POD-based identification approach for powder mixing mechanism in Eulerian–Lagrangian simulations

Numerous products are manufactured through powder mixing. Understanding the mixing mechanism is essential to improve product quality. Convection, diffusion, and shear are well-known classifications in the powder mixing mechanism. During powder mixing, plural mixing mechanisms may occur simultaneously. In this study, to identify the main mixing mechanisms and investigate the transition of the main mixing mechanisms, an advanced identification technique is developed by incorporating the proper orthogonal decomposition (POD) method into numerical modeling for powder mixing. The discrete element method (DEM) coupled with computational fluid dynamics (CFD) is employed to simulate powder mixing. Several investigations are performed to show the adequacy of the developed technique. First, numerous CFD–DEM simulations for solid–liquid flows are performed in a rotating paddle mixer. Next, an efficient Lanczos-based POD (LPOD) method is proposed to characterize the main features of powder mixing via the POD analysis. The results show that the mixing mechanism is dominated by convection in the early stage and by diffusion in the late stage. Besides, a novel mixing identification technique is established by giving the relation between POD modes and mixing mechanisms, namely, clumped and random spatial distributions of the POD modes appear in convective and diffusive mixing, respectively. Consequently, it is shown that combining the CFD–DEM simulation with the LPOD method is effective to identify the main mixing mechanism and to explain the time transition of mixing mechanisms between convective and diffusive mixing.     

Integrated Population Balance Model Development and Validation of a Granulation Process

This study is concerned with the development of an integrated three-dimensional population balance model (PBM) that describes the combined effect of key granulation mechanisms that occur during the course of a granulation process. Results demonstrate the importance of simulating the different mechanisms within a population balance model framework to elucidate realistic granulation dynamics. The incorporation of liquid addition in the model also aids in demarcating the dynamics in different regimes such as premixing, granulation (during liquid addition) and wet massing (after liquid addition). For the first time, the effect of primary particle size distributions and mode of binder addition on key granule properties was studied using an integrated PBM. Experimental data confirms the validity of the overall model as compared to traditional models in the literature that do not integrate the different granulation mechanisms.     

Comprehensive numerical modelling of the hot isostatic pressing of Ti-6Al-4V powder: From filling to consolidation

Hot Isostatic Pressing (HIP) is a manufacturing process for production of near-net-shape components, where models based on Finite Element Method (FEM) are generally used for reducing the expensive experimental trials for canister design. Researches up to date implement in the simulation a uniform powder relative density distribution prior HIPping. However, it has been experimentally observed that the powder distribution is inhomogeneous after filling, leading to a non-uniform tool shrinkage. In this study a comprehensive numerical model for HIPping of Ti-6Al-4V powder is developed to improve model prediction by simulating powder filling and pre-consolidation by means of a two-dimensional Discrete Element Method (DEM). Particles’ dimension has been scaled up in order to reduce the computational cost of the analysis. An analytical model has been developed to calculate the relative density distribution from powder particle distribution provided by DEM, which is then passed in information to a three-dimensional FEM implementing the Abouaf and co-workers model for simulating powder densification during HIPping. Results obtained implementing the initial relative density distribution calculated from DEM are compared with those obtained considering a uniform relative density distribution over the powder domain (classic approach) at the beginning of the analysis. Experimental work has been carried out for validating the DEM (filling) and FEM (HIP) model. Comparison between experimental and numerical results shows the ability of the DEM model to represent the powder flow during filling and pre-consolidation, providing also a reliable values of the relative density distribution. It also highlights that taking into account the non-uniform powder distribution inside the canister prior HIP is vital to improve numerical results and produce near-net-shape components.     

Recent progress on the discrete element method simulations for powder transport systems: A review

Powder transport systems are ubiquitous in various industries, where they can encounter single powder flow, two-phase flow with solids carried by gas or liquid, and gas–solid–liquid three-phase flow. System geometry, operating conditions, and particle properties have significant impacts on the flow behavior, making it difficult to achieve good transportation of granular materials. Compared to experimental trials and theoretical studies, the numerical approach provides unparalleled advantages over the investigation and prediction of detailed flow behavior, of which the discrete element method (DEM) can precisely capture complex particle-scale information and attract a plethora of research interests. This is the first study to review recent progress in the DEM and coupled DEM with computational fluid dynamics for extensive powder transport systems, including single-particle, gas–solid/solid–liquid, and gas–solid–liquid flows. Some important aspects (i.e., powder electrification during pneumatic conveying, pipe bend erosion, non-spherical particle transport) that have not been well summarized previously are given special attention, as is the application in some new-rising fields (ocean mining, hydraulic fracturing, and gas/oil production). Studies involving important large-scale computation methods, such as the coarse grained DEM, graphical processing unit-based technique, and periodic boundary condition, are also introduced to provide insight for industrial application. This review study conducts a comprehensive survey of the DEM studies in powder transport systems.     

