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A particle scale model based on a full two-way coupling of the Discrete Element Method (DEM) and Smoothed Particle Hydrodynamics (SPHs) methods is applied to SAG mills. Motion and collisions of resolved coarser particles within an SAG mill are performed by the DEM component. Fine particles in the feed combine with the water to form a slurry, which is represented by the SPH component of the model. Slurry rheology is controlled by solid loading and fine particle size distribution for each volume of slurry. Transport, dispersion, and grinding of the slurry phase particle size distribution are predicted by solving additional coupled advection–diffusion equations in the SPH component of the model. Grinding of the finer particles in the slurry due to collisions and shear of the coarser particles (rocks and grinding media) is achieved via the inclusion of population balance terms in these equations for each SPH particle. This allows prediction of the transport of both coarser and finer material within the grinding and pulp chambers of an SAG mill, including the discharge performance of the mill. This particle-scale model is used to investigate the relative performance (throughput, product size distribution, resident particle size distribution, net power draw, wear) for an SAG mill at a pilot scale and a 36 ft industrial scale. The 36′ SAG mill considered is a geometrically scaled-up version of the 1.8 m Hardinge pilot scale mill but with a longer belly length, reflecting current SAG mill design preferences. The belly lifters are scaled to a lesser degree with a larger number of lifters used (but still many fewer liners than would typically be used in a large SAG mill based on conventional liner selection rules). The model shows that despite reasonable qualitative similarities, many aspects of the charge structure, slurry transport, coarse particle and slurry discharge through the grates, and the collision energy spectra vary in important ways. This demonstrates that a near purely geometric scale-up of an SAG mill is not sufficient to produce a comparable performance at the two physical mill scales. [ABSTRACT FROM AUTHOR]

A series of challenging fluid flow applications are used to demonstrate the powerful capabilities of the SPH method. The applications are classified according to whether they are industrial, geophysical or biophysical in nature. The versatility and flexibility of SPH allows it to be used to predict wide ranges of flow types with diverse coupled secondary physics and chemistry. The demonstration examples span free surface hydrodynamics, fluid-structure interactions, multiphase flows (bubbles and/or solids immersed in a fluid and multiple fluids with large density differences), and flows involving reactions and phase change. For the studies presented SPH demonstrates at least one and often several key advantages that make the method well suited to these applications. These include the natural handling of free surfaces (especially when splashing), strong advection (arising from the method being Lagrangian), very high deformation levels (due to being meshfree) and intrinsic history tracking (which provides specific benefits for flows with multiple materials, reactions and phase change). [ABSTRACT FROM AUTHOR]

• Advanced particle-based modelling methods are presented for use with grinding mills. • Tumbling mill end walls generate strong curtain flows which strongly affect dynamics. • Liner life cycle for mills can be predicted for complex realistic liner geometries. • Curtain flows control slurry pool volume and discharge from overflow ball mills. • Grinding efficiency in a wet tumbling mill decreases with increasing mill speed. This second part paper explores rock breakage mechanisms, the life cycle of rocks in mills and the strong influence of end walls on charge motion within mills. We present recent advances in particle-based modelling of mills for comminution focused around wear and the effect of slurry and slurry phase grinding. Three mill scenarios are considered: 1. Media flow and the resulting wear evolution of the belly and end wall liners and the resulting change in mill performance for a full industrial scale dry ball mill (modelled using DEM) 2. Axial slurry transport and mixing in a wet overflow industrial scale ball mill (modelled using fully coupled DEM and SPH) 3. Effect of mill speed on slurry and solid charge motion and the resulting grinding of fine particles in a 1.8 m diameter wet Hardinge pilot mill (modelled using fully coupled DEM and SPH with advection-diffusion-population balance equations solved for the slurry size distribution for each SPH particle) These demonstrate the nature and level of fidelity that is now possible to include in particle-scale comminution models. They provide insights into the critical importance of curtain flows generated by the end walls of tumbling mills, on wear behaviour on liners, on the structure of slurry pools and mill discharge and on the adverse effect on grinding of increasing mill speed. [ABSTRACT FROM AUTHOR]

