Material model calibration using Static Angle of Repose test with EDEM
Altair Employee1. Introduction
The static angle of repose test is a common method of material model calibration for Discrete Element Method (DEM)--based simulation. The test is suitable for evaluating particle interaction properties through bulk matter behavior under dynamic flow regimes. Static Angle of Repose (SAoR) is the cone angle a stable particle pile makes relative to the horizontal. Several variants of static angle repose tests exist in the literature[1], some of which are shown in Figure 01.
Using an example of the 'lifting-cylinder' method to form a particle pile, this article demonstrates the workflow of running the simulation and extracting relevant data for material calibration. An EDEM model of the Static Angle of Repose test and an EDEMpy post-processing script are available in the EDEM calibration kits.
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| Figure 1: Method of creating a particle pile (a) lifting a particle-filled cylinder, (b) base provided with a lip (applicable for free-flowing media), (c) opening a flap/side of the box containing the bulk material, (d) releasing confined bulk material through a mechanized opening, and (e) creating a consistent stream of particle flow |
2. Modeling Methodology
The virtual geometric elements required to run the EDEM model are summarized in Figure 3 and include factory, funnel, cylinder, and base. These can be modeled as rigid bodies in EDEM, except for the factory, which is modeled as a virtual geometry. The bulk solid can be modeled using the two-sphere particle shape with an aspect ratio 1.5 to prevent artificial crystallization in the granular assembly.
The model uses EDEM's static factory to generate bulk material of fixed mass, which is then guided into the hollow cylinder through a funnel. This creates a granular assembly for further processing. Using EDEM's add motion functionality, a linear upward translation is provided to the cylinder with fixed velocity, releasing the confined bulk material on the base, as shown in Figure 3. The following are a few recommendations for achieving a repeatable angle of repose.
- The cylinder diameter should be approximately twenty times the particle average diameter, and the cylinder height should be twice its diameter.
- The base diameter should be four times the cylinder diameter.
- A 'lip' can be introduced around the edge of the base for free-flowing bulk material, as illustrated in Figure 2.
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| Figure 2: Introducing a lip around the base to contain free-flowing particles for a stable angle of repose test |
- Add motion to the cylinder after allowing the bulk material a settling time. Further, settling time must be added after the cylinder is lifted and the particle pile achieves stability.
- In case the particle pile is created using a steady stream of discharging bulk material, as shown in Figure 1(d), the distance between the base and the stream outlet should match the experimental characteristics impact velocity of the particles.
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| Figure 3: Lifting cylinder method of SAoR test (a) simulation setup, (b) creation of stress-free granular assembly using static factory, (c) linear upward translation to the cylinder, and (d) formation of particle pile |
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| Figure 4: Assigning a constant upward translation to the cylinder using EDEM's add motion tool |
3. Post Processing with EDEMpy
The results from the SAoR test can be automatically exported from the completed EDEM simulation deck using the Python script provided in the EDEM calibration kits. The script utilizes the EDEMpy library of functions for post-processing EDEM simulation data to compute and export the results in graphs and comma-delimited files such as the one shown in Figure 5(d).
The SAoR is determined by considering a radial array of bins, as shown in Figures 5(a) and 5(b). Each bin identifies the Center of Mass (CoM) of the highest particle within its domain. A least-squares linear fit approximates a straight line through these CoMs, as illustrated in Figure 5(c). The angle of inclination of this straight line provides the SAoR of the particle pile. To achieve a reliable result, the array of radial bins is considered within the high and low limits of the particle pile. These limits are defined through two geometry bins with radius 'rl' and 'rh' representing low and high limits, respectively. It is recommended that the user select the limit values such that a stable and steady angle of inclination is obtained for the fitted line. Also, overlapping of bins should be avoided by adjusting their diameters d.
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| Figure 5: Post-processing of conical pile for angle of repose measurement (a) side and (b) top view of conical pile schematically showing limits within which multiple bins are placed for SAoR measurement, (c) evaluating SAoR across seven equiangular locations along the circumference of the pile, and (d) measurement value collated into an excel file |
Multiple measurements at equidistant angular spacing can be obtained across the circumference of the conical particle pile, as shown in Figure 5(c). These measurements are later averaged to arrive at the final value of SAoR. The recorded values around the particle pile for each orientation are presented in a CSV file 'Static_angle_of_repose_example_Report.csv,' as shown in Figure 5(d).
The Python script file is accompanied by the settings file 'Static_angle_of_repose_analyst_settings. txt' as shown in Figure 6, which defines the domain limits, bin diameter, number of radial measurements, and the total simulation time.
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| Figure 6: Setting file accompanying the Python script for post-processing and reporting of static angle of repose test |
Multiple simulation decks can be post-processed by arranging files into one of two configurations, as shown in Figure 7. In configuration two (Figure 7(b)), each simulation deck can be post-processed with its custom setting file, whereas, in configuration one (Figure 7(a)), a single setting file is read for post-processing of all the EDEM decks. The following sequence outlines the workflow for post-processing.
- Arrange the files as shown in Figure 7.
- Open an existing EDEM simulation file and go to EDEM Analyst --> Run EDEMpy Script.
- Select ‘Static_angle_of_repose_analyst_v3.py’ --> Run Script.
- Reports and graphs will be generated in the master folder.
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| Figure 7: Configuration of folders for post-processing using the 'Static_angle_of_repose_analyst_v3.py' script (a) single setting applicable to all EDEM decks, and (b) provision for custom settings for each simulation deck. |
Only complete simulations with setting files will be post-processed; otherwise, an error message will be generated, as shown in Figure 8. To avoid file overwriting, all simulation files should have unique folders and simulation names.
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| Figure 8: Possible error messages that could be encountered during post-processing |
4. Further Reading and Resources
There is an ever-increasing library of tutorials, webinars, and HowTo videos available online. The user can explore a variety of topics and consider subscribing to the Altair How-To YouTube channel to remain updated with our latest posts.
More information on material model calibration using EDEM and Hyperstudy can be accessed through the following resources.
- Discrete Element Method Calibration with EDEM
- How to Calibrate Material Model with EDEM and Hyperstudy (YouTube)
- Modeling FT4 Rheometer Test with EDEM
- Modeling a Shear Cell Test with EDEM
For further information on EDEM applications, we have plenty more on the Altair Community:
- Applications of Discrete Element Method: Altair EDEM
- Altair Community EDEM
- EDEM Webinars
- Accelerate your EDEM learning curve
References
[1] S. Bin Yeom, E. Ha, M. Kim, S. H. Jeong, S. J. Hwang, and D. H. Choi, “Application of the discrete element method for manufacturing process simulation in the pharmaceutical industry,” Pharmaceutics, vol. 11, no. 8, 2019, doi: 10.3390/pharmaceutics11080414.