Harald Kruggel-Emden

Selection of an appropriate time integration scheme for the discrete element method (DEM)

Abstract With increasing computer power simulation methods addressing discrete problems in a broad range of scientific fields become more and more available. The discrete element method is one of these discontinuous approaches used for modeling granular assemblies. Within this method the dynamics of a system of particles is modeled by tracking the motion of individual particles and their interaction with their adjacencies over time. For the interaction of particles, force models need to be specified. The resulting equations of motion are of coupled ordinary differential configuration, which are usually solved by explicit numerical schemes. In large-scale systems like avalanches, planetary rings, hoppers or chemical reactors vast numbers of particles need to be addressed. Therefore, integration schemes need to be accurate on the one hand, but also numerically efficient on the other hand. This numerical efficiency is characterized by the methods demand for memory and CPU-time. In this paper a number of mostly explicit numerical integration schemes are reviewed and applied to the benchmark problem of a particle impacting a fixed wall as investigated experimentally by Gorham and Kharaz [Gorham, D. A., & Kharaz, A. H. (2000). The measurement of particle rebound characteristics. Powder Technology , 112 (3), 193–202]. The accurate modeling which includes the correct integration of the equations of motion is essential. In discrete simulation methods the accuracy of properties on the single particle level directly influence the global properties of the granular assembly like velocity distributions, porosities or flow rates, whereas their correct knowledge is often of key interest in engineering applications. The impact experiment is modeled with simple force displacement approaches which allow an analytical solution of the problem. Aspects discussed are the dependency of the step size on the accuracy of certain collision properties and the related computing time. The effect of a fixed time step is analyzed. Guidelines for the efficient selection of an integration scheme considering the additional computational cost by contact detection and force calculation are presented.

Modeling of Granular Flow and Combined Heat Transfer in Hoppers by the Discrete Element Method (DEM)

The discrete element method can be used for modeling moving granular media in which heat and mass transport takes place. In this paper the concept of discrete element modeling with special emphasis on applicable force laws is introduced and the necessary equations for heat transport within particle assemblies are derived. Possible flow regimes in moving granular media are discussed. The developed discrete element model is applied to a new staged reforming process for biomass and waste utilization which employs a solid heat carrier. Results are presented for the flow regime and heat transport in substantial vessels of the process.

A Comparative Numerical Study of Particle Mixing on Different Grate Designs Through the Discrete Element Method

Based on LEAT’s discrete element codes, granular flow and mixing on conveying equipment are studied in two and three dimensions. Discrete element simulations, which are briefly introduced, provide detailed information on particle positions and velocities over time. This information is used to derive quantities characterizing the dynamic process of mixing. The main focus of the study presented is the mixing process of inhomogeneous particle ensembles on different grate types. For this purpose, the introduced mixing parameters are used to compare the mixing in a 3D situation with the corresponding 2D approximation on identical grates and to compare different grate designs in two dimensions.

An Experimental and Numerical Study of Transversal Dispersion of Granular Material on a Vibrating Conveyor

The mixing of thin granular layers transported on the surface of an oscillating trough is experimentally and numerically examined. The particle dispersion was experimentally quantified by an image processing system recording the growth of the mixing layer thickness of two differently colored but otherwise identical sand particle streams along the longitudinal position within the transporting channel. Granular flow and dispersion on the vibrating conveyor were studied numerically based on a three-dimensional discrete element code. Both experiments and simulations were used to derive quantities characterizing the transversal dispersion. The mixing was found to be directly proportional to the vertical acceleration of the conveyor and inversely proportional to the mass flow of the transported material. Keeping the above-mentioned parameters constant, the dispersion increases with increasing mean particle diameter. When performing the experiments with materials of different mean particle diameters and tuning the mass flow to achieve the same level of dimensionless bed height, the magnitude of the dispersion coefficient remains constant, as was also confirmed by the numerical simulation.

Applicable Contact Force Models for the Discrete Element Method: The Single Particle Perspective

Several processes in nature as well as many industrial applications involve static or dynamic granular materials. Granulates can adopt solid-, liquid-, or gaslike states and thereby reveal intriguing physical phenomena not observable in its versatility for any other form of matter. The frequent occurrence of phase transitions and the related characteristics thereby strongly affect their processing quality and economics. This situation demands for prediction methods for the behavior of granulates. In this context simulations provide a feasible alternative to experimental investigations. Several different simulation approaches are applicable to granular materials. The time-driven discrete element method turns out to be not only the most complex but also the most general simulation approach. Discrete element simulations have been used in a wide variety of scientific fields for more than 30 years. With the tremendous increase in available computer power, especially in the past years, the method is more and more developing to the state of the art simulation technique for granular materials not only in science but also in industrial applications. Several commercial software packages utilizing the time-driven discrete element method have emerged and are becoming more and more popular within the engineering community. Despite the long time of usage of the time-driven discrete element method, model advances derived and theoretical and experimental studies performed in the different branches of application lack harmonization. They thereby provide potential for improvements. Therefore, the scope of this paper is a review of methods and models for contact forces based on theoretical considerations and experimental data from literature. Particles considered are of spherical shape. Through model advances it is intended to contribute to a general enhancement of simulation techniques, which help improve products and the design of the related equipment.

