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Screw conveyors are extensively used in modern industry such as metallurgy, architecture and pharmaceutical due to their high-efficiency in the transportation of granular materials. And substantial efforts have been devoted to the study of the screw conveyors. Numerical method is an effective way to study screw conveyor. However, previous studies have mainly focused in the regime of spherical particles while the in-depth investigations for non-spherical particles that should be the most encountered in practical applications are still limited. In view of the above situations, discrete element method (DEM), which has been widely accepted in simulating the discrete systems, is utilized to investigate the conveying process of non-spherical particles in a horizontal screw conveyor, with particles being modeled by super-ellipsoids. In addition, a wear model called SIEM (Shear Impact Energy Model) is incorporated into DEM to predict the wear of screw conveyor. The DEM simulation results demonstrate that the particle shape is influential for the flow behaviors of particles and the wear of conveyor. The conveying performance evaluated quantitatively of both mass flow rate and power consumption is subsequently obtained to investigate the effect of sphericity of particle with different operation parameters. Moreover, particle collision frequency and collision energy consumption are acquired to investigate the possible particle breakage between particles and screw blade. The comparisons between particle–particle collision and particle–wall collision reveal that particles with large shape index have more possibility to be damaged in particle–wall impingement.

Vibrating separation is a significant method for liquid–solid separation. A typical example is the vibrating screen to dewater wet granular matter. The properties of granular matter and the vibrating parameters significantly affect the separation efficiency. This study investigates the effect of vibration parameters in separation based on the breakage of large-scale liquid bridge numerically by using a calibrated simulation model. Through analysing the simulation results, the liquid bridge shape and the volume between two sphere particles for various particle sizes and particle distances were studied in the static condition under the effect of gravity. The results show a general reducing trend of liquid bridge volume when the radius ratio of two particles increases, particularly when the ratio increases to 5. Additionally, a set of vibrating motion was applied to the liquid bridge in the simulation model. A group of experiments were also performed to validate the simulation model with vibration. Then, the effect of vibrating peak acceleration, distance between spheres and radius on the separation efficiency which was reflected by the residual water were investigated. It is found that separation efficiency increased obviously with the peak acceleration and the increase slowed down after the peak acceleration over 1 m/s2.

In this paper, a rigorous computational study is carried out on the three numerical methods: cell average technique (CAT), weighted finite volume scheme (WFVS), and quadrature method of moments (QMOM). Each method is analyzed to solve the population balance equation coupled with hydrodynamics. Different test cases have been considered for aggregation, breakage, simultaneous aggregation and breakage processes with four different aggregation kernels and uniform breakage function. Both the advantages and disadvantages of those methods are thoroughly investigated for the PBE coupled with hydrodynamics. Based on accuracy and efficiency, it is recommended that the WFVS is a smart choice for computing number density and moments in the case of inhomogeneous PBE.

Scale-up of the liquid-liquid extraction columns like asymmetric rotating impeller column (ARIC) from laboratory to industry is an expensive procedure in terms of resources, inventory, human resources, and time. Local hydrodynamics of the column governs the breakage and coalescence of the drop and thus the mass transfer performance of the column. The correlations developed for scale-up procedures by experimentation at laboratory scale cannot ensure the local properties like velocities, turbulence, and dispersed phase holdup to be the same in the large scale columns. In the present work, the CFD methodology has been proposed for the scale-up of ARICs. CFD simulations have been carried out in three geometrically similar ARICs, to check for the kinematic similarity. The predicted dispersed phase holdup is found to agree with the experimental results with an average absolute value of the relative error within 20%. The local velocities and turbulence properties are compared for three scales. The local velocities and turbulence are observed to scale with the tip speed. CFD simulations show that the flow patterns and turbulence scale with increased column diameter and scale-up can be made based on geometric similarity at equal specific power and tip speed.

Pneumatic conveying of coal particles widely used for environmental friendliness and automation. In this study, orthogonal experiments were carried out in 90° elbows of large coal particles (7–15 mm) to study the effect of the elbow shape, particle size, airflow velocity, and gas supply pressure on elbow erosion. Elbows with double-layer wall structures were designed to present the erosion characteristics, particle breakage ratio, and pressure drop. Results indicate that the angle between the erosion center and the tangential direction of the elbow inlet is approximately 25°–30°. The elbow shape and airflow velocity have significant effects on all three evaluation indices, whereas the particle size and gas supply pressure have significant effects on the pressure drop. The optimal parameters of each factor were confirmed: the blind elbow with a plug, particle size of 9–11 mm, airflow velocity of 20 m/s, and gas supply pressure of 0.4 MPa.

Impact breakage is one of the main cause of rice injury during harvest and processing. In this work, the effect of impact velocity on breakage probability and modes of rice is studied by experiments. Furthermore, the impact process of rice is simulated by finite element method. The results indicate that the breakage of rice is closely related to the impact velocity. The initiation and propagation of the single meridian crack is one of the important mechanisms leading to rice breaking. A conical region is formed below the contact region when the rice is hit at high velocity. The multiple oblique meridian cracks with irregular propagation are produced under the effect of high tensile stress at the edge of region. Meanwhile, a mathematical model can describe the relationship between impact velocity and breakage probability well. These findings provide a basis for reducing the loss of agricultural products in harvest and processing.

This paper presents a breakage model of particulate solids under impact loading based on a mechanical approach. Existing breakage models are assessed using the experimental data from single particle impact tests, indicating a more general breakage model is required. Indentation fracture mechanics is used to account for surface damage under dynamic loading. The effect of impact angle is considered in the model, which rationalizes the contributions of both the normal and tangential impact velocity. A unified curve of breakage propensity is constructed using the equivalent velocity under oblique impact based on the experimental data from this study and the literature. This model provides a basis to evaluate breakage propensity of brittle/semi-brittle particles subject to oblique impact and the proposed equivalent velocity has a potential to improve the description of impact energy spectra for milling processes where oblique impact of particle is common and typically ignored.