Highlights • A combined DEM-SPH model is developed for spray impingement into a pool of liquid. • Momentum and mass are transferred from the discrete spray into the fluid phase. • The model is evaluated using experimental pressure measurements for 1–3 sprays. • Comparison of pressure predictions with experiment shows very good agreement. • Collisions of droplets from different sprays have a small but noticeable effect. Abstract In this paper we detail the development of a combined DEM-SPH model for spray impingement into a pool of water or onto a flat surface on which a pool of water can build up. The spray is represented by discrete particles which can collide with solid objects, each other and also merge with liquid surfaces. The liquid pool dynamics are solved for using the SPH method. The proposed coupling allows momentum to be transferred from the discrete spray phase into the fluid phase in the pool. The performance of this coupled DEM-SPH method is evaluated by comparing to experiments performed for simple spray arrangements in which the pressure in the pool just above the solid surface is carefully measured by a probe that is moved systematically across the surface. A comparison of the simulated pressure distribution with those from the experiments shows very good agreement for the size of the high pressure region, the average pressure the pressure distribution within this region generated by the spray impingement for cases with one, two and three overlapping sprays. Collisions between spray droplets in the case of multiple sprays are found to have a small but noticeable effect on the details of the high pressures in the regions of overlap of the sprays. [ABSTRACT FROM AUTHOR]

Highlights • A coupled DEM+SPH model is extended to include coarse breakage and slurry rheology. • SPH slurry model includes unresolved progeny allowing prediction of fines transport. • Particles rebounding from the liner produce the strongest incremental damage. • Strong damage is also generated by cascading material arriving in the toe region. • The presence of a slurry pool restricts the opportunity for incremental damage. Abstract Coupled DEM+SPH models are able to predict the motion of the coarse particulates and the slurry phase in a SAG mill. An extension of this model is proposed in which breakage of coarser particles (which are resolved in the DEM sub-model) in accordance with the incremental damage theory is included. This allows direct prediction of the resident size distribution of the rock component of the charge. It also allows the finer unresolved progeny from the breakage to be added to the slurry whose rheological properties then become a dynamic prediction of the model via the evolving local solids density of the slurry. It also allows transport of the fine material within and from the mill to be predicted. This model is demonstrated for an industry standard 1.8 m diameter by 0.6 m long pilot SAG mill. It allows the nature of the damage accumulation by the rock particles and its linkage to the flow structure of the charge to be explored. A flux of particles rebounding from the liner in the impact zone of the mill colliding with cataracting material produces the strongest incremental damage. Damage is also generated by cascading material arriving in the toe region. The presence of a slurry pool restricts the opportunity for incremental damage from the rebounding particles in the impact zone by damping rebound in places where particles fall directly into slurry. Finally, the coupled DEM+breakage+SPH model enables a mechanistic linkage between the slurry properties and the rock breakage. [ABSTRACT FROM AUTHOR]

This paper reports on the development and evaluation of an SPH (Smoothed Particle Hydrodynamics) model for high pressure water flow through and from a nozzle and prediction of its break up into a spray of high speed water droplets. This appears to be the first application of the SPH technique to fully model a high pressure nozzle. The model predicts the internal flow and pressure distribution and enables exploration of the role of the internal geometric insert used in this design of the nozzle. It also predicts exit velocities from the nozzle as well as the pressure distribution generated by the nozzle and droplet size distribution of the resulting spray. Three different nozzle inflow rates were simulated and for all cases the numerical simulation of nozzle and spray gave generally good agreement with experiments, but complete agreement was not achieved. For better agreement, higher resolution for the SPH solution is required. The SPH simulations also show the role that the insert in the nozzle has on the flow and the resulting jet. It produces a flat inclined high velocity liquid jet within the second half of the nozzle which will generate turbulent eddies that may enhance the nucleation of the droplets in the fragmenting jet after it exits the nozzle. Overall, SPH has been shown to have a very good capacity to model high pressure nozzles and with further refinements of the technique should be able to yield accurate, quantitative data. [ABSTRACT FROM AUTHOR]

