Document [original]

Benchmarking a DEM-CFD Model of an Optical

Belt Sorter by Experimental Comparison

Albert Bauer

*, Georg Maier

, Marcel Reith-Braun

, Harald Kruggel-Emden

, Florian Pfaff

Robin Gruna

, Uwe Hanebeck

, and Thomas La¨ngle

DOI: 10.1002/cite.202200124

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any

medium, provided the original work is properly cited.

Dedicated to Prof. Dr.-Ing. Joachim Werther on the occasion of his 80th birthday

A DEM-CFD (discrete element method – computational fluid dynamics) model of an optical belt sorter was extensively

compared with experiments of a laboratory-scale sorter to assess the model’s accuracy. Brick and sand-lime brick were

considered as materials. First, the transport characteristics on the conveyor belt, involving mass flow, lateral particle distri-

bution and proximity, were compared. Second, sorting results were benchmarked for varying mixture proportions at dif-

fering mass flows. It was found that the numerical model is able to reproduce the experimental results with high accuracy.

Keywords: DEM-CFD, Experimental benchmarking, Optical sorting, Sensor-based sorting

Received: June 29, 2022; revised: August 25, 2022; accepted: October 10, 2022

1 Introduction

With the continuous increase in computational power, sim-

ulations of natural and technical processes have become

more and more widespread in the last decades. Particularly

for systems that involve large amounts of particles, which

are usually found in the fields of geoscience, civil and pro-

cess engineering, the discrete element method (DEM)

showed to be valuable for a wide range of applications. In

the DEM, each particle is modeled discreetly. The interac-

tion between particles as well as particles and walls over

time is then computed by using contact modeling incorpo-

rating physical properties, with parameters typically ob-

tained by calibration experiments.

The DEM can address dynamic problems involving large

and complex geometries due to the absence of mesh discret-

ization. Transport processes [1] of rock material [2, 3] and

granular matter or powder flow in mixers, drums or

hoppers are simulated with the DEM [4, 5]. Coupling to

other simulation methods is also feasible to extend the

investigable fields. In particular, coupling with the finite ele-

ment method (FEM) [6, 7] or computational fluid dynamics

(CFD) [8–10] is commonly used to investigate multiphysics

processes, involving mechanical/thermomechanical phe-

nomena at particles or particle/fluid interaction. Challenges

up to now of DEM simulations are the treatment of vast

particle amounts of more than 10

, the consideration of

highly irregularly shaped particles and the calibration pro-

cedure itself [5].

For this study, the DEM-CFD method was applied to

model an optical belt sorter. Optical belt sorting belongs to

the field of sensor-based sorting, where a bulk material is

separated based upon its physical properties. The general

work principle can be summarized as follows. The material

is fed on a conveyor belt, where it is transported towards a

sensor, which measures certain properties. After discharge

from the conveyor belt, the sorting step is applied at which

the material is separated into at least two fractions based on

the identified properties. Properties of the material to be

sorted may be optical properties or other physical proper-

ties. The separation can be realized for example mechani-

cally or by magnets, eddy currents as well as air jets. An

extensive overview of sensor-based sorting of municipal

waste, which is also one of the most prominent applications,

is given in [11]. Further applications are in food processing

[12–14], minerals processing [15–17], and sorting of con-

struction and demolition waste (C&DW) [18, 19].

www.cit-journal.com ª2022 The Authors. Chemie Ingenieur Technik published by Wiley-VCH GmbH Chem. Ing. Tech. 2023,95, No. 1–2, 256–265

–

Albert Bauer https://orcid.org/0000-0002-7906-4036,

Harald Kruggel-Emden

([email protected])

Technische Universita¨t Berlin, Chair of Mechanical Process

Engineering and Solids Processing, Ernst-Reuter-Platz 1, 10587

Berlin, Germany.

Georg Maier, Robin Gruna, Thomas La¨ngle

Fraunhofer IOSB, Institute of Optronics, System Technologies and

Image Exploitation, Fraunhoferstraße 1, 76131 Karlsruhe, Germany.

Marcel Reith-Braun, Florian Pfaff, Uwe Hanebeck

Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Karlsruhe

Institute of Technology, Adenauerring 2, 76131 Karlsruhe, Ger-

many.

