model to simulate turbulent fluid flows, and the fluid-particle interactions are solved by momentum exchange method. Several benchmarks, such as 3D duct flow, single particle settling, and DKT processes, are validated, and the dynamics of particle pair in turbulent structures are further discussed. All the results indicate that this numerical scheme provides a promising method for the simulation of adhesive and cohesive particle-laden turbulent flows.

An improved semi-resolved computational fluid dynamics-discrete element method for simulating liquid–solid systems with wide particle size distributions

Vertical hydraulic transport of particles with wide particle size distributions is a crucial process for coal physical fluidized mining. In the present study, an improved semi-resolved computational fluid dynamics (CFD)-discrete element method was developed to simulate particle flows with wide particle size distributions. In this model, the CFD cells allocated to the particle volume and the momentum source term were defined as the dependent domain and the influential domain, respectively. On this basis, the two-way domain expansion method and the one-way domain expansion method were adopted for the liquid–solid simulation of coarse and fine particles, respectively. The dependent domain expansion coefficient and the influential domain expansion coefficient were proposed to determine the spatial range of the dependent domain and influential domain for the coarse particles, and the optimal modeling strategy for the dependent domain and influential domain expansion coefficient for the coarse particles was determined. Furthermore, a volume expansion method and a momentum source expansion method were proposed for calculating the solid volume fraction of the dependent domain and the source term of the influential domain for the coarse particles. Furthermore, the sample point method was adopted to obtain the solid volume fraction in the dependent domain for the fine particles, and the momentum source term was only updated to the particle-located cell. Subsequently, single-particle settling and binary-particle fluidizing numerical experiments were used to verify the calculation accuracy of the model. The investigation can provide a new method for numerical simulation of liquid–solid flow with wide particle size distributions.

Development of Particle Resolved - Subgrid Corrected Simulations: Hydrodynamic force calculation and flow sub-resolution corrections

Particle Resolved - Direct Numerical Simulation (PR-DNS) of fluid–solid particles is conducted to study hydrodynamic interactions at the interface between phases. An original distinction is proposed between Particle Resolved Simulation (PRS) and Particle Resolved - Direct Numerical Simulation (PR-DNS). In PR-DNS, velocity gradients and pressure are fully resolved, which required several dozens of meshes in the diameter of the particles (40 in Stokes configuration), whereas for PRS, with grid resolution of 10 meshes per diameter, the gradients are only partly resolved, resulting in a sub-resolution of hydrodynamic forces exerted by the fluid to the interface of solid particles. The very high computational cost, associated to PR-DNS, limits its application to academic cases, even though, it was originally developed to study the collective physical effects of a fluid–particle assembly. It explains why numerous simulations with a grid resolution of only a dozen meshes in the particle’s diameter – typically between 10 and 16 – referred to here as PRS, can be found in the literature. In these cases, the velocity gradients and pressure are not accurately computed, inducing an error in the hydrodynamic forces exerted by the fluid to the interface of particles. This paper aims to clarify the hydrodynamic interactions at this scale for a single particle settling in an infinite medium under Stokes configuration. For this purpose, an original method, designed for solid particles, is proposed to compute hydrodynamic forces. A mesh-dependent correlation is then built to numerically correct the partially resolved hydrodynamic forces obtained with PRS, in what we call Particle Resolved - Subgrid Corrected Simulations (PR-SCS). Finally, the correction is assessed for various Reynolds numbers and density ratios under the Stokes assumption.

In situ measurement of hindered settling function in decanter centrifuge by periodic segmentation technique in wireless electrical resistance detector (psWERD)