Several tests are normally used to analyze the resistance of rocks and ores to breakage in the mining/aggregate industries. Some of these tests yield results that serve as basis for either simple mathematical expressions or comprehensive models, whereas others are essentially only used to classify a rock or ore in comparison with others. The present work demonstrates that the outcomes of three of these tests, namely the Bond crushability index, the JK Drop Weight Test and the Los Angeles abrasion test, can be predicted from simulations using the discrete element method with polyhedral particles with a particle replacement model. In addition to that, a sensitivity analysis of the predictions for the drop weight test results on the basis of selected simulation variables is analyzed, resulting in recommendation of optimal values. The work demonstrates the validity of the breakage model and its ability to describe outcomes of tests that are recognized to capture different aspects of the breakage response of brittle particulate materials.

An approach for particle breakage simulation based on the framework of discrete element method was proposed in the current study. Convex polyhedron blocks were adopted as elementary particles for the complex particle shapes, and the variability of particle breakage strength is modeled using the invertible function method. Additionally, the traditional modified “Brazilian” criterion was adopted as the breakage criterion. Under the assumption that the eventual fractures within a particle can be determined according to the contact points and the centroid of the particle, once a target particle fulfilled the breakage criterion, it was cut into several fragments by a series of virtual cutting faces, which are consistent with the eventual fractures. With this, the production of local stress and the non-conservation of mass and volume can be avoided. A pre-defined fragmentation mode was also unnecessary for this approach. A series of numerical triaxial tests adopting this new presented approach was then conducted according to the configurations reported in the literature and comparisons made with experimental results. It revealed that while the presented approach is capable of reproducing the macroscopic shear responses and particle breakage characteristics of breakable particle assemblies, some fragmentation modes of particles such as surface grinding and corner abrasion cannot be captured using this approach, presenting an area for future investigation.

Breakage occurs in several particulate systems that are simulated using the discrete element method (DEM), namely crushing and grinding as well as inadvertently in several others that include transportation, handling, mixing, separation and geotechnical applications. Different approaches may be used to describe particle breakage using DEM, but in cases in which particle breakage influences significantly the flow behaviour of the material, imbedding the breakage description in DEM provides the only valid alternative. This study describes the implementation of a detailed breakage model based on particle replacement with spheres in the commercial software EDEM. It accounts for variability and size-dependency in particle fracture energies, weakening of particles by unsuccessful stressing events, as well as addressing several reported shortcomings in sphere replacement schemes. The model is verified in great detail on the basis of single-particle breakage information and validated using measurements in unconfined particle beds of mineral ores.

A study was performed to analyze the evolution of particle size distribution in the chocolate roller refining process. A mathematical model based on the continuity and population balance equations was developed to interpret industrial data. The industrial data were provided for chocolate pastes with powder/crystalline sugar particles at low/high shear rates. The parameters of the breakage frequency and fragment distribution function were estimated using industrial data. After parameter fitting, the model shows good agreement with the experimental results for varying conditions with a single consistently chosen set of parameters. This provides confidence that the general model structure is suitable for process evaluation. The population balance model was used to analyze the influence of changing some process variables on the efficiency of grinding. The results show that there might exist optimum values of the roll’s diameter and rotational velocity for a specific configuration of the equipment.

The mechanism that leads to fine particle production during pulse combustion drying is still unclear. Although droplet breakup could happen, it cannot result in particles below micron-size. Here production of fine particles during pulse combustion drying is investigated experimentally and numerically. Experiments with three different materials, namely SiO2, TiO2, and maltodextrin, have been conducted to see how the material types and process conditions influence the physical properties of the products. The results show that fine particles can be obtained with and without pulsation, and no significant differences are observed with the variation of pulsation frequency. The volume fraction of the fine particles is, however, very low. Based on these results, a model of particle production through repetitive crust breakage and drying cycles is proposed. The obtained results are in agreement with the experimental data, and the proposed mechanism could explain the production of fine particles with and without gas pulsation.

Ball milling is widely used in industry to mill particulate material. The primary purpose of this process is to attain an appropriate product size with the least possible energy consumption. The process is also extensively utilised in pharmaceuticals for the comminution of the excipients or drugs. Surprisingly, for ball mill, little is known concerning the mechanism of size reduction. Traditional prediction approaches are not deemed useful to provide significant insights into the operation or facilitate radical step changes in performance. Therefore, the discrete element method (DEM) as a computational modelling approach has been used in this paper. In previous research, DEM has been applied to simulate breaking behaviour through the impact energy of all ball collisions as the driving force for fracturing. However, the nature of pharmaceutical material fragmentation during ball milling is more complex. Suitable functional equations which link broken media and applied energy do not consider the collision of particulate media of different shapes or collisions of particulate media (such as granules) with balls and rotating mill drum. This could have a significant impact on fragmentation. Therefore, this paper aimed to investigate the fragmentation of bounded particles into DEM granules of different shape/size during the ball milling process. A systematic study was undertaken to explore the effect of milling speed on breakage behaviour. Also, in this study, a combination of a density-based clustering method and discrete element method was employed to numerically investigate the number and size of the fragments generated during the ball milling process over time. It was discovered that the collisions of the ball increased proportionally with rotation speed until reaching the critical rotation speed. Consequently, results illustrate that with an increase of rotation speed, the mill power increased correspondingly. The caratacting motion of mill material together with balls was identified as the most effective regime regarding the fragmentation, and fewer breakage events occurred for centrifugal motion. Higher quantities of the fines in each batch were produced with increased milling speed with less quantities of grain fragments. Moreover, the relationship between the number of produced fragment and milling speed at the end of the process exhibited a linear tendency.

