Document [original]

Powder Technology 443 (2024) 119907

Available online 22 May 2024

Exploring transverse particle motion in rotary drums: DEM analysis of the

influence of cross-shaped internals on material transport

Alina Lange

, Claudia Meitzner

, Eckehard Specht

, Harald Kruggel-Emden

Technische Universit¨

at Berlin, Chair of Mechanical Process Engineering and Solids Processing, Ernst-Reuter-Platz 1, 10587 Berlin, Germany

Otto von Guericke University Magdeburg, Institute of Fluid Dynamics and Thermodynamics, Universit¨

atsplatz 2, 39106 Magdeburg, Germany

HIGHLIGHTS GRAPHICAL ABSTRACT

•Proposing a new DEM model to predict

the behavior of biomass in rotary dryers.

•Analysis of the effect of lifters and in-

ternals on transverse particle motion.

•Validation of contact parameters of dry

and wet wooden particles.

•Evaluation of bulk porosity, particle

trajectories, and residence time.

•Comparing results for various rotational

speeds, fill levels and particle moisture.

ARTICLE INFO

Keywords:

Simulation

Discrete element method

Rotary drum

Particle motion

Internals

Biomass

ABSTRACT

This study investigates the impact of lifters and cross-shaped internals on the transversal movement of wooden

spheres within rotary drums. Utilizing Discrete Element Method (DEM) simulations, the research evaluates the

influence of these internal configurations on evolving bulk porosity, particle trajectories and residence time of

particles in the central area of the drum. The study analyzes three distinct internal geometries and the influences

of parameters such as drum rotational speed, drum fill level, and particle water content. Analysis of the simu-

lation results shows that the mean bulk porosity increases by 4% for a single internal cross and by 7% for four

internal crosses compared to a configuration without internals. Additionally, it is observed that the residence

time for particles in the center of the drum increases by an average of 2.5 times for a single internal cross and 5.5

times for four internal crosses compared to a configuration without internals.

1. Introduction

Pretreatment of biomass for further use in industry includes trans-

portation, storage, chipping, shredding and drying. This process de-

pends on the feedstock, but in all cases, drying is probably the most

difficult step [1,2]. The main objective of drying is to reduce the water

content; in the case of biomass, this is important to reduce the rate of

deterioration of the products during storage, handling and processing

periods [3]. In addition, drying reduces the bulk weight of the product,

which helps to reduce transportation costs [4].

* Corresponding author.

E-mail address: [email protected] (A. Lange).

Contents lists available at ScienceDirect

Powder Technology

journal homepage: www.journals.elsevier.com/powder-technology

https://doi.org/10.1016/j.powtec.2024.119907

Received 26 March 2024; Received in revised form 7 May 2024; Accepted 20 May 2024

Powder Technology 443 (2024) 119907

Several review papers have been published on the drying of partic-

ulate solids, and rotary dryers are the most discussed [5–7]. In this

equipment, the drying process occurs in a cylindrical casing which is

slightly inclined toward the outlet and is internally equipped with a

series of lifters. Fig. 1 (a) shows a simplified diagram of a rotary dryer

where the wet material enters the upper end of the dryer, and the dry

material exits at the lower end. The hot gas used as the drying medium

can be countercurrent or co-current to the solid flow [8].

The efficiency of the dryer depends to a large extent on the contact

surface between the particulate material and the drying gas. This contact

surface increases when the material is well distributed over the trans-

versal section of the dryer; in general, the better the material is

distributed, the higher the drying efficiency [9,10]. A correct design and

operation of the lifters within the dryer can significantly enhance this

contact surface, as the lifters, lift and then release gradually a large

number of solids ensuring a better distribution of the material and

therefore a more efficient utilization of the energy [11,12]. Multiple

researchers have studied the design of lifters. Revol et al. [13] examined

the impact of lifter geometry on solids cascades. Meanwhile, Sunkara

et al. [14,15] and Seidenbacher et al. [16] focused on studying the size

and length ratio for square lifters. Additionally, Karali et al. [17], Sun-

kara et al. [18] and Seidenbacher et al. [19] explored the influence of the

number of lifters in their respective studies. An example of different

lifters design is shown in Fig. 1 (b).

Another application of rotating drums is the mixing of granular

materials. This application finds extensive use in various industries, such

as agriculture, pharmaceuticals, and mining, where precise blending of

granular components is crucial for product quality and consistency [20].

To enhance the mixing, different shapes and sizes of internals are used,

as shown in Fig. 1 (c) [21]. Priessen et al. [22–24] studied how sectional

internals impact the axial movement of solids in rotating drums. In this

study, the drum was divided into transverse segments and both the

number and length of these segments were varied to observe their effect

on the residence time of particles in the drum. Liu et al. [25] varied the

length of cross-shaped internals to explore its impact on the segregation

of particles differing in density. Heat transfer was also analyzed, as the

particles had different initial temperatures.

To model the mentioned processes, several authors have used the

Discrete Element Method (DEM), with different strategies and

complexity. Previous studies by Komossa et al. [26] and Santos et al.

[27] utilized DEM to investigate particle motion within rotating drums

without lifters, examining various operational conditions and diverse

particle shapes. Meanwhile, He et al. [28] and Zhang et al. [29] inves-

tigated how the quantity of lifters influences particle motion and

segregation within binary mixtures. Additionally, researchers have

employed coupled Computational Fluid Dynamics - Discrete Element

Method (CFD-DEM) approaches to explore the impact of air on residence

time within the drum [30]. Other studies, such as those by Scherer et al.

[31] and Hobbs et al. [32], employed DEM-CFD simulations to research

heat transfer mechanisms and particle drying processes within rotating

drums.

Despite extensive research in optimizing rotary dryer components,

there has been relatively limited exploration into the combined impact

of lifters and internals within these systems. While lifters aid in material

movement and distribution, internals contribute to mixing and heat

transfer. Yet, studies focusing on their combined effects on drying effi-

ciency remain scarce. Understanding how lifters and internals work

together could potentially boost rotary dryer design, enhancing not only

drying rates but also ensuring uniformity in moisture removal across

different materials. With that purpose, in the present study, a combi-

nation of experimental investigations and numerical simulations utiliz-

ing the Discrete Element Method (DEM) was conducted to analyze the

transverse movement of wooden particles within rotating drums, with

lifters and different internal configurations.