Coupled DEM/SPH flow models of rock/slurry flow are developed in order to investigate the effect of feed rate on the operation of the feed box which is used to pre-mix the solid feed with water before it is presented as slurry to the screen. For the feed box, rocks were fed into the feed box from a conveyor and travelled through a series of intermediate ledges before being combined with water from an assembly of pipe jets and spray nozzles, and then exiting to the screen. Two dispersal geometries were considered for distributing the water. Wide nozzle sprays were found to provide much more uniform delivery of water to the rock stream than jets from cylindrical pipes. The details of the feed and slurry mixture exiting the bottom chute does not appear to change significantly with conveyor feed rate. [ABSTRACT FROM AUTHOR]

This paper presents recent work on modelling of industrial particle and multiphase flows using combinations of DEM for resolved particle flow and either grid based CFD or meshless SPH for gas-particle and free surface fluid-particle flows respectively. Current examples of such modelling for dry industrial granular flows (DEM only applications) focuses on mixing and digging of non-ideal shaped particles in complex moving geometries. For the mixer, increasing the number of plough blades improves the rate of mixing due to a larger overlap of the swept paths of the blades with the bed and reduces the size of the dead zones between the blades and between the blades and the end of the mixer. For the dragline filling, the impact with a large mostly submerged boulder creates lateral forces and yawing components to the torque but the rock flow and dragline motion are collectively able to force the boulder into the dragline indicating that that boulders of up to 2 m length can still be easily be excavated. Industrial application of coupled DEM-SPH to fluid-particulate free surface flows is shown for both SAG and tower mills. In the SAG mill, the slurry largely follows the motion of the particulate phase of the charge. However, near the shoulder where the charge dilates the slurry is much more mobile leading to a lower slurry shoulder and the formation of a small slurry pool above the toe. For a tower mill, this coupled model is able to identify the viscosity controlled transition from the slurry being able to support itself with a largely hydrostatic pressure gradient to one where the slurry is supported by the grinding media and with pressure that is independent of height. For gas-particulate flows the important impact of grain shape in fluidised beds, pneumatic conveying and flow generated by high speed gas injection into granular beds are examined. These examples highlight the inability of simple spherical particle models to adequately resolve the complex granular dynamics of such gas driven systems for realistic shaped particulates. The generation and transport of dust in an industrial flow context is also demonstrated for a realistic hood-and-spoon conveyor transfer chute. [ABSTRACT FROM AUTHOR]

Food transport through different sections of the gastrointestinal tract for the purposes of digestion and waste removal is an essential physiological function for life. Mechanical and chemical breakdown of food takes place throughout the gastrointestinal tract. Periodic muscular contraction and relaxation of the intestinal walls agitate, mix and propel the multiphase digesta along the intestines. Experimental measurement of flow inside the intestines is difficult therefore understanding of food transport through the majority of the gut is limited. Computational models for predicting the transient behaviour of intestinal content subject to peristaltic activity offer the possibility for assessing the digestive performance of different foods. We present a numerical model for peristalsis in the duodenum using a suspension of rigid particulates in a viscous Newtonian fluid to represent simple digesta. This consists of a thin viscoelastic membrane representing the gut wall coupled to the particle-based methods Smoothed Particle Hydrodynamics (SPH) and Discrete Element Method (DEM) which are used to predict the motion of liquid and solids content respectively. Peristaltic waves travel along the gut wall resulting in active muscular contractions and relaxations of the gut. The bulk motion of the content shows both phases move together due to the laminar nature of the flow with only very short-term inter-phase differences found in the relaxation region and in the wake of the contraction. Propulsive events were found to cause significant non-homogeneity of the solids distribution along the length of the duodenum. The inclusion of solids mildly modifies the overall propulsive flow behaviour and the retrograde jet in the wake of the contraction. In the absence of solids and connective tissue constraints, a transverse wobbling instability in the fluid filled viscoelastic tube is observed. [ABSTRACT FROM AUTHOR]