The timescale difference between the “fast” flow dynamics of fluidized bed reactors and the relatively “slow” rate of particle degradation makes the direct computational prediction of attrition challenging. An approach to this challenge is a multi-fidelity strategy where a high fidelity model for the flow dynamics is coupled with a lower fidelity model for the long-time resolution of the bulk attrition of the reactor inventory. We implement this approach using high-fidelity kinetic theory simulations to calculate the flow dynamics which are post-processed to calculate the frequency and intensity of the particle-particle and particle-wall collisions (e.g. collision energy spectra). This is combined with the particle breakage properties to construct the coefficients for a low-fidelity model [e.g. Monazam et al., 2018, Powder Technology 340, p. 528–536]. Simulations are performed of a jet cup attrition system containing Canadian hematite (Monazam et al. 2018). These are first analyzed using the collision energy spectra. Quantitative predictions of the mass loss are made using a low-fidelity model derived from the collision-spectra and a calibrated material breakage coefficient. The results are found to compare favorably with the experimental measurements.

Hydrodynamics of fluidization of hydrophilic titanium nanoparticles with vibration was investigated through pressure fluctuations using recurrence quantification analysis. The bed expansion revealed that the bed operates in the ABF regime. The standard deviation of the pressure fluctuations indicated that vibration reduces the minimum fluidization velocity. Hydrodynamic structures were defined using the wavelet transform analysis of pressure fluctuations and the effect of vibration was investigated through the energy of the pressure signal and the recurrence analysis. It was shown that the agglomerates have the most impact on the fluidization of the nanoparticles and vibration has a significant effect on this structure. Using the energy of the signal and recurrence analysis, characteristics of the vibration on the fluidization were defined. The energy of finer structures is higher in the vibrated bed, indicating a more stochastic pattern in this case. The recurrence rate showed the dynamic behavior of formation and breakage of agglomerates in the bed.

A numerical degradation model based on two key-functions, the so-called selection and breakage functions, is developed and implemented into a coupled DEM-CFD approach for investigating wood pellet degradation and fines formation during pneumatic conveying by particle-wall impact. The influence of operating conditions like air flow, product flow and solids loading ratio as well as of pipe component geometry on degradation is examined. Detailed insights into the flow field and particle motion are obtained. The inter-particle and particle-wall collisions are statistically analysed since they are the major cause of particle degradation. Apart from operating conditions, the bend radius is varied in four steps, supplemented by a 90°-Elbow as the worst-case scenario and a straight pipe section for reference. Increasing air flow rates, and thus higher particle velocities, as well as decreasing pellet mass flows and smaller bend radii result in progressive particle degradation. Particle-wall collisions turned out to be the major reason for particle breakage. Numerical results are compared to experimental data and show good agreement.

Force-chain is the main load-bearing structure in the granular materials. The study of force chains and particle breakage is of great significance to understand the mechanical properties of the granular materials. At present, the internal relationship between the force chains and particle breakage is still unclear. It also has no idea about the crushing mode of the particle system with complex gradation and stress path. Therefore, in the present paper, the continuous-discontinuous numerical method (Numerical Manifold Method, NMM) is utilized to simulate the process of the force chains generation and particle breakage in granular material and to explore their internal connection mechanism. The simulation results show that the particle breakage is directly related to the force-chain network, and the particle breakage morphology is basically consistent with the direction of the force-chain network in the granular system. Small particles are broken firstly, producing large displacement to fill the voids in the system. Although the larger particles can also be broken, it is difficult to produce large displacement due to the influence of coordination number among particles. Furthermore, particle breakage can reduce the strength of the force-chain, resulting in that the larger particles in the force-chain will be broken slightly or not.

When considering the bomb explosion damage effect, the air shock wave and high-speed fragments of the bomb case are two major threats. In experiments, the air shock wave was studied by the bare explosives superseding the real cased bomb; in contrast, the bomb case influence was ignored to reduce risk. The air explosion simulations of the MK84 warhead with and without the case were conducted. The numerical simulation results showed that the bomb case significantly influenced the shock wave generated by the bomb: the spatial distribution of shock wave in the near field changed, and the peak value of shock wave was reduced. Breakage of the case and kinetic energy of the fragmentation consumed 3 and 38% of the explosion energy, respectively. The increasing factors of the peak overpressure induced by the bare explosive on the ground and in the air were 1.43–3.04 and 1.37–1.57, respectively. Four typical stages of case breakage were defined. The mass distribution of the fragments follows the Mott distribution. The initial velocity distribution of the fragments agreed well with the Gurney equation.

A bi-directional coupling between the Discrete Element Method (DEM) and Population Balance Modelling (PBM) is suggested to model the failure of pharmaceutical tablets under abrasive conditions such as bulk flow of impact. DEM provides the description of kinetics and permits the extraction of collision energy distributions. Representation of the primary shape of the tablets is achieved by using the multi-sphere approach, a rigid assembly of systematically connected spheres to resemble non-spherical shape. Based on the collision energy distribution and the abrasion characteristics of the tablets by solving the PBM equations, the mass loss of tablets according to their mechanical resistance, as well as the fragment size distribution progeny can be computed. For the description of the abrasive failure characteristics, a multi-stage calibration procedure for the empirical breakage kernels of Vogel and Peukert as well as of Ghadiri and Zhang is also applied. The novelty of the presented approach is the bi-directional coupling: tablet and fragment distribution masses are dynamically updated for subsequent time steps in DEM by the particle replacement method according to the stress history of the system. The outcome of this methodology helps to get a deeper understanding of the process-property relationships, to evaluate the effect of any process or geometry modifications in processing operations, such as drum coating, and to reduce the requirements of experimental investigations.

