Numerical Methods for Simulating Separation in a Vacuum...

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Numerical Methods for Simulating Separation in a Vacuum Cleaner Cyclone (58)

Author

Patrik Lans Date

08/07/2016

Numerical Methods for Simulating Separation in a Vacuum Cleaner Cyclone

Thesis for the degree of Master of Science

Department of Mechanics

Engineering Mechanics

KTH ROYAL INSTITUTE OF TECHNOLOGY

Stockholm, Sweden, 2016

MASTER’S THESIS

Date: 08/07/2016 Numerical Methods for Simulating Separation in a Vacuum Cleaner Cyclone (58)

MASTER’S THESIS


Thesis for the degree of Master of Science

Numerical Methods for Simulating Separation in a

Vacuum Cleaner Cyclone

Patrik Lans

Department of Mechanics

KTH ROYAL INSTITUE OF TECHNOLOGY


MASTER’S THESIS


Numerical Methods for Simulating Separation in a Vacuum Cleaner Cyclone

© Patrik Lans, 2016

KTH Royal Institute of Technology

SE-100 44 Stockholm

Sweden

Telephone +46 (0)8-790 60 00

Printed by KTH


MASTER’S THESIS


Abstract

This thesis includes a numerical comparison of different turbulence models and particle

models in terms of convergence time and physical accuracy. A cyclone is used as the

computational domain. Cyclones are common devices for separating two or more

substances. The work is divided into an experimental part and a numerical part.

In the experiments, characteristics of the cyclone were measured. This data is then

used to evaluate different numerical modeling approaches.

The numerical part consists of two parts, namely single phase flow and multiphase

flow, where different modeling aspects are examined and presented. Furthermore,

important parameters that characterize a cyclone, such as pressure drop and

separation efficiency, are calculated. The separation efficiency, i.e. how much dust that

actually goes to the dust bin, is calculated for two different types of dust. The software

used for the numerical simulations has been Star-CCM+.

Key words: computational fluid dynamics (CFD), cyclone, separation efficiency,

pressure drop, turbulence, dispersed phase

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Sammanfattning

Detta examensarbete omfattar en numerisk jämförelse av olika turbulensmodeller och

partikelmodeller med avseende på konvergenstid och fysikalisk precision. Den

beräkningsgeometri som används är en cyklon. Cykloner är vanliga anordningar för

separering av två eller fler ämnen. Examensarbetet är uppdelat i en experimentell del

och en numerisk del. Vid experimenten uppmättes cyklonens egenskaper. Mätdata från

experimenten jämförs sedan med numeriska modelleringsmetoder.

Den numeriska delen består av en singelfasdel och en multifasdel, där olika

modelleringsaspekter undersöks och presenteras. Vidare beräknas viktiga parametrar

som karaktäriserar en cyklon såsom tryckfall och separationsgrad. Separationsgraden,

d.v.s. hur mycket damm som faktiskt hamnar i dammlådan och därmed anses

separerat, beräknas för två olika dammtyper. För de numeriska beräkningarna har

programvaran Star-CCM+ använts.

Nyckelord: CFD, cyklon, separationsgrad, tryckfall, turbulens, diskret fas

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Acknowledgements

First of all, I would like to thank my supervisors Christian Wollblad and Johan Spång

for all the guidance and support during the whole period of writing.

Additionally I would like to thank Jens Leffler for helping me during the experiments.

Also a special thank is directed towards instructor Christian Windisch from CD-adapco

who held the Star-CCM+ custom technical course about particle-laden flows.

Arne V Johansson, thank you for being my contact person and examiner at KTH.

Stockholm, July 2016

Patrik Lans

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Contents Symbols .................................................................................................... 11

1 Introduction ............................................................................................... 13

1.1 Background ...................................................................................... 13

1.2 Purpose of thesis ............................................................................... 14

1.3 Limitations ....................................................................................... 14

1.4 Other information .............................................................................. 15

2 Theory ...................................................................................................... 16

2.1 Cyclones .......................................................................................... 16

2.2 Working principle of a cyclone ............................................................. 16

2.3 Flow types ........................................................................................ 17

2.3.1 Multiphase flow .................................................................... 17

2.3.2 Dilute versus dense flow fields ............................................... 18

2.3.3 Turbulence .......................................................................... 19

2.4 Characteristics of gas cyclones ............................................................ 20

2.4.1 Pressure drop and Euler number ............................................ 20

2.4.2 Overall separation efficiency .................................................. 20

2.4.3 Grade efficiency curve .......................................................... 21

2.4.4 Stokes number .................................................................... 22

2.4.5 Particle-wall interactions ....................................................... 23

2.5 Physics of particles ............................................................................ 23

2.5.1 Drag forces on particle .......................................................... 23

2.5.2 Particle-fluid interaction ........................................................ 24

2.5.3 Particles and turbulence ........................................................ 24

2.6 Boundary layer ................................................................................. 25

3 Experiments .............................................................................................. 26

3.1 Method ............................................................................................ 26

3.2 Results ............................................................................................ 28

3.2.1 Overall separation efficiency .................................................. 28

3.2.2 Cut size .............................................................................. 29

4 Method...................................................................................................... 30

4.1 Geometry ......................................................................................... 30

4.2 Models ............................................................................................. 31

4.2.1 Boundaries .......................................................................... 32

4.2.2 Pressure drop evaluation ....................................................... 33

4.2.3 Wall treatments ................................................................... 33

4.2.4 Dispersed phase .................................................................. 34

4.2.5 Particle-boundary interactions ............................................... 36

4.3 Meshing ........................................................................................... 37

4.3.1 Mesh quality ........................................................................ 39

4.4 Solver settings and convergence ......................................................... 42

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4.4.1 Lagrangian multiphase solver ................................................ 43

5 Results and discussion ................................................................................ 44

5.1 Flow visualization .............................................................................. 44

5.2 Analysis of dust bin boundary condition................................................ 45

5.3 Single-phase with dust bin ................................................................. 47

5.4 Multiphase ........................................................................................ 50

5.4.1 Calculation of Euler number and Stokes number ...................... 53

6 Conclusions ............................................................................................... 55

7 Further work .............................................................................................. 57

References....................................................................................................... 58

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Nomenclature

Symbols

C Mass concentration

CD Drag coefficient

D Diameter

Eu Euler number

Fss Steady state drag force

g Acceleration of gravity

I Sharpness of cut size

Ir Relative turbulence intensity

k Turbulent kinetic energy

L Characteristic length scale

m Mass

Mc Captured mass

Mf Fed mass

p Pressure

Re Reynolds number

Rep Particle Reynolds number

Stk Stokes number

t Time

U Characteristic velocity scale

𝑢∗ Friction (shear) velocity

ujk Velocity component of bulk phase

vijk Velocity component of second phase

V Velocity

V Volume

x50 Cut size

x Particle diameter

Xi Measurement number i

xijk Position component for i,j,k directions

y Wall-normal height component

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y+ Non-dimensional wall-normal height component

Greek symbols

αd Volume fraction of dispersed phase

ε Dissipation rate of turbulent kinetic energy

η Separation efficiency

μ Expected value

μ Dynamic viscosity

μt Eddy (turbulent) viscosity

ν Kinematic viscosity

ρ Density

σ Standard deviation

σij Stress tensor

τ Period of time

τij Shear stress tensor

ω Specific dissipation rate of turbulent kinetic energy

∇ Nabla operator

Abbreviations

CAD Computer-Aided Design

CDF Cumulative Distribution Function

CFD Computational Fluid Dynamics

GEC Grade Efficiency Curve

RANS Reynolds-Averaged Navier-Stokes

SST Shear Stress Transport

TKE Turbulent Kinetic Energy

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1 Introduction

1.1 Background

The Swedish engineering company Electrolux has over the last years replaced the dust

bags in some of their vacuum cleaners with cyclones instead. An example is shown

Figure 1 where the cyclone is horizontally placed on top of the vacuum cleaner. The

advantage of this solution is that less dust passes through a cyclone than through a

dust bag, which means that the motor filters do not clog so quickly. Moreover, the

users do not need to change the bag every time it is full, but can simply empty the

container instead.

Figure 1: A generic view of the vacuum cleaner with the cyclone placed horizontally and the dust bin placed vertically.