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Our research was motivated by the goal to model the

entire sorting process of an optical belt sorter. A precise

simulation model would not only open new possibilities

regarding the optimization of the sorting process and dras-

tically decrease the amount of labor and cost intensive

experimental work but would also allow the investigation of

the sorting process of potentially harmful substances, such

as hazardous substances in C&DW. For this purpose, a

laboratory-scale optical belt sorter was modeled with a

DEM-CFD approach. A rubble bulk material consisting of

brick and sand-lime brick was considered. The two materi-

als were discriminated by their color and ejected using

pneumatic separation. The particles and the walls were sim-

ulated by the DEM, the air jets were simulated by the CFD.

Both phases were coupled in the region where particles are

deflected by air jets. For a more comprehensive understand-

ing of the analyzed sorting system, the transport and the

sorting phase were investigated separately in the simula-

tions and the experiments.

Only few studies exist concerning research on the numer-

ical investigation of optical belt sorting. In [20], the authors

used a Monte-Carlo simulation method to investigate the

feed characteristics of an automated sorter. In [21], a

DEM-CFD framework was utilized to investigate the parti-

cle ejection of flat and cubic particles in a simplified sorting

step involving a single valve. The transport of a bulk of

spheres, cylinders, and plates on an automated sorter was

compared with experiments in [22]. A MATLAB model was

used to assess the influence of belt length and other param-

eters on the sorting efficiency. In [23], the authors numeri-

cally studied the influence of the sorting algorithm and sev-

eral other parameters on the sorting accuracy of an optical

belt sorter with a DEM-CFD approach. Exiting mass flows

at the feeder and sorting results at one input composition

were also experimentally compared.

Regarding the aforementioned publications, the contribu-

tions of this work can be summarized as follows. An exten-

sive comparison of transport and sorting characteristics for

various input feed conditions is conducted for the first time.

Also, the complexity of our modeling approach is increased

in two ways compared to preceding work. Firstly, a real bulk

material is considered in the DEM-CFD. Secondly, the com-

putation of the number and duration of active fluid jets is

performed identically to the experimental system. Finally,

the possibility to model a full sorting system with accurate

results by utilizing the DEM-CFD is proven.

The article is divided into five sections. In Sect. 2, the

sorting task, setup and numerical model are introduced. In

Sect. 3, the investigation procedure is outlined. The results

of the transport and sorting experiments and simulations

are presented and discussed in Sect. 4. Lastly, conclusions

are drawn in Sect. 5.

2 Setup and Methods

2.1 Sorting Task and Belt Sorter Setup

As a sorting task, we chose a sorting scenario from the field

of C&DW. We consider a binary mixture of brick and sand-

lime brick, as shown in Fig. 1. The densities of the materials

were 2541 kg m

–3

for brick and 2565 kg m

–3

for sand-lime

brick with a size range of 4–8 mm determined by sieving

analysis. The laboratory-scale sorting system is shown in

Fig. 2a. Its model replicate is outlined in Fig. 2b.

Both brick and sand-lime brick are fed into the system by

a combination of a silo and an electromagnetic feeder (see

Fig. 2a) that operates at a constant frequency of 50 Hz. The

amplitude is adjustable and used to steer the intended mass

flow. The lower feeder is used to transport sand-lime brick,

the upper feeder is transporting brick. From the feeders, the

materials are mixed and pre-accelerated via a chute onto a

conveyor belt. The conveyor belt has a length of 600 mm

and a width of 140 mm. The system is equipped with a color

line-scan camera (not shown in Fig. 2a). This inspection

camera observes the material 25 mm after being discharged

from the belt. The line width of the camera model used is

1365 pixel and the maximum line frequency is 14.8 kHz. In

the course of this study, the mixed material is sorted based

on the color. Additional to this inspection camera, the

system is equipped with an area-scan camera (shown in

Fig. 2a). This camera is used to observe the material on the

conveyor belt to evaluate the particle positions. It is not

used as an inspection camera for the calculation of sorting

decisions in this study. The area-scan camera has a CMOS

sensor with global shutter and offers 2320 ·1726 pixel at a

maximum frame rate of 192 Hz. Note that no cameras

(area-scan, line-scan) are foreseen in the numerical model

of the optical belt sorter (Fig. 2b) as colors, positions and

velocities of particles are fully accessible over time.