The paper is structured as follows: In Section 2, a brief overview of

the numerical model is given. In this study, uncoupled DEM simulations

have been used to illustrate the particle behavior, so the following sec-

tion details the primary equations and the model used to solve them. In

Section 3, the considered setup is outlined. This includes a description of

the rotary drum design, all geometric configurations used, and the

specific operational parameters chosen for the study. In a second part of

this section, the methodology to measure the contact parameters and the

calibration methods are described. Once the numerical frame and con-

figurations are set, in Section 4, a detailed analysis of the simulation

results is presented. This includes a detailed study of the particle tra-

jectories and the calculation of the residence time of the particles in the

center of the drum, for the different geometric configurations. In addi-

tion, the average bulk porosity and the distribution of the bulk porosity

over time are examined. In the last section of this paper (Section 5),

conclusions are drawn, where also issues for future research are

discussed.

2. Model description

The discrete element method, proposed by Cundall and Stack in 1979

[33], is the most frequently used method to simulate granular flow. To

model the mechanical behavior of particles with this method, it is

necessary to solve Newton’s second law to describe linear motion (Eq.

(1)) and Euler’s equation to describe angular motion (Eq. (2)). For a

particle i with mass mi, both equations can be written as follows

→i=∑jF

→ij +F

→f

i+F

→g

i,(1)

→i=∑jM

→c

ij +M

→h

i,(2)

where

→i represents the acceleration of particle i, Fij

→the contact forces

Fig. 1. (a) Illustration of typical co-current rotary dryer, (b) examples of different lifters, (c) examples of internal configurations.

A. Lange et al.

Powder Technology 443 (2024) 119907

between adjacent particles and with walls, F

→f

i is the force resulting from

the interaction with the surrounding fluid, F

→g

i is the gravitational force,

→i is the angular acceleration, M

→c

ij and M

→h

i are the external moments,

resulting out of particle contact forces as well as rolling resistance and

hydrodynamic forces respectively, and Ii the moment of inertia. In the

context of this study, the interactions between the fluid and particles are

neglected, resulting in F

→f

i=0 and M

→h

i=0.

According to the Hertz-Mindlin contact model [34], the contact

forces between particles can be written as

Fij

→=Fnn

→ij +Ftt

→ij,(3)

with normal vector n

→ij and tangential vector t

→ij

→ij =(x

→i−x

→j)/x

→i−x

→j,(4)

→ij =(v

→t)/v

→t,(5)

calculated from the particle midpoints x

→i and x

→j and the relative

translational velocity in tangential direction. Note that particle-wall

contacts can be treated accordingly.

Fn in Eq. (3) is the contact force in normal direction, which can be

decomposed into an elastic component, modelled by a non-linear con-

tact model based on the Hertz theory [35] and a dissipative component,

modelled according to Tsuji et al. [36]

Fn= − knδn−

nvn.(6)

In Eq. (6) δn is the normal overlap and vn the relative translational

particle velocity in normal direction, while kn and

n represent stiffness

and damping calculated as

kn=4/3Eij 

Rijδn

√,(7)

n

mijkn

√,(8)

where

n is the damping coefficient. Rij and mij are the effective radius

and mass respectively and Eij is the effective Young’s modulus calculated

Rij =1/(1/Ri+1/Rj),(9)

mij =1/(1/mi+1/mj),(10)

Eij =1/((1−

i)/Ei+(1−

j)/Ej),(11)

where

represents the Poisson ratio. Note that Eqs. (9)–(11) can also

easily be extended to particle-wall contacts.

Ft in Eq. (3) is the contact force in tangential direction, and is

calculated from a linear spring model and assumed to be limited by

Coulomb friction [34].

Ft=min(kt|ξt|,

c|Fn|),(12)

with ξt

→the absolute value of the tangential displacement and

c the

coefficient of Coulomb friction. The tangential stiffness kt is calculated

kt=8Gij 

Rijδt

√,(13)

where δt is the tangential overlap and Gij the effective shear modulus

with

Gij =1/((2−

i)/Gi+(2−

j)/Gj).(14)

To model rolling resistance M

→r

ij as considered as part of M

→c

ij in Eq. (2),

a constant torque model is used as proposed by Zhou et al. [37]

→r

ij = −

rFn

→((

→−

→)/

→−

→),(15)

where

r is the rolling friction coefficient and Fn

→=Fnn

→ij bases on the

normal force from Eq. (6).

3. Considered setup

As explained in Section 1, rotary dryers consist of inclined cylinders

where the solid and the air are in contact and exchange energy and mass.

Since this study focuses on the particle’s transverse motion, only a cross-

section of the drum was simulated, neglecting the longitudinal motion of

the particles. Both, the front and back sides of the drum are simulated as

walls, and the inclination of the drum is not considered.

3.1. Rotary drum design and operation parameters

The geometry chosen for this study was a rotating drum of 500 mm

diameter and 150 mm length made of stainless steel (grade 316) with a

density of 8.030 kg⋅m

−3

, an arithmetic average roughness of 1.2

m, a

Rockwell hardness B of 80, a Young’s modulus of 1.93E-11 Pa and a

Poisson ratio of 0.33, in which different internal configurations were

installed over the full length of the drum. An overview of the different

configurations is shown in Fig. 2.

Fig. 2 (a) shows the geometry with 0 lifters and 0 internals (0 L +0 I).

This geometry was used to determinate the dynamic angle of repose

(Section 3.2.2) and as a reference geometry for assessing the effect of

internal components on particle behavior. Fig. 2 (b) shows the geometry

with lifters only (10 L +0 I), in which 10 lifters with an axial and radial

length of 50 mm were uniformly arranged. Note that the size and

number of lifters chosen for this work is based on a previous study by

Seidenbecher et al. [19], which studied the optimal configuration for a

Fig. 2. Illustration of the considered combinations of lifters and internals. (a)

Geometry with 0 lifters and 0 internals, (b) geometry with 10 lifters and 0 in-

ternals, (c) geometry with 10 lifters and 1 internal, (d) geometry with 10 lifters

and 4 internals.

A. Lange et al.

Powder Technology 443 (2024) 119907

drum of the same diameter as the one under study. Fig. 2 (c) shows the

configuration with 10 lifters and a single internal cross (10 L +1 I). In

this geometry the center of the cross is aligned with the center of the

drum, while the length of the four arms is 150 mm each. Lastly Fig. 2 (d)

shows the configuration with 10 lifters and four internal crosses (10 L +

4 I). These crosses are evenly positioned at a radius of 120 mm, and each

cross has a length of the four individual arms of 70 mm.

To study the influence of operational and material parameters on the

movement and distribution of particles in the drum, variations of these

were carried out. A summary of these parameters, including the

resulting Froude number (Fr) and parameters characterizing the

considered material, are presented in Table 1 and thereafter discussed in

detail. Note that the Froude number is calculated as Fr = (2

Ω)2R/g,

with R being the drum radius of 250 mm, Ω the rotational speed in s

−1

the drum and g the gravitational acceleration.