Since September 2014, new vacuum cleaners are provided with an energy label such

as the one shown in Figure 2. The label indicates how much energy that the machine

consumes, and it also shows the dust absorption, noise level and how much dust that

passes through the vacuum cleaner. When the label was introduced back in 2014, the

upper limit of the vacuum cleaner power was set to 1600 W. This limit has been

achieved by vacuum-cleaner manufacturers relatively easy. However, by political

decrees, the limit will be lowered to 900 W, which is much more difficult to comply

with sustained suction. In addition, the vacuum cleaners are classified by energy

classes A+, A++ and A+++. The input power has to be significant lower for a

classification of A+++.

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Figure 2: Energy label for vacuum cleaners initiated by the European Union [12].

Computational Fluid Dynamics (CFD) will be an important tool for the development of

vacuum cleaners that meet tougher energy requirements. CFD is already self-evident

in the design of some parts of vacuum cleaners. One example is the design of fans.

But it is a greater challenge to simulate the separation of dust, especially when the

separation takes place in a cyclone whose flow is a challenge to simulate even without

considering the separation process.

1.2 Purpose of thesis

In their projects, Electrolux need to study large numbers of possible geometries. The

selected CFD models must therefore be cost-effective. There is plenty of literature on

how to improve prediction efficiency in multiphase flow, but it is often less well

investigated how much this improvement costs in terms of computational time,

especially when different methods and models are combined.

The goal of this thesis is to select a number of physically significant parameters and

modeling aspects that could be important for the prediction of separation efficiency in

a cyclone and examine their impact, in terms of accuracy, computational time and

convergence properties.

1.3 Limitations

The suction capacity stated by the label in Figure 2 is measured with a standard dust

consisting of a sand component and two different fiber components. Of these, the sand

is the most difficult to separate with a cyclone. Tests during the development phase

are therefore usually performed with clean sand. It fits the thesis work well to limit the

investigation to sand grains because the small particles can be described fairly well by

the methods typically implemented in commercial softwares. Simulation of fiber

suspensions, on the other hand, is regarded to belong to the research front.

Consequently, CFD of fibers in a cyclone would require more effort than fits in the

framework of a master’s thesis.

It would be possible to obtain measurement data directly from Electrolux but in order

to get a first-hand view of the measurement method, the work comprises a smaller

experimental part. Since the cyclone is transparent, the trajectories of the particles are

observable during the experiments, which clearly help to get a deeper understanding

of the flow physics.

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1.4 Other information

The work was performed at the main office of ÅF and supervised by Christian Wollblad.

Electrolux provided facilities and equipment for the experimental part of the project.

The experiments were supervised by John Spång and Jens Leffler (Electrolux

Appliances). Johan also served as supervisor and facilitator at Electrolux.

Cyclone geometry and CAD files were provided by Electrolux. The project deals with

the cyclone shown in Figure 1. Since this product is on the market, there is no obstacle

to include the results in a publicly available report.

The simulations were performed in the commercial software Star-CCM+ because it is

the software used for CFD computations at Electrolux.

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2 Theory

2.1 Cyclones

Cyclones are devices constructed to separate materials of different phases based on

difference in density between the phases. Typical industrial applications are separation

of droplets or solid particles from a gas flow. There are two main types of cyclones,

namely reverse flow cyclone and uniflow cyclone. For uniflow cyclones, the fluid enters

and exits straightly. Reverse flow cyclones have two separated outlets. In industrial

applications, the reverse flow cyclone is much more common. The principle of the

reverse cyclone, with a tangential velocity inlet, is shown in Figure 3. In reverse

cyclone, the bulk flow can be injected in four different configurations, namely

tangential, axial, helical and spiral [9]. The cyclone in Figure 4 has tangential velocity

injection, and only such cyclones are investigated in this thesis.

Cyclones are also categorized depending on what kind of phase the bulk flow has.

Cyclones where the bulk flow consists of a liquid, is called hydro-cyclones and cyclones

where the bulk flow consists of a gas, is denoted gas cyclones. In further

considerations, only gas cyclones are covered in this work since the carrier fluid always

constitutes a gas for vacuum cleaners.

Figure 3: Simplified sketch showing the fundamental cyclone construction [2].

2.2 Working principle of a cyclone

A sketch of a reversed flow cyclone with tangential inlet is shown in Figure 3. Reversed

flow cyclones have an inlet and two outlets, one for the dust and the one for the

purified air. The flow in the cyclone consists of a swirling motion tangentially. Axial and

radial flow velocity components are also present, however the radial velocity is small

compared to the tangential and axial ones [2].

The incoming airflow starts to swirl when entering the separation space due to the

curvature of the cyclone. Since rotational motion is created, centrifugal forces start to

act on the fluid. Larger particles (typically larger than 5 microns) contain more inertia

and are therefore pushed more rapidly towards the wall [2]. Main forces acting on the

particle are drag force and centrifugal force. The drag force for a single particle is

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pointed radially inwards, and the centrifugal force is directed radially outwards. The

drag force is created due to relative motion between the particles and the conveying

fluid [1]. This is explained more deeply in Section 2.5.1.

The axial velocity component at the wall tends to push the particles downwards and

finally they assemble in the dust bin, see Figure 4. At the center of the cyclone body, a

reversed flow field points upwards. The reversed flow mainly consists of clean air but

usually contains some smaller particles. However, installation of a vortex finder

hinders smaller non-separated particles from entering the air outlet.

Figure 4: CAD-model of the cyclone used for the numerical simulations.

2.3 Flow types

A flow field consists of either one phase or two or more phases simultaneously, these

are called single-phase and multiphase respectively. Depending on the numbers of

chemical species of the bulk flow, the fluid is referred to as single component or

multicomponent fluid respectively. Four types of fluid flows exist, see Table 1 [1].

Table 1: Examples of different flow types and their corresponding names.

Number of phases Single component Multicomponent

Single-phase Water flow Nitrogen flow

Gas mixture flow Flow of emulsions

Multiphase Stream-water flow Nitrogen-sand grains flow

Gas mixture-water flow Slurry flow

Observe that even though air theoretically is classified as a gas mixture, it is in the

context of numerical modeling often treated as a single component gas.

2.3.1 Multiphase flow

Multiphase flows generally result in more complex flow fields than single-phase flows

since different phases co-exist and can therefore interact with each other. The second

phase can be regarded as either separated or dispersed. A separated phase means

that one phase is only connected with another phase by an interface, see Figure 5. On

the other hand, a dispersed phase means that it is distributed in another phase. For

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gas cyclones, a dispersed phase means that the particles are regarded as discrete

points spatially distributed in the airflow phase.

Figure 5: Separated phase (left) and dispersed phase (right)[13][14] .

There exist two reference frame works on how to model the motion of particles or

droplets in space, the Eulerian and Lagrangian approach respectively [2][7]. The

Eulerian modeling approach focuses on modeling the particles by storing flow physics

at different points in space and time. It could be described as sitting on the beach and

seeing a boat going by. The Lagrangian approach however describes the particles

instantaneously, it is like sitting in the boat [7]. The bulk flow itself is continuous, so

normally the entire flow field is called Euler-Euler or Euler-Lagrangian. For dispersed

phase flows, the second phase can be further characterized by introducing the concept

of dilute and dense flow.

2.3.2 Dilute versus dense flow fields

A dilute flow for a dispersed phase is characterized by low volume fraction and thereby

governed by dynamic fluid forces, namely drag and lift. A dense flow consists of higher

volume fraction and thereby governed by particle collisions or regular contact. The

response time can also be used to determine if a flow is dilute or dense. The response

time tells how quickly the particles react to fluid dynamic forces of the bulk flow. The

particles in a dense flow collide before the response from the change of properties of

the carrier phase is finished [1]. The volume fraction of the dispersed phase, see

Figure 6, is defined by,

𝛼𝑑 =𝑉𝑑

𝑉𝑑 + 𝑉𝑐

1

and gives a general indication of what kind of dispersed phase that is present in the

flow field [1].

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Figure 6: Flow types depending on the volume fraction of particles [1].

