rotatingDrum

Overview

Template Info

Target Parameters: c_frict_xx c_rollingFrict_xx initCohStress_xx maxCohesiveStress_xx cohStrength_xx cohEnDens_xx
Contact Models: tangential no_history tangential history rolling_friction off rolling_friction epsd rolling_friction epsd2 cohesion off cohesion adaptive cohesion sjkr cohesion sjkr2
Particle Shapes: sphere multisphere

This calibration template simulates a rotating drum that is scalable in both depth and diameter. The template is very similar to the GranuDrum template, but offers more options for configuration.

This setup is designed to be sensitive to the particle-particle static/rolling friction and cohesion coefficients. Hence, one or more of these target parameters can be iteratively modified during the calibration process to achieve the optimal correspondence between simulation and reference results. To calibrate friction, set c_frict_pp and/or c_rollFrict_pp as target parameters. For cohesion, the adaptive, the simplified jkr, and the modified sjkr models are supported.

To calibrate the adaptive model, the user is invited to select the maxCohStress_exp_pp and the cohStrength_pp as target parameters, while to calibrate the sjkr and sjkr2 models, the user it invited to select the cohEnDens_pp as target parameter. Here, it should be specified that maxCohStress_exp_xx is equal to the logarithm of the maximum cohesive stress as defined in the adaptive model (i.e., maxCohStress_exp_pp = 2 corresponds to maxCohesiveStress_pp = 10^2). The parameters initCohStress_pp and initCohStress_pw of the adaptive model are typically set to zero; hence, they are rarely calibrated. The calibration of the particle-wall interaction parameters such as c_frict_pw, c_rollFrict_pw, maxCohStress_exp_pw, cohStrength_pw and cohEnDens_pw is possible as well; however, other tests might be better suited to calibrate them, like for example the inclination test and the wall friction test.

It is possible to calibrate cohesion and friction at the same time. Note that this will increase the parameter space and hence the number of simulations required to obtain a properly calibrated parameter set.

The load balancing is disabled by default due to the non-deterministic nature of the algorithm which can effect the results of calibration. If the number of particles is sufficiently high ( $10^5$ and above), the non-deterministic effect induced by the load balancing algorithm is negligible and load balancing should be enabled by setting the parameter useLoadBalancing to 1. Be aware that the load balancing can substantially speed-up the calibration process.

Simulation phases

Filling

During this phase, particles are inserted into the drum. The amount of particles depends on the desired filling level, which can specified through the fillLevel variable.

Settling

During this phase, the inserted particles settle down. The simulation stops when the total kinetic energy is below a certain threshold.

Rotation

During this phase, the drum is rotated. Rotation starts instantaneously, but measurement will only commence after a time interval of simEquilTime has passed. The simulation then continues for a period speicfied through simMeasTime, during which images of the simulation are being written. The time interval for writing is specified through dumpT.

Note

It is recommended to use at least one quarter of the rotation period (or $\frac{60}{4\mathrm{RPMMeas}}$ ) for both simEquilTime and simMeasTime.

Quality function

The images of the granular material obtained from the simulations during the rotation phase are used to calculate the average interface position and the dynamic cohesive index, where the latter is defined as the standard deviation of the interface position; see Neveu et al.. From the average interface position, the average dynamic angle of repose is computed as the inclination of the slope between two points. These points can be defined via measWindowLeft and measWindowRight. Both values are given in fractions of the radius, and indicate a signed distance from the rotation axis. So, for example, a value of -0.2 for measWindowLeft means that the left point lies $0.2 R_{drum}$ left of the axis, and a value of 0.3 for measWindowRight puts the right point at $0.3 R_{drum}$ right of the axis.

The quality function is calculated as follows:

$f_q = \sqrt{(\alpha_{f,s} - \alpha_{f,e})^2+ c_w (\sigma_{f,s} - \sigma_{f,e})^2 }$

where $\alpha_{f,s}$ and $\alpha_{f,e}$ are the simulated and reference dynamic angle of repose, $\sigma_{f,s}$ and $\sigma_{f,e}$ are the simulated and reference dynamic cohesive index, and $c_w$ is a weight factor for modulating the contribution of the dynamic cohesive index to the quality function. The factor $c_w$ , which by default is equal to zero, can be defined using the keyword cohesiveIndexWeight.