Modeling of Powder Blending Using On-line Near-Infrared Measurements

A model to quantify the degree of mixing in pharmaceutical powder mixing operations was developed. The additive volume mixing model is based on the determination of the characteristic volume of agitation for a given blender, which is dependent on process parameters such as the formulation ingredients, the geometry of the mixer, and the batch load. The calculation of this characteristic volume of agitation is based on the determination of the fitted fraction of formulation mixed after the first blender rotation. A variation of this model, denominated the iterative mixing model, was also developed. On-line near-infrared (NIR) measurements were taken throughout the runs to obtain the mixing profile and the dynamics of the powder bed as a function of blender rotations. Studies were conducted at two scales using two different formulations to study and compare the calculated characteristic volume of agitation for each blender-formulation system. This approach elucidates the existing relationship between the characteristic mixing parameters and critical rotations (required rotations to achieve content uniformity) for a given system and represents a step toward scale-up of solids mixing operations.     

DEM simulation for optimal design of powder mixing in a ribbon mixer

A ribbon mixer is often employed in powder mixing in a wide range of engineering fields. The structure of the ribbon mixer is extremely complicated. This structure makes it difficult to understand the mixing mechanism by experimental approaches due to problems related to accurate sampling. At present, the mixing mechanism in the ribbon mixer is empirically identified as convection, despite a lack of precise assessment. Additionally, experimental investigations to find the optimal design of the ribbon mixer have not been sufficiently conducted because of its prohibitive cost. As such, there is a lack of sufficient discussion concerning the design for better mixing in the ribbon mixer. Numerical technologies represent a promising approach for solving the aforementioned problems. Significant improvements in computer hardware have enabled numerical models such as the discrete element method (DEM) to be positively employed in powder mixing. In the current study, an identification approach is developed for convective mixing, and besides, the study explores an effective parameter for better mixing in the ribbon mixer using the DEM. A swept volume measurement approach due to paddle movement is newly developed to identify the main mixing mechanism as convection. Sensitivity analyses are performed to find an effective parameter for better mixing. Through the sensitive analyses, the blade width is indicated as an important factor for achieving better mixing. Moreover, this study shows that the relationship between the swept volume and mixing index remains, even if the paddle width changes. Thus, the swept volume measurement method is revealed as useful for identifying the mechanism as convection in the ribbon mixer. Thus, not only novel finding regarding the blade width for better mixing but also the development of an approach for identifying convective mixing in the ribbon mixer is presented herein. Incidentally, convection being the dominant mechanism is consistent with the novel finding regarding blade width achieving better mixing.     

橡胶连续混炼粉料混合均匀性仿真及实验研究

为了提高橡胶连续混炼中混炼胶质量稳定性,实现炭黑等粉体物料精确配比和均匀性混合问题,针对粉体物料在混合和输送过程存在复杂的物理性质,建立了炭黑等混合粉料的球体颗粒模型和Hertz接触力-位移模型,采用EDEM对典型粉体物料混合均匀性进行模拟仿真和粉体物料混合实验,对炭黑等粉体物料在橡胶连续混炼工艺中的混合均匀性进行分析,探求橡胶粉料连续混合和输送机理.研究发现:粉体物料混合仿真与实验测试结果具有较高的拟合性,表明在橡胶连续混炼工艺中可以在保证混合均匀性的前提下实现多粉体混合物的连续称量和输送,同时也验证了运用EDEM数据模拟仿真粉体物料混合的可行性.     

