Modeling FT4 Rheometer test with EDEM

1.0 Introduction


The FT4 Rheometer test is used for the determination of the flowability of bulk materials under dynamic flow conditions and finds application in domains such as bulk material conveying, dosing, feeding, and mixing [1]. The dynamic flow condition is characterized by low stress and high strain rate. A rheometer offers a means of characterizing and differentiating amongst the flowability of bulk materials which otherwise, under quasi-static conditions (observed in Shear cell tests), could exhibit very similar behavior [1,2].

 An EDEM model of the FT4 Rheometer test, along with an EDEMpy post-processing script for the determination of the force and torque curves, is available in the EDEM calibration kits.


2.0 Modeling Methodology


The test procedure for the FT4 Rheometer is summarized in Figure 1. It consists of a cylindrical vessel of known volume filled with powder under gravity using EDEM’s Dynamic Factory method (Figure 1(a)). A rotating impeller is driven into this powder-filled vessel and retracted creating a lightly packed test sample, as illustrated in Figure 1(b) and Figure 1(c). This process of obtaining a lightly packed state of the test sample is called ‘conditioning’.


Figure 1: Test sequence for DEM material calibration using FT4 rheometer (a) filling of test vessel, powder bed conditioning through (b) downward and (c) upwards motion of impeller, (d) splitting, (e) state of sample for bulk density evaluation, (f) conditioning downwards post-splitting, (g) impeller rotation and translation upwards for SE measurement, and (h) bulldozing for BFE measurement


After conditioning, the test sample is split, and the bulk density is evaluated. Subsequently, the impeller is lowered for conditioning post-splitting, as shown in Figure 1(f). In the next step, as the impeller traverses from bottom to top, illustrated in Figure 1(g), the Specific Energy (SE) of the test sample is evaluated. In the final stage, shown in Figure 1(h), referred to as bulldozing [2], the vertical force and torque on the impeller are recorded for the assessment of bulk material flowability.

The benchmark measurement used for characterizing powder flowability/ rheology is Basic Flowability Energy (BFE). The BFE is quantified as the summation of the total work (rotational and translational) required to drive a standard rotating impeller a certain distance into a bed of conditioned powder. This total work or flow energy Ef is expressed as





where 'H' is the penetration depth of the impeller with radius 'r' rotating with torque 'T,' 'Fv' is a vertical force, and is the helix angle (depicted in Figure 2). The specific energy ('Es') quantifies powder flowability under low stress and unconfined state and is expressed as





where 'm' is the mass of the test sample.

The CAD model of the blade, as illustrated in Figure 2, is used to perform the standard FT4 rheometer test, the tip speed on the impeller blade ('Vb') is expressed as










where 'r' is the radius of the impeller rotating at angular velocity. 'Vv' is the linear vertical velocity of the impeller traversing within the test sample. The combined linear and rotational motion of the impeller results in a helical path of travel with an angle of helix . Expressions (3) and (4) can be utilized to evaluate the rotational and linear components of blade velocity for a selected ‘standard’ blade-tip speed during simulation. These values can be implemented to achieve desired blade kinematics using EDEM’s Add Motion feature, summarized in Figure 3. The Hertz-Mindlin (no slip) model is used to define the mechanics of particle contact.



Figure 2: Helical path of blade motion resulting from combined rotation and translation



Figure 3: Use of EDEM’s ‘Add Motion’ feature to assign appropriate kinematic to the impeller blade


The material calibration kit for the FT4 rheometer test has eight simulation decks with the naming convention FT4_<cell volume>_<blade speed>. For instance, a folder name of FT4_50_10 implies a test sample of size 50 ml processed with an impeller blade-tip speed of 10 mm/s. Two standard sizes of cell volumes, 50 ml, and 160 ml, are provided with the calibration kit. Appropriate modifications can be made to these decks to accommodate longer simulation times with revised motion kinematics.


3.0 Post Processing with EDEMpy


The results from the rheometer 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 4(b-c). Accompanying this script file is its settings file (‘FT4_analyst_settings.txt’ shown in Figure (a)), which defines key time simulation steps and settings for post-processing the completed EDEM deck.


Figure 4: (a) Setting file for Python script, (b) report file containing calibration parameters extracted from completed EDEM deck, variation of (c) vertical force, and (d) torque against penetration depth of impeller blade into the conditioned test sample


Multiple simulations can be post-processed using the provided Python script. This can be done by arranging simulation files in one of two configurations, as shown in Figure 5. In configuration one, a single settings file is used to post-process all EDEM decks, whereas, in configuration two, each simulation deck can have its own custom settings file. Configuration two is recommended for post-processing multiple simulations each with different time steps and duration for SE and BFE test cycles. The following sequence outlines the workflow for post-processing.


Figure. 5: Configuration of folders for post-processing using the ‘’ 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, as shown in Figure 6, will be generated. To avoid file overwriting, all simulation files should have unique folders and simulation names.


Figure. 6: 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


For further information on EDEM applications, we have plenty more on the Altair Community:


5. References

[1]   C. Hare, U. Zafar, M. Ghadiri, T. Freeman, J. Clayton, M.J. Murtagh, Analysis of the dynamics of the FT4 powder rheometer, Powder Technol. 285 (2015) 123–127.

[2]   R. Freeman, Measuring the flow properties of consolidated, conditioned and aerated powders - A comparative study using a powder rheometer and a rotational shear cell, Powder Technol. 174 (2007) 25–33.