Computational Prediction of Paste Separation from Industrial Waste by

a Dry Separator Equipped with a Rotor

SUNG UK PARK1, YOUNG SU KANG2, SANGMO KANG1, YONG KWEON SUH1*

1Department of Mechanical Engineering, Dong-A University, 840 Hadan-dong, Busan, KOREA

2Kumho Machinery, Gimhae, Gyeong-nam, KOREA

Abstract: - Recycling of aggregates separated from industrial wastes becomes more important than ever

because of increasing demand of urban redevelopment. The purpose of this study is to investigate the operating

principle of a newly developed paste separator equipped with a rotor. We constructed one-dimensional model

for the air flow and the particle motion is assumed to be governed by the air drag, centrifugal and gravitational

forces. We demonstrate that there are several sections on the air flow route, where particle motions are

stationary along the stream-wise direction while rotating in the azimuthal direction, called quasi-stagnant state.

It was shown that it plays a key role in separation of particles. We report the critical curve in the parametric

space where we can predict separation or non-separation of a given particle size, flow rate and rotor speed.

Key-Words: - Industrial waste, paste separation, numerical prediction, aggregate, rotor

1 Introduction

As per the continuing demand of urban re-

development, the issue of “how to recycle the

wastes including cement aggregates” has been

uttermost important. Various technologies for pro-

ducing the recycling materials from the wastes have

been developed so far [1]. Detailed discussion on

the technological process of manufacturing recy-

cling products has been given, e.g., in [2].

The process is composed of complicated

engineering stages, such as removing extra materials,

crushing coarse aggregates, removing cement and

mortar, and sorting the particles depending on their

size, etc. [2] Not only the mechanical but also even

the chemical principle (see e.g. [3]) is also utilized

in the process. In the sorting process, in particular,

liquid can also be used [4, 5], which is called

wetting method compared with dry method.

In this study, we report the mechanism of

sorting the fine size particles (pastes or cementitious

powder [6]) by using a dry separator equipped with

a rotor. We employ both theoretical and numerical

methods to reveal the mechanism. In order to make

the analysis feasible, we assume one-dimensional

flow field and steady-state drag-force formula acting

on the particles. It turns out that the rotor plays a

key role in separating pastes from the wastes.

2 Problem Formulation

Figure 1 s hows the geometry of the rotor rotating

around the

-axis. We designate three regions; the

inlet region,

rR>

, the rotor channel,

21bb

R rR<<

and the core,

rR<

. Air carrying the solid particles

is pushed into the rotor from the inlet section at

rR=

, enters the inlet of the rotor channel at

rR=

, flows through the channel in between the

rotating radial blades and exits the channel outlet at

rR=

. In the core region,

rR<

, air is guided to

flow upward as well as t oward the central axis,

while showing a spiral trajectory due to the

conservation of angular momentum.

Fig. 1 Geometry of the rotor for separation of paste

particles from wastes and the cylindrical coordinates

for describing the motion of air and particles.

EQUATIONS

DOI: 10.37394/232021.2022.2.3

Sung Uk Park, Young Su Kang,

Sangmo Kang, Yong Kweon Suh

E-ISSN: 2732-9976

Volume 2, 2022

For the theoretical treatise to be feasible, we

develop a much simplified flow model. In the inlet

region, the air flow is assumed to be radial and

uniformly distributed on the azimuthal plane. The

flow velocity is inversely proportional to

. Within

the rotor channel, too, the air flow is assumed to be

purely radial and uniform. Its velocity is computed

from the continuity equation. Since the area of the

channel is reduced further due to the finite thickness

of the blades, the velocity is suddenly increased at

the interface,

rR=

, while the fluid enters the

channel. In the core, the air flow must be upward to

be drawn to the outlet. So, in this region we propose

an axi-symmetric flow model, where the vertical

velocity component is taken to be proportional to

and is dependent on t he radial position by a cubic

polynomial function of

, from which the radial

velocity component is decided from the continuity

equation. On the other hand, the azimuthal

component is determined from the principle of

conservation of angular momentum applied

throughout the core region. In the region connected

to the outlet from there, the vertical component is

taken to be independent of

and so the radial

component is zero and the azimuthal component

still follows the angular momentum conservation.

In terms of the inertial frame of reference, the

particle motion is governed by the Newton’s 2nd

law of motion, where the air drag force acts along

the air’s relative velocity referred to the particle

velocity, and the gravitational force acts downward

with a constant magnitude. The air drag coefficient

is given from

0.06

1.52

6 Re

24 0.194 Re

Re 11.55 Re

c=++

(1)

where Re /

p ap p

ρµ

= is the particle Reynolds

number,

the air density,

the magnitude of the

relative velocity of air,

the particle diameter, and

the dynamic viscosity of air. Since cylindrical

coordinates are used in the expression of the particle

motion, both the centripetal and Coriolis accelera-

tion terms appear on the left-hand side of the

equations, but these are moved to the right-hand

side and are treated as t he centrifugal and Coriolis

forces, respectively, for better understanding of the

physics to be given in the discussion.