Wooden spheres with a nominal diameter of 10 mm made out of

European beech (Fagus sylvatica) were chosen as the study material (see

Fig. 3) having an arithmetic average roughness of 32.3

m, a Janka

Hardness of 6460 N, a Young’s modulus of 1.33E-09 Pa and a Poisson

ratio of 0.35. Due to its structural composition, wood can absorb water

both at the micro level (cell wall) and at the macro level (intracellular

cavities). The moisture point at which the entire cell wall system is

saturated with water is called the fiber saturation point (FSP) and ranges

from 22 to 35% depending on the wood species. Above this point, the

wood loses the water accumulated in the cell cavities without changing

its size, below this points the wood begins to shrink as it loses water

[38]. To assess how changes in wood moisture content (w) affect both,

physical properties and mechanical properties, studies were carried out

at two moisture levels, w =0% as dry particles (moisture content below

FSP) and w =37% as wet particles (moisture content above FSP).

Chen et al. [39] analyzed the influence of rotational speed on a drum

with lifters. The result of this study indicates that if the rotational speed

is either too high or too low, the material curtain will move toward the

outer edges of the drum. As a result, the material curtain does not cover

the entire transversal section evenly, which has a negative effect on the

drying process. To investigate whether this phenomenon is modified for

the geometry with internals, a variation of the rotational speed between

3 rpm and 15 rpm (Fr =2.5E-03 and Fr =6.3E-02) was carried out.

The material curtain is influenced not only by the rotational speed

but also by the fill level [40]. Karali et al. [17] categorized the loading

condition of a drum into three states: under-loaded, optimally loaded

and over-loaded. When the drum is under-loaded, the lifters ascend

without being entirely filled and their discharge starts at the top of the

drum (12 o’ clock position), resulting in reduced particle-air contact

time. When the drum is over-loaded, a particle bed forms at the bottom,

reducing the chances of a particle being picked up by the lifters and

subsequently reducing particle-air contact time. When the drum is

optimally loaded, the particles are picked up by the lifters immediately

after they have fallen and will start falling when the lifter is on the 9

o’clock position, maximizing the transversal area of the curtain. The

optimal fill level ranges between 10% and 15% [41] and is strongly

influenced by the change in the number of lifters and the lifter geometry

[17]. Since the presence of internals in the drum results in a higher

number of particles in the center of it, the number of particles at the

bottom is reduced. Therefore, the presence of internals could change the

optimum fill level. To study this phenomenon, the fill level was chosen

between 10% (optimum load for the 10 L +0 I geometry) and increased

to 15% and 20%.

3.2. Material model

To simulate the behavior of particles and ensure an accurate repre-

sentation of bulk materials, it is necessary to specify several input pa-

rameters. These parameters can be divided into two essential categories

[42], those representing intrinsic material properties, such as particle

density, particle shape and particle size distribution (see Section 3.2.1)

and those required to emulate particle-particle or particle-wall contact

such as coefficients of sliding and rolling friction and coefficient of

restitution (Section 3.2.2) with the latter being related to the damping in

normal direction

3.2.1. Particle representation for simulations

As explained in Section 3.1, wood shrinks as it loses moisture below

the FSP point. Wood shrinkage is anisotropic relative to fiber directions,

according to Simpson [43]. In the direction perpendicular to the longi-

tudinal axis of the tree it is usually small enough to be neglected, in the

Table 1

Operational and material parameters considered.

Water content (w) 0% | 37%

Fill level (F) 10% | 15% | 20%

Rotational speed (Ω) 3 rpm | 5 rpm | 10 rpm | 15 rpm

Froude number (Fr) 2.5E-03 | 7.0E-03 | 2.8E-02 | 6.3E-02

Geometry 0 L +0 I | 10 L +0 I | 10 L +1 I | 10 L +4 I

Fig. 3. (a) Examples of particle diameters, w =0% in blue and w =37% in

yellow and (b) histograms of diameter distribution for particles at different

water contents. (For interpretation of the references to color in this figure

legend, the reader is referred to the web version of this article.)

A. Lange et al.

Powder Technology 443 (2024) 119907

direction of the growth ring boundaries (tangential), it shrinks between

5% and 10%, and in the direction perpendicular to the rings (radial), it

shrinks between 3% and 6%. Since the particles have a diameter of

approximately 10 mm, they are small enough to disregard such anisot-

ropy and assume that they shrink equally in each direction and are

perfect spheres at all water contents. Therefore, to determine the

diameter, the length in the three directions was measured and averaged.

Fig. 3 (a) shows examples of particles at both water contents, and Fig. 3

(b) shows a histogram of the variation in the diameter at both humidity

levels and thereby in which way particle size was realized in the DEM

simulations.

The histogram illustrates particle distribution at different water

content levels: particles with 0% water content (represented in blue,

Fig. 3 (b)) exhibit diameters ranging from 9.5 mm to 10.1 mm, with a

predominant 65% of particles measuring 9.9 mm. Conversely, for par-

ticles with 37% water content (represented in yellow, Fig. 3 (b)), di-

ameters vary from 10.1 mm to 10.7 mm. In this instance, the distribution

is more uniform, with 45% of particles having a diameter of 10.5 mm.

Following the characterization of particle shape and size, the average

particle volume was determined. Using this volume and the average

particle mass, the density was calculated to be 727 kg⋅m

−3

for w =0%

and 800 kg⋅m

−3

for w =37%.

3.2.2. Single particle calibration of wood spheres and bulk validation

To use DEM to predict the motion of the bulk material, it is important

to accurately model the particle-particle (PP) and particle-wall (PW)

contacts. To achieve this, the sliding friction coefficients

c,PP,

c,PW from

Eq. (12) and the rolling friction coefficients

r,PP,

r,PW from Eq. (15)

must be determined for the material under study. A third variable to be

determined is the damping constant

n from Eq. (6), which is related to

the coefficient of restitution. An overview of the parameter values used

are given in Table 2.

There are two general approaches to determining contact parame-

ters: the direct measurement approach and the bulk calibration

approach. In the direct measurement approach, each parameter is

measured at the micro level, i.e. for each individual particle [44]. This

method was first used to determine the values of the coefficients (see

Table 2, column 3). A detailed description of the experiments carried out

to obtain these coefficients can be found in Elskamp et al. [45] work.

The imperfection on the surface and the irregular shape of wood

particles do not guarantee an accurate representation of the bulk

behavior from the parameters determined by a direct measurement

approach [46]. For this reason, using the second approach (bulk cali-

bration) is necessary to improve parameter estimation and to finally

validate the model. In this approach, laboratory experiments are carried

out where the behavior of the bulk can be accurately measured. These

experiments are then repeated numerically, and the parameter values

are adjusted until the simulation results are within an acceptable level of

accuracy. In this study, two different bulk experiments were conducted:

one to determine the dynamic angle of repose (see Fig. 4), which is

performed on the 0 L +0 I geometry and the other to determine the final

angle of discharge (see Fig. 5), which is performed on the geometries

with lifters. The results of the coefficients after the bulk calibration are

shown in Table 2, column 4 and together with those of the coefficient of

restitution from Table 2, column 3 represent the final values used in the

DEM simulations of the rotary drum.

