Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media

DEM modelling of the motion of coarse fractions of the charge inside SAG mills has now been well established for more than a decade. In these models the effect of slurry has broadly been ignored due to its complexity. Smoothed particle hydrodynamics (SPH) provides a particle based method for modelling complex free surface fluid flows and is well suited to modelling fluid flow in mills. Previous modelling has demonstrated the powerful ability of SPH to capture dynamic fluid flow effects such as lifters crashing into slurry pools, fluid draining from lifters, flow through grates and pulp lifter discharge. However, all these examples were limited by the ability to model only the slurry in the mill without the charge.In this paper, we represent the charge as a dynamic porous media through which the SPH fluid is then able to flow. The porous media properties (specifically the spatial distribution of porosity and velocity) are predicted by time averaging the mill charge predicted using a large scale DEM model. This allows prediction of transient and steady state slurry distributions in the mill and allows its variation with operating parameters, slurry viscosity and slurry volume, to be explored.     

Slurry flow in a tower mill

Tower mills are a commonly used device for fine grinding in the mineral processing industry and can be used for dry or wet-grinding applications. In wet grinding, the nature of the slurry flow plays an important role in transporting feed rock and ground fines inside the mill and also assists discharge from the mill. Operating conditions and impeller design can affect the slurry distribution within the mill with some regions of the charge potentially being drier and others saturated. To help understand the slurry distribution and transport we use a two stage modelling process. The Discrete Element Method (DEM) is used to characterise the motion and distribution of the grinding media in the tower mill. The averaged voidage distribution and steady velocity field from the DEM model is then used to define a dynamic porous media in the fluid model. The Smoothed Particle Hydrodynamics (SPH) method is used for modelling the fluid flow because of the free surface and the moving impeller. The one way coupled DEM/SPH model is then used to assess how the fluid distribution and flow pattern of the slurry in a tower mill are to variations in the slurry viscosity.     

Using SPH one-way coupled to DEM to model wet industrial banana screens

Large banana screens with multiple decks are used extensively in the process separation of many valuable export commodities. They are high capacity vibrating screens with a curved profile. Discrete Element Method (DEM) modelling using non-spherical particles has previously provided significant insight into the operation of these dry industrial screens. Here we introduce the use of Smoothed Particle Hydrodynamics (SPH) to model the flow of slurry (water and fine material) through a double deck banana screen. This paper firstly reports on the underlying DEM model of the coarse particulate flow on a full-scale banana screen. We then use Smoothed Particle Hydrodynamics (SPH) to model the transport of fine particle slurry over and through the double deck banana screen. Finally, we combine the DEM with SPH models using a one-way coupling to simulate the effects of adding a slurry flow to coarse particulates on the banana screen. The key outcomes from this study are that; SPH is ideally suited for the high speeds and the high fragmented and filamentary nature of the fluid flow through the screen deck openings; the fluid only (SPH) model of slurry behaves similarly to the DEM approach in that more fluid is screened as the velocity slows, except near the earlier panels on the top deck; and, use of a porous media derived from DEM in one-way coupled approach with SPH produces clear and reasonable changes in fluid structure, separation and wetting of the screens consistent with slurry behaviour. Specifically, the fluid layer was much thicker in the coupled case, with slurry being trapped inside a coarse particle bed and which is sensitive to the fluid viscosity.     

Validation of a model for physical interactions between pulp,charge and mill structure in tumbling mills

Modelling the pulp fluid and its simultaneous interactions with both the charge and the mill structure is an interesting challenge. The interactions have previously been modelled for dry grinding with a combination of discrete element method (DEM), smoothed particle hydrodynamics (SPH) and the finite element method (FEM), where the DEM particles or SPH particles represent the grinding balls and FEM is used to model the mill structure. In this work, the previous model is extended to include fluids with SPH. Wet milling with water and a magnetite pulp, for graded and mono-size charges are numerically modelled and validated. The internal working of the charge and the physical interaction between the charge and the mill structure is studied. The combined SPH–DEM–FEM model presented here can predict the classical DEM results, but can also predict responses from the mill structure, as well as the pulp liquid flow and pressure. Validation is conducted by comparing numerical results with experimental measurements from grinding in an instrumented small-scale batch ball mill equipped with an accurate torque metre. The simulated charge movement is also compared with high speed video of the charge movement for a number of cases. Numerical results are in good agreement with experimental measurements.     