When soil particles break, the particle size distribution (PSD) becomes a variable in the same way as other variables like void ratio, soil structure and anisotropy, etc. To consider particle breakage in a constitutive model, we need three key components: (i) quantification of PSD in a realistically simple manner, (ii) evolution of PSD during particle breakage, and (iii) influences of PSD on other soil properties like strength and stiffness. This paper firstly summarizes the latest advances in the first two components, discusses new ways of quantifying PSD effects, and finally presents a new critical state model where the PSD is treated as a variable. In discussing the PSD effects, we focus on the movement of the critical state line (CSL) due to particle breakage. We introduce a new state parameter and a new evolution law of the CSL. We assume that the CSL shifts downwards in the v—lnp space with increasing particle breakage under relatively low stresses, but all the CSLs for different PSDs converge to a steady state at high stresses where particle breakage eventually stops and is no longer the main mechanism for soil deformation. The proposed model is compared with other constitutive model in the literature and validated against experimental data, which demonstrates its satisfactory performance.

In the framework of the Euler-Euler gas–solid two-fluid model, the particle population balance equation is solved by the direct quadrature method of moment. The dynamic process of ultrafine particle movement and aggregation in an internally circulating fluidized bed is simulated. The distribution of the concentration and velocity of the agglomerates in the flow process is given, and the changes of the moments in the bed are shown. The effects of different breakage coefficients and inlet gas rates on the concentration distribution of agglomerates are compared. The results show that the particle size decreases with the increase of breakage coefficient, and the time required to reach steady fluidization state increases; the higher the inlet velocity, the better the effect of circulating particles in the bed. When there is a certain gas velocity difference between the two sides, the effect of circulating particles in the bed is better.

The particle based Discrete Element Method (DEM) can be applied to examine comminution processes. In this study, a DEM framework has been extended to model particle breakage without mass loss. After a breakage event occurs, spherical particles, as often considered in the DEM, are replaced by size reduced spherical fragments. During the following time steps, the fragments grow to their desired sizes, so that the mass loss can be counterbalanced. Previously defined overlaps with adjacent unbroken and broken particles (fragments) as well as walls are allowed. The breakage model has been realized in a parallelized DEM framework because comminution processes are often attributed to large numbers of particles and by parallelization the computational time can be reduced efficiently. An oedometer (one-dimensional compression in axial direction of a confined particle bed) has been modelled to investigate the parallelization efficiency and the influence of the permitted overlaps during the growth process on the growth duration. A simplified roller mill has been considered to examine the applicability of the breakage procedure considering parallelization. The results show that parallelization reduces computational time considerably. The breakage procedure is suitable to model comminution processes involving even densely packed particle systems and is superior to existing approaches.

Bubble columns are widely used as multiphase reactors for gas–liquid reactions in industrial applications. For the sensitivity and usability analysis of the bubble column in the process development, a model is needed that incorporates couplings between the fluid dynamics, the population balance equation (PBE) and the thermodynamics. Thereby the model should be as fast and reliable as possible. A suitable candidate is the kinetic theory approach with size resolution (KTAWSR), as one of the most rigorous combined multifluid-PBE models. A steady-state and one-dimensional version of the KTAWSR model was used and extended to batch bubble columns. For this purpose, a new approach for the determination of the integral gas holdup was developed which does not require additional empirical correlations. The spectral orthogonal collocation method was used to solve the model equations. Different breakage and coalescence model combinations were calibrated, compared and investigated on the basis of measured bubble size distributions. To validate the model, the integral gas holdup and the bubble size distribution were measured at four axial positions at three gas volume fluxes reaching the transition flow regime in a batch water–air bubble column. The novel integral gas holdup calculation approach could be predictively confirmed with measured data.

A multiphase computational fluid dynamics (CFD) model coupled with the population balance equation (PBE) was developed in a homogeneous air–kerosene bubble column under elevated pressure (P). The specific pressure drop (ΔP/L), gas holdup (αG), and Sauter mean diameter (d32) were experimentally measured in the bubble column with 1.8 m height and 0.1 m inner diameter, which was operated at a superficial gas velocity of 12.3 mm·s−1, and P = 1–35 bar (1 bar = 105 Pa). A modified drag coefficient model was proposed to consider the effect of bubble swarm and pressure on hydrodynamics of the bubble column. The Luo breakage model was modified to account for liquid density, viscosity, surface tension and gas density. The ΔP/L, αG, and d32 obtained from the CFD model were compared with experimental data, and the gas density-dependent parameters of the CFD model were identified. With increasing P from 1 to 35 bar, the αG varied from 5.4% to 7.2% and the d32 decreased from 2.3 to 1.5 mm. The CFD-PBE model is applicable to predict hydrodynamics of pressurized bubble columns for gas–organic liquid in the homogeneous regime.