To determine the dynamic angle of repose, tests were performed on

the empty drum geometry (0 L +0 I) for particles at both water content

levels, with four different velocities and three different fill levels (see

Table 1). Thereby in the experiments frontal photographs of the drum

were taken at 200 different points in time. These photos were then

binarized and the boundary between the particles and the background

was determined. A linear regression was then performed on all points of

this boundary. Finally, the angle of repose was determined by calcu-

lating the slope of this line. The same procedure was followed in the

simulations, starting with the parameters of Table 2, column 3. These

parameters were adjusted until reaching the values in Table 2, column 4,

for which the dynamic angle of repose of the experiments and the sim-

ulations show a good agreement, with differences smaller than the

standard deviations (see Fig. 4).

Looking at the results in more detail, it can be concluded for the 6

configurations shown in Fig. 4 that the angle of repose increases with

rotational speed / Froude number, fill level and particle moisture both in

experiments and simulations. Regarding Froude number the

transverse motion of a bulk material in a drum can be divided into three

basic types, slipping motion (Fr <10 −4), cascading motion

(10 −5<Fr <10 −1), and cataracting motion (Fr >10 −1). The cases

under study (2.5E−3<Fr <6.3E−2) belong to the cascading motion

type, which is divided into three subcategories [47]:

•Slumping (10 −5<Fr <10 −3): Due to the rotational friction be-

tween the particles and the wall, the solid bed continuously rises and

is then leveled by successive avalanches on the surface. This flow is

characterized by an oscillation between two different angles of

repose.

•Rolling (10 −4<Fr <10 −2): The dynamic bed is transported up-

ward by the rotational friction between the particles and the drum

walls, while the bed surface is leveled by a constant cascading mo-

tion. This flow is characterized by having a relatively constant angle

of repose.

•Cascading (10 −3<Fr <10 −1): This mechanism occurs when the

rotational speed of the drum is increased, thus increasing the friction

between the wall and the particles. This causes the particles to rise to

a greater height and the dynamic bed surface arches.

Looking at the standard deviation of the experiments, it can be seen

that at lower rotational speeds, fill levels and for higher particle mois-

ture, the system has a slumping dynamic, where the system varies be-

tween different dynamic angles of repose and therefore the standard

deviation is higher. At higher fill levels, the system has a slumping or

rolling dynamic, which produces a more homogeneous motion and

therefore the standard deviation decreases. The same is noticeable in the

results from the simulations (not depicted in Fig. 4) which should be

however not discussed further.

The final discharge angle considered as the second parameter is

defined as the position of the lifter tip where the last particle is dis-

charged and is determined by referencing the 9 o’clock position of the

drum as θ=0, and increasing clockwise from this point until the lifter

tip position is reached (see Fig. 5 (a)).

Tests were conducted for particles at both water content levels, for

four different velocities and on the three geometries with lifters. Vari-

ations in the fill level were also made, but this parameter had no effect

on the final discharge angle. For the experimental results and the DEM

simulations, the final angle of discharge was measured / obtained at 10

different points in time for one complete turn of the drum and averaged.

The results are shown in Fig. 5 (b-d) for a 20% fill level and show a

Table 2

Contact parameters for wooden spheres made out of European beech.

Water

Content

As obtained from direct

measuring approach

After bulk

calibration

Coefficient of restitution PP [−] 0% 0.68 –

37% 0.60 –

Coefficient of restitution PW [−] 0% 0.57 –

37% 0.42 –

Sliding friction PP [−] 0% 0.27 0.32

37% 0.62 0.62

Sliding friction PW [−] 0% 0.38 0.47

37% 0.42 0.42

Rolling friction PP [−] 0% 1.1E-04 0.1E-04

37% 2.7E-04 1.6E-04

Rolling friction PW [−] 0% 1.7E-04 0.5E-04

37% 1.7E-04 1.7E-04

A. Lange et al.

Powder Technology 443 (2024) 119907

general agreement between simulations and experiments for the cali-

brated DEM parameters (see Table 2, column 4). The mean average error

is in the range of 0.4% to 2.3% and remains below the maximum stan-

dard deviation of 2.5%.

Based on the results shown in Fig. 4 and Fig. 5 obtained with the

parameters depicted in Table 2, column 4 together with those of the

coefficient of restitution from Table 2, column 3 a valid set of DEM

parameters in terms of sliding friction coefficient

c,PP,

c,PW, rolling

Fig. 4. Experimental results of the dynamic angle of repose compared to the results of DEM simulations for varying combinations of fill level (F) and particle water

content (w) over applied drum rotational speed and mean absolute error (MAE) depicted for each plot.

Fig. 5. (a) Final angle of discharge definition. (b-d) Example of angle of discharge for a fill level of 20% and varying rotational speed (b) geometry with 10 lifters, (c)

geometry with 10 lifters and one internal, (d) geometry with 10 lifters and 4 internals. The mean absolute error (MAE) is depicted for each plot.

A. Lange et al.

Powder Technology 443 (2024) 119907

friction coefficient

r,PP,

r,PW and damping in normal direction

n are

available, which reliably allows for investigating transvers particle

motion in drums with different internal configurations for which

detailed results are shown in the next section.

4. Detailed analysis of obtained simulation results

In this section, two main parameters were analyzed to evaluate the

results of the simulations. First, the trajectories of the particles are

considered, studying also how long the particles are in the different

areas of the drum (see Section 4.1). Then, the bulk porosity is evaluated

on a particle basis, considering that a higher porosity means a higher

contact of the particles with the air, and thus is potentially guaranteeing

a better drying (see Section 4.2). Finally it is considered how bulk po-

rosities are temporally distributed (see Section 4.3).

4.1. Particle trajectories and residence times

This section examines how the different internal configurations

affect the transverse motion of particles inside the drum in terms of

trajectories and residence times.

4.1.1. Particle trajectories

To qualitatively study the particle trajectories inside the drum, a

particle was randomly selected for the different configurations and its

trajectory was plotted over 7 revolutions. Fig. 6 (a-d) shows the move-

ment of the particles for a fill level (F) of 10%, (e-h) for F =15% and (i-l)

for F =20%. Note that in Fig. 6 particles with w =0% at 5 rpm are

considered. As the results for other rotational speeds and for wet parti-

cles do not differ qualitatively, they are not shown separately.