Computational prediction of performance for a full scale Isamill: Part 2 – Wet models of charge and slurry transport

The Isamill is a horizontal stirred media mill used for fine and ultrafine grinding of slurry transported rock particles. The charge motion is analysed using two different approaches, (1) a fluid only model, and (2) a 1-way coupled DEM + SPH model. The flow pattern when the classifier is closed is regular with a pair of oppositely oriented vortices between each pair of grinding discs. A strong radial outflow from the middle of the classifier is generated by the high centrifugal force which creates a pair of toroidal vortices at the discharge end of the mill. The classifier, when open, acts as a pump drawing slurry axially along the mill. It enters the classifier through the holes in its end plate and is then forced radially outward by rotational acceleration of the classifier cage. The enhanced outflow significantly strengthens the large toroidal vortices on the outside of the classifier. This produces a strong retrograde annular flow along the mill shell that penetrates a significant distance back into the grinding chamber. The effect of the classifier is significant and strongly influences the flow over much of the mill and controls slurry (feed and product) transport and discharge. The predictions of the different models are qualitatively similar but with important differences including the fluid only model predicting higher flow speeds because it cannot capture the strong slip between the media and the grinding discs. The strength of the axial transport is strongly dependent on the slurry viscosity. A critical viscosity can be identified above which there is insufficient axial transport to enable mill operation.     

What is required from DEM simulations to model breakage in mills?

It is quite common to encounter discrete element method (DEM) simulations of mills that present images of the motion of grinding media, summaries of tangential and normal forces, and mill power. The usefulness of this data is questioned, with respect to modelling breakage. This work presents hypotheses of how the DEM simulations can be used as input to comminution modelling, and this guides the data logging and analysis requirements. Techniques are proposed for collecting and using this data in a manner useful for predicting breakage in a comminution device. Individual particle impact histories of contact angle, force, and impulse are required to realistically model breakage. It is argued that the majority of breakage results from cumulative damage, thus it is essential to track individual particle histories to realistically predict the breakage product from a mill.     

基于CG VOF-DEM和CG Mixture-DEM模型的水力旋流器多相流数值模拟

针对水力旋流器进料固体颗粒的分离过程内部流场复杂,颗粒运动规律难以掌握的问题.基于颗粒动力学理论并引入粗颗粒(CG)概念,提出了两种数值模型来对水力旋流器中的多相流进行建模:一种是将多相流(VOF)模型与离散元法(DEM)结合起来的CG VOF-DEM模型;另一种是将混合(Mixture)模型和DEM模型结合起来的CG...     

Prediction of wear and its effect on the multiphase flow and separation performance of dense medium cyclone

Dense medium cyclone (DMC) is a high-tonnage device that is widely used to upgrade run-of-mine coal in modern coal preparation plants. It is known that wear is one of the problems in the operation of DMCs, but it is not well understood. In this work, the wear rate of DMC walls due to the impact of coal particles is predicted by a combined computational fluid dynamics and discrete element method (CFD-DEM) approach, using the Finnie wear model from the literature. In the CFD-DEM model, DEM is used to model the motion of discrete coal particles by applying Newton’s laws of motion and CFD is used to model the motion of the slurry medium by numerically solving the local-averaged Navier–Stokes equations together with the volume of fluid (VOF) and mixture multiphase flow models. According to the Finnie wear model, the wear rate is calculated according to the impact angle of particles on the wall, particle velocity during an impact and the yield stress of wall material; the relevant particle-scale information can be readily obtained from the CFD-DEM simulation. The numerical results show that the severe wear locations are generally the inside wall of the spigot and the outside wall of the vortex finder. The wear rate depends on both the operational conditions and solids properties. It increases generally with the decrease of medium-to-coal (M:C) ratio. For a given constant M:C ratio, the wear rate for thermal coal is higher than that for coking coal, especially at the spigot. Large particles may cause a non-symmetric wear rate due to the gravity effect. The effect of a worn spigot wall on the multiphase flow and separation performance is also studied. This work suggests that the proposed approach could be a useful tool to study the effect of wear in DMCs under different conditions.     

Using Smooth Particle Hydrodynamics (SPH) to model multiphase mineral processing systems

A characteristic of most minerals processing systems is that they are multi-phase. The Lagrangian nature of SPH means that it is well suited to modelling these systems as it can naturally track interfaces and free surfaces. In this paper we describe a massively parallel SPH simulator that we have developed and highlight some of the features that have been implemented. These features include surface tension and contact angles, two way coupled solid fluid-interactions and animated geometries. The capabilities of this simulator are illustrated by means of examples showing its ability to simulate a wide range of different minerals processing related systems including particle scale heap flow, multi-phase interactions in a sheared slurry and multi-phase mixing.     