The connections between swimming technique and the fluid dynamical interactions they generate are important for assisting performance improvement. Computational fluid dynamics (CFD) modeling provides a controlled and unobtrusive way for understanding the fundamentals of swimming. A coupled biomechanical-smoothed particle hydrodynamics (SPH) fluid model is used to analyze the thrust and drag generation of a freestyle swimmer. The swimmer model was generated using a three-dimensional laser body scan of the athlete and digitization of multi-angle video footage. Two large distinct peaks in net streamwise thrust are found during the stroke, which coincide with the underwater arm strokes. The hand motions generate vortical structures that travel along the body toward the kicking legs and the hands are shown to produce thrust using both lift and drag. These findings advance understanding of the freestyle stroke and may be used to improve athlete technique. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A coupled DEM (discrete element method) and SPH (smoothed particle hydrodynamics) method is used to predict the motion of the solid particles interacting with slurry flow. DEM simulates the motion of the coarser particulates while SPH simulates the slurry (water and finer particulates). This three dimensional method is demonstrated for multiphase mixing flow on a chute, in a central slice of a 36′ SAG mill and in a Hardinge pilot mill. It is shown to be robust and stable and able to predict complex coupled free surface particle and slurry flows including splashing with saturation levels varying from dry to fully saturated. It is suitable for prediction of multiphase flow in moving equipment including small scale structures such as classification grates. [ABSTRACT FROM AUTHOR]

Patient-specific geometric factors together with traditional risk factors may aid the early identification of patients at high risk of developing carotid artery disease requiring surgical intervention. Recent studies have linked aspects of carotid geometry to the pathogenesis of internal carotid artery (ICA) stenosis. Abnormal wall shear stress (WSS) is found for large ICA angles. Low WSS is believed to correspond to plaque formation whereas high WSS may result in plaque rupture and clotting. Here, the meshless method, smoothed particle hydrodynamics, is used to simulate Newtonian flow through a clinical, rigid walled, carotid bifurcation. The resulting flow field and WSS are reported for a range of different ICA angles. Varying the angle without changing boundary pressure conditions produces minimal change in flow and WSS. Greater ICA downstream pressures appear important for maintaining well-behaved flow through the bifurcation by suppressing flow separation downstream of the stenosis resulting in more uniform wall stress. [ABSTRACT FROM AUTHOR]

Abstract: Slurry flow, including flow through the charge in the grinding chamber, through the discharge grates, along the pulp lifters and its discharge from the mill is an important contributor to the efficiency of the grinding process within a SAG mill. Poor transport of finer ground material can adversely affect grinding leading to excess energy consumption and over-grinding of fine material. This paper uses a 1-way coupled DEM–SPH method in three dimensions to analyse the full slurry flow for a 1.8m diameter by 0.6m long AG/SAG pilot mill. This provides detailed information on the internal flow of slurry within a SAG mill, including the prediction of dry regions and of slurry pooling. The importance of the end walls in generating complex three dimensional recirculation patterns in the charge and its influence on axial flow is demonstrated. Such a full 3D analysis ensures that the slurry is presented to the grate with a realistic spatial distribution and allows prediction of the flow through the grates and then within the pulp chamber. The rate of filling of the pulp chambers, the point of initiation of flow down along the rising pulp lifters, back flow into the grinding chamber and flow onto the discharge cone are all investigated. It is shown that the end wall lifters are critical to the flow through the grate generating pumping and shadowing effects which produce strongly non-uniform flow through different grate panels. [Copyright &y& Elsevier]

