number of particles to a base plate, which is then placed on the inclining wall. The inclining wall test will provide the friction values only for low contact forces. It is known that under higher pressures, the friction might be different and needs to be measured under similar conditions in a direct shear tester. However, this would require access to such an apparatus or laboratory to perform the testing. Values for the particle-wall coefficient of friction obtained in any of these two tests can be directly used in the DEM model without the need for further calibration.
Contact stiffness
The values specified for the stiffness will depend on the specific contact model used. If the linear model is used, the stiffness is specified in the normal and tangential directions in units of N/m. These two stiffness values are independent of each other, although the tangential stiffness is usually taken between 0.5 and 1.0 times the normal stiffness. The value of the normal stiffness can be estimated using kn = 4.E.R where E is the effective Young’s modulus at the contact and R the radius of curvature (usually taken as the radius of the particle or that of a volume equivalent sphere). If the Hertz-Mindlin contact model is used, the user needs to specify the contact effective elastic properties namely Young’s modulus E, or the shear modulus G, and Poisson’s ratio (usually assumed as n = 0.3). Equipment is usually manufactured from hard materials such as steel or ceramics and it is sufficient to specify the particle-wall stiffness twice that of the particle-particle contacts. The contact stiffness and elastic properties are difficult to measure at contact or particle level and are best calibrated using a confined uniaxial compression test. A container (usually cylindrical) is filled with the material, closed with a lid and compressed, Figure 5.
The load-displacement response is measured while the sample is compressed to a maximum pressure which should be of the same order as expected in the final application to be modelled. The slope of the load-displacement curve is defined as the bulk stiffness. The experiment is repeated in DEM under similar boundary conditions and the contact stiffness adjusted iteratively until the bulk stiffness is accurately modelled. The relation between contact stiffness and bulk stiffness is close to linear. The container should be large enough to minimise any wall effects and should be at least equal to 10 particles in diameter. The integration time step is inversely proportional to the square root of the contact stiffness and it is usually impractical to model large industrial scale applications without reducing the modelled stiffness. Research has shown that the stiffness can be scaled down by a factor of 10 when modelling bulk material flow under relatively low pressures. In some cases, the stiffness can even be reduced by a factor 100 without any significant loss in accuracy. Using the linear contact model, a minimum value of kn = 1.103 N/m is recommended for free flowing conditions under low pressures for materials with low bulk densities (less than 1 000kg/m3). However, a value between kn = 1.104 N/m and 1.105 N/m is appropriate in most cases. Using the Hertz-Mindlin model, the proposed minimum value for the shear modulus is G = 1.107 N/m2.
Particle and bulk density
The bulk density should be accurately modelled if both the volume flow rate and mass flow rate are to be modelled accurately. For example, if a transfer chute is analysed and the throughput is specified in ton per hour, the DEM model can be setup to ensure the correct mass flow. However, to accurately predict any blockage and build-up, the volume flow rate should also be accurately modelled. Modelling the bulk density accurately ensures that both the mass flow and volume flow rates are accurately modelled. The bulk density can be measured by filling a container with known volume and weighing it to get the mass (weight). This process is then repeated in DEM and the particle density adjusted until the measured bulk density is achieved. Note that, depending on the accuracy of the particle shape, the particle density used in DEM will not necessarily be equal to that of the real particles.
Figure 5 – Confined uniaxial compression test of corn grains
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BULK HANDLING TODAY
August 2019
In modelling bulk materials handling, the aim is always to accurately model the bulk density rather than the particle density. Also note that at this stage in the calibration process, guesstimated values of the coefficients of friction are used which might influence the bulk density. For that reason, the density at the end of the calibration process should be re-checked and the