In Fig. 6 (a), (e) and (i) the particle moves in the dynamic bed

forming at the bottom of the drum within the empty drum geometry.

Thereby dark blue represents the initial position of the particle and dark

red represents the final position of the particle. In this geometry, the

only phenomena affecting particle motion are particle-wall and particle-

particle friction, so particles can only move within the volume occupied

by the dynamic bed. This is reflected in the area on the image occupied

by the trajectories for each fill level. As the fill level increases, the area

over which the particle moves also increases.

For the 10 L +0 I geometry (Fig. 6 (b), (f) and (j)), the particle is

picked up by the lifter and falls at different positions, crossing the drum

section. As outlined in Section 3.1, F =10% (Fig. 6 (b)) is the optimum

fill level for this configuration. This is reflected in the trajectory of the

particle, which is picked up by the lifter immediately after falling. In the

case of F =15% (Fig. 6 (f)), the persistence of a dynamic bed at the

Fig. 6. Particle trajectory of one randomly selected particle over 7 revolutions with w =0%, for 5 rpm and (a-d) 10% fill level, (e-h) 15% fill level and (i-l) 20% fill

level. Initial position of the particle is depicted in dark blue and final position in dark red. A trajectory represented by a solid line resembles a slow moving particle; a

trajectory represented by individual dots is associated to a fast moving particle. (For interpretation of the references to color in this figure legend, the reader is

referred to the web version of this article.)

A. Lange et al.

Powder Technology 443 (2024) 119907

bottom of the drum indicates an overload condition. This phenomenon

is more pronounced for F =20% (Fig. 6 (j)), where the area of the dy-

namic bed is larger. In Fig. 6 each dot symbolizes the particle position at

a given time step; at higher particle velocities the dots are further apart,

while a solid line represents lower particle velocities. During the fall, the

widening gap between the dots indicates a higher velocity and thus a

shorter duration of the particle in the central region of the drum,

compared to its trajectory when it is in the lifter or within the dynamic

bed.

As shown in Fig. 6 (c-d), the presence of internals prolongs the par-

ticle residence in the center of the drum. This occurs because the particle

trajectory is interrupted by the internals, reducing its speed and ulti-

mately increasing the time it spends in this zone. The difference shown

between geometry 10 L +1 I (Fig. 6 (c), (g) and (k)) and 10 L +4 I (Fig. 6

(d), (h) and (l)) is a more uniform distribution of the particle trajectory

over time for the four-cross configuration. Comparing the fill levels for

the geometries with internals, the overall particle trajectory is similar,

although for F =10% there is no dynamic bed, for F =15% the presence

of a dynamic bed is shown for the 10 L +4 I but not for the 10 L +1 I

geometry, and for F =20% there is a dynamic bed forming for both

geometries.

4.1.2. Particle residence times

To evaluate particle residence times the drum can be divided into

two areas: a central area where the particles are in greater contact with

the air, and an outer area where the particles are packed on the lifters or

prevail in the dynamic bed forming at the bottom of the drum. Most of

the drying process takes place in the central zone [48]. Fig. 7 shows an

example of the central (blue) and the outer (red) zones for three different

fill levels for the 10 L +1 I geometry operated with particles with w =

0% at 5 rpm. The lifter area is the same for all configurations, but the

dynamic bed area depends on the operational parameters and material

properties. For F =10% (Fig. 7 (a)), the dynamic bed volume is equal to

zero and therefore the outer area is equal to the lifter area. For F =15%

and 20% (Fig. 7 (b-c)) the dynamic bed volume is not equal to zero and

furthermore depends on the rotational speed and water content of par-

ticles (not depicted in Fig. 7); at higher rotational speed or water content

the dynamic angle is also higher and therefore the dynamic bed forming

is steeper. Another parameter that affects the extension of the dynamic

bed is the drum geometry with its applied internals. As shown in Fig. 6

(g), (h), (k) and (l), the presence of internals keeps more particles in the

central zone of the drum and reduces the volume of the prevailing dy-

namic bed. For this reason, the central zone is defined differently for

each configuration.

To quantitatively assess the geometries, the residence time of parti-

cles within the central zone was determined. This involved averaging

the cumulative time spent by each particle in this zone across all par-

ticles. To facilitate comparisons across different rotational speeds, a

normalization step was implemented by dividing the average residence

time by the total evaluated time. Fig. 8 shows the results for the obtained

normalized residence time

N averaged over all particles np according to

N=1/np∑np

i=1

N,i for each configuration, divided into three plots, one

for each fill level. Each plot shows a curve in purple for the 10 L +0 I

geometry, in green for the 10 L +1 I geometry and in orange for the 10 L

+4 I geometry. The solid line represents results for the dry material and

the dashed line represents results for the material with 37% water

content.

Fig. 8 illustrates the normalized residence time (

N) as a function of

the rotational speed. In the graph for F =10%, an increase in the number

of internals correlates with an increase in

N for each rotational speed.

On average, the particles spend 5.1% more time in the central zone for

the 10 L +1 I geometry and 10.3% more for the 10 L +4 I geometry

compared to the 10 L +0 I geometry. For all configurations, it is

observed that

N is slightly higher for dry particles (between 0.5% and

up to 1.2%). Due to a higher particle-particle and particle-wall friction,

particles with w =37% have a higher final discharge angle (see Fig. 5).

As a result, the particles remain on the lifter longer and the residence

time in the central zone is lower.

In the case of the 10 L +0 I geometry, the curve exhibits a rise with

increasing rotational speed until it reaches 10 rpm, and then remains

constant. As explained in Section 3.1, this phenomenon occurs because

at higher rotational speeds the material curtain shifts to the right side of

the drum, thereby reducing the total area of the material curtain and

also

N. This behavior is not observed for geometries with internals,

where in both cases

N decreases with increasing rotational speed. As the

drum rotates at higher velocities, the particles spend less time on the

internals and fall to the bottom of the drum, reducing

For F =15% Fig. 8 shows that the increment of

N with the number of

internals is more pronounced, with an average increase of 6.5% between

the 10 L +0 I and 10 L +1 I configurations, and a more significant

increase of 16.5% between the 10 L +0 I and 10 L +4 I configurations.

N is also larger for dry particles, the gap in the results between w =0%

and w =37% increases with the number of internals, in average from

0.9% for 10 L +0 I to 1.6% for 10 L +1 I and 2.5% for 10 L +4 I.

For the 10 L +0 I geometry,

N increases with increasing speed,

unlike F =10%, does not reach a maximum at 10 rpm. This is also

justified by the phenomenon explained in Section 3.1, since the geom-

etry is overloaded, there is enough material to maintain the material

curtain through the transversal section of the drum at all rotational

speeds, therefore

N is higher at higher rotational speeds. The same

phenomenon occurs with the 10 L +1 I geometry.