A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media

A hierarchical multiscale framework is proposed to model the mechanical behaviour of granular media. The framework employs a rigorous hierarchical coupling between the FEM and the discrete element method (DEM). To solve a BVP, the FEM is used to discretise the macroscopic geometric domain into an FEM mesh. A DEM assembly with memory of its loading history is embedded at each Gauss integration point of the mesh to serve as the representative volume element (RVE). The DEM assembly receives the global deformation at its Gauss point from the FEM as input boundary conditions and is solved to derive the required constitutive relation at the specific material point to advance the FEM computation. The DEM computation employs simple physically based contact laws in conjunction with Coulomb's friction for interparticle contacts to capture the loading‐history dependence and highly nonlinear dissipative response of a granular material. The hierarchical scheme helps to avoid the phenomenological assumptions on constitutive relation in conventional continuum modelling and retains the computational efficiency of FEM in solving large‐scale BVPs. The hierarchical structure also makes it ideal for distributed parallel computing to fully unleash its predictive power. Importantly, the framework offers rich information on the particle level with direct link to the macroscopic material response, which helps to shed lights on cross‐scale understanding of granular media. The developed framework is first benchmarked by a simulation of single‐element drained test and is then applied to the predictions of strain localisation for sand subject to monotonic biaxial compression, as well as the liquefaction and cyclic mobility of sand in cyclic simple shear tests. It is demonstrated that the proposed method may reproduce interesting experimental observations that are otherwise difficult to be captured by conventional FEM or pure DEM simulations, such as the inception of shear band under smooth symmetric boundary conditions, non‐coaxial granular response, large dilation and rotation at the edges of shear band and critical state reached within the shear band. Copyright © 2014 John Wiley & Sons, Ltd.     

Modeling collective dynamics of particulate systems under time-varying operating conditions based on Markov chains

This paper develops an approach to modeling and analyzing the overall dynamics of monodisperse particulate systems in a horizontal rotating drum under time-varying drum rotational speeds. This approach captures the above collective dynamics using stochastic models in the form of Markov chains. The characteristics of such dynamics can be obtained from the Markov chain operator. It provides a systematic way to the analysis of features of collective particle movements, which is in contrast to the existing qualitative analysis. In this paper, Markov chains models are developed based on DEM simulation results to show the effectiveness of the proposed approach. The obtained operators are used to estimate the spatial particle distribution and particulate mixing as examples of collective dynamic features of particulate systems.     

A numerical study on dynamic inertial focusing of microparticles in a confined flow

Inertial microfluidics is regarded as a promising approach to facilitate precise, robust and continuous manipulation of particles through inertial focusing of particles in microchannels. Although there is a need to gain rich insights into the focusing dynamics of particles, it has been hardly studied numerically. In this study, the complex focusing dynamics of particles is simulated numerically for multi-particle suspensions in confined microchannels. To this end, we develop a new method that couples the discrete element method (DEM) with the direct numerical simulation (DNS). This method is referred to as the DEM–DNS method. In order to validate the DEM–DNS method, we then investigate complex dependence of particle behaviour on Reynolds number and channel geometries. With good agreement between the numerical results and existing observations, it is shown for the first time that the DEM–DNS method can simulate the counterintuitive focusing dynamics of particles. This study thus establishes that the DEM–DNS method is a powerful tool to examine the focusing dynamics of particles in inertial microfluidics.     

Benchmark tests for verifying discrete element modelling codes at particle impact level

Over the past 30 years, the Discrete Element Method (DEM) has rapidly gained popularity as a tool for modelling the behaviour of granular assemblies and is being used extensively in both scientific and industrial applications. However, it is far from clear from reviewing the literature whether the large number of DEM codes have been verified and checked against fundamental benchmark problems. DEM simulates the dynamics of each particle in an assembly by calculating the acceleration resulting from all the contact forces and body forces. It is clearly necessary that such a model be validated or verified by comparing with experimental results, analytical solutions or other numerical results (e.g. Finite Element Analysis (FEA) results) at particle impact level. There appears to be no standard benchmark tests against which DEM codes can be verified. It is thus essential and useful to establish a set of standard benchmark tests to confirm that these DEM codes are modelling the particle dynamics as intended. This paper proposes a set of benchmark tests to verify DEM codes at particle impact level for spherical particles. The analytical solutions derived from elasticity theory for elastic normal collision of two spheres or a sphere with a rigid plane are first reviewed. These analytical solutions apply only to the elastic regime for normal impact. Secondly, the analytical solutions of frictional oblique impact between two spheres or a sphere with a rigid plane are scrutinized and derived. These analytical solutions originate from the dynamics principles and should be satisfied for any DEM contact force model with prescribed friction and restitution coefficients. A set of eight benchmark tests are designed and performed using commercial DEM codes. Test 1 and Test 2 consider the elastic normal impact of two spheres or a sphere with a rigid plane, whereas the other tests (Test 3–Test 8) investigate the energy dissipation due to the collision. These benchmark tests also involve different types of material. The DEM results were compared with the analytical solutions, experimental or FEA results found in the literature. All benchmark tests showed good to excellent match, providing a quantitative verification for the codes used in this study. These benchmark tests not only verify DEM codes but also enhance the understanding of fundamental impact phenomena for modelling a large number of particles.     