Material separation is carried out by means of a series of

pneumatic fast-switching valves, which activate related

nozzles (see Fig. 2a). The nozzle bar is equipped with

Chem. Ing. Tech. 2023,95, No. 1–2, 256–265 ª2022 The Authors. Chemie Ingenieur Technik published by Wiley-VCH GmbH www.cit-journal.com

Figure 1. Mixture of bulk material to be sorted. Brick (orange)

and sand-lime brick (grey).

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32 nozzles in total. Besides the classification of individual

particles, the control signals for material separation are

calculated based on an image processing algorithm. A

so-called deflection window is obtained. It describes the du-

ration and point in time for the deflection of a single parti-

cle. The extent of the window perpendicular to the trans-

port direction is based on the extend of the particle in this

direction and determines which valves are opened. Alike,

the opening duration of the valves is based on the extend of

the particle in transport direction. By assuming the particle

velocity to be equal to the belt velocity, a fixed time delay is

used to compute the point in time for valve activation,

including the activation delay of the valves themselves. It is

further assumed that there exists no velocity of the particles

crosswise to the transport direction.

Additionally, a system for the online assessment of the

sorting quality during an experiment was implemented.

The resulting setup is shown in terms of a CAD drawing in

Fig. 3. It consists of two chutes, onto which the fractions of

the reject and accept containers are fed. A line-scan camera

is used to record both material streams and classify individ-

ual particles. Using this information, time resolved statistics

regarding the ratio of the materials can be calculated for

both sorting fractions, such as the true positive rate and true

negative rate, see Sect. 3.2.

2.2 Numerical Model

2.2.1 Governing Equations of the DEM-CFD

Mostly adapting the DEM-CFD approach of [23], force

equilibrium yields

€

ﬁmi¼Fc

!þFg

!þFf

!(1)

where the acceleration xi

€

ﬁof particle iwith mass m

caused by acting forces on that particle: Fc

!is the summed

contact force originating from contact with other particles

and walls, Fg

!is the gravitational force and Ff

!is the force

caused by interaction with the surrounding fluid. Rotational

motion is given by

Jiwi

ﬁþwi

!·Jiwi



¼L1

iTc

!(2)

where Tc

!is the summed torques induced by wall and par-

ticle interactions through sliding friction and Tr

!by rolling

friction. No torques are induced by fluid interaction. J

the mass tensor of inertia given in the principal axes, wi

ﬁ

denotes the angular acceleration in the body fixed frame, wi

represents the angular velocity in the body fixed frame and

L1

iis the rotation matrix converting a vector from the iner-

tial into the body fixed frame. The contact forces were mod-

www.cit-journal.com ª2022 The Authors. Chemie Ingenieur Technik published by Wiley-VCH GmbH Chem. Ing. Tech. 2023,95, No. 1–2, 256–265

Figure 2. a) Experimental setup of the optical belt sorter. In this photo, only the area-scan camera used to observe the mate-

rial on the conveyor belt is shown. b) Numerical model of the optical belt sorter.

Figure 3. CAD drawing of the resulting setup for online assess-

ment of the time resolved sorting quality.

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eled by a linear spring-dashpot model. For computation,

each force was split into a normal and a tangential

component. Both components yield Fn

!¼knd~

nþgn~

rel

and Ft

!¼min ktxt

;mcFn

!





tfor the normal and tan-

gential force, respectively. Superscripts nand tdenote nor-

mal and tangential components, respectively. k

is the nor-

mal spring stiffness, dthe virtual overlap, ~

nthe normal

vector, g

the normal damping coefficient and ~

rel the rela-

tive velocity in normal direction at the contact point. k

the tangential spring stiffness, xt

!is the tangential displace-

ment, m

is the coefficient of Coulomb friction and ~

tis the

tangential vector. The rolling friction model [24] was

adapted, which yields Tr

!¼mrFn

!

Rrwrel

!

wrel

!

, with rolling

friction m

, the rolling radius R

and the relative angular ve-

locity wrel

!between two contacting particles.