Abstract: In solid metal forming processes, such as forging, large distortions in the material present challenging problems for numerical simulation using grid based methods. Computations invariably fail after some level of mesh distortion is reached unless suitable re-meshing is implemented to cope with the mesh distortion arising from the material deformation. The issue of mesh distortion and the subsequent re-meshing are topics of much research for grid based methods. These problems can be overcome by using a mesh-less numerical framework. In this paper, the application of a mesh-less method called Smoothed Particle Hydrodynamics (SPH) for modelling three-dimensional complex forging processes is demonstrated. It is shown that SPH is a useful simulation method for obtaining insights into the material deformation and flow pattern during forging of realistic industrial components. The effect of process parameters and material properties on the quality of the forged component is evaluated via SPH simulations. This includes the determination of forging force required for adequate die filling which is an important criterion for die designs. Material hardening, controlled by the degree of heat treatment, is found to have a profound effect on the material deformation pattern and the final product. Forging defects such as incomplete die filling, asymmetry in forged components, flashing and lap formation are shown to be predicted by SPH. SPH can thus potentially be used both for assessment of the quality of forged products and evaluation of prototype forging system designs. [Copyright &y& Elsevier]

Understanding how the permeability of a porous medium changes as function of solid fraction and pore geometry is vital in many significant areas. Here, we construct a number of different porous media via computer methods. We then simulate the flow of a viscous liquid through the solid packing using the Smoothed Particle Hydrodynamics (SPH) and Lattice Boltzmann (LB) methods. Qualitative comparisons of flow between the two methods are generally good as are the quantitative permeability comparisons. The relative computational efficiency of both methods is examined with the LB method being superior to SPH for this application. [ABSTRACT FROM AUTHOR]

Abstract: Low pressure die casting is used to manufacture complex metal components where there is a need for high structural integrity. In this process, liquid metal is fed from below into the die used to form the component under a positive pressure. Smoothed particle hydrodynamics (SPH) is a meshfree Lagrangian method that has specific advantages for modelling such material forming applications. This paper describes extensions to the SPH method for predicting shrinkage of the cooling metal, tracking of oxide formation, prediction of feeding, solidification front dynamics and finally direct prediction of the residual pressure distribution in the solidified metal and of cavity defect formation. These are demonstrated using a simple two dimensional example which contains the essential features of an engine block. [Copyright &y& Elsevier]

Aluminium melt transfer operations lead to dross formation via splashing/turbulence. Optimisation may be achieved by employing computational modelling to explore the effects of various process parameters. Existing mesh-based modelling techniques are limited due to their inability to carry history information such as accumulated oxide mass per-node. Instead, the grid-free Smoothed Particle Hydrodynamics method with its Lagrangian framework is used to predict the oxide mass generated during a melt transfer from a tilting furnace into a sow mould. An oxidation model based on laboratory-scale skimming trials is used. Favourable comparisons with experimentally measured oxide levels are obtained for various transfer rates. [ABSTRACT FROM AUTHOR]

This study involves simulation of blood flow through a non-pulsatile, axial pump consisting of a complex multi-sectioned impeller with rotating and stationary components, and a stationary housing. We use a particle-based method, Smoothed Particle Hydrodynamics (SPH), to investigate the effects of varying the impeller blade pitch angle and the gap size between the rotor and housing. We show that the impeller blade inclination affects pump performance and the level of shear-related blood damage. The inclusion of a rotor-housing clearance results in flow losses that reduce the efficiency of the pump but also reduce the viscous energy losses in the pump. [ABSTRACT FROM AUTHOR]

Abstract: The geometric complexity and high fluid speeds involved in high pressure die casting (HPDC) combine to give strongly three dimensional fluid flow with significant free surface fragmentation and splashing. A simulation method that has proved particularly suited to modelling HPDC is Smoothed Particle Hydrodynamics (SPH). Materials are approximated by particles that are free to move around rather than by fixed grids, enabling more accurate prediction of fluid flows involving complex free surface motion. Three practical industrial case studies of SPH simulated HPDC flows are presented; aluminium casting of a differential cover (automotive), an electronic housing and zinc casting of a door lock plate. These show significant detail in the fragmented fluid free surfaces and allow us to understand the predisposition to create defects such as porosity in the castings. The validation of flow predictions coupled with heat transfer and solidification is an important area for such modelling. One powerful approach is to use short shots, where insufficient metal is used in the casting or the casting shot is halted part way through, to leave the die cavity only partially filled. The frozen partial castings capture significant detail about the order of fill and the flow structures occurring during different stages of filling. Validation can occur by matching experimental and simulated short shots. Here we explore the effect of die temperature, metal super-heat and volume fill on the short shots for the casting of a simple coaster. The bulk features of the final solid castings are found to be in good agreement with the predictions, but the fine details appear to depend on surface behaviour of the solidifying metals. This potentially has significant implications for modelling HPDC. [Copyright &y& Elsevier]