Modeling Continuous Powder Mixing by Means of the Theory of Markov Chains

This article demonstrates the efficiency of the application of the theory of Markov chains as a tool to model and simulate continuous powder mixing to aid in better design of such equipment. Markov chain models allow calculating practically all parameters of the process necessary for its characterization, and in particular those related to particle residence time distribution (RTD). Some numerical examples from the model, which are important for better understanding the process, are also included. It is shown that the main factor defining the efficiency of continuous mixing, through the variance reduction ratio (VRR), is the ratio of the mean residence time and the period of inflows fluctuation, rather than the variance of the RTD. Also, the influence of the dimensions of the mixer outlet on the mean residence time, and in turn on the VRR, is examined as another way of improving the design.     

Analysis of powder behaviour in bin blending processes at different scales using DEM

Obtaining a desired content uniformity with satisfactory flowability is one of the main challenges during blending process of the pre-mixture with lubricants. In this study, Discrete Element Method (DEM) simulations were implemented to examine blending time and mixing behaviour during the blending process on the lab and industrial scales. The main goal was to investigate the possible influence of operational conditions on the blending behaviour and the change in powder cohesivity during the scale-up process. The effects of rotational speed and filling mass on the particles' travelled distance, velocity, shear stress and blending time were studied in the simulations. Based on the simulations, blending time and particle exposure to shear during the blending process were calculated for different scales. It was observed that the system's mass significantly influences them, and the effect of rotational speed could be neglected. The novelty of this paper is connecting particle exposure to shear from DEM to the flow function coefficient (ffc) of powder from experiments. It was done to define a critical range of exposure to shear that changes the powder flowability in different scales.     

Modeling Continuous Powder Mixing by Means of the Theory of Markov Chains

This article demonstrates the efficiency of the application of the theory of Markov chains as a tool to model and simulate continuous powder mixing to aid in better design of such equipment. Markov chain models allow calculating practically all parameters of the process necessary for its characterization, and in particular those related to particle residence time distribution (RTD). Some numerical examples from the model, which are important for better understanding the process, are also included. It is shown that the main factor defining the efficiency of continuous mixing, through the variance reduction ratio (VRR), is the ratio of the mean residence time and the period of inflows fluctuation, rather than the variance of the RTD. Also, the influence of the dimensions of the mixer outlet on the mean residence time, and in turn on the VRR, is examined as another way of improving the design.     

Realizing fragment spawning and fragment growth in the parallelized Discrete Element Method (DEM) during modelling of comminution

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.     

Study on a large-scale discrete element model for fine particles in a fluidized bed

The discrete element method (DEM) is widely used to comprehend complicated phenomena such as gas–solid flows. This is because the DEM enables us to investigate the characteristics of the granular flow at the particle level. The DEM is a Lagrangian approach where each individual particle is calculated based on Newton’s second law of motion. However, it is difficult to use the DEM to model industrial powder processes, where over a billion particles are dealt with, because the calculation cost becomes too expensive when the number of particles is huge. To solve this issue, we have developed a coarse grain model to simulate the non-cohesive particle behavior in large-scale powder systems. The coarse grain particle represents a group of original particles. Accordingly, the coarse grain model makes it possible to perform the simulations by using a smaller number of calculated particles than are physically present. As might be expected, handling of fine particles involving cohesive force is often required in industry. In the present study, we evolved the coarse grain model to simulate these fine particles. Numerical simulations were performed to show the adequacy of this model in a fluidized bed, which is a typical gas–solid flow situation. The results obtained from our model and for the original particle systems were compared in terms of the transient change of the bed height and pressure drop. The new model can simulate the original particle behavior accurately.     

基于GPU的杆系离散元并行算法在大型工程结构中的应用

杆系DEM(离散元,discrete element method)是求解结构强非线性问题的有效方法,但随着结构数值计算规模的扩大,杆系DEM所需要的计算时间也随之急剧膨胀.为了提高杆系DEM的计算效率,该研究提出单元级并行、节点级并行的计算方法,基于CPU-GPU异构平台,建构了杆系DEM并行计算框架,编制了相应的几...