The fluid phase which is present in the area of the nozzle

jets is described by conservation of mass (Eq. (3))

¶rf

¶tþrf~



¼0 (3)

and conservation of momentum (Eq. (4)), respectively

¶rf~



¶tþrf~



¼pþtþrf~

g(4)

In Eqs. (3) and (4) r

is the fluid density, ~

uthe fluid veloc-

ity, pthe pressure, ~

gthe gravitational acceleration and tthe

stress tensor. For turbulence modeling, we use the

Reynolds-averaged Navier-Stokes equations, so that the

stress tensor can be written as

t¼he~

uðÞþ~

uðÞ

1

 (5)

where h

is the effective viscosity which is obtained through

turbulence modeling. For calculation of the fluid force Ff

on the particles in Eq. (1) in the coupling region, the drag

model of [25] was utilized. It is applicable to non-spherical

particle shapes and calculated by

!¼Fd

!þFp

!¼1

2rf~

u~

cDA?e1c

u~

vðÞ (6)

The fluid force is the sum of drag Fd

!and pressure gra-

dient force Fp

!. Velocities of fluid and particles are denoted

by ~

uand~

v, respectively. c

denotes the drag coefficient of a

particle, A?the projection area perpendicular to the flow

direction, r

the fluid density and e

is the local voidage. It

holds that 0 <ef<1 due to the solid phase in the fluid. c

is an empirical correction factor and depends on the parti-

cle Reynolds-number Re They are given by

c¼3:70:65exp 1:5log ReðÞðÞ

(7)

and

Re ¼1

efrfdp~

u~

jj (8)

The drag coefficient c

of the individual particle was

computed by the correlation of [26], which yields

CD¼8

ﬃﬃﬃﬃﬃﬃ

pþ16

ﬃﬃﬃ

pþ3

pRe

f3=4

þ0:42 ·100:4log fðÞðÞ

0:21

(9)

To our knowledge, the drag correlation is the most accu-

rate formulation for arbitrary particle shapes, since it takes

the particle shape into account by using the crosswise

sphericity f?. Note that the fluid flow around the individual

particles was not resolved. A one-way coupling strategy was

used to model the particle-fluid interaction. The fluid fields

were computed once and were then coupled to the

DEM-CFD each time a particle reached the area of the noz-

zles. Hence, the particle was influenced by the fluid field,

but not vice versa.

2.2.2 Representation of the Nozzle Bar Fluid Field

The preparation of the fluid field to be used in the

DEM-CFD resulting from individual nozzle activation re-

quired several steps. First, the fluid field of a single nozzle

was simulated with the CFD software Ansys Fluent based

on the available CAD data of the nozzle (details not given

here). We used a stationary RANS simulation with a k-etur-

bulence model, which is well suited for free stream phe-

nomena [27]. The pressure difference between nozzle inlet

and ambient room was set at 0.75 bar. Second, the fine CFD

mesh with about 6.5 million cells was coarsened to about

10 000 cells. Third, the field of the single nozzle was con-

catenated 32 times to form the full fluid field of the nozzle

bar.

2.2.3 Particle Model and Contact Parameters

To model both materials as part of the DEM-CFD exem-

plary particle shapes were obtained by tomographic recon-

struction (13 sand-lime brick particles and 11 brick par-

ticles). The obtained shapes were then approximated by a

certain number of clustered spheres per particle (15–20

spheres). For each exemplary particle shape the genetic al-

gorithm of MATLAB was utilized to reduce the difference

between the volume of the tomographically obtained shape

and the volume of the clustered spheres. A resulting exem-

plary cluster particle is shown in Fig. 4a. A major advantage

of clustered particles is that complex shapes can be approxi-

mated while computing time and complexity of contact

detection remains relatively low. The principle of a cluster

particle contact is shown in Fig. 4 b for the collision of two

exemplary particles, A and B. Utilizing a linear spring-dash-

Chem. Ing. Tech. 2023,95, No. 1–2, 256–265 ª2022 The Authors. Chemie Ingenieur Technik published by Wiley-VCH GmbH www.cit-journal.com

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pot model (see Sect. 2.2.1) leads to an overlap dbetween the

respective contacting subspheres with centroids C

and

. As particles comprise of subspheres, contact detection

of clustered sphere particles is analogue to contact detection

of individual spherical particles. Contact force models as for

spheres can be used (see Sect. 2.2.1). Only the integration of

rotational motion is more complex as Eq. (2) has to be

solved instead of just Jiwi

ﬁ¼Tc

!þTr

!, as it is the case for

spheres.

