TUNRA Bulk Solids consulting engineer Dr Daniel Grasser discusses the practicalities of calibrating DEM models to adequately represent the behaviour of bulk materials.
A brief introduction to DEM applications
The Discrete Element Method (DEM) is a commonly used numerical method in the bulk materials handling and mining sector. For example, DEM is a useful tool to predict the material flow behaviour, to assess the blockage potential of handling equipment and to study the build-up behaviour of material in rock boxes of transfer chutes.
In addition, quantities resulting from the material flow acting on wall liners can be analysed. This includes, for example, the resulting loads on the liners and wall pressure on bins. These loads are of interest for the assessment of wear hot spots and enable an indicative service life prediction if reference data form the mine site is available. Moreover, the velocity of the particles can be quantified and shown as flow trajectories.
DEM can be coupled with other techniques, such as Smoothed Particle Hydrodynamics (SPH) to predict the moisture migration or fluid separation between the bulk material and a liquid phase, such as water. This is important when hang up or carry back on conveyor belts is an issue and good designs to minimise these unwanted effects is desired. Moreover, in addition to DEM, similar assessments in terms of material flow and wear can be conducted, for example, on conveyor belts using DEM-SPH.
Importantly, most of the commercial DEM packages are user-friendly. Hence, most DEM packages can be used under guidance of experts or senior users after a short learning period. However, the adequate calibration of the DEM model is often overlooked. To retain the predictive nature of DEM, which is its main purpose, a comprehensive set of thoroughly conducted independent calibration tests is of utmost importance. Each of these tests must represent a different flow regime and be similar to the regimes found in the desired industrial application, for example, a transfer chute. Otherwise, the DEM model is deduced to an illustrative purpose, without substantial scientific or engineering value. This article highlights the importance of DEM calibration and provides examples of several important DEM calibration techniques for mining and bulk materials handling applications.
Basic parameters
The Young’s modulus – sometimes referred to as contact stiffness – determines the overlapping distance between particles (i.e. rocks) and boundaries (i.e. a wall liner) in a DEM simulation. The higher the Young’s modulus, the larger the number of numerical steps which are required to calculate the loads resulting from these interactions. As a result, the computational efforts increase. An overview of several important DEM parameters and their effect on the computational time required to solve a simulation is given in Table 1.
Hence, the Young’s modulus should be chosen to be as low as possible and as high as necessary. For most simulations, a Young’s Modulus of 107 is sufficient. However, there is no one-size-fits-all solution and the Young’s Modulus needs to be adjusted until an acceptable overlapping error is achieved. Generally, low Young’s moduli are sufficient when the bulk material is of main interest; in contrast, high moduli are required when the extraction of wall loads and pressures is desired.
In addition to the Young’s Modulus, the particle size and shape are important factors determining the quality of a DEM simulation and the computational time required. As a basic rule, smaller particles (6 mm) and odd-shaped particle are more computationally intensive than bigger (30-40 mm) and spherical particles. At the same tonnage of handled bulk material, smaller particles lead to a higher number of particles and therefore increase the computational effort.
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As a guidance, the larger the size of the particles, the higher the importance of the particle shape. Generally, the bulk material flow can be represented in a good approximation using small spherical particles, especially when a DEM parameter termed “Rolling Resistance” is applied. This parameter adds an additional momentum to each particle, hence supporting the realistic motion of the spherical particles. However, larger boulders, for example, should be modelled by implementing the actual shape. This is important to achieve a good approximation of the bulk density (i.e. solids fraction), which becomes increasingly difficult to achieve for an increasing particle size when spherical particles are used. For a realistic particle shape, no additional Rolling Resistance (value close to or equal to 0) is required, while values up to 1 are commonly applied for spherical particles. Similar to the Young’s Modulus, the particle size and shape strongly depend on the required level of realism and can only be determined in the context of each individual application.