2.3.3 Turbulence

A flow is either laminar or turbulent. A laminar flow consists of a velocity field without

velocity fluctuations. It can be one, two or three-dimensional and only incorporates

shear stress. A turbulent flow field is more complex. Only three-dimensional, sudden

fluctuations in space and time occur, the flow has high diffusivity and a high Reynolds

number [4]. Since the majority of flows in nature are turbulent, there is a reasonable

modeling approach in this context as well.

Reynolds number is an indicator of the characteristics of the flow. As with many other

quantities within fluid mechanics, the Reynolds number is dimensionless. The number

is defined as,

𝑅𝑒 ≡𝐿𝑈

𝜐~

𝑖𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝑓𝑜𝑟𝑐𝑒𝑠

𝑣𝑖𝑠𝑐𝑜𝑢𝑠 𝑓𝑜𝑟𝑐𝑒𝑠

2

where L is the characteristic length scale of the flow, U the magnitude of the velocity

and ν the kinematic viscosity of the fluid. By replacing L by the inlet diameter, the

Reynolds number for the cyclone in consideration can be computed, see Figure 4. For

this cyclone, at normal operating conditions, the velocity magnitude, U, is 16.6 m/s,

with the viscosity of air known as νair=1.5∙10-5 m2/s, the Reynolds number becomes,

𝑅𝑒 =0.0384•16.6

1.5•10−5 ~42500 3

The transition from laminar to turbulent state depends on the geometric configuration

among other things; however the number above clearly shows the need of turbulence

modeling in this application.

Two-equation eddy viscosity models such as k-ε and k-ω for cyclones are commonly

used for simulating turbulence in industry. Nevertheless, these models tend to have

some problems concerning curvatures and to model satisfactorily the anisotropy of the

turbulence [6]. This can to some degree be remedied by adding correction terms, but

in general it requires the use of more sophisticated turbulence models such as

Reynolds stress models or Large eddy simulation (LES) [6].

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2.4 Characteristics of gas cyclones

There are different ways to characterize a cyclone when it comes to performance. The

most commonly used parameters are the overall separation efficiency and the

pressure drop. The aim when designing a cyclone is to increase the separation

efficiency and decrease the pressure drop of the gas cyclone. A higher quality of

separation usually implicates an increased pressure drop [2]. The separation occurs

due to significant differences of material densities between the bulk phase and the

dispersed phase. Thereby the separation is heavily dependent on the material in

consideration. The separation of smaller particles is less efficient since they tend to

follow the airflow to a larger extent, therefore the simulation of smaller particles is of

high interest.

Generally speaking, for tangential flow cyclones, a quite high inlet velocity is necessary

to give the particles sufficient momentum. Higher inlet velocity tends to give a

stronger vortex motion but it also results in higher pressure drop.

2.4.1 Pressure drop and Euler number

The pressure drop is a measure of total loss in energy between the inlet and the air

outlet and is of importance in cyclone manufacturing in order to improve the cyclone

performance. The pressure drop is proportional to shear forces acting within the fluid

itself and at the walls. Additionally, the pressure drop tends to vary with wall friction,

concentration of solids and the dimension of the cyclone [2]. Increased solid loading

amplifies the particle interactions, therefore losses are more probable. Smoother

surface at the wall gives a higher dynamic pressure, thus a higher velocity in the core

of the cyclone body. This velocity difference facilitates the separation.

The quantification of pressure drop in cyclonic modeling is often non-dimensional. The

Euler number is defined as a local pressure drop over the volumetric kinetic energy.

Another name of Equation 4 is the resistance coefficient as it represents the ratio of

pressure forces to inertial forces. The Euler number is defined as follows,

𝐸𝑢 ≡𝑝𝑢𝑝𝑠𝑡𝑟𝑒𝑎𝑚 − 𝑝𝑑𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚

12

𝑝𝑣𝑧2

4

where the nominator represents the difference in total pressure. The velocity in the

denominator is in academic context often the mean axial velocity of the cyclone body.

The mean axial velocity along the center line of the cyclone body, see Figure 3, can be

determined by the following equation,

𝑣 =4𝑄

𝜋𝐷2 5

where Q is the volumetric flow rate and D is the mean. However, most engineering

applications employ the use of inlet velocity or mean velocity in the vortex finder

[2][6]. Euler number, within this range of application, is independent of the Reynolds

number, low solid loading, and gravity. It is constant for geometrically similar

cyclones. The Euler number hence gives an estimate of the expectation when it comes

to performance of different operational cyclones.

2.4.2 Overall separation efficiency

There are various variants of how to measure the separation efficiency. The overall or

total efficiency, η, is normally of high interest and is calculated as follows,

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𝜂 =𝑀𝑐

𝑀𝑓= 1 −

𝑀𝑒

𝑀𝑓

6

The denominator denotes the mass (or mass flow rate) of fed particles. Similarly,

subscripts c and e, denote the captured and emitted (lost) mass (or mass flow rate)

respectively [2]. However, another approach is necessary to broaden the analysis to

include separation efficiency of each particle size range.

2.4.3 Grade efficiency curve

Since most applications of practical interest involve a particle size distribution, the

degree of separation for a particular particle size range is desirable. In a similar

manner to the computation of the overall separation efficiency, the collected mass

divided by the feed mass gives the separation efficiency for a specific particle size

range, ∆x or specific particle size, x:

𝐺(∆𝑥) =𝑚𝑐

𝑚𝑓

7

The relation between the overall separation efficiency and the separation of a specific

particle size is as follows,

𝜂(𝑥) = 𝜂𝑓𝑐(𝑥)

𝑓𝑓(𝑥)

8

where fc and fc are the distribution functions for the collected mass and fed mass

respectively. By tabulating these values for each particle size range, a plot can be

obtained that shows the separation efficiency as function of the particle size, see

Figure 7.

At a certain particle size x, where the probability η(x) that separation occurs is 50 %,

is defined as the cyclonic cut size. It is commonly denoted by x50 [2][6]. The boundary

conditions of the grade efficiency curve are given below,

𝜂(𝑥) → 0 𝑎𝑠 𝑥 → 0

𝜂(𝑥) = 0.5 𝑎𝑡 𝑥 = 𝑥50

𝜂(𝑥) → 1 𝑎𝑠 𝑥 → ∞

The boundary conditions are valid for the graph in Figure 7.

Figure 7: Graph showing a typical s-shaped grade efficiency curve [2].

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If the separation in the cyclone was ideally sharp, the grade-efficiency curve would be

a vertical line at the ‘critical’ or ‘cut’ size. The x-axis and the y-axis show particle sizes

and overall separation efficiency respectively. The interval to the left of x is the crucial

particle size that is poorly separated. The cut size could also be dimensionless by use

of Stokes number, see Section 2.4.4.

The sharpness of cut expresses the slope of the curve at the cut size [2]. This relation

can be described by,

𝐼75/25 =𝑥75

𝑥25

9

Other relations also exist. Since the curve grows monotonically, the slope coefficient

must be greater or equal to unity. A sharp limit is given by unity and it is only possible

in theory. Why the limit is not sharp depends on several factors, for instance inlet

position for an individual particle, agglomeration between smaller and larger particles,

and back-mixing due to wall roughness [2].

2.4.4 Stokes number

Stokes number relates the momentum response time of the particle to the some

macroscopic time scale of the flow. The importance of the Stokes number is to give an

indication of how quickly the particles react to a change in a macroscopic flow quantity

such as velocity or momentum. If velocity equilibrium is valid, the particles have

sufficient time to adjust to abrupt changes in the continuous phase.

An empirical relationship between Euler number and Stokes number exists where

parameters are scaled to be able to compare separation efficiency between cyclones of

different geometrical configuration for instance. The scaling is only done for one-way

coupling, i.e. the dispersed phase does not influence the carrier phase. The

dimensionless Stokes number for the cut size is given by,

𝑆𝑡𝑘50 ≡𝑑𝑠

𝐷𝑥

10

where ds is the stopping distance and Dx a characteristic cyclone length, for instance

the diameter of the vortex finder. The stopping distance is defined as the length that

the particles shaped by the cut size would travel against fluid drag if the motion of the

airflow ceases abruptly. Stokes number shows a clear independence of inlet Reynolds

number above 2∙104 [2]. The inlet Reynolds number for this cyclone is 4.2∙104, see

Section 2.3.3.