Fine grinding based on compression stresses is an important industrial process step, which is often applied in mineral, chemical and pharmaceutical industries, for example by using stirred media mills. For this stress mechanism, several studies investigate how to predict the breakage behavior depending on process and formulation conditions by population balance modelling. Breakage rate and breakage function are essential to describe the evolution in particle size distribution over time. Hereby, the division in a mill and a material model has already been shown to be a successful approach for different mills. Especially for fine particles the determination of the breakage function is a particular challenge. In order to predictively model breakage characteristics of materials, such as the breakage function for different energies applied to break the material, it is required to develop a new method, which is easy, fast, and inexpensive to carry out. For this purpose, we present a newly designed breakage tester consisting of a rigidly-mounted two-roll mill. First, a recommendation for the use of a breakage tester is developed. In this step, the investigated machine parameters include the gap size, feed rate, and roller velocity. Furthermore, the influence of feed particle size on the resulting particle size distribution was researched. All tests have been conducted with soda-lime glass as a model material. Second, the applicability of different models for the breakage function, focusing on the tnt10-model, is demonstrated. The breakage can be predicted for new energy values and is in very good agreement with the experimental data. This new breakage tester allows the fast characterization of particle breakage in lower micron range.

In the traditional Mohr–Coulomb criterion, the shear strength is determined by cohesion and friction angle. However, the particle breakage that occurs on the shear failure surface of rockfill makes it difficult to express the shear strength of rockfill using the traditional Mohr–Coulomb criterion. It is assumed that the shear strength is the friction force of the particle contact surface, and the power function relationship between the shear strength of rockfill and the normal stress is derived, where the index is a function of the particle fractal dimension. The discrete element software PFC-2D was used for numerical simulation of rock single particle crushing and rockfill direct shear test. The single particle crushing test simulates the whole process of particle crushing and verifies the size effect of particle crushing strength. In the direct shear test simulation, 8 different test parameter groups are set up to explore the effects of basic particle adhesion, single particle porosity, rockfill porosity on shear strength and body strain and verify the correctness of the derived power law shear strength formula.

This paper addresses the influence of relative density on the particle breakage of non-uniform grading coral sand by 45 one-dimensional compression tests. Dyeing tracking and image segmentation methods are adopted to reveal the particle breakage of the coral sand. The test results show that D50 (1 mm) is the critical size in deciding the breakage possibility. The number of total broken particles and the broken fine particles (d D50) are significantly greater than those of the fine particle groups (d

Population balance model is crucial for improving the method of aluminum hydroxide massive crystallization and enhancing the quality of control over industrial precipitation trains. This paper presents the updated population balance model, which can be used for simulation of industrial-scale precipitation. Processes of birth-and-spread and particle breakage are considered integral parts of the precipitation process along with secondary nucleation, growth and agglomeration of particles. The conceptual difference of the proposed system of equations is its ability to reproduce the oscillatory process that occurs in precipitation circuits as a result of cyclic changes in the quality of the seed surface. It is demonstrated that self-oscillations can occur in the system without any external influence. The updated model is adjusted and verified using historical industrial data. The simulation of seed-recycle precipitation circuit showed an exact correspondence between the calculated dynamic pattern of changes in particle size distribution of aluminum hydroxide and the actual data.

application/pdf, Chemical Engineering Research and Design. 2021, 167, P.84-95

Fragmentation of desired size in large scale open cast blasting operations is a challenge often met with limited success. Literature review on fragmentation mechanics and modelling provided a comprehensive understanding on influencing parameters affecting the mean fragment size. Scientific methods of investigation such as scaled in-situ face mapping, seismic refraction tomography and in-hole continuous velocity of detonation measurement were carried out to generate necessary data. Impedance ratio, average inter-row delay and dynamic Poisson's ratio were found to influence the mean fragment size as the key affecting parameters. A multiple linear regression model was developed to predict mean fragment size relating the key variables. Near-field vibration signatures were used to identify the role of reflection breakage mechanism, using reflection breakage index (RBI). Near-field peak vector sum was observed with mean fragment size and consequently the optimum charge configuration was determined. Using the developed fragmentation model, an effective row to row delay of 14–18 ms/m of effective burden and maximum charge per delay of 1000 kg was found to be optimum to achieve the desired mean fragment size in the range 43–57 cm. This was in addition to reduction in near-field vibrations, superior bench slope conditions and negligible backbreak. The modifications were simulated in JKSimblast to observe the delay contours. Implementation of suggested blast design yielded a 12–15% increase in dragline productivity apart from appreciably reducing the dragline breakdowns.

Frozen soil is a multiphase heterogeneous composite, whose mechanical properties are controlled by the different constituent materials properties and the internal breakage mechanism. In response to this issue, a multiscale incremental elastoplastic constitutive model for frozen soil is derived to reflect this internal mechanical mechanism through micro-thermo-mechanics and homogenization theory, which includes two homogenization steps: breakage stage (I step) and constituent materials stage (II step). Firstly, the nonlinear homogenization process in the first step is transformed into linear homogenization through Hill's linearization method and the incremental constitutive model is given with the elastic/plastic increment strain concentration tensors by the self-consistent theory, which considers the breakage mechanism, and a new method for determining the volumetric breakage ratio is developed by means of thermodynamic theory, which has a more rigorous theoretical framework than previous methods. Secondly, in the second homogenization process, the elastic stiffness tensor of bonded elements, which is composed of unbroken material with elastic properties, is given by M-T method (incremental constitutive model). Meanwhile, the elastical-plastic stiffness tensor of frictional elements is determined by using a new Eshelby's tensor for elastic-plastic medium (incremental constitutive model). Finally, the specific application of this model for frozen soil is given, and the rationality is demonstrated by comparing the computed and tested results under conventional triaxial compression test.