As a next step after addressing the particle approximation,

sliding friction, rolling friction and coefficient of restitution

(COR) were calibrated for all possible material pairs analo-

gous to [28]. Small scale laboratory experiments were con-

ducted and simulated. The parameters of interest were varied

until the results of experiments and simulations matched.

Static angle of repose, dynamic angle of repose and a plate

impact experiment were performed to obtain the desired

parameter sets for brick and sand-lime brick which can get in

contact with itself, each other or wall materials made of rub-

ber (conveyor belt) or steel (sorter walls). Tab. 1 summarizes

the calibrated parameters. Note that all obtained contact

parameters can either be directly applied in the DEM-CFD

or in case of the COR be used to calculate a corresponding

normal stiffness k

and a damping coefficient g

. The tangen-

tial stiffness k

is calculated based on mechanical material

properties (Poisson’s ratio and Young’s modulus).

2.2.4 Modeling of the Vibrating Feeder Plates

To model the vibrating feeder plates, the vibration ampli-

tudes in all three directions were measured at all four cor-

ners of both material feeders described in Sect. 2.1 with a

3D accelerometer. Due to lack of accessibility, the vibration

could not be measured at the center of the plates. The time

signals were transformed into phase averaged periods by

utilizing a Hilbert-transformation, yielding the instantane-

ous phase and amplitude of a signal

[29]. The phase averaged amplitudes

showed a clear dependency on the

accelerometer position. While the

difference between the back and the

front region of the feeder is a desired

behavior to transport the bulk to the

front, the disbalance between the

amplitudes of the left and right side

of a feeder is unwanted. Further-

more, both feeders behaved differ-

ently. To approximate the vibration

pattern of the plates, a linear interpo-

lation of the amplitude between the

four measured corners was used for

the simulations. Each contact point

between a particle and the plate was

evaluated by weighting the proximity

to each plate corner, where the am-

plitude was known.

3 Investigation Procedure

For a comprehensive benchmarking of the capabilities of the

sorter model with respect to experiments, the analysis of the

sorting process was divided into two steps. First, material

transport investigations with a pure bulk material were con-

ducted both experimentally and numerically without per-

forming sorting. Thereby, a critical evaluation of the particle

model, the DEM contact representation and the model of the

vibrating feeder plates was feasible. Second, sorting investiga-

tions with premixed material were carried out. This way, both

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a) b)

Figure 4. Exemplary cluster particle in the hull to be approximated (a). Relevant quantities

for cluster particle collision (b).

Table 1. Calibrated mechanical parameters of both materials

with all contact partners. (P) refers to the contacting particle

either sand-lime brick or brick which gets in contact with either

sand-lime brick (SB), brick (B), conveyor belt (CB) or sorter wall

(SW) material.

Material Sand-lime brick Brick

COR P-SB [–] 0.19 0.215

COR P-B [–] 0.215 0.24

COR P-CB [–] 0.19 0.1

COR P-SW [–] 0.19 0.1

Sliding friction P-SB [–] 0.19 0.18

Sliding friction P-B [–] 0.18 0.17

Sliding friction P-CB [–] 0.4 0.56

Sliding friction P-SW [–] 0.4 0.56

Rolling friction P-SB [–] 2 10

–2

1.2 10

–2

Rolling friction P-B [–] 1.2 10

–2

3.8 10

–3

Rolling friction P-CB [–] 7.5 10

–3

5.8 10

–3

Rolling friction P-SW [–] 7.5 10

–3

5.8 10

–3

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stages of the sorting process could be analyzed separately.

Additionally, potential errors in the simulated material feed

did not affect the sorting results in the simulations.

3.1 Bulk Transport Analysis

In the material transport investigations, each silo (brick,

sand-lime brick) was half filled both in the experiments and

the numerical investigations. After being transported onto

the conveyor belt, each material was captured individually

by the area-scan camera towards the end of the conveyor

belt in the experiments. The same observation window was

applied in the simulations where particle positions were

known. The observation window had a length of 10 cm in

transport direction and was aligned with the end of the con-

veyor belt. For both materials, it was recorded:

1) mass flows intended to be 10 g s

–1

,15gs

–1

,20gs

–1

applying the amplitudes from the experiments,

2) lateral distribution on the conveyor belt,

3) average closest distance to neighbor particles.