Abstract: The Smoothed Particle Hydrodynamics method for elastic solid deformation is modified to include von Mises plasticity with linear isotropic hardening and is then used to investigate high speed collisions of elastic and elastoplastic bodies. The Lagrangian mesh-free nature of SPH makes is very well suited to these extreme deformation problems eliminating issues relating to poor element quality at high strains that limits finite element usage for these types of problems. It demonstrates excellent numerical stability at very high strains (of more than 200%). SPH can naturally track history dependent material properties such as the cumulative plastic strain and the degree of work hardening produced by its strain history. The high speed collisions modelled here demonstrate that the method can cope easily with collisions of multiple bodies and can also naturally resolve self-collisions of bodies undergoing high levels of plastic strain. The nature and the extent of the elastic and plastic deformation of a rectangular body impacting on an elastic wall and of an elastic projectile impacting on a thin elastic wall are investigated. The final plastically deformed shapes of the projectile and wall are compared for a range of material properties and the evolution of the maximum plastic strain throughout each collision and the coefficient of restitution are used to make quantitative comparisons. Both the elastoplastic projectile–elastic wall and the elastic projectile–elastoplastic wall type collisions have two distinct plastic flow regimes that create complex relationships between the yield stress and the responses of the solid bodies. [Copyright &y& Elsevier]

The present study reports on the extension of smoothed particle hydrodynamics (SPH) of high pressure die casting to realistic three-dimensional components. Predictions of the isothermal filling of a moderately complex die in 3D demonstrates the importance of flow separation off corners, edges and faces with high curvature and the non-intuitive order of fill resulting from complicated back flows. The free surface behaviour involves significant transient void formation and free surface fragmentation. The predictions are shown to be insensitive to the Reynolds numbers. Their accuracy is confirmed by comparing simulations with coarser and finer resolutions. [ABSTRACT FROM AUTHOR]

In this paper we present the extension of smoothed particle hydrodynamics (SPH) modelling of high pressure die casting (HPDC) to both three-dimensions (3D) and to realistic die geometries. The SPH method is well established in other areas and is now used for HPDC. The SPH method (in 3D) and the methodology used to represent complex three-dimensional die shapes are described. The use of this SPH system to model the filling of a representative generic HPDC component is presented. The importance of the order of the die filling, first seen in two dimensions, is demonstrated as is the role of flow separation from corners and even moderately curved surfaces. The degree of surface fragmentation, droplet formation and the strongly transient nature of the voidage are also shown. Finally the filling of the runner, gate and die for a real automotive piston head from an automatic transmission is shown and the difficulties inherent in such large scale computations are discussed. [Copyright &y& Elsevier]