Applicability of a coarse-grained CFD–DEM model on dense medium cyclone

The combined computational fluid dynamics and discrete element method (CFD–DEM) approach has been proved to be an effective tool to study the fundamentals of different particle–fluid flow systems, but suffers high computational cost problem. Recently, various treatments such as parcel–particle concept, coarse-grained model, similar particle assembly and representative particle model have been developed to reduce the computational cost of CFD–DEM approaches. These treatments are basically empirical and thus their applicability is likely system-dependent. Until now, there are still no general agreements on the formulation of those models and their accuracy and general applicability are largely unknown.In this work, a coarse-grained (CG) (CFD–DEM) model is developed to model the swirling multiphase flow in a dense medium cyclone (DMC) and the error caused by the CG concept is quantified by carrying out controlled numerical calculations to directly compare the simulated results between a standard CFD–DEM model and a CG CFD–DEM model. It demonstrates that when the flow is dilute, the results are independent on the size of the grain (also called as parcel or model particle in this work). Nonetheless, when the flow is dense, small discrepancies are observed between the two models. This work suggests that the CG CFD–DEM model is indeed a useful tool to quickly evaluate the flow and performance of large-scale DMCs and the simulation results should be useful at least qualitatively, if not quantitatively.     

CFD–DEM modelling of particle flow in IsaMills – Comparison between simulations and PEPT measurements

The IsaMill? is a high speed stirred mill with a horizontal configuration that offers advantages such as energy efficiency and an inert grinding environment. A combined computational fluid dynamics (CFD) and discrete element method (DEM) approach was developed to investigate the particle and fluid flows inside a simplified IsaMill?. The configuration of the mill was simpler than that of an actual IsaMill? and no feed flow or rotor was considered. The CFD–DEM model is a progression from earlier DEM only models of “dry” systems which did not account for the fluid phase. The properties of flows at a macroscopically steady state, such as velocity field, distributions of particle velocity and acceleration in the radial direction and power draw, were analysed. Detailed comparisons were carried out between the simulation results and Positron Emission Particle Tracking (PEPT) measurements under similar conditions. The comparisons showed reasonable agreements, confirming that both techniques can capture the key features of the flow. The discrepancies between simulated and measured results were discussed. The findings indicated that the proposed model can be used to generate microdynamic information that is useful in leading to a better understanding of the underpinning physics of flow inside mills.     

DEM simulation of the flow of grinding media in IsaMill

IsaMill is a high speed stirred mill for high efficiency grinding of mineral ores and concentrates. A numerical model based on the discrete element method (DEM) was developed to study flow of grinding media in IsaMill. The DEM model was first verified by comparing the simulated results of the flow patter, mixing pattern and power draw from those measured from a 1:1 scale lab mill. Then the flow properties were analysed in terms of flow pattern, flow velocity, force field and power draw. The effects of parameters relating to particle material (i.e., sliding friction coefficient and damping coefficient) and operational conditions (i.e., rotation speed and solid loading) were investigated. While the damping coefficient showed a negligible effect for the range considered, other three parameters had strong effects on the flow properties. Increasing the sliding friction caused the flow velocity and compressive force to have minimum values due to the competitive mechanisms for energy transfer and dissipation, but increased the power draw. The increase in the rotation speed and solid loading also increased the flow velocity, compressive force and power draw of mill. The particle scale information obtained would be useful to understand the fundamentals governing the flow of grinding media in IsaMill.     

Applying discrete element modelling to vertical and horizontal shaft impact crushers

The PFC3D (particle flow code) that models the movement and interaction of particles by the DEM techniques was employed to simulate the particle movement and to calculate the velocity and energy distribution of collision in two types of impact crusher: the Canica vertical shaft crusher and the BJD horizontal shaft swing hammer mill. The distribution of collision energies was then converted into a product size distribution for a particular ore type using JKMRC impact breakage test data. Experimental data of the Canica VSI crusher treating quarry and the BJD hammer mill treating coal were used to verify the DEM simulation results.Upon the DEM procedures being validated, a detailed simulation study was conducted to investigate the effects of the machine design and operational conditions on velocity and energy distributions of collision inside the milling chamber and on the particle breakage behaviour.     

