Hindered Settling Effect Research Articles

Study on the Application of a Reflux Classifier in the Classification of Ultrafine Ilmenite

Mineral classification is an important preparation operation in the process of beneficiation. The classification effect directly affects the production capacity of grinding machines, product quality, subsequent separation of the concentrate grade, and recovery. To improve mineral classification accuracy and provide technical ideas for enriching the separation of fine materials, this paper proposes the use of a trapezoidal inclined channel agitated reflux classifier (TARC) to classify ultra-fine ilmenite. The principle of this separating system is based on a hindered settling effect and fluidization theory. This study focuses on the factors influencing the particle separation through the optimization of different experimental conditions. A satisfactory 10 µm classification efficiency of 67.89% could be obtained when the ore pulp concentration was 15%, the agitation speed was 350 r/min, and the underflow flux was 16 cm3/min. The TARC realized a continuous feeding classification of fine particles within a narrow particle size range, with 10 µm as the limit size, and an effective reduction in the entrainment of fine particles in the underflow and coarse particles in the overflow phenomena, thus achieving improved classification efficiency.

Generalized non-equilibrium suspended sediment transport model with hindered settling effect for open channel flows

The present paper formulates a generalized model for non-equilibrium suspended sediment transport through an open channel turbulent flow that contains all the existing models in literature as special cases. The two-dimensional (2D) unsteady model for suspended concentration distribution contains the effect of hindered settling and the bottom boundary condition considers deposition velocity together with equilibrium bottom concentration. OpenFOAM, an open-source Finite Volume (FV) method based framework, has been used for the numerical approximation of the model. The proposed model addresses the non-linearity in the governing equation as well as the non-linearity in boundary conditions. Picard iteration approach has been utilized to ensure the convergence of the numerical solution. With different physical parameters and conditions, concentration profiles of suspended sediment particles have been analysed theoretically and graphically. It greatly extends the domain of the numerical solutions for determining sediment distribution in suspension through an open channel turbulent flow in a non-equilibrium state.

Blood, lead and spheres: A hindered settling equation for sedimentologists based on metadata analysis

AbstractA revision of the popular equation of Richardson and Zaki (1954a, Transactions of the Institute of Chemical Engineering, 32, 35–53) for the hindered settling of suspensions of non‐cohesive particles in fluids is proposed, based on 548 data sets from a broad range of scientific disciplines. The new hindered settling equation enables predictions of settling velocity for a wide range of particle sizes and densities, and liquid densities and viscosities, but with a focus on sediment particles in water. The analysis of the relationship between hindered settling velocity and particle size presented here shows that the hindered settling effect increases as the particle size decreases, for example, a 50% reduction in settling velocity is reached for 0.025 mm silt and 4 mm pebbles at particle concentrations of 13% and 25% respectively. Moreover, hindered settling starts to influence the settling behaviour of sediment particles at volumetric concentrations of merely a few per cent. For example, the particle settling velocity in flows that carry 5% silt is reduced by at least 22%. These observations suggest that hindered settling greatly increases the efficiency of natural flows to transport sediment particles, but also particulate carbon and pollutants, such as plastics, over large distances.

A Two‐Layer Numerical Model for Coastal Sheet‐Flow Sediment Transport

AbstractSheet‐flow sediment transport is an important topic for coastal sediment research. In this study, a two‐layer numerical model is proposed for coastal sheet‐flow sediment transport. The bottom pick‐up layer, in which sediment motion is usually treated as bedload transport, is resolved in an empirical way, so no bedload model is required. For the suspension layer, the model solves the turbulent diffusion equation for sediment concentration, while the hydrodynamic part is described by Reynolds‐averaged Navier‐Stokes equations. The damping of turbulence due to concentration gradient and the hindered settling effect due to particle‐particle interactions are both incorporated in the present model. A predetermined erosion depth is taken as an input for determining the no‐motion sand bed level. This two‐layer model is capable of describing the detailed spatial‐temporal variations of flow velocity and sediment concentration within the sheet‐flow layer, and the model's fidelity is comparable to that of some two‐phase‐flow models. A large campaign of model validation is carried out to demonstrate that the models works well for wave‐driven sheet‐flow sediment transport.