• A coupled DEM + SPH model is extended to include fine rock slurry size fractions. • Shear induced fine particle dispersion is represented as diffusion solved using SPH. • A local PBM is solved for each SPH particle to predict grinding of the slurry. • Fine particle grinding is controlled by the rate of DEM energy dissipation. • The model is demonstrated in a 1.8 m diameter by 0.6 m long Hardinge pilot mill. A coupled DEM + SPH model can be used to predict the motion and breakage of resolved coarser particles within a SAG mill. The fine product from coarse particle fracture can then be included in the slurry phase modelled using SPH. This allows, in principle, the prediction of the breakage and transport of coarser material and the transport of the finer material within the grinding and pulp chambers of a SAG mill including discharge performance of the mill. It also allows the effect of the changing solids loading on the slurry rheology to be included. In this paper we will explore the development of an extension of this model that also allows prediction of the grinding of the finer particles embedded in the slurry phase due to the collisions and shear of the coarser particles (rocks and grinding media). The size distribution of the slurry fines is discretised into a set of size fractions so that its change due to grinding can be tracked at each point in the slurry. This is formulated as a system of coupled advection-diffusion equations. An SPH discretisation of this system is then developed. The resulting coupled SPH ODE's are solved using the SPH method in a way that is fully coupled to the DEM and SPH parts of the model. The proposed model includes a diffusive component that allows for the shear induced dispersion of the slurry size fractions and allows prediction of the spatial distribution of these fine size fractions within the slurry phase. The advection of the slurry is automatically accounted for by the motion of the SPH particles which is an important benefit of using the SPH method for such wet mill modelling. The local fine grinding behaviour arising from the coarse DEM resolved components of the charge are characterised at each location in terms of the local energy dissipation rate. This information is used in conjunction with a first order grinding law to predict the grinding of each slurry size fraction at each location in the mill due to the collisional action of the coarser particles. The ability of this new model to predict fine particle grinding and transport within the slurry phase is demonstrated for an industry standard 1.8 m diameter by 0.6 m long AG/SAG pilot mill. [ABSTRACT FROM AUTHOR]

• SPH and FVM models have been compared for buoyant flow in a stomach geometry. • The curved shape of the stomach leads to rapid layer inversion due to the development of a swirling flow. • Rayleigh–Taylor instability (RTI) is well–captured in the SPH model. • The FVM leads to more complete final separation. • SPH kernels with smaller compact support behave better in separation processes. The primary functions of the stomach, including mixing, digestion, and emptying, are affected by the spatial distribution of content properties, and how this distribution changes in response to gravity and wall contraction forces. One aspect that is not well studied is the buoyancy effects that result from content with heterogenous density. A buoyancy–driven flow in a non–deforming stomach is simulated using the Smoothed Particle Hydrodynamics (SPH) and Finite Volume Method (FVM). An aqueous liquid layer is initially placed above a fatty layer of the same volume. The buoyancy effect driven by gravity and strongly influenced by the stomach shape, causes the fat to rise to the top layer and the aqueous liquid to sink to the bottom. Rayleigh–Taylor Instability (RTI) is well–captured in the SPH model in the initial interface flow development. Some detailed flow behaviours are slightly different between the two models once the bulk turnover flow is established, but both models show that the separation process happens rapidly (within 6 s) in the curved geometry of the stomach. The final phase separation is more complete in the FVM compared with the SPH. Sensitivity analysis is conducted in both models to examine the solution accuracy. This work suggests that buoyancy driven flow effects, which have not been investigated previously, occur on a much shorter timescale (6 s) than peristaltic (20 – 60 s) and digestion timescales (hours). This result may help basic understanding of digestive processes and be used to guide food and drug design. [ABSTRACT FROM AUTHOR]

Two-way coupling of the effects of wave impact on moored offshore structures is a challenging problem, especially in the case of large amplitude motions produced by extreme wave impact. We explore fully-3D wave impact behaviour on a semi-submersible platform using Smoothed Particle Hydrodynamics (SPH). Wave impact and propagation around and through the structure is complex and induces non-trivial motion. Large waves can impact the underside of the production deck or the upper superstructure. Such impacts can induce dangerous motions, threaten the structural integrity of the platform and create significant risk to people and equipment. These issues are investigated for different mooring configurations and a range of wave heights. [ABSTRACT FROM AUTHOR]

SPH is a powerful mesh free method that is now able to solve very complex multi-physics flow and deformation problems in a broad number of fields. This paper concentrates on the use of SPH to simulate a broad range of complex industrial fluid flow problems. These include free surface fluid flow for the generation of digital content, geophysical flows such as volcanic lava flows and tsunamis, several types of die casting (gravity, high pressure and ingot casting), resin transfer moulding and flow in porous media, mixing of particulates in liquid, pyrometallurgy and slurry flow in semi-autogenous grinding mills. The strengths and weaknesses of SPH will be explored and future opportunities for using the method to make major modelling advances are discussed. [ABSTRACT FROM AUTHOR]