The last graphic to analyze of Fig. 8 is for a fill level of 20%, in this

case

N also increases if the number of internals increases, on average by

5.9% more between geometry 10 L +0 I and 10 L +1 I, and up to 23%

more for the 10 L +4 I. Comparing the curves for different water con-

tents, for the 10 L +0 I geometry it is again observed that

N is higher for

dry particles (0.6% on average). For the other two geometries, the

opposite phenomenon occurs, with moist particles having a higher

than dry particles (1.2% for the 10 L +1 I geometry and 2.5% for the 10

L +4 I geometry).

Fig. 7. Example of central and outer zones for 5 rpm, 10 L +1 I geometry and particles with w =0%, (a) F =10%, (b) F =15% and (c) F =20%.

A. Lange et al.

Powder Technology 443 (2024) 119907

An exemplary visualization of the DEM simulations and photos of the

experiment can be seen in Fig. 9, for F =20%, 3 rpm and w =37%. In

figure (a) and (b) (taken at t =t

), the internal 4 is on the left side of the

drum. Due to friction, the humid particles are caught between the in-

ternal and the wall of the lifter and lifted out of the dynamic bed. This

phenomenon does not occur in figure (c) and (d) (taken at t =t

), where

the internal 4 is at the top of the drum. Therefore, depending on the

position of the internals, a greater quantity of particles enters the central

zone. For particles with w =0% where the particle-particle and particle-

wall friction is lower, the particles slip between the walls of the lifter and

internals and remain in the dynamic bed. For this reason

N is higher for

particles with w =37%.

For both 10 L +0 I and 10 L +1 I an increase in

N is seen with

increasing drum rotational speed. In the case of geometry 10 L +4 I a

maximum is seen for 10 rpm.

To assess the distribution of

N, the standard deviation, calculated as

follows

=

1/np∑

i=1(

N,i−

N)2

√

√,(16)

and its percentage of the mean

N are calculated and shown in Table 3.

This calculation involved determining

N,i for each particle and evalu-

ating the dispersion of these values for each configuration over all

particles np. To facilitate the analysis, the values were exemplarily

evaluated at a rotational speed of 5 rpm and for w =0%, as variations in

these parameters (rotational speed, water content) resulted in similar

standard deviation values for all considered variations.

In the 10 L +0 I geometry, it can be seen that

increases slightly at

higher fill levels, while

N decreases. Consequently,

N increases with

the fill level. This phenomenon corresponds to what is illustrated in

Fig. 6, where for an increased fill level, a dynamic bed forms at the

bottom of the drum and the particles may stay longer there before being

picked up by the lifters. As a result the dispersion of

N,ibetween par-

ticles is higher.

For the 10 L +1 I geometry, it is also observed that

slightly in-

creases or remains constant for higher fill levels, while

N decreases.

However, the percentage values of

N are notably higher compared to

the 10 L +0 I geometry. This is because in the absence of internals,

gravitational forces primarily dictate particle movement, while the

presence of internals introduces additional factors such as particle-

particle or particle-wall friction, resulting in a higher dispersion of

N,i.

For the geometry 10 L +4 I, both

N and

increase with increasing

Fig. 8. Normalized residence time of particles in the central zone of the drum at w =0% and w =37% water content for varying rotational speeds and fill levels for

the geometries studied throughout this paper, neglecting those without lifters.

Fig. 9. Photo examples of simulation results (b) and (d) and comparison to

experiments (a) and (c) for a drum operated with F =20%, at 3 rpm and

particles of w =37%.

Table 3

Normalized averaged residence time of particles

N as depicted in Fig. 8 and its

standard deviation

at w =0% and 5 rpm for the geometries studied throughout

this paper, neglecting the one without lifters.

Geometry F [%]

N[%]

[%]

N [%]

10 L +0 I 10 3.6 0.5 15%

15 2.8 0.6 22%

20 1.5 0.7 44%

10 L +1 I

10 9.5 3.7 39%

15 8.9 4.1 46%

20 6.8 4.1 60%

10 L +4 I

10 14.8 4.6 31%

15 18.4 5.3 29%

20 25.2 8.4 33%

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Powder Technology 443 (2024) 119907

fill level. This results in a relatively constant value of

N because the

random motion of the particles in the center of the drum becomes more

important as more internals are introduced.

4.2. Bulk porosity evaluated at the particle level

The higher efficiency of drying at the drum’s center primarily stems

from the increase in the contact surface area between particles and the

surrounding air, which is an important factor for the heat and mass

transfer [19,31]. This phenomenon has been studied for the 10 L +0 I

geometry by several authors [10], [12–20], but since in the 10 L +1 I

and 10 L +4 I geometries the particles group at the internals, this

conclusion cannot be directly transferred. A good parameter to study the

contact between particles and air is the local bulk porosity (also known

as local void fraction) since it characterizes the ratio between the local

void volume and the local total volume. For this reason, the bulk

porosity attributed on the individual particle level is examined for each

configuration, to determine whether the presence of internals not only

affects the particle trajectory and residency time, but also increases

particle contact with the air.

For numeric calculation of the local bulk porosity, Hoomans et al.

[49] proposed dividing the calculation domain into equally sized cubic

cells. Then the local bulk porosity can be obtained as follows

=1−1

Vcell ∑

i=1

φiVpi (17)

where Vcell is the volume of the cells the calculation domain is divided

into, pv is the number of particles located within the cell, φi denotes the

volume fraction of particle i that belongs to the cell, and Vpi the total

volume of particle i. To simplify the calculation of φi, instead of calcu-

lating it for the wooden spheres considered in the DEM simulations, it is

calculated based on bounding cubes (see Link et al. [50]). Since the

porosity calculation can lead to non-meaningful values if Vpi approaches

Vcell, the edge length of each cube is chosen to be 2 times the nominal

particle diameter of 10 mm.

In the following section, bulk porosity is analyzed in three forms, as

local porosity, spatially averaged porosity and time averaged porosity.

As a cell based approach is used to obtain the porosity in the calculation

domain (Eq. (17)) the particle based local bulk porosity

i can be ob-

tained by assigning each particle the porosity

of the cell in which its

centroid is located. To study how the porosity varies for the different

positions of the lifters and internals as a function of time, the average

porosity over all particles was calculated for each time step as

s=1

np∑

i=1

i(18)

where np is the number of particles considered. Finally, to evaluate the

influence of the water content and to get an overview of the influence of

each configuration, the time averaged porosity was calculated for one

full revolution of the drum as

s=1

tf−ti∑

t=ti

s,t(19)

Fig. 10. Particle based spatially averaged bulk porosity plotted over normalized time for particles with 0% water content.