Another way of calculating the Stokes number is given by [9],

𝑆𝑡𝑘50 =𝑥50

2 𝜌𝑠𝑣

18𝜇𝐷 11

where 𝜌𝑠 is the particle density, v is the particle velocity and D is the diameter of the

separation space, see Figure 3. The Stokes number in Equation 11 describes the ratio

of centrifugal force to drag force, where a decrease of Stokes number improves the

separation efficiency [9].

Svarovsky derived an empirical relationship for cyclones of conventional design and

low solid loading, i.e. the relationship between the mass flows of each phase [2],

𝐸𝑢𝑏√𝑆𝑡𝑘𝑏,50 = √12 12

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where the subscript b stands for cyclone body. The equation above is a rough

estimate, but gives at least a hint about the performance of this particular cyclone

compared to others in the same geometric range [2]. Several assumptions have been

done in order to obtain the relation above, for a complete derivation see [2].

2.4.5 Particle-wall interactions

Particle-wall interactions are of high interest for cyclonic separation since wall contact

affects the trajectory of particles. These interactions are mainly caused by particle

mass loading, geometrical dimensions, particle response time, bulk velocity,

turbulence intensity, particle shape, wall roughness and combination of particle and

wall material [2].

A rule of thumb is to estimate the importance of particle-wall interactions by

comparing the particle response distance, 𝜆𝑃, to the diameter of the system, 𝐷. If

𝜆𝑃 ≫ 𝐷, the particles do not have sufficient time to react to velocity flow changes

before they collide with the nearest wall [5]. Hence the particle motion is primarily

dominated by wall collisions.

2.5 Physics of particles

2.5.1 Drag forces on particle

In industrial applications, it is common to model particles as spheres. As these spheres

move through space, forces act on them. In order to get a reliable estimate of the

separation efficiency, a drag force must be included. In gas-particle flows the drag

force determines the particle motion and it consists of both friction and form drag. The

particle Reynolds number is defined as,

𝑅𝑒𝑃 =𝜌𝐹𝑑𝑃|𝑢𝐹 − 𝑢𝑃|

𝜇𝐹

13

where subscripts F and P denote flow and particle respectively. The drag coefficient of

the particle may change due to several physical phenomena including turbulence of

the carrier phase, surface roughness, shape, wall effects and the concentration of the

particles (particle mass ratio) [1].

The equation of motion for small particles in unsteady laminar flow is given by,

𝑚𝑑𝑣𝑖

𝑑𝑡= 𝑚𝑔𝑖 + 𝑉𝑑 (−

𝜕𝑝

𝜕𝑥𝑖+

𝜕𝜏𝑖𝑗

𝜕𝑥𝑗) + 3𝜋𝜇𝑐𝐷 [(𝑢𝑖 + 𝑣𝑖) +

𝐷2

24∇2𝑢𝑖]

+1

2𝜌𝑐𝑉𝑑

𝑑

𝑑𝑡[(𝑢𝑖 − 𝑣𝑖) +

𝐷2

40∇2𝑢𝑖]

+3

2𝜋𝜇𝑐𝐷2 ∫ [

𝑑𝑑𝜏⁄ (𝑢𝑖 − 𝑣𝑖 + 𝐷2

24⁄ × ∇2𝑢𝑖)

𝜋𝜈𝑐(𝑡 − 𝜏)1/2] 𝑑𝜏

𝑡

0

14

where the first term of the right-hand side represents body force due to gravity, the

second undisturbed flow, the third steady state drag, the fourth virtual or apparent

mass term and the last Basset or history term. The undisturbed flow consists of

pressure and shear stress fields and can be a major part of the force acting on a

particle. However, for gas-solid flows this term can be neglected since 𝜌𝐹 𝜌𝑃⁄ ≪ 1

[1][5]. The virtual mass is the local conveying fluid of a particle that is accelerated or

decelerated due to acceleration or deceleration of a particle. The Basset force depicts

MASTER’S THESIS


the development of a boundary layer on a particle. In case of steady bulk flow, the last

two terms are removed. This reduces Equation 14 to describe the steady state drag as,

𝐹𝑠𝑠,𝑖 = 3𝜋𝜇𝑐𝐷(𝑢𝑖 − 𝑣𝑖) + 𝜇𝑐𝜋𝐷3

8∇2𝑢𝑖 15

The steady-state drag force is the drag (air resistance) where the relative velocity

between the two phases is constant. The latter term can usually be neglected in

industrial applications since the effects of Reynolds number are more important [1].

The latter term represents the Faxen force which corrects the Stokes drag in the

conveying flow field [1]. For turbulent flows, the steady-state force is given by the

drag coefficient based on empirical relations,

𝐹𝑠𝑠,𝑖 =1

2𝜌𝑐𝐶𝐷𝐴|𝑢𝑖 − 𝑣𝑖|(𝑢𝑖 − 𝑣𝑖) 16

where 𝜌𝑐 is the carrier density and 𝐴 the projected area of a particle. The drag

coefficient must be modeled in some way and that is presented in Section 4.2.4.1.

2.5.2 Particle-fluid interaction

The interactions between particles and carrier flow field are referred to as phase

couplings. One-way coupling means that the carrier phase affects the dispersed phase,

not the opposite. Two-way coupling means that reciprocal effects exist [1]. Two-way

coupling can be interesting to model in order to get an estimate of how much the

presence of particles affect the redistribution of turbulence. Phase coupling occurs

either by transfer of mass, momentum or energy. All three quantities could be coupled

simultaneously [1][2].

The properties of the mean flow have an important impact for the particles, but it is

usually necessary to include the reverse action as well. If two-way coupled, the

particles affect the carrier phase and have a suppressing effect on the turbulence for

small particles. Correspondingly, the rate of dissipation increases. Conversely, large

particles tend to increase turbulence due to a larger wake region of the particles.

For cases considered in this work, the particles are solid at all times, therefore no

mass coupling occurs. Energy coupling can also be excluded since no heat transfer

(thermal equilibrium) between the two phases is present. The temperature of the

system is spatially and temporally uniform. Momentum coupling is significant due to

high mass concentrations, i.e. large differences in material density of each phase.

2.5.3 Particles and turbulence

The drag force of a particle is also dependent on the turbulence present in the bulk

flow. An important aspect of turbulence modeling is to correctly model the interactions

of particles with large turbulent eddies since they carry the main part of the turbulent

kinetic energy (TKE). The turbulence mixes the bulk flow over the entire domain and

can thereby affect the trajectory of a particle.

Since the particles are of the same order of magnitude as the turbulent eddies,

interactions between particles and turbulence are important. The turbulence affects

the separation of particles but the particles can also affect the turbulence since

transportation of particles can play a major role of velocity fluctuations in the

continuous phase. Usually, smaller particles suppress the turbulence and larger

particles increase the turbulence, because of a more significant wake region for the

MASTER’S THESIS


larger particles. The interaction between velocity fluctuations and varying volume

fractions can generate further turbulence augmentation or reduction [8].

2.6 Boundary layer

A typical boundary layer velocity profile is shown in Figure 8.

Figure 8: Image of a boundary layer, indicating the sublayers of interest [15].

A boundary layer is the physical description of the flow close to a solid boundary. The

boundary can be divided into three sublayers, see Figure 8. In the viscous layer,

viscous stresses dominate totally. The buffer layer is the region where both viscous

and turbulent stresses are important. Finally, the log-layer is the region where

turbulent stresses (Reynolds stresses) are predominant.

The height of the boundary layer is often measured in so called viscous units, denoted

y+ and defined as,

𝑦+ ≡𝑢∗𝑦

𝜈

17

where 𝑢∗ is the friction velocity, y distance to the nearest wall and ν is the local

kinematic viscosity of the fluid. Typical ranges for the different layers are, 1 < y+< 5

for the viscous layer, 5 < y+< 30 for the buffer layer and y+ > 30 for the log-layer. In

early years of turbulence modeling, the boundary layer was either modeled using wall

functions, where the first cell was required to be located in the log-layer, or a so-called

low-Reynolds number model, that required resolution of the whole boundary layer, i.e.

the first cell was required to have y+<1. Nowadays all-y+ wall formulation exist which

blend the high y+ wall treatment made for the log-layer and the low y+ wall treatment

made for the viscous layer [8].