As the first step of comparison, it was assessed if the sim-

ulated mass flows coincided with the experimental mass

flows. As a next step, the lateral particle position was eval-

uated along a fixed line in y-direction (see coordinate sys-

tem in Fig. 2b). The line of evaluation was set 5 cm ahead of

the end of the conveyor belt. Another spatial quantity was

given by analyzing the average minimal particle distance. It

was calculated by

i¼1min ~

xi~





n(10)

with I≠jand jrunning from 1 to nneighbor particles as

observed in the observation window in each camera frame

and simulation time step.

3.2 Sorting Investigations

The second part of the benchmark focused on

the sorting step. To compare experimental and

numerical efficiency at several operating condi-

tions, three compositions of material were sorted

at two mass flows. Proportions of 90:10, 75:25

and 50:50 were processed at 10 g s

–1

and 20 g s

–1

The first percentage denotes the accept material,

i.e., sand-lime brick, and the second percentage

denotes the reject material, i.e., brick. Each in-

vestigation in both experiment and simulation

covered a sorting duration of 60 s.

The true positive rate and true negative rate

were computed to measure the sorting accuracy.

They were defined as

TNR ¼True negatives

True negatives þFalse positives (11)

TPR ¼True positives

True positives þFalse negatives (12)

and denote the rates of correctly sorted reject and accept

material, respectively. To decouple possible uncertainties in

material feed, the feed of both vibration feeders was

replaced with a mass flow inlet of premixed material above

the chute in the simulations. In the experimental system,

the feeder of sand-lime brick was used to transport a man-

ually premixed bulk material onto the chute.

4 Results

In the following, the results of the benchmarking are pre-

sented starting with the bulk transport and followed by the

sorting. In the figures a fixed shade was assigned to each

analyzed mass flow: 10 g s

–1

is depicted white, 15 g s

–1

colored bright grey and 20 g s

–1

is colored dark grey.

4.1 Comparison of Bulk Transport

The evaluated mass flows are shown in Fig. 5 a for sand-

lime brick and in b for brick. The values are averaged over

30 s of experimental and simulation time. Continuous lines

indicate experimental results and dashed lines show numer-

ical data.

For sand-lime brick at intended 10 g s

–1

, the experimental

mass flow of 9.6 g s

–1

is clearly overestimated by the simula-

tion, which reports 13.2 g s

–1

(24.2 % deviation). This dis-

crepancy decreases at the higher mass flows, where the devi-

ations are 0.6 g s

–1

(4 %) at intended 15 g s

–1

and 1.2 g s

–1

(6 %) at intended 20 g s

–1

. The mass flow rates of brick show

better agreement between simulation and experiment. The

most prominent discrepancy of 0.6 g s

–1

is found at intended

15 g s

–1

. The other mass flows coincide with a deviation of

less than 1 %.

Fig. 6 summarizes the results of the lateral particle distri-

bution. Particles along a line orthogonal to the transport

Chem. Ing. Tech. 2023,95, No. 1–2, 256–265 ª2022 The Authors. Chemie Ingenieur Technik published by Wiley-VCH GmbH www.cit-journal.com

Figure 5. Comparison of experimental (continuous lines) and numerical (dashed

lines) mass flows for both bulk materials. Sand-lime brick is shown in (a), brick in

(b). Values are averaged over 30 s.

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direction were counted and evaluated in histograms with

20 bins. Experimental data is shown in (a) and (c), numeri-

cal data is presented in (b) and (d). The histograms show

the relative frequency of particle presence along the width

of the conveyor belt. Additionally, all histograms were fitted

with a normal distribution.

The simulated transport of sand-lime brick coincides well

with the experiment, cf. Fig. 6a and 6b. Both plots show rel-

ative frequencies of around 8 % at the center,

which decline at the rate of a normal distribu-

tion. The distribution in the simulation is

slightly narrower than in the experiment and

nearly identical for all mass flows.

The histogram of brick in the experiment

shows to follow almost a normal distribution,

comp. Fig. 6c. Around 8 % of the particles move

near the center of the conveyor belt. The relative

frequency declines towards the edges of the belt.