In situ measurement of hindered settling function Hϕ as a function of particle volume fraction ϕ in a decanter centrifuge has been proposed by periodic segmentation technique in wireless electrical resistance detector (psWERD). The processes to calculate Hϕ has three steps which are (1) segmentation of measured resistance R(z,t) in three settling periods; (2) elimination of the screw conveyor’s (SC’s) adverse effect; (3) calculation of ϕ which is important to determine the in situ hindered settling velocity uhinins and calculation of the proposed uhinfit from the proposed Hϕ. In the 1st step, R(z,t) are segmented based on the phases of liquid L, screw S, and particle P under three settling periods which are pre settling (pre), transient settling (tran), and post settling (post). In the 2nd step, the segmented R(z,t) is categorized by fourier transfrom (FT) based on the frequency of the liquid fL, screw fS, and liquid-particle fLP phases with a focus on eliminating SC’s adverse effect which causes fluctuating R(z,t). In the 3rd step, the ϕz,t is obtained by applying the effective medium theory (EMT) based on the conductivity of each phase which are liquid σ¯L, particle σP, and slurry σLPz,t. Each conductivity is calculated based on the average liquid resistance R¯Lz, the static particle resistance RP under closed-pack particle volume fraction ϕcp, and the slurry (liquid-particle) resistance RLPz,t from the 2nd step. Afterward, the uhinins is obtained from the distribution of ϕ which refers to the length parameter in the settling radius rset. Hence, the uhinins is calculated by time t needed for particle to settle from ϕ0 to ϕcp in tran. The proposed Hϕ is developed by considering the influence of ϕcp and the increasing distribution of ϕ due to the particle settling which is presented by fitting parameters of k and p. Take into account the importance of single particle settling in Stokes settling velocity uSt, the proposed uhinfit is determined by calculating the uSt and fitting parameters in the Hϕ to fit the uhinins. To evaluate the psWERD, a decanter centrifuge was used in the industrial scale experiment by appliying three operational parameters which are types of SC, centrifugal forces G, and the differential speeds ω. Two types of SC which are SC1 and SC2 were used to investigate the effect of G to the in situHϕ under constant ω. While SC2 was used to investigate the effect of ω to the insituHϕ under contant G. The in situ measurement is conducted in three measurement points z which represents the particle settling condition at different locations. In order to verify the experiment results, simulation on electrical measurement in the boundary of particle sensitivity area APSA of psWERD and on particle settling behavior in centrifugal fields are done by Multiphysic software. As a result, the psWERD is successful in determining the best fitting parameters for the in situHϕ with good average root mean square error 〈RMSE¯〉≤10-3. The in situHϕ also has a good agreement to the previous work of Hϕ determined in decanter centrifuges with the similar operational condition. Finally, the Hϕ shows the potential for evaluating the in situ separation process in decanter centrifuges under specific operational conditions.

A resolved CFD-DEM coupling model for modeling two-phase fluids interaction with irregularly shaped particles

In this paper, we develop a resolved coupling model to simulate interaction between two-phase fluids and irregularly shaped particles by using Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM). The Volume of Fluid (VoF) method is introduced to solve two-phase fluids, and irregularly shaped particles are represented by multi-sphere clumps in DEM. The resolved CFD-DEM coupling approach calculates meso-scale flow around particles, and an integration scheme is proposed to directly calculate the fluid forces on multi-sphere particles without resorting to empirical drag force models. A number of benchmark cases are conducted, including a single particle settling in a two-phase fluid, settling of two particles, disk-shaped particles and irregularly shaped particles. The numerical simulations compare well with experimental works and previous studies, showing the accuracy of this model. Finally, a case study of dambreak wave impact on a rock pile demonstrates great potential to apply this model in coastal engineering.

A Coupled CFD-DEM Model for Resolved Simulation of Filter Cake Formation during Solid-Liquid Separation

In cake filtration processes, where particles in a suspension are separated by forming a filter cake on the filter medium, the resistances of filter cake and filter medium cause a specific pressure drop which consequently defines the process energy effort. The micromechanics of the filter cake formation (interactions between particles, fluid, other particles and filter medium) must be considered to describe pore clogging, filter cake growth and consolidation correctly. A precise 3D modeling approach to describe these effects is the resolved coupling of the Computational Fluid Dynamics with the Discrete Element Method (CFD-DEM). This work focuses on the development and validation of a CFD-DEM model, which is capable to predict the filter cake formation during solid-liquid separation accurately. The model uses the Lattice-Boltzmann Method (LBM) to directly solve the flow equations in the CFD part of the coupling and the DEM for the calculation of particle interactions. The developed model enables the 4-way coupling to consider particle-fluid and particle-particle interactions. The results of this work are presented in two steps. First, the developed model is validated with an empirical model of the single particle settling velocity in the transition regime of the fluid-particle flow. The model is also enhanced with additional particles to determine the particle-particle influence. Second, the separation of silica glass particles from water in a pressurized housing at constant pressure is experimentally investigated. The measured filter cake, filter medium and interference resistances are in a good agreement with the results of the 3D simulations, demonstrating the applicability of the resolved CFD-DEM coupling for analyzing and optimizing cake filtration processes.