In mineral processing, stirred mills have become a common device due to their high energy efficiency. In this work, the kinetics of batch wet grinding studies were studied using six mono-sized fractions of quartz. The population balance model (PBM) was used to simulate the evolution behavior of the particle size distribution in a laboratory scale stirred mill. The parameters of PBM were obtained by calculations performed on experimental data. The results showed that the breakage behavior of each class followed a first-order model in the grinding process. Furthermore, the particle size distribution was back calculated from the determined parameters of the PBM. The simulated results were analyzed by the attainable region (AR) method to maximize the volume fraction of the desired size (−45 + 10 μm) in grinding products. The results obtained indicated that the turning point and switch point were largely dependent on the feed size. These results suggest that a finer feed size is a better choice if the objective is to maximize the volume fraction of the desired size in the shortest residence time possible in a grinding circuit with a classifier. In addition, at the initial stage of grinding, the influence of the specific energy input on the yield of the desired size and overgrinding size for different feed sizes was significant.

Droplet breakage is a common phenomenon in converting a pipe flow to a swirl flow in a vane-type pipe separator (VTPS)’ inlet. The evaluation of the dispersed droplet sizes after breakage is crucial to the optimum design of the inlet structure and the estimation of the oil-water separation performance. This paper studies the droplet behavior in a swirl flow produced by guiding vanes. Experiments are performed with two different guiding vanes at the inlet of the VTPS. The sizes of the produced oil droplets at the downstream of the guiding vanes are measured in situ using a Malvern Insitec SX. The results indicate that the streamlined deflector is superior to the semi-elliptical plate for the VTPS’ optimization based on the comparison of the droplet sizes in their respective induced swirl flow fields, which can be explained by a modified T-model. Our study suggests that the use of the modified T-model is a reliable method to optimize the design of the guiding vane in the swirling generating stage.

The bubble breakage rate in gas-liquid bubble columns increases for organic liquid and at high pressure. This study developed a breakage model that accounts for different liquid properties in gas-liquid pressurized bubble columns in the homogeneous regime. The Luo (1996), Lehr (2002), and Wang (2003) breakage models, which are widely used for the population balance equation (PBE) of bubble columns, were compared in terms of the total breakage rate, daughter size distribution, and computational time. The model with two empirical equations, modified from Luo’s breakage kernel, was proposed. One represented bubble deformation behavior in different liquid properties in terms of buoyancy, surface tension, and viscosity. The other considered the effect of operating pressure (or gas density) on the breakage rate. The modified model was compared with experimental data and a rigorous breakage model from the literature. The proposed breakage model shows good agreement with experimental data and computational efficiency. This breakage model is applicable for computational fluid dynamics with PBE in pressurized bubble columns with organic liquids.

The scale effect is an unavoidable problem in the laboratory test of coarse-grained materials. By combining the self-developed cellular automaton program with laboratory experiments, a method of simulating the triaxial test of coarse-grained materials was proposed in this paper, and a triaxial test numerical specimen that can characterize the discontinuous, nonuniform, and heterogeneous characteristics of bulk geotechnical materials was established. The parallel grading method was adopted to create six grading curves for numerical simulation based on one in situ grading curve. The failure process and the scale effect on the strength and deformation of coarse-grained materials were analyzed and discussed. The results showed that under the same confining pressure, the peak stress and initial deformation modulus E i increased with the increase of the maximum particle size d max , while the degree of shear shrinkage and Poisson’s ration υ decreased. As the confining pressure increased, the scale effect of coarse-grained materials would be magnified. If particle breakage and migration were assumed to be neglected, the internal friction angle φ and d max would be roughly proportional, the cohesive force c fluctuated with the increase of d max , and the empirical relations between d max and c and φ were established, respectively, which provides a reference for estimating the actual shear strength parameters of coarse-grained materials on-site. The research results can provide a way of thinking for the study of the scale effect of coarse-grained materials and also have certain reference significance for inferring the strength parameters of the original-graded coarse-grained materials.

This paper presents a computational study on the interactive evolution of particle shape and particle breakage for granular material under confined compression. A novel multiscale approach combining peridynamics and non-smooth contact dynamics is employed. Breakage of more than 12,700 particles with different size, shape, and loading condition are simulated with results examined statistically. It is found that, with the progress of particle breakage, the shape of fragments tends to achieve a steady state distribution. Particle shape has profound influence on the strength and crushing pattern of individual particles and such influence is best reflected by sphericity. The average particle strength appears linearly correlated with particle shape factors and sphere-like particles tend to possess higher strength and break in a major-splitting mode. The findings help to decode the intricate crushing behavior in granular media and shed lights on future development of physically informed, simplified models for predicting particle breakage.

A novel device has been developed for continuous shearing and repeated impact of granules in order to simulate granule attrition and dust formation under realistic plant conditions of mechanical stresses, shear strains and strain rates. The device subjects the granules to multiple impacts at a range of velocities prevailing in typical process plants, and to shear deformations using two rollers with an adjustable gap to simulate the level of shear stresses and strains experienced during bulk motion, e.g. discharge from silos onto conveyor belts, etc. In this paper, the device operation and tests carried out to determine the settings required for attaining a desired impact velocity and shear strain rate are described. Subsequently, the extent of breakage of the granules is determined for the specified settings and the results are compared with data obtained by more established methods, e.g. annular shear cell and single particle impact tests.

The knowledge of size reduction of wood pellets during pneumatic conveying is important to achieve failure-free system operation and to set-up adequate quality assurance processes. In the present study, experiments are performed with a single particle impact test facility. A stereoscopic high-speed camera set allows 3D-particle tracking and visual analysis of the particles' degradation properties. Based on the data obtained, empirical correlations for the statistical description of the pellets' breakage behaviour are presented depending on particle length, impact velocity and collision angle. These relationships are expressed mathematically by two key functions: the so-called selection function (breakage probability) and the breakage function (fragment size distribution). As expected, higher impact velocities lead to more damage, especially at normal collisions (90°) due to the maximum change of momentum. Furthermore, smaller particles tend to be more breakage resistant as they contain less impurities and cracks. Finally, an outlook on the influence of pellet quality and target material on the particles' degradation behaviour is given. Here, pellets with higher durability tend to break at higher impact loads and into larger fragments. In addition, a softer target material (e.g. HDPE) causes less particle breakage than e.g. steel.