There is only minor difference between the mass

flows. For the simulation, the distribution of

particles is broader and not symmetric, see Fig. 6

d. On the left side of the conveyor belt, around

50 % more material is being transported than on

the right side. There are also notable peaks at

both edges of the conveyor belt. While the trans-

port at the center of the belt is predicted

accurately by the numerical model, it

shows clear deviations towards the edges

of the belt. A cause may be the vibration

amplitudes at the corners of the feeder

for brick, which differ much less than at

the feeder of sand-lime brick. As a conse-

quence, the resulting particle distribution

is broader and interaction with the con-

veyor belt side walls may occur resulting

in the distribution as seen in Fig. 6d.

In Fig. 7a, the average minimal distan-

ces of sand-lime brick particles are pre-

sented for experiment and simulation.

The average minimal distance is around

3 cm at intended 10 g s

–1

and decreases

slightly with increasing mass flow. The

distances in the simulations decrease

analogously but are around 0.15 cm

higher (5 % deviation). A cause could be

the slightly higher mass flows in the sim-

ulation. Similar trends can be observed

for the averaged minimal distances of

brick particles, depicted in Fig. 7b. In the

simulation, the distances of the brick

particles are slightly overestimated, with

the highest deviation of 0.37 cm at preset

20 g s

–1

(11.4 %). At the other mass flows,

the discrepancy is 0.05 cm (1.5 %) and

0.2 cm (5 %).

To conclude on the bulk transport,

there is good agreement between experiment and simula-

tion with accordance of 95 % or above in most cases. How-

ever, for some quantities the errors are around 20 %. More

data of the vibration amplitudes of the feeders would be

beneficial to improve the modeling approach.

www.cit-journal.com ª2022 The Authors. Chemie Ingenieur Technik published by Wiley-VCH GmbH Chem. Ing. Tech. 2023,95, No. 1–2, 256–265

Figure 6. Relative frequency of lateral particle distribution orthogonal to transport

direction. Experimental data of sand-lime brick is shown in (a), numerical data in (b).

Experimental data of brick is shown in (c), numerical data in (d).

Figure 7. Comparison of average minimal particle distance on the conveyor

belt. Sand-lime brick is shown in (a), brick in (b). Experimental data is indicated

with continuous lines, numerical data with dashed lines.

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4.2 Comparison of Sorting

In the second part of the comparison, sorting experiments

and simulations were performed. As described in Sect. 3.2,

the sorting results were compared for six different scenarios.

All scenarios were evaluated in terms of the TNR and TPR,

see Eqs. (11) and (12). The TNR denotes the rate of cor-

rectly sorted particles, the TPR denotes the rate of correctly

not separated particles. Fig. 8a and b present the deviation

of the TNR and TPR between experiment and simulation

for all scenarios. As before, scenarios with a mass flow of

10 g s

–1

are depicted in white, 20 g s

–1

are depicted dark grey.

The proportion of brick, which was sorted out, is given by

the second number of the proportion and is also the param-

eter on the x-axis in Fig. 8. As for the TNR in Fig. 8a, the

highest errors of 3.5 % are observed at a 75:25 mixture. The

errors of the other two mixtures are 3 % for 90:10 and 1.8 %

for 50:50. The TPR in Fig. 8b shows similar results. The

mean error has a maximum value of 1.4 % at 50:50 and

20 g s

–1

. There is only minor difference in TNR and TPR, if

the mass flow is changed.

Absolute values of both TNR and TPR are shown in

Tab. 2. The TNR is around 97 % for all scenarios and shows

a slight tendency to decrease with an increasing proportion

of brick. The TPR is above 99 % at all sorting scenarios.

Here, a clear tendency is not visible.

To conclude on the sorting, with maximal errors of 3.5 %,

the sorter model proved to yield very good agreement with

the experiments. A broad range of input compositions at

two distinct mass flows showed to be reproduced well by

the simulations, independently of the scenario.

5 Conclusions

In this study, a DEM-CFD model was utilized to model a

laboratory-scale optical belt sorter. The experimental sort-

ing system was used to benchmark the numerical model for

various scenarios. C&DW waste consisting of brick and

sand-lime brick was considered to conduct the experiments.

The particles of differing shapes and sizes were approxi-

mated with multi-sphere clusters.