An efficient framework for particle-fluid interaction using Discrete Element Lattice Boltzmann Method: Coupling scheme and periodic boundary condition

Discrete modeling of particle-fluid interaction was of great importance for its wide applications in chemical, petroleum and geotechnical engineering. Using Immersed Boundary Method (IBM) to couple Discrete Element Method (DEM) with Lattice Boltzmann Method (LBM) was adopted by many researchers to study particle-fluid systems. However, to accurately simulate the behavior of a large number of particles in the fluid, a huge computational power wasrequired to fully resolved the motion of each particle and an intensive search of particles’ contacts was needed to account for the collision between particles. In this paper, a periodic boundary was proposed for coupling DEM with LBM using IBM and an efficient particle contact detection algorithm was developed to further reduce the computation cost. The model was validated by several well-defined benchmark including: a single particle settling in a box, particle spinning in a channel and the well-known ‘Drafting, Kissing and Tumbling’ (DKT) effect of two settling disks. The model's applicability was exhibited in the simulation of sediments movement in a channel, which agreed well with previous experiments. These results showed the potential usage of present numerical model to investigate in particle-fluid interaction systems.

A Unique Settling Pattern for Two Circular Particles Having Different Densities

In this work the sedimentation of two circular particles having different densities in a vertical channel has been numerically studied using the lattice Boltzmann method (LBM). The case of a single particle settling in a narrow channel has been simulated to validate the computational code. The relationship between the Reynolds number and the particle-to-fluid density ratio was presented. For the case of two particles, a unique pattern of motion, represented by the process of “drafting-kissing-oscillating-separating”, has been revealed. The vortex structures along with the particle displacements are shown to illustrate this pattern.

An efficient Discrete Element Lattice Boltzmann model for simulation of particle-fluid, particle-particle interactions

In this study, an efficient Discrete Element Lattice Boltzmann Model (DE-LBM) is introduced to simulate mechanical behaviours of multiphase systems involving particle-fluid and particle-particle interactions. The LBM is based on the Multiple Relaxation Time (MRT-LBM) formalism for the fluid phase and the Discrete Element Method for particle motions. A novel algorithm is developed for detecting the particle contact base on particle overlapping areas computed directly from the grid-based LBM data. This contact algorithm achieves the same accuracy in determining the particle contact as provided by the Hertz contact model but is far more efficient computationally. The DE-LBM coupling approach is also modified to unify the different schemes developed previously. A modified Verlet List method for updating the solid occupation fraction is proposed to further speed up the simulation. The new model is validated by a series of simulations including the single particle settling and well-known ‘Drafting, Kissing and Tumbling’ (DKT) phenomenon found in suspensions. The settling of a large number (2500) of particles in a still fluid is also simulated with predicted concentration profiles matching well the analytic solution. These applications demonstrate the potential of the present DE-LBM model as a powerful numerical tool for simulating multiphase particulate systems encountered in many engineering and science disciplines.

Validation of fluid–particle interaction force relationships in binary-solid suspensions

In this work several relationships governing solid–fluid dynamic interaction forces were validated against experimental data for a single particle settling in a suspension of other smaller particles. It was observed that force relationships based on Lattice-Boltzmann simulations did not perform as well as other interaction types tested. Nonetheless, it is apparent that, in the case of a suspension of different particle types, it is important that the correct choice is made as to how the contribution to the overall fluid–particle interaction force is split between buoyancy and drag. Experimental evidence clearly suggests that the “generalized” Archimedes’ principle (where the foreign particle is considered to displace the whole suspension and not just the fluid) provides the best result.