MASTER’S THESIS


3 Experiments The experiments were carried out at the department of Appliances at Electrolux in

Stockholm, Sweden. The purpose of the experiments was to measure the separation

efficiency and pressure drop of an existing gas cyclone in a vacuum cleaner

manufactured by Electrolux. Two test dusts with different particle size compositions

were used during the experiments. Firstly, the Dolomite sand was used which is the

main component (ca 70 %) of the DMT sand which is the international standard dust

when it comes to investigate cyclone performances within the requirements of EU,

stated in Section 1. Other components of the DMT dust are cellulose and cotton fibers.

Secondly, the Arizona dust has been investigated. The Arizona dust is of interest since

it contains a larger amount of small particles which are harder to separate in general.

Figure 9 Names of different sections of the experimental setup

3.1 Method

The experimental set up is shown in Figure 9 and Figure 10. The inlet pipe is extended

by a feeding pipe in order to make the flow more uniform and to obtain a fully

developed flow profile before the flow reaches the cyclone inlet. A funnel, whose end is

located 4 mm from the wall surface, was used to facilitate the feeding process. The air

intake is quantified by the volumetric flow rate. A device which has the possibility of

changing the cross-sectional area, is used to keep the value of the volumetric flow to

25 L/s. Its location is shown in Figure 10. Two probes, which are connected to a

pressure gauge, have been installed to measure the pressure drop over the cyclone.

These probes are located at the inlet and the outlet, see Figure 9. They are mounted

just at the wall surface for each boundary.

Before running the experiment, all parts were weighed. After each measurement, the

cyclone, the dust bin and the filter were weighed. The dust bin was subsequently

cleaned by air in a fume hood after each measurement. Air was used instead of water

in order to avoid creation of humidity at the walls of the dust bin. Twelve

measurements for each dust type were performed.

MASTER’S THESIS


Figure 10: The end of the setup, including two filters which are absorbing non-separated test dust.

As mentioned above, two different dusts are examined, Dolomite and Arizona. Both

test dusts are polydisperse, i.e. there are different particle sizes in the same material.

For the Dolomite, 35 g during 2 minutes are used. The amount of dust for the Arizona

is 5 g during 1 minute. Mass densities of Dolomite and Arizona are 2900 kg/m3 and

2650 kg/m3 respectively. The corresponding mass concentrations are,

𝐶𝐷𝑜𝑙 =𝜌𝑑

𝜌𝑐=

2900

1.18415≈ 2449

18

𝐶𝐴𝑟𝑖 =𝜌𝑑

𝜌𝑐=

2650

1.18415≈ 2238

19

A larger mass concentration means higher solid loading and normally better particle

separation [2]. The properties of the dust are often given by particle size distribution,

where the particle size means either the diameter or the mass. Table 2 and

Table 3 show the distributions for each dust given by the manufacturer [11].

Table 2: Particle size distribution for the Dolomite dust.

Particle size range (microns) % Parts by mass

< 5 9 5 < 10 5 10 < 20 8 20 < 40 11 40 < 75 10 75 < 125 7

125 < 250 20 250 < 500 24 500 < 1000 6 1000 < 2000 0

Table 3: Particle size distribution for the Arizona dust.

Particle size range (microns) % Parts by mass

0.97 4.5 – 5.5 1.38 8.0 – 9.5 2.75 21.3 – 23.3

MASTER’S THESIS


5.50 39.5 – 42.5

11.00 57.0 – 59.5 22.00 73.5 – 76.0 44.00 89.5 – 91.5 88.00 97.9 – 98.9 124.50 99.0 – 100.0 176.00 100.0

3.2 Results

The ambient pressure and temperature of the laboratory were 99.2 kPa and 20 °C

respectively. A pressure drop of 1510 Pa was measured. The static pressure at the

inlet is fairly simple to measure since the flow field is almost uniform. The outlet is

more difficult since vortices from the vortex finder persist quite far downstream, and

this vortex is associated with a radially varying static pressure. The measured static

pressure hence depends on the exact location of the pressure probe.

3.2.1 Overall separation efficiency

To know if the measurements are close to the expected value, the law of large

numbers can be used. Let Xn be a sequence of independent random variables,

𝑋𝑛 = ∑ 𝑋𝑖

𝑛

𝑖=1

20

where the average is,

𝑋𝑛 =1

𝑛∑ 𝑋𝑖

𝑛

𝑖=1

21

For any ε > 0, 𝑃(|𝑋𝑛 − 𝜇| > 𝜀) → 0 as 𝑛 → ∞ where µ is the expected value. By a large

number of measurements, 𝑋𝑛 will be close to the expected value but how close

remains unknown. The variance of the measurement error is therefore introduced as

Var(𝑋) = 𝜎2. It is desirable to find 𝑃(|𝑋𝑛 − 𝜇| < 𝑐) for a constant c. By assuming that the

central limit theorem is valid, saying that the arithmetic mean for a sufficient number

of independent random variables gives a normal distribution regardless of the

distribution properties of each random variable [3], it is equal to 𝑃(|𝑋𝑛 − 𝜇| < 𝑐) =

𝑃(−𝑐 < 𝑋𝑛 − 𝜇 < 𝑐) = 𝑃 (−𝑐

𝜎√𝑛⁄

<𝑋−𝜇𝜎

√𝑛⁄<

𝑐𝜎

√𝑛⁄) ≈ ∅ (

𝑐𝜎

√𝑛⁄) − ∅ (−

𝑐𝜎

√𝑛⁄), where σ is the standard

deviation and n the sample size.

By assuming Gaussian distribution, the confidence coefficient is 1.96 for 95 %

confidence level. The first six measurements of the Arizona dust are excluded due to

saturation at the walls. Since the Arizona dust mainly consists of particles less than 5

microns, the probability of saturation increases. It means that the particles stick to the

wall surface and remain there. By use of the central limit theorem stated above it is

also motivated statistically. The expression to the right of the plus-minus sign

represents the margin of error,

𝜇 ≈ 𝑋 ± 1,96𝜎

√𝑛

22 Results are shown in Table 4.

MASTER’S THESIS


Table 4: Results for each dust.

Dust name Separation efficiency by mass (g)

Separation efficiency by percentage (%)

Injected mass in total (g)

Dolomite 33.48 ±0.14 96±0.4 35 Arizona 4.2±0.30 84.0±6 5

The results follow the expected results stated in Section 3.1, i.e. the dust with higher

mass concentration obtains higher separation efficiency. The Arizona dust has

apparently a greater margin of error than the Dolomite dust which can partially be

explained by the lower amount of measurements. Other error sources could be that

the injected mass was not injected continuously and that sometimes incomplete

cleaning occurred. Observing important saturation effects, maybe additional

measurements for the Arizona would have been desirable.

3.2.2 Cut size

A simple approximation to calculate the cut size from the overall separation efficiency

is seen in Figure 11. It is here assumed that the cut size is sharp meaning that,

particles smaller than the cut size is not separated at all and all particles above the cut

size are separated completely [2].

Figure 11: Determination of the cut size by means of overall separation efficiency η [2].

Here 𝐹𝑓(𝑥) is the particle size distribution by parts of mass, a cumulative undersize

distribution of the feed. By using the experimental values computed in Section 3.2.1,

the cut size for each dust is seen in Table 5.

Table 5: Results showing degree of separation.

Dust Overall separation efficiency (%)

Cut size (µm)

Dolomite 96 ± 0.4 1.93 - 2.33 Arizona 84 ± 6 1.5 - 2.7

MASTER’S THESIS


4 Method As mentioned in Section 1, the focus of this thesis is to investigate different models

when it comes to predicting the performance of the cyclone. To do this the pressure

drop across the cyclone is a suitable parameter to use. The aim is also to run

simulations with as simple models as possible without losing too much physics that

could possibly affect the properties of the flow. The first step before running the

simulation is to import the geometry and to do smaller simplifications of the geometry.

Then the physics is defined and a mesh is generated.

In order to represent the physics pointed out in Section 2.4 and 2.5, different

modeling approaches are run and compared to experiments to evaluate the suitability

of these models.

4.1 Geometry

The used CAD-model is of identical dimensions as an existing gas cyclone in

Electrolux’s product range, see Figure 13. All dimensions are identical with the cyclone

used in the experiments. The inner diameter of the cyclone body is 9 cm, the height of

the cyclone is approximately 19 cm, and the inlet diameter is 3.8 cm.