Semi-analytical solution for one-dimensional unsteady sediment transport model in open channel with concentration-dependent settling velocity

This paper aims to solve the one-dimensional unsteady suspended sediment transport equation in open channels through a semi-analytical approach. The presence of a large amount of particles in flow change the settling velocity of a particle, and this phenomenon, commonly known as hindered settling effect, must be taken into account to deal with high concentrated flows. Inclusion of this mechanism makes the governing equation nonlinear, and together with this nonlinear governing equation, a generalized bottom boundary condition is taken in terms of deposition velocity and equilibrium bottom concentration. An explicit series solution is presented using the method of lines based homotopy analysis method, and the convergence of the series solution is gained through a convergence control parameter. The solution is validated by comparing it with the existing solution as well as a numerical one. Apart from that, the solution has also been validated under a steady-state condition with available experimental data. Results are interpreted both graphically and physically. It is found that the hindered settling effect is dominant in the main flow region only, for sediment free inlet for all types of turbulent diffusion coefficients. On the other hand, in the case of uniform sediment concentration at the inlet, hindered settling affects the concentration in the top portion of the channel too for linear and parabolic profiles of turbulent diffusion coefficients.

Development of a two-phase SPH model for sediment laden flows

A SPH model based on a general formulation for solid–fluid two-phase flows is proposed for suspended sediment motion in free surface flows. The water and the sediment are treated as two miscible fluids, and the multi-fluid system is discretized by a single set of SPH particles, which move with the water velocity and carry properties of the two phases. Large eddy simulation (LES) is introduced to deal with the turbulence effect, and the widely used Smagorinsky model is modified to take into account the influence of sediment particles on the turbulence. The drag force is accurately formulated by including the hindered settling effect. In the model, the water is assumed to be weakly compressible while the sediment is incompressible, and a new equation of state is proposed for the pressure in the sediment–water mixture. Dynamic boundary condition is employed to treat wall boundaries, and a new strategy of Shepard filtering is adopted to damp the pressure oscillation. The developed two-phase SPH model is validated by comparing the numerical results with analytical solutions for idealized cases of still water containing both neutrally buoyant and naturally settling sand and for plane Poiseuille flows carrying neutrally buoyant particles, and is then applied to sand dumping from a line source into a water tank, where the sand cloud settles with a response of the free water surface. It is shown that the numerical results are in good agreement with the experimental data as well as the empirical formulas. The characteristics of the settling sand cloud, the pressure field, and the flow vortices are studied. The motion of the free water surface is also discussed. The proposed two-phase SPH model is proven to be effective for numerical simulation of sand dumping into waters.

Reprint of: A numerical investigation of fine sediment resuspension in the wave boundary layer—Uncertainties in particle inertia and hindered settling

The wave bottom boundary layer is a major conduit delivering fine terrestrial sediments to continental margins. Hence, studying fine sediment resuspensions in the wave boundary layer is crucial to the understanding of various components of the earth system, such as carbon cycles. By assuming the settling velocity to be a constant in each simulation, previous turbulence-resolving numerical simulations reveal the existence of three transport modes in the wave boundary layer associated with sediment availabilities. As the sediment availability and hence the sediment-induced stable stratification increases, a sequence of transport modes, namely, (I) well-mixed transport, (II) formulation of lutocline resembling a two-layer system, and (III) completely laminarized transport are observed. In general, the settling velocity is a flow variable due to hindered settling and particle inertia effects. Present numerical simulations including the particle inertia suggest that for a typical wave condition in continental shelves, the effect of particle inertia is negligible. Through additional numerical experiments, we also confirm that the particle inertia tends (up to the Stokes number St = 0.2) to attenuate flow turbulence. On the other hand, for flocs with lower gelling concentrations, the hindered settling can play a key role in sustaining a large amount of suspended sediments and results in the laminarized transport (III). For the simulation with a very significant hindered settling effect due to a low gelling concentration, results also indicate the occurrence of gelling ignition, a state in which the erosion rate is always higher than the deposition rate. A sufficient condition for the occurrence of gelling ignition is hypothesized for a range of wave intensities as a function of sediment/floc properties and erodibility parameters.