Effect of slurry properties on particle motion in IsaMills

IsaMill? is a high-speed stirred mill for a range of milling duties from ultra-fine to relatively coarse grinding in the mineral processing industry. This work investigated particle and slurry flow in a mill using a combined Discrete Element Method and Computational Fluid Dynamics (DEM-CFD) approach. Slurry properties, such as flow density and viscosity, were varied to study their effects on the flow properties in terms of flow velocity, power draw, collision frequency, collision energy and total impact energy. Significant differences were observed when slurry was introduced and other conditions unchanged. With increasing density, fluid and particle flows showed stronger circulation in the axial direction due to the larger drag forces. Increased relative velocity and interaction between particles with disc led to higher collision frequency and collision energy. Increase in flow viscosity limited particles from moving towards the outer wall and the particles were more dispersed due to the larger circulating velocity in the axial direction. The total impact energy of the media and power draw also increase with slurry density and viscosity. The developed model provides a useful framework for further analysis of particle–slurry interactions in IsaMills?.     

CFD–DEM study of the effect of particle density distribution on the multiphase flow and performance of dense medium cyclone

A mathematical model is developed to study the coal-medium flow in a dense medium cyclone (DMC) of 1000 mm body diameter. In the model, the motion of coal particles is obtained using the Discrete Element Method (DEM) facilitated with the concept of “parcel–particle” while the flow of medium as a liquid-magnetite mixture Computational Fluid Dynamics (CFD) based on the local averaged Navier–Stokes equations. In addition the Reynolds Stress Model (RSM) is adopted to describe the anisotropic turbulence, the Volume of Fluid (VOF) model is used to describe the air-core position and multiphase mixture model used to estimate the flow of fine magnetite particles. The simulated medium and coal flows allow estimates to be made of pressure drop, efflux stream medium densities and partition curves for coal particles of different sizes and densities. These estimates are compared favourably with industrial scale measurements of a 1000 mm DMC operating under similar conditions. On this base, the effect of particle density distribution that represents the major difference between two major coal type, i.e., coking coal and thermal coal, is studied. The results are analysed in terms of medium flow pattern, particle flow pattern, partition performance and particle–fluid, particle–wall and particle–particle interaction forces.     

Estimating energy in grinding using DEM modelling

The latest state of the art on Discrete Element Method (DEM) and the increased computational power are capable of incorporating and resolving complex physics in comminution devices such as tumbling mills. A full 3D simulation providing a comprehensive prediction of bulk particle dynamics in a grinding mill is now possible using the latest DEM software tools.This paper explores the breakage environment in mills using DEM techniques, and how these techniques may be expanded to provide more useful data for mill and comminution device modelling. A campaign of DEM simulations were performed by varying the mill size and charge particle size distribution to explore and understand the breakage environment in mills using DEM techniques. Analysis of each mill was conducted through consideration of the total energy dissipation and the nature of the collision environment that leads to comminution.The DEM simulations show that the mill charge particle size distribution has a strong influence on the mill input power and on the way the energy is distributed across the charge. The smaller particles experience higher energies while the larger experience less, but this variation is strongly dependent on the mill size. The results also showed that the average particle collision energy increases with increasing mill size, whereas its distribution over particle size is strongly influenced by the mill content particle size distribution. The simulations also captured the energy distribution within different regions of the tumbling charge, with the toe impact region having higher impact energies and the bulk shear region having higher tangential energies. Regardless of the mill size most of the energy is consumed by the particles in the mid-size range, which has the highest percentage mass of the total charge distribution.     

DEM modelling of liner evolution and its influence on grinding rate in ball mills

Wear of grinding mill liners and lifters plays a major role in the overall efficiency and economics of mineral processing. Change in the shape of lifters as they wear has a significant influence on grinding efficiency, and the annual cost of maintenance and mill down-time depends on the life of both liners and lifters. The Discrete Element Method (DEM) is a computational method for simulating the dynamics of particle processes. This paper presents an analysis of 3D simulation of a grinding mill carried out using the EDEM software package customised to predict the rate of wear of lifter geometry and to enable progressive updating of worn lifter geometry profiles. A simplified breakage rate model is developed as a tool to correlate liner profile to mill performance.The combination of the prediction of liner profile and grinding rate shows promise to provide a powerful tool for advanced mill liner design – providing a means to balance liner life and mill performance over the life of the liner at the liner design stage.     

Discrete element method (DEM) modelling of evolving mill liner profiles due to wear. Part I: DEM validation

Since the early 1990s the discrete element method (DEM) gained considerable success in its ability to predict the power draw and the load behaviour in mills as affected by operating conditions. The DEM can also be used to design milling equipment and predict the breakage of particles. A detailed validation of this method is required in order to produce accurate results. In this paper, we assess the ability of the DEM to predict forces exerted by the mill charge on liners. Data obtained on an experimental two-dimensional mill designed in order to record the normal and tangential forces exerted on an instrumented lifter bar was available. The measured results are compared to the DEM simulated results. Good agreement has been found in terms of amplitude of forces and positions of shoulder and toe at low speed.