A. Lange et al.

Powder Technology 443 (2024) 119907

where ti is defined as the time when the second rotation of the drum

begins and tf is the time when the second rotation ends and the third

begins.

4.2.1. Bulk porosity for dry particles

A first study only for dry particles was performed, in which

s is

plotted for each rotational speed, fill level and geometry. Fig. 10 shows

the results for one rotation of the drum, to facilitate comparison between

different rotational speeds, the porosity was plotted as a function of

normalized time.

Looking at the graph for a rotational speed of 3 rpm and F =10%,

is represented in blue for the geometry 0 L +0 I, maintaining a rather

constant value at

s=0.46. In the case of the 10 L +0 I geometry

(purple line) an oscillation around the mean value

s=0.55 is observed.

This oscillation, with an amplitude of 0.02, is caused by the number of

lifters discharging particles, which varies between 3 and 4. At the

culmination of a lifter’s discharge, a higher quantity of particles is

released within a short timeframe and a maximum at

s is observed.

Subsequently, when only 3 lifters are discharging particles, a minimum

is reached in the oscillation pattern. For the 10 L+1 I geometry (shown

in green), the average value is higher (

s=0.57) and although the value

also varies over time, there is a deviation from a typical oscillating

pattern around the mean. Instead, peaks on

s occur at the time when

the internal cross is unloaded. The same observation applies for the

geometry 10 L +4 I, but in this case the peaks are more pronounced

(because 4 internals are unloaded instead of 1) and the average value is

s=0.57.

Fig. 10 also shows that for F =10% as the drum rotates at higher

speeds, there is an increase in

s across all geometries. The most sig-

nificant increase is observed in the 10 L +0 I geometry, exhibiting a

6.3% rise in

s between 3 rpm and 15 rpm, compared to 5.6% for the 10

L +1 I geometry and 4.5% for the 10 L +4 I geometry. Consequently, at

15 rpm, the curves overlap more compared to other rotational speeds.

The oscillations in the curves also become less cyclic as the speed in-

creases, showing nearly no regular pattern at 15 rpm.

For the 0 L +0 I geometry a more moderate increase in

s is seen. The

only difference between the rotational speeds in this configuration is a

higher dynamic angle of repose (see Fig. 4) which slightly increases the

contact surface between particles and air, and therefore

A decrease in

s can be seen for each configuration as the fill level

increases. This was expected as the number of particles (and thus their

total volume) increases but the volume of the drum remains constant.

For F =15%, this decrease is more pronounced for a rotational speed of

3 rpm (2.5% on average) than for 15 rpm (1.7% on average), which

means that as the fill level increases, the rotational speed has a greater

influence on

In the case of the 10 L +0 I geometry, and F =15%, there is also an

oscillating behavior around the mean value, with an amplitude ranging

between 0.01 for 3 rpm to 0.014 for 15 rpm. For the 10 L +1 I geometry

an oscillating behavior is seen, and the presence of peaks is less

noticeable. For the 10 L +4 I geometry there is also a presence of peaks

for the moment where the internals are being discharged. These peaks

are more visible for a rotational speed of 3 rpm. At a rotational speed of

15 rpm (if compared with F =10%) these oscillations are still present

and the difference between the geometries is more visible.

The graphs in Fig. 10 for a 20% fill level (figures on the right) show a

greater difference between the geometries for all rotational speeds. In

this case the curves do not substantially overlap, indicating a greater

influence of the geometries on the average porosity for this fill level. This

is explained by the differences observed between the fill levels in Fig. 6.

For F =10%, the particles are already uniformly distributed for the 10 L

+0 I geometry and the presence of internals does not significantly

modify

s. However, for F =20%, the presence of internals keeps a

higher percentage of particles in the upper part of the drum, reducing

the volume of particles in the dynamic bed and thus increasing

Consequently, the influence of the internals (reflected in the difference

between the curves for each geometry) becomes more pronounced at

higher fill levels. Another difference to see for F =20% is for the ge-

ometry 10 L +0 I, where the oscillations disappeared, and the

s value

remains relatively constant over time (between

s=0.51 for 3 rpm and

s=0.55 for 15 rpm). The increase in the total number of particles does

not interfere with the amount of particles that are taken up by the lifter.

Hence for F =20%, where a significant number of particles reside in the

dynamic bed, the lifter discharge has a minor influence on

s. Conse-

quently, this results in the absence of oscillations on the graph, main-

taining a relatively steady and constant value instead.

4.2.2. Influence of particle water content on bulk porosity

To investigate the effect of water content on

s the values in Fig. 10

were averaged over time and plotted as a function of rotational speed.

Additionally particles with w =37% were considered. The results are

shown in Fig. 11. The general behavior of the porosity for particles with

w =37% is the same as for w =0% particles, the porosity increases with

rotational speed and geometry complexity, and decreases with fill level.

For all configurations, particles with w =37% are attributed to a higher

porosity than particles with w =0%. This difference is greater for higher

fill level and particularly pronounced for the 0 L +0 I geometry.

To explain the variations in average porosity observed across

different water contents, two configurations were chosen, and snapshots

/ photo examples were taken for DEM simulations and laboratory ex-

periments. Fig. 12 (a-d) shows the first configuration, set at F =10%, 10

rpm, and 0 L +0 I geometry, while Fig. 12 (e-f) shows the second

configuration, for F =20%, 3 rpm and 10 L +4 I geometry. In both cases,

the upper images exhibit material with w =0%, while the lower images

exhibit material with w =37%. In the simulation images, the particle

color indicates local porosity (

i), and the view of the drum is not a

frontal view, but a cross section positioned at the mid-point along the

length of the drum. The observed porosity is therefore in the mid-section

of the dynamic bed.

For the first configuration it is observed that the particles with w =

0% exhibit a blue (porosity between 0.35 and 0.4) or turquoise color

(porosity between 0.4 and 0.45), whereas particles with w =37% mostly

exhibit an aquamarine color (porosity between 0.45 and 0.5). These

results align with images of experiments (Fig. 12 (a) and (c)), where the

spaces between particles with w =37% are larger compared to those

with w =0%.

For the second configuration the same phenomenon is seen, in the

areas where the particles accumulate (either in the dynamic bed or in the

internals) the particles are assigned a lower porosity for w =0%

compared to w =37%. This distinction in porosities results from particle

distribution within the packed bed, which is directly related to the

particle surface, and therefore to the contact parameters.

Note that configurations with more particle accumulation (such as

the 0 L +0 I geometry across all fill levels or all geometries for F =20%)

exhibit more pronounced differences in average porosity due to the

difference in the contact parameters and therefore the distribution of the

particles in the packed bed. However this does not directly benefit the

drying process, since the higher porosity is for particles that are not

necessarily in contact with the main air flow.