One thing to investigate is if the dust bin should be included in further computations at

Electrolux or not. To examine the difference, simulations are done by use of both

geometries. Initially the cyclone also contained a vortex finder but this part of the

cyclone is removed since the perforation surface of the vortex finder is too complex to

model. The location of the removed vortex finder is shown in Figure 12.

Figure 12: Black contours indicating the shape of the vortex finder.

The geometry is saved as a step file in order to be able to import it to any commercial

CFD software on the market. Some geometrical smoothing operations are used before

the surface meshing is executed in Star-CCM+. The ‘repair surface’ command is

executed to reconstruct crucial regions of the surface.

MASTER’S THESIS


Figure 13: Complete geometry, cyclone and dust bin.

Figure 14: The geometry of the cyclone only.

4.2 Models

To meet the requirements stated in Section 1, some different turbulence models are

used and compared. In industrial applications of today, the standard method is the use

of two-equation turbulence models but more complex models are present as well

[6][8]. The two-equation models are referred to complete models as they do not need

prior knowledge about the turbulent nature of the flow [10].

The two-equation model relies on the Boussinesq eddy viscosity assumption which

determines that the Reynolds stress tensor is proportional to the mean strain rate

tensor. The constant of proportionality is called turbulent viscosity. It is based on the

principle that turbulent eddies could be modelled by eddy (turbulent) viscosity in the

MASTER’S THESIS


same way as molecular motion could be modelled by molecular viscosity. The two-

equation model is based on the Reynolds-Averaged Navier-Stokes equations, and

describes the flow field through two transport equations. Normally these models are

robust and easy to converge. However, some concerns exist when it comes to strong

rotation and sudden change of strain rate [10].

The Reynolds Stress Models (RSM) belong to a branch of more complex models, where

each unique individual stress component of the Reynolds stress tensor is resolved. This

results in a seven-equation model, one equation for each unique Reynolds stress

component and one for the dissipation rate (the conversion of turbulent kinetic energy

into thermal internal energy). The motivation of also investigating the RSM is the

better representation of rotational effects. Other advantages of the RSM are the

modeling of flow history and the increased sensitivity for streamline curvature. The

drawback of the RSM is the numerical instability and that it often requires a very fine

mesh.

One goal is to investigate whether the RSM is reasonable or even possible to use,

compared to the two-equation model, for predicting the cyclone performance in terms

of computational cost and physical accuracy. An alternative modeling approach in-

between these two models is to start the simulations with a two-equation model and

then after while change it to a RSM model to improve the possibility of obtaining a

converged solution. By starting the RSM simulations with a two-equation model, the k-

ε is selected since both models compute the dissipation rate by use of ε. From the

reasoning mentioned above three different modeling approaches are selected:

1. SST k-ω

2. RSM

3. k-ε RSM

The selected two-equation model is the SST k-ω, which is hybrid model consisting of

k-ε in the free-stream and k-ω in the boundary layer. These modeling approaches are

relevant to achieve the purpose of this thesis. For SST k-ω, an ad-hoc solution such as

curvature correction, which takes local rotation and vorticity rates into account [8], is

also investigated.

4.2.1 Boundaries

Depending on whether the dust bin should be included or not, one or two outlets exist.

When excluding the dust bin, three different boundary conditions for the dust outlet

are examined:

1. Wall with slip condition

2. Wall with no-slip condition

3. Pressure outlet

Wall means obviously a closed boundary but the effect of a slip condition is

investigated as well. Slip condition means that the tangential velocity at the wall is

allowed to be non-zero. Pressure outlet is an open boundary condition where the net

mass flow over the boundary is set to zero by a static pressure that must be

computed. When the dust bin is included, the walls are set with a no-slip condition

meaning that the velocity attains zero at the wall boundary.

Settings of remaining boundaries are detailed in Table 6. At the inlet, a mass-flow inlet

is set, and at the air outlet, the average pressure option is set in order to allow a

pressure profile with a radial dependence, see Figure 15.

MASTER’S THESIS


Figure 15: Location of each boundary and their corresponding names.

No-slip condition is selected at the walls of the cyclone. The turbulence intensity is set

(default) to 1 % and the turbulent viscosity ratio is set to 10 for non-wall boundaries.

These values are used as back-flow conditions on non-inlets.

Table 6: Settings for each boundary.

Boundary Selected b.c Selected option Physical values

Inlet Mass flow Mass flow rate 0.0296kg/s Air outlet Pressure Average pressure 0 Pa

Cyclone Wall No-slip -

4.2.2 Pressure drop evaluation

As mentioned in Section 3.2, the experimental value of the pressure drop was

obtained by probes located in close proximity to the wall. However, there is a radial

pressure gradient present in the air outlet due to the high tangential velocity field in

the separation space [2]. The radial dependence of the pressure means that the static

pressure may vary across the cross section of the air outlet. The radial dependence is

hence important to evaluate to see if it is significant or not. To handle this numerically,

the position of the outlet probe is marked in the CFD model. At this position a plane

section is created so the radial dependence of the static pressure can be plotted, see

Figure 26. The mean value of the two extreme points at the wall is selected as the

numerical static pressure of the outlet probe.

Since this radial dependence is negligible at the inlet, assuming fully developed flow,

the averaged static pressure of the inlet boundary cross-sectional surface is the same

as the static pressure measured at the wall by the inlet probe.

4.2.3 Wall treatments

The boundary layer of the wall region should be modelled with sufficient discretization

in order to avoid unphysical results. The all y+ wall treatment is enabled for the SST k-

ω model, i.e. the first cell height in terms of viscous units is assumed to be unknown.

This approach uses a blended wall law to predict the shear stress, and is more

independent of the mesh resolution than other available wall treatments within this

MASTER’S THESIS


category of models. The all y+ wall law formulation is enabled automatically when

selecting the SST k-ω model.

In order to get a good mesh quality of the wall region for the RSM, the elliptic blending

model is used since it consists of an all y+ formulation that is preferred for coarse

meshes and for meshes of intermediate/fine quality. Other possible wall treatments

that are developed for very fine meshes is the two-layer all y+ formulation, which is a

hybrid model of a low y+ formulation and high y+ formulation.

4.2.4 Dispersed phase

As mentioned in Section 3, the mass of Dolomite particles added during the

experiments was 35 g during 2 minutes. The volumetric flow rate of air is constant and

is set to 25 liters/s during the experiments. By inserting known values in Equation 1,

the particle volume fraction is determined to 4 ∙10-6. Since the particle volume fraction

is below 0.001, the flow is considered to be dilute and can be treated as a Lagrangian

phase, see Section 2.3.2. Low volume fraction means that particle-particle interactions

probably can be excluded.

To make the computations regarding the particles feasible, particles are modelled by

parcels. Each parcel represents a localized group (cluster) of dispersed particles or

droplets possessing the same properties (diameter, mass, temperature). Parcels are a

discretization of the population of dispersed phases in the same way that cells are a

discretization of a continuous volume. Since the dispersed phase is considered to be

Lagrangian, the Lagrangian multiphase model is enabled. Detailed information about

each parcel is available, such as position, velocity, composition and temperature [8].

The particles are modelled with a spherical shape. One-way coupling is initially enabled

to get a faster predication of the cyclone performance. However, an analysis including

two-way coupling is also performed to investigate how much the particles actually

affect the airflow even if the particle mass fraction is considered to be low.

Mathematically, Lagrangian source terms are added in the continuous phase equations

when two-way coupling is activated [8].

As mentioned in Section 2.5.3, the need of modeling the interaction between

turbulence and particles is also investigated. The so-called turbulent dispersion model

accounts for the interactions from turbulent eddies to particles, but not the reverse

effect, by adding an extra random velocity component to the particles [1][8]. This

option can be necessary since the dispersion of particles in a turbulent flow state is

higher than for a laminar one [8]. In order to obtain reliable statistics, additional

parcels must be injected. In Star-CCM+ this can be done by increasing the parcel

streams. This option sets the number of parcels which each injection point can inject.

By default it is set to 1, i.e. one parcel per injection point, see Figure 16.