Measurement file

The measurement file can contain:

both the average dynamic of angle of repose and the dynamic cohesive index, or
the average dynamic of angle of repose alone, or
the path to the images of the rotating drum

Here are some examples of potential measurement files:

angle=62.34
cohesive_index=20.0

angle=62.34

image_path=path/to/image/directory

By specifying the average dynamic of angle of repose alone, the quality function is calulated as follows:

$f_q = \sqrt{(\alpha_{f,s} - \alpha_{f,e})^2}$

In case the path to the images of the rotating drum is specified, Aspherix® Calibration loads all .png files in the given folder and computes both the average dynamic of angle of repose and the dynamic cohesive index from those images. In order to be usable, the images require some pre-processing. Below is a typical image from a rotating drum measurement:

The final image to be used needs to

be square (same amount of pixels in width and height) and depict exactly the whole rotating drum (assumption: the width/height in pixel is exactly the drum diameter)
have a black background. The angle of repose is extracted from non-black pixels
have high contrast

A processed image could look like the one below:

The processing was performed using this python script:

#! /usr/bin/python3

import cv2 as cv
import numpy as np
import argparse
import glob
import os

parser = argparse.ArgumentParser()
parser.add_argument("directory")
parser.add_argument("--xlo",type=int)
parser.add_argument("--ylo",type=int)
parser.add_argument("--dx",type=int)
parser.add_argument("--radius-offset",type=int)
parser.add_argument("--threshold",type=int)

args = parser.parse_args()

xlo = args.xlo
ylo = args.ylo
dx = args.dx
r = int(dx/2)-args.radius_offset
cx = xlo+r+1
cy = ylo+r+1
threshold = args.threshold

srcdir = args.directory
destdir = os.path.join(srcdir,"processed")

for f in glob.glob(os.path.join(srcdir,"*gs*.png")):
    infile = f
    outfile = os.path.join(destdir,os.path.basename(infile))
    img = cv.imread(infile)
    img_crop = img[xlo:xlo+dx, ylo:ylo+dx]
    img_inv = cv.bitwise_not(img_crop, img_crop)
    mask = np.zeros((img_crop.shape[0],img_crop.shape[1]),np.uint8)
    circle_mask = cv.circle(mask,(int(dx/2),int(dx/2)),r,(255,255,255),thickness=-1)
    img_masked = cv.bitwise_and(img_inv, img_inv, mask=circle_mask)
    ret,img_thresh = cv.threshold(img_masked,threshold,255,cv.THRESH_TOZERO)
    cv.imwrite(outfile,img_thresh)

which was called with the parameters

./convert.py --xlo 56 --ylo 448 --dx 981 --radius-offset 5 --threshold 70 path/to/image/dir

Template parameters

General settings

Parameter	Default
scaleweight	1
pairGranModel	hertz
pairTangential	history
pairCohesion	sjkr
pairRollingFriction	epsd
torsionTorque	on
pairSurface	default
NPROC	4
dumpT	0.01 s
dump	0
nChunks	1
coresPerChunk	1
useLoadBalancing	0

Specific settings

Variable	Default	Meaning
simEquilTime	0.5	Interval of time [s] after reaching the prescribed rotation velocity. Needs to be large enough for the system to reach an equilibrium state.
simMeasTime	2	Interval of time [s] during which the images of the granular material are taken.
RPMMeas	undefined	Rotations per minute used in the experiment
fillLevel	0.5	Fraction of the drum volume to be filled with particles. 0.5 corresponds to a half-full drum. Values higher than 0.5 are not recommended due to limitations of particle insertion. [-]
measWindowLeft	-0.2	Left boundary of the measurement window for the dynamic angle of repose. Given as a fraction of the radius, where negative numbers indicate left from the center and positive numbers indicate right of the center. [-]
measWindowRight	0.2	Left and right boundaries of the measurment window for the measurement of the dynamic angle (see above) [-]
cohesiveIndexWeight	1	Weight for the calculation of the quality function [-]
drumLength	undefined	axial lenght of the drum [m]
drumRadius	undefined	radius of the drum [m]

Literature

[1] Neveu, A., Francqui, F., & Lumay, G. (2022). Measuring powder flow properties in a rotating drum. Measurement, 200, 111548.