Shear Box
The Shear Box test is governed by particle-to-particle interactions and the internal strength of the material at low consolidation pressures. The test consists of a cubical box with a side wall that can be rapidly removed. Once the side wall has been removed, the material slumps over itself and the angle of the resulting shear plane is quantified. It is vital that the width of box is significantly larger – at least 20 to 50 times – than the size of the largest DEM particle. This is important to avoid secondary effects and to minimise the effect of the wall friction, which is not part of the calibration parameters in the Shear Box test. In this test, the Coefficient of Friction, the Rolling Resistance and adhesion between the DEM particles are adjusted until the shear angle matches the experimental observation. Overall, the Shear Box test is an important test to calibrate the particle-to-particle interactions of mainly free-flowing bulk materials.
Angle of Repose
The Angle of Repose test is likely the most well-known DEM calibration test. In this test, the angle formed by a conical pile of bulk material formed by the discharge from a funnel or pipe is measured. It can be conducted as a static or dynamic test. For the static case, a quasi-static choked flow is retained. For the dynamic case, the conical pile is created by dynamically discharging the material by either.
Applying a higher lifting velocity than used for the static case or unloading the bulk material from a set height. Depending on the targeted application, the material can be unloaded on a wear liner or a bed of accumulated material. Similar to the Shear Box test, the opening of the funnel must be significantly larger (at least 20 times) than the largest size of the DEM particles. While this test is one of the most applied DEM calibration tests, the angle formed by the conical pile is not sufficient for a DEM calibration without additional tests. The Angle of Repose test often is used as an indicative comparison between bulk materials under quasi-static and dynamic flow regimes.
Inclined Wall Friction
The Inclined Wall Friction test is an important DEM calibration test, which aims to replicate the frictional behaviour between an inclining plate, often a wear liner or a conveyor belt, and the bulk material under quasi-static conditions. Using the particle-to-particle parameters which previously have been calibrated using the Shear Box test, the particle-to-boundary (e.g. wall liner) friction is adjusted until the slip angle in the DEM simulation is matching the experimental results. The bulk material can be loosely placed on the wall liner. Alternatively, if a consolidation pressure is desired, the material can be placed into a cell and then loaded with weights. Different adhesion models can be applied to capture the effect of the consolidation pressure on the wall friction angle. Similar to the previous tests, the cell should be relatively large to contain a sufficient amount of DEM particles. In summary, the Inclined Wall Friction test is an important test to calibrate the frictional behaviour between the bulk material and the wall liner under quasi-static conditions.
The Dynamic Adhesion Drop Test
The Dynamic Adhesion Drop Test is used to calibrate and validate the dynamic adhesion between the bulk material and a boundary (for example, a wall liner). The bulk material is discharged rapidly from a conveyor belt on an inclined wall liner. Depending on the type of material, the wall liner usually is inclined between 30° and 45°. The adhesive parameters of the DEM model are adjusted to replicate the amount of bulk material which accumulated on the inclined wall liners and is retained due to frictional and consolidation effects. Additionally, the distribution of the bulk material on the wear liners is replicated qualitatively. The Dynamic Adhesion Drop Test is important to calibrate the adhesive behaviour under a dynamic regime, similar to the regimes occurring in transfer chutes and during the loading procedure of tipper trays.
Comments on the calibration of a DEM-SPH model
For the calibration of a DEM-Smoothed Particle Hydrodynamics (SPH) model, similar sets of comprehensive tests are recommended. However, the purpose of coupling SPH with DEM is often to predict the behaviour of highly adhesive bulk materials, which can be difficult to capture solely using DEM. Examples include highly cohesive pastes leading to consolidation effects inside bins, carry-back on conveyor belts and issues related to phase-separation between the solid fraction and the liquid fraction, such as water. For this purpose, additional calibration tests are required. For example, bench scale tests replicating the consolidation pressure, scaled bins and conveyor belts, and vibration tests to replicate the phase separation observed on mine sites.
Conclusion
Overall, a comprehensive set of experimental tests is crucial for the calibration of a Discrete Element Method (DEM) simulation. It is essential that the DEM model adequately replicates the bulk material behaviour across different flow regimes, including quasi-static and dynamic regimes. The predictive nature of a DEM simulation, hence the success of a bulk materials handling or mining project involving DEM, depends on the quality of the calibration.