4.2.4.1 Particle surface forces

The drag force occurs due to the relative motion between the continuous phase and

the dispersed phase as stated in Section 2.5. The default Schiller-Naumann correlation

is recommended for spherical particles if the carrier phase is viscous [8]. The

correlation is given by,

𝐶𝑑 = {

24

𝑅𝑒𝑝(1 + 0.15𝑅𝑒𝑝

0.687) 𝑅𝑒𝑝 ≤ 103

0.44 𝑅𝑒𝑝 > 103

MASTER’S THESIS


The presence of particle rotation in the flow field contributes to lift forces acting on the

particles. The rotation is mainly created by particle interactions, velocity gradients and

rebounds at wall surfaces [1]. The modeling of particle rotation is not available within

the Lagrangian phase model in Star-CCM+, so consequently this potential effect is not

included. However since the particle-particle interactions are concluded to be

negligible, the impact of particle rotation is considered the same.

The virtual mass force and pressure gradient force are disabled in the particle

simulations since the impact of the virtual mass to the bulk flow is considered to be

insignificant for steady flows [1].

4.2.4.2 Particle body forces

Gravity plays a role when it comes to the collection of particles in the dust bin and is

hence included. The Coulomb forces between particles are not considered here

because there are other parameters that are more important to evaluate.

Thermophoretic forces are not necessary to include since it is assumed that the

temperature is constant throughout the computational domain, i.e. no temperature

gradients are present [1].

4.2.4.3 Injectors

To inject the particles into the domain, injectors are created and defined. In order to

be able to inject all particles from the same plane independent of the mesh structure,

so-called part injectors are preferable. The particles are initiated by grid points defined

equidistantly close to the inlet boundary as shown in Figure 16. The two methods

below are evaluated:

1. One single injector by use of particle size distribution

2. Several injectors where each injector contains one discrete particle size

For the first approach, a cumulative distribution function is set in Star-CCM+ by

importing a user-defined table with a particle diameter column and a CDF column. A

drawback with the first approach is that the injector inject particles of different sizes

randomly, hence it is hard to know how many parcels per particle size range that are

injected. As a result the first approach made it difficult to post-process the particle

data and was therefore finally regarded as an unusable method for this case. The flow

rate specification, particle rate or mass flow rate, is set to mass flow rate since it is

known from the experiments.

Table 7: Settings for injectors.

Dust Injection points Mass flow rate in (kg/s)

Dolomite 329 2.92∙10-4 Arizona 329 8.33∙10-5

All one-way coupled multiphase simulations are run transiently by letting parcels pass

through once in the computational domain. That is sufficient since the multiphase

solver starts from converged single-phase simulations. Particle size (diameter)

distributions for each dust are given in Table 2 and

Table 3. Particle velocity is set to the same value as the bulk velocity, see Section

2.3.3.

MASTER’S THESIS


Figure 16: A presentation grid indicating the injection points of particles.

Particles larger than 5 microns are assumed to be completely separated, hence they

are not included in the one-way coupled simulations but included when the separation

efficiency is computed. However, for the two-way coupling the larger particles are

included as well since their presence alters the flow field and thereby affects the

results.

It is recommended to introduce more parcels when enabling the turbulent dispersion

model and two-way coupling [8]. The two-way coupling is used to question the

assumption of negligible reverse effect, i.e. particles to bulk flow.

Table 8: Number of parcels per particle size.

Case Number of parcels per particle size

Parcels per injection point

Non-dispersion 329 1 Turbulent dispersion 1645 5

Two-way coupled + Turbulent dispersion

3290 10

As seen in Table 8, ten parcels per injection point are used for the two-way coupling to

avoid too large parcels, which results in 3290 parcels per each discrete particle

diameter.

4.2.5 Particle-boundary interactions

As stated in Section 2.4, it is important to include the interactions between particles

and boundaries in order to get accurate information of the cyclone performance. The

specification for the boundary interaction mode at the wall is defined as default

‘rebound’, i.e. the particles bounce back at a finite velocity. Restitution coefficients are

set to default for both the wall-normal and tangential directions, i.e. ideal (elastic)

bounce is assumed. The mathematical concept is based on the difference in relative

velocity before and after the wall collision, where the selected value is between 0 and

1. Elastic rebounds correspond to 1 and sticking conditions correspond to 0.

Mathematically, the relationship is given by,

(𝒗𝑝 − 𝒗𝑤)𝑡𝑅 = 𝑒𝑡(𝒗𝑝 − 𝒗𝑤)𝑡

𝐼

23 (𝒗𝑝 − 𝒗𝑤)𝑛

𝑅 = 𝑒𝑛(𝒗𝑝 − 𝒗𝑤)𝑛𝐼

24 The particle-particle interactions are not modelled because it was concluded that these

interactions can be ignored since the dispersed phase is dilute, see Section 4.2.4.

MASTER’S THESIS


A function called ‘boundary sampling’ model is used to store data about particles

hitting boundaries, see Section 4.4.1. The boundary sampling can only be activated for

real boundaries and therefore activated for the air outlet and the dust bin. Additional

data is however also available for removed parcels. For all calculations involving

separation efficiency, the particles are classified as ‘separated’ as soon as they touch

the walls of the dust bin. In Star-CCM+ this setting is called ‘escape mode’. Here other

approaches are obviously possible and maybe equally trustful. For instance, the upper

surface of the dust bin can have rebound properties which can be more realistic.

4.3 Meshing

The mesh is the discretization of a volume into a finite number of cells. This is a

conventional method in order to resolve the flow field numerically. One of the main

goals in this section is to achieve an economical meshing. Depending on field of

application, the mesh cell size varies. Parameters as mesh resolution and mesh quality

give a picture of how well the meshing is performed, for instance by checking the

skewness of cells. Due to areas of complex geometry it can be necessary to repair the

surfaces in order to minimize problems of convergence for instance.

The cyclone is meshed by using tetrahedral cells where the surface remesher is

activated to remove bad cells at walls and boundaries. A cylinder (purple-colored), see

Figure 17, is added to refine the mesh along the horizontal axis (z-axis) of the cyclone.

The use of volumetric control makes it possible to capture more exactly the flow

behavior in this region of the geometry.

Figure 17: The volumetric control is highlighted in purple.

Two meshes are generated, a finer one and a coarser one. The fine mesh is generated

by decreasing the base cell size from 5 mm to 3 mm, see Table 9.

Table 9: Number of cells for each mesh.

Mesh type Base cell size (mm) # Cells without dust bin # Cells with dust bin

Coarse 5 ~ 1.6 million ~ 6.3 million

Fine 3 ~ 2.2 million ~ 7.9 million

Additional prism layers are generated at the walls to represent the boundary layer and

to get a smoother cell transition within it, see Section 2.6. The y+ value shows how

well the height of the first cell is chosen [8]. Possible variables to modify within the

prism layer mesher are thickness, stretching (growth rate), and number of prisms.

MASTER’S THESIS


Table 10: Values of parameters within the prism layer mesher.

Mesh type Thickness (mm)

Stretching Number of prisms

Coarse 1 1.2 3 Fine 0.36 1.2 5

Figure 18 and Figure 19 show the generated mesh when using a base cell size of 5

mm.

Figure 18: Coarse mesh of the cyclone.

Figure 19: Coarse mesh of cyclone and dust bin.

Interior mesh structures are seen in Figure 20 and Figure 21.

Figure 20: A plane section of the mesh refinement at the vortex finder by use of volumetric control.

MASTER’S THESIS


Figure 21: Plane section of the grid in the dust bin.

4.3.1 Mesh quality

Mesh quality indicates of how good the discretization is. There are five measures to

validate the mesh quality in Star-CCM+, namely cell skewness angle, boundary

skewness angle, face validity metric, cell quality metric and volume change metric [8].

Some mesh quality measures are not universal and can therefore only be applied to

specific cell shapes. Since tetrahedral cells are selected, the skewness angle is

descriptive. The cell quality measure is also selected. The cell quality tells about the

cell orthogonality, where a cubic cell attains a value of 1. The cell quality is given

between 0 and 1, where 1 represents perfect cells. Cells less than 10-5 indicate bad

cells [8].

The skewness angle measures the interface angle of two cells compared to their

centroid. It simply shows the inclination of one cell to another. The skewness angle is

given between 0 and 90 degrees, where 0 degrees mean complete orthogonal and

perfect cells. A skewness angle of more than 85 degrees is considered bad [8]. Cells

exceeding 85 degrees give a non-desirable unboundedness when it comes to calculate

the diffusion between neighboring cells [8].