Water-only laboratory coal fractionation using the reflux classifier

Due to health and environmental factors involved with standard float-sink analytical methods, a water-only fractionation procedure was investigated. A laboratory scale 105×105mm reflux classifier was built and used to fractionate fine coal into a number of density classes. The procedure was tested against standard float and sink methods. The reflux classifier was found to be an effective fractionation method, especially if the fractioned samples were to be used in further chemical or reactivity investigations that could be affected by the dense medium adhering to the coal particle surfaces. The procedure was easier, safer and less tedious to perform in the laboratory. Higher density cuts could be achieved, and any number of density intervals could be prepared. It was also confirmed that the separation in the reflux classifier was not totally independent of particle size but it operated well for narrow size distributions above 355μm. Tracer tests were also done, and it was shown that tracer partition results were a poor predictor of the reflux classifier performance because of hindered settling effects.

A numerical investigation of fine sediment resuspension in the wave boundary layer—Uncertainties in particle inertia and hindered settling

The wave bottom boundary layer is a major conduit delivering fine terrestrial sediments to continental margins. Hence, studying fine sediment resuspensions in the wave boundary layer is crucial to the understanding of various components of the earth system, such as carbon cycles. By assuming the settling velocity to be a constant in each simulation, previous turbulence-resolving numerical simulations reveal the existence of three transport modes in the wave boundary layer associated with sediment availabilities. As the sediment availability and hence the sediment-induced stable stratification increases, a sequence of transport modes, namely, (I) well-mixed transport, (II) formulation of lutocline resembling a two-layer system, and (III) completely laminarized transport are observed. In general, the settling velocity is a flow variable due to hindered settling and particle inertia effects. Present numerical simulations including the particle inertia suggest that for a typical wave condition in continental shelves, the effect of particle inertia is negligible. Through additional numerical experiments, we also confirm that the particle inertia tends (up to the Stokes number St = 0.2) to attenuate flow turbulence. On the other hand, for flocs with lower gelling concentrations, the hindered settling can play a key role in sustaining a large amount of suspended sediments and results in the laminarized transport (III). For the simulation with a very significant hindered settling effect due to a low gelling concentration, results also indicate the occurrence of gelling ignition, a state in which the erosion rate is always higher than the deposition rate. A sufficient condition for the occurrence of gelling ignition is hypothesized for a range of wave intensities as a function of sediment/floc properties and erodibility parameters.

Hindered Settling of Silt

AbstractSediment particles smaller than 64 μm, with a noncohesive base mineral, are referred to as silt. The settling velocity of suspended sediment decreases with increasing concentration due to hindered settling effects. Compared with clay and sand, hindered settling of silt is poorly documented and understood. A formulation is proposed for the hindered settling of silt-water mixtures, derived from physical reasoning. The effect of silt on the mixture’s viscosity is addressed in particular. The formulation compares favorably with laboratory experiments on the settling of silt-sized sediment. This study shows that effective settling velocities can be derived from a single concentration time series measured within the settling mixture, provided that the sediment is initially homogeneously distributed.