Convective instability in sedimentation: 3-D numerical study

To provide a probable explanation on the field observed rapid sedimentation process near river mouths, we investigate the convective sedimentation in stably stratified saltwater using 3-D numerical simulations. Guided by the linear stability analysis, this study focuses on the nonlinear interactions of several mechanisms, which lead to various sediment finger patterns, and the effective settling velocity for sediment ranging from clay (single-particle settling velocity V0 = 0.0036 and 0.0144 mm/s, or particle diameter d = 2 and 4 μm) to silt (V0 = 0.36 mm/s, or d = 20 μm). For very fine sediment with V0 = 0.0036 mm/s, the convective instability is dominated by double diffusion, characterized by millimeter-scale fingers. Gravitational settling slightly increases the growth rate; however, it has notable effect on the downward development of vertical mixing shortly after the sediment interface migrates below the salt interface. For sediment with V0 = 0.0144 mm/s, Rayleigh-Taylor instabilities become dominant before double-diffusive modes grow sufficiently large. Centimeter-scale and highly asymmetric sediment fingers are obtained due to nonlinear interactions between different modes. For sediment with V0 = 0.36 mm/s, Rayleigh-Taylor mechanism dominates and the resulting centimeter-scale sediment fingers show a plume-like structure. The flow pattern is similar to that without ambient salt stratification. Rapid sedimentation with effective settling velocity on the order of 1 cm/s is likely driven by convective sedimentation for sediment with V0 greater than 0.1 mm/s at concentration greater than 10–20 g/L.

Numerical investigation on the role of discrete element method in combined LBM–IBM–DEM modeling

Particle collisions play a very important role in determining the fluid–particle multiphase flow, and thus it is crucial to treat the particle–particle interaction using a felicitous method in numerical simulations. A novel combined lattice Boltzmann method (LBM)–immersed boundary method (IBM)–discrete element method (DEM) scheme is presented in this study with its application to model the sedimentation of 2D circular particles in incompressible Newtonian flows. The hydrodynamic model of the incompressible Newtonian flow is based on the Bhatnagar–Gross–Krook LBM, and a momentum exchange-based IBM is adopted to calculate the fluid–solid interaction force. The kinematics and trajectory of the discrete particles are evaluated by DEM, in which the particle–particle interaction rules are governed by theoretical contact mechanics to enable the direct use of real particle properties. This eliminates the need of artificial parameters and also improves the reliability of the numerical results. By using a more accurate and physical description of particle interaction, a ‘safe zone’ or threshold is also no longer required. Case studies of single particle settling in a cavity, and two particles settling in a channel were carried out, the velocity characteristics of the particle during settling and near the bottom were examined. A numerical example of sedimentation involving 504 particles was finally presented to demonstrate the capability of the combined scheme.

Experimental Research on the Characteristics of Bamboo Powder Model Sediment

Physical characteristics (including unit weight, dry unit weight and submarine rest angle) and motion characteristics (including settlement characteristics, incipient velocity and resistance characteristics) of bamboo powder model sediment were studied by test in this paper. Experimental study on physical characteristics showed that particle size variation had little effect on unit weight, dry unit weight increased with the particle size,submarine rest angle increased with the decrease in particle size and an empirical formula for calculating submarine rest angle of bamboo powder model sediment was proposed. Experimental study on motion characteristics found that the single particle settling velocity of bamboo powder model sediment increased with particle size, the relative settling velocity initially increased and then decreased with sediment concentration, the incipient velocity increased with the particle size and water depth, the roughness decreased with water depth and increased with the flow velocity and an empirical formula for calculating the incipient velocity of bamboo powder model sediment is proposed.