4.3. Temporal distribution of bulk porosity

In this section, the previous analyses of residence time and porosity

are combined to examine the percentage of time particles exhibit a given

porosity. Theoretical porosity ranges from 0 to 1. In this study, this range

was divided into 10 intervals, and for each particle it was determined

how much time (for a whole rotation) it presented a porosity belonging

to one of these intervals. This was then averaged across all particles.

Fig. 13 illustrates the results of this study, where each bar represents the

percentage of time particles have a porosity within two interval values.

The overall effect of fill level and rotational speed on this parameter is

A. Lange et al.

Powder Technology 443 (2024) 119907

similar to that examined in the previous section. With increasing rota-

tional speed, the particles show higher porosities for a longer period and

with increasing fill level the differences between the geometries with

lifters are more noticeable. For this reason, and to simplify the analysis,

only the results for F =20% and 10 rpm are shown.

The maximum porosity a particle can acquire occurs when 1/8 of a

particle is in a cell. In this case, given that the cell has a size of

0.02 0.02 ×0.02 m and the particles have a diameter of approximately

0.01 m, the porosity is 0.992. The minimum porosity a particle can ac-

quire is the fixed bed porosity, which is estimated to be between 0.36

and 0.4 [51].

According to the results in Fig. 13, no geometry exhibits particles

with porosities below 0.3. Within intervals where

s<0.5, particles

show prolonged residence times in these porosity ranges for the 0 L +0 I

geometry. For instance, considering the porosity interval between 0.3

and 0.4, which represents the packed bed porosity, particles maintain

Fig. 11. Comparison of time averaged porosity at different water content for various fill levels and rotational speeds.

Fig. 12. Snapshots / photo examples of simulation results (b), (d), (f), (h) for particle local porosity (

i)and comparison to experiments (a), (c), (e), (g) for a drum (0

L +0 I) operated with F =10%, at 10 rpm and particles of w =0% and w =37% (a-d) as well as for a drum (10 L +4 I) operated with F =20%, at 3 rpm and particles

of w =0% and w =37% (e-h).

Fig. 13. Time distributed porosity for four geometries and particles with 0%

water content, for F =20% and 10 rpm.

A. Lange et al.

Powder Technology 443 (2024) 119907

such porosities for 16% of the time in the 0 L +0 I geometry and

approximately 5% of the time for the other geometries.

In the range 0.4 to 0.5, all geometries show a maximum in the per-

centage of time, however the maximum is less pronounced as the ge-

ometry complexity increases. Specifically, for the 0 L +0 I geometry,

this percentage reaches a maximum of 67% and decreases to 51% for the

10 L +0 I geometry, 46% for the 10 L +1 I geometry, and 35% for the

10 L +4 I geometry.

For

s>0.5 this phenomenon is reversed, and it is seen that for each

interval, the percentage of time in which the particles exhibit these

porosities increases as the complexity of the geometry increases.

The porosity intervals between 0.9 and 1, represent the porosity

acquired by free-falling particles. For the 10 L +4 I geometry, particles

maintain this porosity for 4% of the time, a slight increase compared to

the 3.6% duration observed for particles in the 10 L +0 I geometry. This

suggests that the presence of internals despite causing particle clus-

tering, extends the period of free-fall time. For the 0 L +0 I geometry the

particles do not exhibit

s>0.9, and only 0.5% of the time have po-

rosities in the interval between 0.8 and 0.9.

5. Conclusions

In the current study the movement of wooden spheres in rotating

drums were investigated at different fill levels, rotational velocities and

water content. The simulations were conducted in a drum with a

diameter of 500 mm and length of 150 mm, and three other internal

geometries including:

•10 L-shaped lifters

•10 L-shaped lifters and one central cross-shaped internal

•10 L-shaped lifters and four cross-shaped internals

DEM simulations were conducted, and corresponding experiments

were recorded with a digital camera for comparison. After calibration of

DEM parameters, the dynamic angle of repose and the final angle of

discharge showed a reasonable agreement with the experiments,

showing a maximum deviation of about 5.6%.

This study reveals that the inclusion of internals in rotary drums has

an influence in particle motion. It is observed that the residence time for

particles in the center of the drum increased by an average of 2.5 times

for a single internal cross and 5.5 times for four internal crosses

compared to a configuration without internals. In addition, the mean

bulk porosity showed an increase of 4% for a single internal cross and an

increase of 7% for four internal crosses, and it was also found that the

presence of internals, although causing particle clustering, extended the

period of free fall time for the particles. These results suggest that the

introduction of internal crosses enhances heat and mass transfer be-

tween air and particles, leading to more efficient drying processes.

In terms of operation parameters, the presence of internals also

contributes to an enhanced optimal fill level. Simulations conducted at a

15% fill level, and the geometry with 4 internal crosses, demonstrated

comparable porosity levels to simulations carried out at a 10% fill level

with the 10 lifters configuration. However, analysis of the simulation

results at different rotational speeds showed that bulk porosity increased

with higher rotational speed, while the residence time of particles in the

center of the drum yielded inconclusive results. The investigation into

the influence of water content on the physical and mechanical properties

of wooden spheres revealed variations in diameter, density, as well as

friction and restitution coefficients. These modifications directly

impacted particle movement within the studied system. However, the

extent to which these changes affect particle-air contact remains

inconclusive.

Further research is required to precisely understand how alterations

in particle properties due to varying water content affect particle-air

contact during drying. A coupled CFD-DEM model should be devel-

oped, where detailed information about the airflow within the drum can

be predicted. Additionally, further research into heat and mass transfer

mechanisms and the influence of internals on the residence time within

the dryer can solidify conclusions about drying processes. Finally, a

study aimed at optimizing the number and shape of internal compo-

nents, as well as their influence on the optimal fill level, would help to

understand how to improve device performance.

CRediT authorship contribution statement

Alina Lange: Writing – review & editing, Writing – original draft,

Visualization, Validation, Software, Resources, Methodology, Investi-

gation, Conceptualization. Claudia Meitzner: Writing – review &

editing, Validation, Resources, Investigation. Eckehard Specht: Writing

– review & editing, Supervision, Funding acquisition, Conceptualiza-

tion. Harald Kruggel-Emden: Writing – review & editing, Writing –

original draft, Supervision, Resources, Methodology, Funding acquisi-

tion, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial

interests or personal relationships that could have appeared to influence

the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgment

The research project IGF 21637 BG of the German Association for

Combustion Research (DVV) is funded by the Federal Ministry for Eco-

nomic Affairs and Climate Action based on a resolution of the German

Bundestag as part of a program for promoting industrial collective

research (IGF).

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