Platform diving injuries are common, especially in the arms, neck and back, and appear to arise from cumulative damage from multiple overload events as well as singular cases of acute loading. Experimental measures of forces on the body are impractical so instead computational simulation is used to estimate this loading. A coupled Biomechanical-Smoothed Particle Hydrodynamics (B-SPH) model for diver and water is developed and applied to a reverse pike dive performed by an elite athlete. The body surface is represented by a mesh that deforms in response to measured skeleton kinematics acquired from multi-camera video. Calculations of the fluid forces on the body and the transmission of torque through the upper body joints are made. Loading on the body segments and joints is found to be closely related to the dynamic behaviour of the body and water. The sensitivity of the results of the model to variations in water entry pitch angle (EPA) is explored. Simulation results suggest that altering the timing of contact between the water and different body segments changes the loading and potentially the injury risk of the dive. The simulation framework presented shows promise as a tool for coaches and sports scientists to evaluate the performance, strength requirements and safety of diving technique. [ABSTRACT FROM AUTHOR]

• Friction modeling capabilities of existing SPH approaches are evaluated. • Limitations associated with these are identified for low velocity elastic impacts. • An improved Collisional SPH approach for friction modeling is presented. • Rebound and deformation predicted by CSPH is validated. • CSPH is found to accurately reproduce both. Accurate modeling of rebound kinematics in particle-substrate collisions is essential in a wide range of applications like milling and mixing. To accurately model these real-world collisions the forces arising due to elastoplastic deformation and friction need to be modelled accurately. In this study the use of frictional boundary conditions in modeling elastic collisions with Smooth Particle Hydrodynamics (SPH) is explored. The collision dynamics for an oblique impact of a 3D spherical granule on an elastic substrate is assessed for SPH (a) without any special treatment for friction and (b) using Coulomb's friction model, and it is identified that these approaches are inaccurate in some instances. To resolve this, spring-based contact models are incorporated in SPH to develop a new method for improved contact modeling. We call this method Collisional SPH. This Collisional SPH method predicts both rebound kinematics and surface deformation accurately. This method opens new avenues for further development in modeling collisional deformations and collision dynamics in granular systems using SPH. [ABSTRACT FROM AUTHOR]

Abstract: Understanding the caving process and material flow is fundamental to block and sublevel cave mining, and also to longwall mining in sedimentary deposits. In this paper, the application of a mesh-free method, called Smoothed Particle Hydrodynamics (SPH), is demonstrated for simulating rock caving in a stratified deposit. The advantages for simulating caving processes using a mesh-free numerical framework are highlighted. Two different examples are chosen, one with elastic-brittle material behaviour with large yield strength (failure by brittle fracture) and the other with elasto-plastic material behaviour with relatively lower yield strength to allow ductile deformation of the rock mass. The modelling results capture the mechanistic aspects observed in caving processes. It is shown that the large-scale deformation and the associated fracture processes in caving can be effectively simulated using SPH. In the authors’ knowledge, this work is the first attempt in demonstrating the application of a mesh-free method for simulating caving processes. [Copyright &y& Elsevier]

Elastoplastic frictional collisions are encountered in a wide range of applications. For modelling these, inclusion of both the elastoplastic material response and history-dependent collisional forces is essential. The Collisional-SPH method, originally developed for elastic collisions, incorporates frictional collision forces into SPH and accounts for their history-dependence. In this paper, CSPH is extended to model elastoplastic collisions by incorporating an elastoplastic material model. A thorough validation of this elastoplastic CSPH method is presented. CSPH is then used to analyse the influence of deformation on history-dependent collision forces. It is found that the elastoplastic deformation and the resulting shape change of the substrate alter the contact-zone mechanics by influencing the local tangential force distribution. These effects become more pronounced with increasing deformation. • Collisional-SPH is extended to model elastoplastic frictional collisions. • Predicted substrate deformation and rebound kinematics are validated with several experiments. • The pure sliding limit is found to increase with substrate deformation. • Substrate deformation also leads to a reduced rebound spin magnitude as the impact angle increases. [ABSTRACT FROM AUTHOR]