Experimental investigation of single particle settling in turbulence generated by oscillating grid

Abstract In this study, turbulence influence on the settling behavior of solid particles was investigated experimentally in confined turbulent aquatic environment generated by oscillating grid. An enhanced PIV system was employed to conduct simultaneous velocity measurements of individual settling particles and ambient fluid. Grains varying in shape (spherical and cylindrical) and diameter (2.78–7.94 mm) were tested with different turbulent conditions. The results showed clearly that the settling behavior of particles subjected to turbulence is significantly modified. First, the settling velocity modification is closely correlated to the mean vertical velocity of the fluid zone (very close to the settling particle), which in size is in the order of a few particle diameters. Second, the relative settling velocity is smaller than the still water terminal velocity for the most cases. Lastly, the fluctuation in the settling velocity is significantly increased, as compared to the still water conditions, and clearly dependent on the turbulence intensity. The experimental data were also analyzed with dimensional considerations. By comparing to literature, turbulence effects on the relative settling velocity were discussed with regard to Stokes number, Richardson number and dimensionless turbulence length scale. Finally, a simple analytical model was proposed for estimating the turbulence-modified settling velocity.

Milling and separation of the multi-component printed circuit board materials and the analysis of elutriation based on a single particle model

Electronic waste, in the form of printed circuit boards (PCBs) or printed wiring boards (PWBs), represents a significant and growing fraction of the waste generated in many communities. It is necessary to identify schemes to manage and dispose this waste in an environmentally safe manner. The present work, examines the use of mechanical means to separate the metallic and non-metallic components present in PCBs. The unique characteristics of PCB construction pose challenges to the mechanical means of separation. In view of these unique characteristics of PCBs, an empirical approach is suggested to evaluate the effectiveness of the mechanical separation process. Two milling operations were used to obtain the feed for the separation using elutriation. Compositions of different size fractions from the milling operations are presented. Experimental data from the separation process is presented and the extent of use of mechanical means that results in optimum separation is identified. The separation efficiency is analyzed in terms of composition, particle size and operating condition of the elutriation flow rate. A probabilistic analysis based on single particle settling velocity shows that separation results with uniform particle size fraction can be described effectively. However, the probabilistic analysis captures only the qualitative features with mixed particle sizes and components.

Local penalty methods for flows interacting with moving solids at high Reynolds numbers

An original numerical modelling of multiphase flows interacting with solids in unsteady regimes is presented. Based on the generalized Navier–Stokes equations for multiphase flows and Volume of Fluid (VOF) formulations, an Uzawa minimization algorithm is implemented for the treatment of incompressibility and solid constraints. Augmented Lagrangian terms are added in the momentum equations to speed the convergence of the iterative solver. Defining a priori the penalty parameters which are dedicated to incompressibility and solid constraints is difficult, or impossible, as soon as the flow involves more than one phase and inertia becomes predominant compared to viscous and gravity forces. The Lagrangian penalty terms are calculated automatically according to an original local estimate of the various physical contributions. Numerical validations have been carried out for single particle settling in confined media and viscous flow through a fixed Cubic Faced Centered array. A very good agreement is obtained between experimental, theoretical and numerical results. Extension to unsteady free surface flow interacting with particles is illustrated with the simulation of a dam break flow over moving obstacles.

On the accuracy of upper ocean particulate organic carbon export fluxes estimated from 234Th/ 238U disequilibrium

An analysis of the 234Th method for determining the export flux of particulate organic carbon ( P POC) from the upper ocean using in situ pumps or water bottles shows that the accuracy of the method (the ratio of the experimental value of P POC divided by the true POC flux, F POC), defined as the p-ratio, is equal to the mean settling velocity of particulate 234Th divided by that of POC. Therefore, P POC is equivalent to the true POC flux ( F POC) and the p-ratio is equal to unity if, and only if, POC and particulate 234Th have the same mean sinking velocities. A simple particle settling model is discussed that invokes Stokes’ Law settling velocities, volume:surface area ( V:SA) fractionation of C: 234Th and two assemblages of particles having different sizes and densities. The model is used to illustrate the ranges of parameter values that conform to values of the p-ratio sufficiently close to unity that the experimentally determined POC flux can be considered to be an accurate representation of the true POC flux. Despite the over-simplification of real systems implicit in the model, the results suggest that p-ratios<1, equivalent to an under-estimate of the POC flux, are representative of single particle settling regimes in which the larger particles dominate the vertical flux. This follows from the assumption that the ratio of C/ 234Th on particles is governed by the volume to surface area ( V:SA) ratio of the particles. This results in a greater proportion of 234Th compared to C being associated with the smaller, more slowly settling particles and, as a result, normalization of the POC flux to the 234Th flux provides an under-estimate of the former quantity. However, when the smaller particle assemblage dominates the vertical flux, as could occur in open ocean regimes having high aeolian inputs of dense, rapidly settling, inorganic particles, then the p-ratio could exceed unity ( p-ratio >1) resulting in an over-estimate of the POC flux using the 234Th method. High levels of flocculation associated with phytoplankton blooms in productive regions of the ocean are likely to produce p-ratios approaching unity, because flocs would tend to preserve the V:SA partitioning of the original particle size distribution and thereby minimize differences in the mean settling speeds of POC and particulate 234Th (Waite, A.W., Hill, P.S., 2006. Flocculation, phytoplankton and the accuracy of 234Th-based estimates of the vertical flux of particulate organic carbon in the sea. Marine Chemistry in press). Selective sampling of the large particle fraction using, for example, 53-μm screens can produce a more accurate estimate of the true POC flux, but may not entirely shift the p-ratio to a value of unity.