In the first part of the investigation, the focus was on the

vibrating feeders and the transport behavior was assessed

on the conveyor belt for each material separately. Mass

flows, lateral particle distributions and minimal average

particle distances were compared. The numerical results

showed good agreement with the experimental data, but a

few larger deviations were also observed. Those arose most

likely from the complex vibration pattern of the feeder. In

the second part of the investigation, the sorting results were

compared in terms of the TNR and TPR. At all investigated

inflow conditions, there was high agreement between exper-

iment and simulation. To sum up, it was shown that the ap-

plied approach to numerically model a full optical sorting

system is suitable to reproduce experimental results. Fur-

thermore, it was demonstrated that computation of ejection

windows and nozzle numbers analogous to the experimen-

tal system yielded precise sorting results.

Similar numerical simulations could be used to predict

the behavior of complex industry-scale sorting machines in

the future. With the possibility to track particle movements

and interaction with other components, for example with

the fluid jets, numerical optimization of such processes

becomes much more feasible. Further investigations could

include data of various operational points, such as higher

mass flows of the bulk material. Particle trajectories could

be analyzed during the flight phase to optimize

the sorting step. Compared to experimental in-

vestigation, a numerical model reduces time

consumption and cost of development drasti-

cally. Moreover, experimentally difficult to han-

dle scenarios such as sorter operation near its

limit or sorting of potentially harmful materials

can be studied. However, a correct set up of

numerical models remains challenging, as the

vibrating feeder plate has shown. Each compo-

nent introduces additional uncertainties into the

system and must be treated with caution. If pos-

sible, an isolated investigation of each compo-

nent is reasonable before considering an entire

system.

Chem. Ing. Tech. 2023,95, No. 1–2, 256–265 ª2022 The Authors. Chemie Ingenieur Technik published by Wiley-VCH GmbH www.cit-journal.com

Figure 8. Comparison of sorting results at three input proportions and two

mass flows. (a) shows the correctly deflected particles (TNR) and (b) the correctly

not-deflected particles (TPR).

Table 2. Values of TNR and TPR in % of sorting experiments

and simulations. Experiments were carried out three times and

averaged for each input configuration.

Scenario TNR [%] TPR [%]

Experiment Simulation Experiment Simulation

90:10 – 10 g s

–1

97.68 95.12 99.83 99.67

90:10 – 20 g s

–1

96.85 98.73 99.75 99.32

75:25 – 10 g s

–1

94.78 98.27 99.38 99.43

75:25 – 20 g s

–1

95.13 98.29 99.60 99.58

50:50 – 10 g s

–1

96.11 97.15 99.44 99.05

50:50 – 20 g s

–1

95.45 97.12 99.32 97.98

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The IGF project 20354 N of the research association

Forschungs-Gesellschaft Verfahrens-Technik e.V. (GVT)

was supported via the AiF in a program to promote the

Industrial Community Research and Development (IGF)

by the Federal Ministry for Economic Affairs and

Climate Action on the basis of a resolution of the

German Bundestag. Computing resources were funded

by the Deutsche Forschungsgemeinschaft (DFG, German

Research Foundation) – Project-ID 463921749. Open

access funding enabled and organized by Projekt DEAL.

Symbols used

A[m

] projecton area

C[–] coefficient

C [–] centroid

F[N] force vector

J[kg m

] mass inertia tensor

k[N m

–1

] spring stiffness

m[kg] mass

n[–] normal vector

n[–] particle number

r[m] radius

R[m] radius

Re [–] Reynolds number

T[N m] torque vector

t[s] time

t[–] tangential vector

u[m s

–1

] fluid velocity vector

v[m s

–1

] particle velocity vector

x[m] particle position vector

Greek letters

g[kg s

–1

] damping coefficient

d[m] overlap

e[–] local voidage

h[N s m

–2

]dynamic fluid viscosity

m[–] friction coefficient

x[m] displacement vector

r[kg m

–3

] density

t[N m

–2

] stress tensor

f[–] sphericity

c[–] correction factor

w[s

–1

] angular velocity vector

L1

i[–] rotation matrix

Sub- and Superscripts

A particle A

B particle B

c Coulomb

c contact

d drag

D drag

e effective

f fluid

g gravitation

i particle index

j particle index

n normal

p pressure

r rolling

rel relative

t tangential

temporal derivation

⊥perpendicular to flow direction

Abbreviations

B brick

CB conveyor belt material

C&DW construction and demolition waste

CFD computational fluid dynamics

CP contact point

DEM discrete element method

FEM finite element method

SB sand-lime brick

SW sorter wall material

TNR true negative rate

TPR true positive rate

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