MODELING THE CHANGE OF BEACH PROFILE UNDER TSUNAMI WAVES: A COMPARISON OF SELECTED SEDIMENT TRANSPORT MODELS

In contrast to the efforts made to develop hydrodynamic models for large-scale tsunami propagation and run-up, little has been done to develop, test, and validate sediment transport models used to simulate tsunami-induced sediment movement. In this study, the performances of six widely-used sediment transport formulas are evaluated through case studies using an open source code XBeach, which is based on 2D depth-averaged nonlinear shallow water equations. Another open source code, Delft3D, is also used to see to what extent XBeach can give reliable results. The benchmarks used for case studies include three laboratory experiments and one field observation from a post-tsunami field survey conducted after the 2004 Indian tsunami. Our results show that most of the surveyed sediment transport formulas can give good results for laboratory-scale problems, but for real-scale problems, all six formulas failed to produce good results compared to those found in laboratory conditions. For laboratory-scale problems, both XBeach and Delft3D can predict satisfactory results with properly-chosen model parameters. For real tsunamis, high suspended sediment concentration may occur, and density stratification and hindered settling effect play an important role; therefore, Delft3D, with both hindered settling and density stratification being considered, may perform better than XBeach. The findings reported here will be useful for researchers and practitioners working on tsunami hazard mitigation.

An acoustic backscatter system for in situ concentration profiling of settling flocculated dispersions

An in situ concentration profiler is demonstrated, using a novel application of a commercial acoustic backscatter system, which is suited to a wide range of dispersion and sludge settling systems. Specifically, the system utilises 2, 4 and 5MHz transducer–receivers that both emit high frequency ultrasonic pulses and receive the echo backscatter signals, with the strength of the return being directly proportional to the particulate concentration. It was found using well mixed flocculated Spheriglass dispersions from 2 to 10wt% that the backscatter signal was attenuated in an approximated linear mode with column depth (on a dB scale). In turn, the gradient of the attenuation was also found to increase linearly with respect to particle concentration, which allowed the formation of a direct correlation relationship. The backscatter response of a 5wt% settling dispersion was also observed. It was found that a peak formed in the measured signal at a depth relating to the cloud-front, and the bulk change in particulate concentration could be measured by comparing the difference in the linear slope of the acoustic attenuation. Further, by taking the interpolated differentiation of the backscatter signal at particular times, concentration changes throughout the column depth could be profiled. High levels of segregation within the sludge at intermediate time intervals were highlighted (due to the heterogeneous distribution of the particulates) as well as a build up in hindered settling effects.

Particle Collisions in a Lumped Particle Model

AbstractThis paper presents an extension of the lumped particle model in [1] to include the effects of particle collisions. The lumped particle model is a flexible framework for the modeling of particle laden flows, that takes into account fundamental features, including advection, diffusion and dispersion of the particles. In this paper, we transform a binary collision model and concepts from kinetic theory into a collision procedure for the lumped particle framework. We apply this new collision procedure to investigate numerically the role of particle collisions in the hindered settling effect. The hindered settling effect is characterized by an increase in the effective drag coefficient CD that influences each particle in the flow. This coefficient is given by , where ϕ is the volume fraction of particles, is the drag coefficient for a single particle, and n ≃ 4.67 for creeping flow. We obtain an approximation for CD/CD by calculating the effective work done by collisions, and comparing that to the work done by the drag force. In our numerical experiments, we observe a minimal value of n = 3.0. Moreover, by allowing high energy dissipation, an approximation for the classical value for creeping flow, n = 4.7, is reproduced. We also obtain high values for n, up to n = 6.5, which is consistent with recent physical experiments on the sedimentation of sand grains.

The structure of the deposit produced by sedimentation of polydisperse suspensions

To interpret the deposits from particle-laden flows it is necessary to understand particle settling at their base. In this paper a quantitative model is developed that not only captures how particles settle out of suspension but also the composition of the final deposit in terms of its vertical distribution of grain sizes. The theoretical model is validated by comparison to published experimental data that has been used to interpret the field deposits of submarine sediment-laden flows (Amy et al., 2006). The model explains two intriguing features of the experimental deposits that are also observed in natural deposits. First, deposits commonly have an ungraded, or poorly normally graded, region overlain by a strongly normally graded region. Second, the normalized thickness of the ungraded region increases as the initial concentration of the suspension is increased. In the theoretical model, the poorly normally graded region results from a constant mass flux into the bed that persists until the largest grain size present within the flow has been completely deposited. The effect of increasing the concentration of the initial suspension is to increase the thickness of the poorly graded part of the deposit and to decrease its average grain size. This work suggests that deposits with relatively thick, poorly graded bases can form from relatively high-concentration polydisperse suspensions, when the initial volume fraction of sediment is greater than approximately 20% and indicates that it is important to include these hindered settling effects in models of depositing flows.