Direct numerical simulation of the sedimentation of solid particles with thermal convection

Dispersed two-phase flows often involve interfacial activities such as chemical reaction and phase change, which couple the fluid dynamics with heat and mass transfer. As a step toward understanding such problems, we numerically simulate the sedimentation of solid bodies in a Newtonian fluid with convection heat transfer. The two-dimensional Navier–Stokes and energy equations are solved at moderate Reynolds numbers by a finite-element method, and the motion of solid particles is tracked using an arbitrary Lagrangian–Eulerian scheme. Results show that thermal convection may fundamentally change the way that particles move and interact. For a single particle settling in a channel, various Grashof-number regimes are identified, where the particle may settle straight down or migrate toward a wall or oscillate laterally. A pair of particles tend to separate if they are colder than the fluid and aggregate if they are hotter. These effects are analysed in terms of the competition between the thermal convection and the external flow relative to the particle. The mechanisms thus revealed have interesting implications for the formation of microstructures in interfacially active two-phase flows.

Simulation of the sedimentation of melting solid particles

This study is motivated by the fact that dispersed two-phase flows are often accompanied by interfacial activities such as chemical reaction and phase change. Toward an understanding of the role of interfacial transport, we numerically simulate the sedimentation of melting solid particles in a Newtonian fluid. The fluid flow and solid motion determine the fluid–solid heat transfer and hence the melting rate. The thermal convection and interfacial morphology, in return, affect the motion of both phases. The two-dimensional Navier–Stokes and energy equations are solved at moderate Reynolds numbers by a finite-element method, and the melting interface is determined from the local heat flux. The motion of each solid particle is tracked using an arbitrary Lagrangian–Eulerian scheme. Results show that the sedimentation of melting particles is largely governed by the competition between the upward flow of the warm upstream fluid and the downward flow of the cold melt. A single particle settling in a channel may be pushed away from the centerline toward the wall. A pair of particles interact in a complex way, separating at low Grashof number Gr and attracting each other at high Gr. These results have interesting implications for the formation of microstructures in interfacially active two-phase flows.

Unexpected phenomena observed in particle settling in non-Newtonian media

Particle settling experiments are seemingly simple but a number of surprising phenomena have been observed in the past. A review of observations on exceedingly long (when compared to the relaxation time of the fluid) velocity transients and time effects is presented. This is complemented with new experimental results on time effects in shear-thinning fluids which are very surprising indeed for Carbopol which on a time scale of hours shows no relaxation of the wake structure at all. In fact the opposite occurs: the time effects seems to become stronger. Also the effect of shear flow on single particle settling is considered. It is shown that for shear-thinning gel-like fluids it is possible to calculate the settling velocity if the viscosity at the prevailing shear rate is entered into Stokes' Law. For shear-thinning gluids which display a low shear rate viscosity plateau this appeared to be possible only in the Newtonian range of shear rates whereas at higher rates, in the shear-thinning regime, the particles settle more slowly than calculated on the basis of the viscosity alone. Experiments with two, or more, settling particles indicate that the interaction between particles is complicated by the time effects in the wake of the leading particle. Also elastic effects are shown to be important and in our experiments seem to cause particle dispersion by themselves.