Mechanical degradation of iron ore pellets can have important economic and environmental implications. The work initially describes a pneumatic gun device that has been developed for characterizing breakage of pellets, by impacting them one-by-one against a target at controlled velocities, angles and against different types of surfaces. It shows that body breakage probability was only a function of the normal component of the impact and that pellets presented higher resistance and lower variability when subjected to impact than to slow compression. Mass loss due to surface breakage was well described using a model that accounts for the energy dissipated in the impact, including both normal and shear components. Parameters capturing their amenability to break either catastrophically or only undergoing surface breakage were estimated from data and the model has been validated on the basis of data from different sequences of impacts, also being used to predict the phenomenon of stabilization.

In the production process of pharmaceutical pellets with a narrow size distribution and a high sphericity, a combined extrusion-spheronization technique is frequently used. The rounding of the wet cylindrical extrudates in the spheronizer after the extrusion step is influenced by various interfering mechanisms, in particular plastic deformation, breakage, attrition and coalescence. Due to the complexity of these mechanisms which depend on the particle dynamics, there is no sufficient description of the particle rounding process in the spheronizer. In this study, the Discrete Element Method (DEM) which runs on the micro scale is coupled with a Particle Shape Evolution (PSE) model on the macro scale to describe how the particle shape changes due to collisions. For the DEM simulation a new contact model was used which was developed to capture the cyclic, dominant visco plastic deformation behaviour. Based on the DEM collision data, the changing particle shape was described in the PSE model by applying the proposed submodels for the different formation mechanisms. The resulting particle shapes obtained with this simulation framework are in a good agreement with experimental data.

The kinetic energy loss in particle-wall impact is distributed between different mechanisms. These mechanisms were modeled using only material mechanical properties, impact conditions and particle area. With this model, the particle breakage probability (BP) was plotted in terms of the available energy to damage the particle. It was found that breakage probability is scaled well with the available energy for softer targets. Thus, a generic BP function can be derived for different types of targets. Additionally, particle fracture energy is modeled in terms of surface energy and the new exposed area. This area was evaluated using Monte-Carlo simulations. The simulation results suggest that SiC fracture energy is larger compare to quartz because of smaller surface energy. For potash, the compression energy obtained in quasi-static compression tests is found to be larger than the fracture energy in impact. But if plastic deformation and fracture is considered, it exceeds the compression energy.

Experimental tests for characterizing bubble breakage dynamics in different locations of a stirred tank with a 6-bladed impeller were carried out for a range of impeller Reynolds number (Re) using water as a continuous phase. The dynamic behavior of the bubble from the injection point until arriving at the impeller region was studied by using a high speed imaging method. The deformation behavior, local breakage probability, and the local number of daughter bubbles produced from the injection point until crossing the impeller region were quantified for the whole range of power input. The dominant breakage mechanisms at different locations in the stirred tank were identified and discussed. The results revealed that during the bubble’s motion in the turbulent field, it experiences different scales of deformation depending on the location of the bubble. Highly deformed shapes were observed in the injection and impeller regions due to the bubble’s interaction with turbulent eddies. Three distinct regions between the injection position and the impeller region were observed in which different breakage mechanisms were found to govern the breakage behavior including turbulent fluctuation, shear forces, and bubble collision with the blade. High breakage probability was observed in front of the blade’s tip, with about 90% occurring within a distance of 0.35Ri from the blade’s tip (Ri is the impeller radius). In the impeller region, around 20% of the breakages occurred above the impeller close to the blade’s top, while the breakage percentage below the impeller was very small (2% as a maximum). The breakage probability and the number of daughter bubbles increased with increasing Re with a dependence of 1.3.

In this paper, was performed by numerical work according to the difference scheme. Analysis of the numerical results showed: one of the important issues of contact interaction is to determine the duration of the impact of the colliding bodies. Obviously, under the condition of a hard clutch, sticking of the striker from the barrier will not occur. To study the process of complete breakage of mechanical contact (appearance of separation zones), we will use boundary conditions that simulate a perfectly smooth impact. Analysis of the dynamics of contact resistance has shown that its magnitude and features of evolution over time substantially depend on the geometric and physicomechanical parameters of the deformable system, as well as on the type of boundary conditions. An increase in the acoustic rigidity of the impactor leads to an increase in the amplitude and duration of the impact. The impact of a less rigid punch or the presence in the barrier of a shielding layer of a polymeric material reduces the contact resistance of the plate, but the force interaction between the impacted bodies is longer. As the analysis of the results shows, the evolution of contact stresses is characterized by a number of specific features. For example, there is a direct correlation between the height of the cylinder and the time of its complete detachment from the obstacle, which corresponds to the vanishing of the function   tk  . An increase in the acoustic rigidity of the impactor leads to a sharp increase in the amplitude of the total resistance and an increase in the duration of the contact interaction. Thus, the contours of the isolines provide a visual representation of the configuration of the areas at which points the stresses develop, immediately preceding the appearance of elastoplastic deformations for spall fractures (for brittle materials).

