Test Descriptions

Untapped Bulk Density Test

A 100 ml cylinder was created with 16 mm radius and 185 mm height. 0.05 kg of powder material was added via a funnel at the top of the cylinder at a rate of 0.2 kg/s and an initial velocity of -0.25 m/s. The material was allowed to settle and the bulk density calculated from the height of the material in the cylinder following a standard experimental process (World Health Organization, 2017[4]). A Time Step of 2e-6 s was used for Bulk Density tests.

Tapped Bulk Density Test

The settled material from the untapped density test was subjected to a repeating tap. A 3 mm drop was added to the cylinder repeating every 0.24 s (250 times per minute). This was introduced to EDEM via two repeating kinematics (show below). Every 60 s the motion was paused for 2 s to allow the material to settle and the bulk density measurement taken. When the bulk density variation between measurements was negligible, the tapped density was recorded. A Time Step of 5e-6 s was used for the tap tests.

Static Angle of Repose Test

0.05 kg of material was filled in a cylinder as per the untapped bulk density test. An additional cone with initial radius 16 mm and final radius 8 mm was added to the end of the cylinder to reduce the velocity at which the material exited the cylinder. The drop height from the base of the cone to the floor was set to 80 mm. The floor consisted of a small cylinder with lip 2 mm in height. Initially the cylinder was filled with material with a stop at the base. The base stop was removed, and the material was allowed to flow out. IN cases 7-9, the material stuck to the cylinder without flowing, and an additional ‘tap’ kinematic was added to enable the material to flow to gain a measurement of angle.

Compressibility Test

0.05 kg of material was filled in a cylinder as per the untapped bulk density test. The sample material was then compressed under a pressure of 3 MPa (using the EDEM Coupling Interface) and the final material height recorded.

The amount of compression is calculated as: ‘Difference in sample height’/‘sample height before compression’, where the difference in sample height is the difference before and after compression.

The Compressibility index and Hausner ratio are calculated as: 100 x (tapped density – untapped density)/tapped density’ and ‘tapped density’/‘untapped density’ respectively.

Estimating Run Times

The following table indicates the recommended Time Step for a solid density of 1150 kg/m3.


Compressibility Ratio	Time step(s)	Cases
0.1	8.00E-07	1, 4, 7
0.5	6.00E-07	2, 5, 8
0.9	3.00E-07	3, 6, 9

However. investigations into the Time Step suggested that the Compression tests and Angle of Repose tests were unaffected by running at higher Time Steps. A value of 2e-6 s was used for the Angle of Repose tests and 5e-6 s for the Tapped Bulk Density tests.

The following table indicates the estimated simulation run times for different hardware.


Time step(s)	Simulation run time (s)	Time per iteration per particle (microseconds)	Number of Particles	Estimated Run Time (days)
2.00E-06	1	1.2	1000000	6.9
2.00E-06	1	1	1000000	5.8
2.00E-06	1	0.8	1000000	4.6
2.00E-06	1	0.6	1000000	3.5
2.00E-06	1	0.4	1000000	2.3
2.00E-06	1	0.2	1000000	1.2

Number of Iterations = EDEM run time/EDEM Time Step.

Seconds Per Iteration = elapsed real time/number of iterations.

Time Per Iteration per particle = Seconds Per Iteration/Number of particles.

The time per iteration per particle is measured from the relevant hardware setup. First, set up a simulation that takes around 1000 iterations. Then use a stopwatch to measure how long the elapsed real time for the simulation is and use this to calculate time per iteration per particle.

This is typically in the range of 1 microsecond for 8-16 processors. Different values will be found depending on how many spheres are used to make up a particle shape and the type of contact model used.

According to the table, the time per iteration ranges from 1.2 which is high-end CPU’s and 0.2 which would be for a high-end GPU.