Sedimentation of bidisperse suspensions

The average settling velocity of a suspension of identical particles through otherwise quiescent fluid is smaller than the settling velocity of a single particle in an unbounded fluid. When a suspension settles out to form a deposit, this hindered settling effect may lead to complicated sedimentation behaviour, even if the initial suspension is uniformly distributed. This study analyses the bulk sedimentation of bidisperse suspensions and calculates the evolution of the volume fraction of each species from an initially vertically uniform state through to the final steady state where both species have fully settled out of suspension and have formed a deposit. These calculations are analytical and employ the method of characteristics to reveal how both particle species evolve. The profiles often include ‘shocks’, across which discontinuous changes in volume fraction occur. Rarefaction fans may also be found across which the gradients of volume fraction are discontinuous. These new analytical solutions reveal the evolving composition of the suspension and the deposit and may be compared to experimental observations. They also provide test cases that can be used to verify recent numerical techniques for computing the bulk sedimentation behaviour of polydisperse suspensions.

Suspended sediment dynamics and morphodynamics in the Yellow River, China

AbstractThe Yellow River in China carries large amounts of sediments in suspension at concentrations up to several hundreds of kilograms per cubic metre; the sediment is composed mainly of silt. These high sediment concentrations influence the hydrodynamics (flow velocity and turbulence) which, in turn, determine the sediment concentration profile, whereas both the high sediment concentrations and pseudo‐cohesive properties of silt determine the morphodynamics of the Yellow River. The effect of sediment on the hydrodynamics is analysed using the Richardson number and the Reynolds number to provide a framework to differentiate between various flow regimes in the Yellow River, which is calibrated and validated with Yellow River data. The flow may be sub‐saturated (stable flow), super‐saturated (unstable flow characterized by high deposition rates, caused by collapse of turbulence), or hyperconcentrated sub‐saturated (stable flow because of hindered settling effects), depending on the Richardson number. Independent of this, the flow may be turbulent, transitional or laminar, depending on the Reynolds number. Analysis of these flow types improves understanding of the flow regimes and morphodynamics of the Yellow River. The morphodynamics of the Yellow River are also affected by pseudo‐cohesive behaviour caused by shear dilatance, which results in increasing critical shear stress for erosion at decreasing grain‐size. This pseudo‐cohesive behaviour may be partly responsible not only for the high deposition rates which characterize the lower Yellow River, but also for mass erosion during river floods.

Stratification effects by fine suspended sediment at low, medium, and very high concentrations

This paper describes results of the second part of a study on stratification effects by cohesive and noncohesive sediment. Winterwerp (2001) applied classical stratified flow theory implemented in a one‐dimensional vertical numerical model (the 1DV POINT MODEL), showing that sediment‐induced stratification effects may occur at already fairly small suspended sediment concentrations (i.e., a few 100 mg/L). We also discussed a basic difference between the behavior of cohesive and noncohesive sediment, which emerges as a result of the large water content of mud flocs. In this paper we elaborate further on the hydrodynamic description of the transport of fine suspended sediment by analyzing field and laboratory observations over a very large range of concentrations. We propose a sediment stability diagram to explain some features of hyperconcentrated flows, such as those observed in the Yellow River. We show that the behavior of hyperconcentrated flows is affected largely by hindered settling effects reducing the energy required to keep the sediment in suspension. The hydrodynamic description of sediment transport is used to predict capacity conditions as a function of a dimensionless stream power, i.e., U3/hgWs. This prediction agrees favorably with observations reported in literature covering four orders of magnitude in suspended sediment concentration.