The gas–solid separator of coupling cyclone with a built-in granular bed filter (GBF) was proposed to capture dust emitted from the industrial source. The coarse dust was separated by the rotatory motion, and the fine dust entrained by the swirl was collected by the GBF. A new geometrical parameter, named as the swirl space ratio, was introduced to characterize the mutual impacts on the coupled separator. Experimental results showed that the pressure drop decreased 10% when the swirl space ratio increased from 0.37 to 0.43, while the collection efficiency was enhanced significantly. The coupled separator with a large swirl space ratio exhibited excellent separation characteristics according to the separation quality factor. Furthermore, the contribution ratio of the cyclone shell was strengthened by increasing the swirl space ratio. The variation in the bed voidage and the pressure drop was completely opposite. The breakage phenomenon was observed in the circulation of the collector particles.

Fluidized bed opposed jet mills are capable of meeting the continuously growing demand for contamination-free fine particles. In this type of jet mill, the solid material is entrained and accelerated by expanding gas jets that are focused onto a focal point inside a fluidized bed. The resulting particle collisions induce breakage. The process is affected by the relative particle velocities and the number of particle–particle collisions. Clearly, both quantities are distributed. However, to date, neither relative particle velocities nor collision frequencies in such units have been determined. The present work introduces an innovative method to assess the stressing conditions in jet mills experimentally. To this end, mixtures of glass and ductile metal microspheres were used, with the latter employed in small amounts. Inter-particle collisions between the aluminum and glass spheres lead to the formation of dents on the microparticles. The size and number of these dents are associated with the individual collision velocities and overall collision frequencies. The correlation between dent size and collision velocity was obtained from finite element calculations based on empirical data. The proposed approach was validated using particle image velocimetry during secondary gas injection into a fluidized bed reactor. In this case the effect of the distance between two opposed nozzles was examined. For a lab-scaled fluidized bed opposed jet mill the effects of gas pressure and hold-up were investigated. Relative particle velocities were found to be significantly lower than the gas velocities, while the number of contacts per particle was determined to be extremely high.

Solid particles heavily affect the hydrodynamics in slurry bubble columns. The effects arise through varying breakup and coalescence behavior of the bubbles with the presence of solid particles where particles in the micrometer range lead to a promotion of coalescence in particular. To simulate the gas-liquid-solid flow in a slurry bubble column, the Eulerian multifluid approach can be employed to couple computational fluid dynamics (CFD) with the population balance equation (PBE) and thus to account for breakup and coalescence of bubbles.In this work, three approaches are presented to modify the breakup and coalescence models to account for enhanced coalescence in the coupled CFD-PBE framework. The approaches are applied to a reference simulation case with available experimental data. In addition, the impacts of the modifications on the simulated bubble size distribution (BSD) and the applicability of the approaches are evaluated. The capabilities as well as the differences and limits of the approaches are demonstrated and explained.

The study is concerned with the development of a model for predicting the particle size distribution resulting from the impact of nearly spherical cohesive agglomerates at a wall under a variety of impact conditions. For the derivation of the model an extensive number of discrete element simulations is carried out. The matrix of impact conditions consists of eight agglomerate size classes between 10 and 104 primary particles and seven impact angles between a flat (7°) and a normal impact (90°). To include the effect of the van-der-Waals bond strength, three primary particle diameters in the micrometer range are considered. Furthermore, the range of velocities allows to reproduce the full breakage spectrum from a rebound of an intact agglomerate to a full disintegration. The model is intended for the application in Euler-Lagrange simulations based on the hard-sphere approach ignoring the time-consuming resolution and tracking of the detailed agglomerate structure. This allows the prediction of turbulent flows with high mass loadings. For the model derivation the impact outcome is quantified by measures enabling the determination of the particle size distribution, i.e., the overall number of resulting fragments (fragmentation ratio) and the number of primary particles incorporated in the three largest fragments. The results concerning the effect of different agglomerate and impact parameters are consistent with the reported literature. Relying on this broad data base a new physically meaningful dimensionless number πimp is derived based on an empirical approach to characterize the breakage phenomenon. The advantage of the proposed dimensionless number reasonably unifying the results obtained under widely varying impact conditions is demonstrated. In addition, the disagreement detected for some of the cases can be attributed to the re-agglomeration of detached fragments due to the van-der-Waals force. Since agglomeration is separately accounted for in the multiphase simulation approach targeted by the breakage model, the data influenced by high re-agglomeration rates are not considered in the derivation of the data-driven model.

To investigate the effect of high-pressure water jet assistance on hard rock breakage by mechanical impact, a rate-dependent constitutive model was adopted to describe the mechanical behavior of the rock. Then, a numerical model of rock breakage was developed using the coupled smoothed particle hydrodynamics (SPH) and finite element method (FEM). The indenter and rock stress and rock breakage features were used to evaluate the assisted effect of the high-pressure water jet. The rock stress perturbation by water jet assistance was more intense than that by indenter impact alone, which could result in more microscopic damage in the hard rock. For the normal indenter and water jet impact velocities, the peak indenter stress could be reduced by more than 30%. As the distance between the indenter and water jet impact points increased from 0 to 12.5 mm, the peak indenter stress decreased accordingly from 71.6% to 14.7% compared with the indenter stress without water jet assistance, and it decreased with increasing distance. The influence rule of the bilateral water jets on rock breakage and indenter stress is analogous to the unilateral condition, but the enhanced degree of breakage performance with bilateral water jets is better than that of the unilateral water jet. The inclined angle of the water jet also has an important effect on the rock breakage performance, and the inclined angle in the range of 80° ~ 90° is better for hard rock breakage. The allowable intersection angle between the impact directions of the water jet and indenter is important and significant for retaining the structural integrity of the indenter.