Convective Drying of Agitated Silica Gel and Beech Wood Particle Beds—Experiments and Transient DEM-CFD Simulations

With coupled discrete element (DEM)–computational fluid dynamics (CFD) simulations, drying processes can be simultaneously described on the system scale while resolving detailed subprocesses on the particle scale. In this contribution, DEM-CFD simulations are used to analyze the transient heat and mass transfer in mechanically agitated particle beds during drying. Results are compared to convective batch-drying experiments with silica gel and beech wood spheres and mixing effects are studied in detail. A good agreement with the measurements of both single-particle and particle bed drying is achieved by resolving heat and moisture transport three-dimensionally inside each particle.

Performance of integration schemes in discrete element simulations of particle systems involving consecutive contacts

In this investigation, which is a follow-up study extending earlier work (Kruggel-Emden, Sturm, Wirtz, & Scherer, 2008), a realistic assessment of the performance of integration schemes in systems of moving particles and consecutive contacts is conducted. Linear contact models are applied throughout this work as they allow for an analytical solution of consecutive oblique impacts. The many-particle systems considered are the discharge of particles from a hopper and particle movement in a shaken container. Results for many-particle systems are robust with respect to the applied integration method and step size once particle interactions are resolved with a sufficient number of steps. The integration schemes are also evaluated based on consecutive particle/wall contacts. Integration of consecutive contacts in a discrete element framework implies repeatedly solving non-continuous systems of differential equations. Various termination conditions for the normal force models and adaptive time stepping for one-step integration methods are investigated. The effect of softened contacts on particle trajectories is discussed. Based on these insights, recommendations for the most accurate integration schemes are made.

Comparative study on mesh-based and mesh-less coupled CFD-DEM methods to model particle-laden flow

A comparative study on mesh-based and mesh-less Computational Fluid Dynamics (CFD) approaches coupled with the Discrete Element Method (DEM) is presented. As the mesh-based CFD approach a Finite Volume Method (FVM) is used. A Smoothed Particle Hydrodynamics (SPH) method represents mesh-less CFD. The unresolved fluid model is governed by the locally averaged Navier-Stokes equations. A newly developed model for applying boundary conditions in the SPH is described and validation tests are performed. With the help of the presented comparative tests, the similarities and differences of DEM-FVM and DEM-SPH methods are discussed. Three test cases, comprised of a single solid particle sedimentation test, flow through a porous block and sedimentation of a porous block, are performed using both methods. Drag forces acting on solid particles highly depend on local fluid fractions. For comparative reasons, the size of a cell in FVM is chosen such that fluid fractions match those computed in SPH. In general, DEM-FVM and DEM-SPH methods exhibit good agreement with analytic reference results. Differences between DEM-SPH and DEM-FVM approaches were found mostly due to differences in computed local fluid fractions.

Fast multitarget tracking via strategy switching for sensor-based sorting

State-of-the-art sensor-based sorting systems provide solutions to sort various products according to quality aspects. Such systems face the challenge of an existing delay between perception and separation of the material. To reliably predict an objects position when reaching the separation stage, information regarding its movement needs to be derived. Multitarget tracking offers approaches through which this can be achieved. However, processing time is typically limited since the sorting decision for each object needs to be derived sufficiently early before it reaches the separation stage. In this paper, an approach for multitarget tracking in sensor-based sorting is proposed which supports establishing an upper bound regarding processing time required for solving the measurement to track association problem. To demonstrate the success of the proposed method, experiments are conducted for data-sets obtained via simulation of a sorting system. This way, it is possible to not only demonstrate the impact on required runtime but also on the quality of the association.

Simulation-based evaluation of predictive tracking for sorting bulk materials

Multitarget tracking problems arise in many real-world applications. The performance of the utilized algorithm strongly depends both on how the data association problem is handled and on the suitability of the motion models employed. Especially the motion models can be hard to validate. Previously, we have proposed to use multitarget tracking to improve optical belt sorters. In this paper, we evaluate both the suitability of our model and the tracking and then of our entire system incorporating the image processing component via the use of highly realistic numerical simulations. We first assess the model using noise-free measurements generated by the simulation and then evaluate the entire system by using synthetically generated image data.