Hindered settling of sand grains

AbstractThe sedimentation rate of sand grains in the hindered settling regime has been considered to assess particle shape effects. The behaviour of various particulate systems involving sand has been compared with the widely used Richardson–Zaki expression. The general form of the expression is found to hold, in as much as remaining as a suitable means to describe the hindered settling of irregular particles. The sedimentation exponent n in the Richardson–Zaki expression is found to be significantly larger for natural sand grains than for regular particles. The hindered settling effect is therefore greater, leading to lower concentration gradients than expected. The effect becomes more pronounced with increasing particle irregularity. At concentrations around 0·4, the hindered settling velocity of fine and medium natural sands reduces to about 70% of the value predicted using existing empirical expressions for n. Using appropriate expressions for the fluidization velocity and the clear water settling velocity, a simple method is discussed to evaluate the sedimentation exponent and to determine the hindered settling effect for sands of various shapes.

Numerical simulation of finite Reynolds number suspension drops settling under gravity

A suspension drop is a swarm of particles that are suspended in initially still fluid. When settling under the influence of gravity a suspension drop may undergo a complex shape evolution including the formation of a torus and eventual disintegration. In the present work the settling process of initially spherical suspension drops is investigated numerically for low and moderate drop Reynolds numbers Red. In the simulations a pseudospectral method is used for the liquid phase combined with a Lagrangian point-particle model for the particulate phase. In the case of low Reynolds numbers (Red<1) the suspension drop retains a roughly spherical shape while settling. A few particles leak away into a tail emanating from the rear of the drop. Due to the use of periodic boundaries a hindered settling effect is observed: the drop settling velocity is decreased compared to a suspension drop in infinite fluid. In the Reynolds number range 1⩽Red⩽100 the suspension drop deforms into a torus that eventually becomes unstable and breaks up into a number of secondary blobs. This Reynolds number range has not been investigated systematically in previous studies and is the focus of the present work. It is shown that the number of secondary blobs is primarily determined by the Reynolds number and the particle distribution inside the initial drop. An increased number of particles making up the suspension, i.e., a finer drop discretization, may result in a delayed torus disintegration with a larger number of secondary blobs. The influence of the initial particle distribution as a source of (natural) perturbations and the effect of initially imposed (artificial) shape perturbations on the breakup process are examined in detail. To gain a better understanding of the substructural effects (inside the suspension) leading to torus breakup, the particle field is analyzed from a spectral point of view. To this end, the time evolution of the Fourier coefficients associated with the particle distribution in the azimuthal direction of the torus is studied.

Numerical study of cluster and particle rebound effects in a circulating fluidised bed

Gas–particle flows in a vertical two-dimensional configuration appropriate for circulating fluidised bed applications were investigated numerically. In the computational study presented herein the motion of particles was calculated based on a Lagrangian approach and particles were assumed to interact through binary, instantaneous, non-frontal, inelastic collisions including friction. The model for the interstitial gas phase is based on the Navier–Stokes equations for two-phase flows. The numerical study of cluster structures has been validated with experimental results from literature in a previous investigation. Numerical experiments were performed in order to study the effects of different cluster and particle rebound characteristics on the gas–particle flow behaviour. Firstly, we investigated the hard sphere collision model and its effect on gas–particle flow behaviour. The coefficient of restitution in an impact depends not only on the material properties of the colliding objects, but also on their relative impact velocity. We compared the effect of a variable restitution coefficient, dependent on the relative impact velocity, with the classical approach, which supposes the coefficient of restitution to be constant and independent of the relative impact velocity. Secondly, we studied the effects of different cluster properties on the gas–particle flow behaviour. Opposing clustering effects have been observed for different particle concentrations: within a range of low concentrations, groups of particles fall faster than individual particles due to cluster formation, and within a well-defined higher concentration range, return flow predominates and hindered settling characterises the suspension. We propose herein a drag law, which takes into account both opposing effects and have compared the resulting flow behaviour with that predicted by a classical drag law, which takes into account only the hindered settling effect.