Two kinds of analysis for the particle motion

have been conducted in this study; the first one is

the quasi-stagnant analysis and the second one the

numerical analysis with the full equations for the

motion of a particle. In the first kind, the particle is

assumed to be stagnant in the radial motion (but is

allowed to rotate) and simultaneously sum of the

horizontal forces (air drag plus centrifugal force) is

assumed to be zero as the basic state. Then a small

perturbation in its location is applied to determine

the basic state’s stability. In the second, after the

particle is introduced at the inlet, its trajectory is

followed with purely numerical integration of the

equations for the particle motion in time so that we

can confirm if the stability predicted in the first

analysis is indeed relevant. Such a s table quasi-

stagnant orbit of a particle turns out to be a crucial

element in understanding the superior capability of

the paste separation provided by the newly

developed separator.

3 Results and Discussion

Figure 2 shows the radial distribution of the air drag,

f−

, and the centrifugal force,

, acting on a

particle at a quasi-stagnant state. At the outlet of the

rotor channel,

rR=

, the drag force D

f− is larger

than

inside the channel, so that the particle tends

to move toward the outlet. On the other hand,

f−

is smaller than ce

f outside the channel, so that the

particle tends to move toward the outlet, too. This

implies that the particle’s quasi-stagnant state is

stable, and so the particle tends to accumulate there.

During that time the gravitational force will make

the particle fall down and be withdrawn through a

hole on the bottom plate of the rotor. Such scenario

is a fundamental route to understanding the superior

capability of the paste separation. On the other hand,

another quasi-stagnant state at the channel inlet,

rR=

, is unstable because

f−

is larger than

inside the channel.

Fig. 2 Typical distribution of air drag and

centrifugal forces along the radial position.

r [m]

- f

, f

[N/kg]

0.45 0.5 0.55 0.6

100

r=R

- f

N=102 rpm

Q=8m

=0.5mm

EQUATIONS

DOI: 10.37394/232021.2022.2.3

Sung Uk Park, Young Su Kang,

Sangmo Kang, Yong Kweon Suh

E-ISSN: 2732-9976

Volume 2, 2022

As the particle size is decreased, the drag force

becomes more important and outside the outlet of

the channel, it overtakes the centrifugal force and

thus the quasi-stagnant state is no longer stable there.

Instead the stable point moves to the core region.

For a larger particle size, the channel inlet position

now provides the stable steady-stagnant state.

(a)

(b)

Fig. 3 Particle trajectories projected on the

(, )xy

plane (solid curve) and on the

(,)xz

plane (dashed

line) for (a)

0.26

mm and (b)

0.25

mm .

Figure 3 shows typical trajectories of particles

having two slightly different diameters obtained

from numerical simulation of the full equations. The

slightly larger and smaller particles fall down (a)

and rise up ( b), respectively leading to non-

separation and separation, respectively. The results

are in good agreement with the prediction given by

the theoretical analysis.

Figure 4 shows the limit curves from which we

can classify, for the particle diameter 0.075mm, its

separation (left-upper region) and non-separation

(right-lower region) result. We ca n see very close

agreement between the two results implying that a

simple theoretical analysis based on the quasi-

stagnant state and its stability analysis is a r eliable

tool in designing the separator.

Fig. 4 Comparison of the limit curve for separation

and non-separation of particles with diameter

0.075mm obtained from the theory (line without

symbols) and the simulation (line with symbols).

4 Conclusion

Various simplifying assumption has been made for

the air-velocity distribution in the fluid-passing

route around the rotor and for forces acting on t he

particle for the theoretical analysis to be possible

regarding the particle separation in a newly devel-

oped separator. It is found that the concept of quasi-

stagnant state and its stability plays a k ey role in

understanding the physical mechanism of the paste

separation. We confirm that the rotation of the rotor

equipped with blades creates the centrifugal force

acting on the particle outward, and pushing the air

from the outer- toward the inner-region through the

rotor channel makes the air-drag force acting inward

so that balance between the two forces can be

achieved. We also confirm that blades of finite

thickness on the rotating disc result in difference in

the air drag force between inside and outside so as

to cause the particle to show quasi-stagnant state in

particular at the exit of the rotor channel such that

the gravitational activity has enough time for the

particles to settle down and be removed from the air.

-0.5 0 0.5

-0.5

0.5

0.1

0.2

0.3

-0.5 0 0.5

-0.5

0.5

0.1

0.2

0.3

N [rpm]

Q [m

/s]

100 150 200 250 300

Theory

Simulation

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DOI: 10.37394/232021.2022.2.3

Sung Uk Park, Young Su Kang,

Sangmo Kang, Yong Kweon Suh

E-ISSN: 2732-9976

Volume 2, 2022

Acknowledgment

This work was supported by NRF grant No. 2009-

0083510 through Multi-phenomena CFD

Engineering Research Center and by the Human

Resources Development of the Korea Institute of

Energy Technology Evaluation and Planning

(KETEP) grant funded by the Korean government

Ministry of Knowledge Economy (No.

20114030200030). It was also supported by Kumho

Machinery.

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[4] M-G Lee, K-O Kwon, G Gayabazar, and H-C

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[5] Y. Kano, S, Akiba, and Y. Kuriyagawa,

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(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the Creative

Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en_US

EQUATIONS

DOI: 10.37394/232021.2022.2.3

Sung Uk Park, Young Su Kang,

Sangmo Kang, Yong Kweon Suh

E-ISSN: 2732-9976

Volume 2, 2022