In Figure 22 and Figure 23, these mesh quality measures for the coarse mesh are

presented. Almost identical results are obtained for the fine mesh and are therefore

not shown here.

MASTER’S THESIS


Figure 22: Histogram of cell quality.

Figure 23: Histogram of skewness angle of neighbouring cells.

MASTER’S THESIS


Figure 24: Parameters for mesh quality.

By the option called ‘Remove invalid cells’, the quality of the cells are checked, see

Figure 24. It displays if some cells of the mesh need refinement. A few cells were

improved. This option is good to use in order to decrease discretization errors and

thereby help the solver to better resolve the flow field.

As seen in Figure 25, the non-dimensional wall distance y+ is within the buffer layer (5

< y+ < 30) which is satisfactorily since the boundary layer is modelled with the all y+

wall formulation [8]. Note that the red area of the first mesh has actually even higher

y+ than 15 at some regions. The wall y+ value is also lower for the fine mesh which is

consistent with the definition of y+.

MASTER’S THESIS


Figure 25: Wall y+ for the computational domain, coarse mesh (first) and fine mesh (second).

4.4 Solver settings and convergence

The numerical solver for the single-phase is a so called segregated flow solver. A

steady, three-dimensional flow field is initiated, including a constant gas density. The

governing equations of the flow are resolved sequentially. This solver is preferred since

the fluid is assumed to be incompressible. Moreover, it is more easily to obtain a

converged solution [8]. The relaxation factor is changed by enabling a linear ramp

function, which aids the first part of the computation. The linear ramp function is

enabled for the first 100 iterations to stabilize the solution to some extent initially.

Additional plots are created to assure a fully converged solution when running the

single-phase simulations. Besides the residuals, which are default, pressure drop,

average tangential velocity at the outlet surface, and axial velocity at a point along the

center line of the cyclone body are monitored to study the level of convergence, see

Figure 26.

MASTER’S THESIS


Figure 26: Position of plane section, point probe and outlet probe, marked in purple.

Regarding the residuals, they are considered to be converged as soon as they are

some magnitudes smaller than the initial ones. Besides, when the other parameters

show no long-term changing after a significant number of iterations, the simulations

are considered to be converged.

4.4.1 Lagrangian multiphase solver

The steady Lagrangian multiphase solver is used for the particle simulations. Before

initiating the simulation, a set of functions in the solver node are modified. Maximum

residence time is the maximal predefined time period that the particles have to be

separated. Particles that exceed this value are deleted from the simulations. However

the number of removed parcels is known during the simulations, to verify that this

number is fairly low. The number of substeps depends on what models that are

enabled. Used values are shown in Table 11.

Table 11: Number of substeps and maximum residence time.

Case Maximum number of substeps

Maximum residence time (s)

Non-dispersion 500 000 15 Turbulent dispersion 100 000 10 Two-way coupled + Turbulent dispersion

100 000 10

In order to get a complete tracking data of the trajectories of the particles, a track file

is stored as a separate file besides the main simulation. This file can later be utilized to

calculate path lines or to obtain the particle residence time. The boundary sampling is

enabled to be able to store data of the flow properties when particles collide with

boundaries. However, these boundaries have to be ‘real’ boundaries. Artificial plane

sections, a sub-category for so called derived parts in Star-CCM+, cannot be used for

boundary sampling.

MASTER’S THESIS


5 Results and discussion The results consist of the analysis of the dust bin boundary condition, the experimental

and numerical comparison of the pressure drop, and finally the results of the

multiphase simulations. The three modeling approaches, stated in Section 4.2, are

used for some of the analysis. The results also clarify the total elapsed time of a

simulation to make it comparable to other simulations of vacuum cleaner cyclones. The

relation between good prediction and needed computational time is a key feature.

5.1 Flow visualization

In Figure 27, the airflow is displayed in order to visualize the theoretic description

given in Section 2.2. The flow starts to rotate almost immediately when entering the

cyclone and continues downwards. A part of the flow is still present at the upper

volume of the dust bin. In Figure 29, it can also be seen that the flow then starts to

reverse along the central axis. Cross-sectional plots of tangential and axial velocity

normalized with inlet velocity are shown in Figure 28 and Figure 29. It is also possible

to observe the strong rotation in the vortex finder which remains at the air outlet.

Figure 27: Streamlines of air in the computational domain.

MASTER’S THESIS


Figure 28: Tangential velocity scaled by inlet velocity for a cross-section in the middle of the

cyclone body for coarse mesh (left) and fine mesh (right). Positive means anti-clockwise and negative means clockwise flow.

Figure 29: Axial velocity scaled by inlet velocity for a cross-section in the middle of the cyclone body for coarse mesh (left) and fine mesh (right). Positive means directed upwards and negative means directed downwards.

5.2 Analysis of dust bin boundary condition

An analysis of appropriate boundary conditions for the dust bin is made. The geometry

that does not include the entire dust bin, has to be supplemented with an adequate

boundary condition replacing the physics of this part of the geometry, see Section

MASTER’S THESIS


4.2.1. A comparative study between three different boundary conditions along with the

complete dust bin is presented here. In order to save computational time and number

of simulations, the k-ω model with coarse mesh settings is used to discover important

differences. The average tangential velocity is measured at the air outlet and the axial

velocity is measured by a probe located at the center line of the outlet pipe, for exact

position see Figure 26.

Table 12: Values of some physical parameters for each boundary condition.

Boundary condition

Pressure drop (Pa)

Average tangential velocity (m/s)

Axial velocity (m/s)

Elapsed time (h)

Pressure outlet 1420 10.6 20.8 ~ 18

Wall (slip) 1419 10.8 21.5 ~ 18

Wall (no-slip) 1422 10.8 21.4 ~ 4

None (dust bin) 1430 10.9 21.8 ~ 8

All boundary conditions predict very similar values of pressure drop and average

tangential velocity at the air outlet. Small differences are observed for the axial

velocity.

Artificial planes at different heights are created to evaluate significant velocity

differences between the boundary conditions. As mentioned in Section 0, for the

‘simplified’ dust bin almost the entire bin is removed. A smaller extruded volume with

a rectangular cross-section replaces the bin, see Figure 30.

Figure 30: Location of plane sections at different heights.

Figure 31 and Figure 32 show the velocity magnitude at the implicit plane sections 1

and 2 previously seen in Figure 30. A qualitative comparison of the different boundary

conditions is presented.

1

2

MASTER’S THESIS


Figure 31: Flow patterns, at plane section 1, depending on defined boundary condition, from left to right; complete dust bin, pressure outlet, wall slip and wall no-slip.

Figure 32: Flow patterns, at plane section 2, depending on defined boundary condition, from left to right; complete dust bin, pressure outlet, wall slip and wall no-slip.

As seen Figure 31 and Figure 32, there is a difference regarding the velocity

distribution. In Figure 27, it is also shown that a part of the flow is still present in the

dust bin. The conclusion is that the entire dust bin should be imported into the

computational domain since the elapsed solution time is also reduced by more than 50

% according to Table 12. Boundary conditions of wall type are not an alternative based

on the fact that the velocity pattern is totally different from when the entire dust bin is

included. Even though additional cells are generated to be able to include the dust bin

into the computational domain, the elapsed solution time is reduced. The cause of that

is probably that a lot of reverse flow is present for the pressure outlet boundary

condition that is numerically heavy to handle. Maybe a better initial guess of the static

pressure, that is needed to obtain a net mass flow rate of zero at the boundary, can

decrease the computational time somewhat. Based on the reasoning above, the dust

bin is included for all further simulations.

5.3 Single-phase with dust bin

In Section 5.2, it was concluded that further simulations are done by including the dust

bin into the geometry. The additional number of cells is in this case are preferred over

defining a boundary condition.

In Figure 33, the numerical pressure drop is presented for different models and mesh

resolution. As seen the k-ε RSM clearly shows a transient behavior as could be

expected but stills at least oscillate around a steady state. By use of RSM all the way in

MASTER’S THESIS


the simulations, the solution diverges almost immediately. A transient behavior also

appears when enabling the curvature correction for the SST k-ω model which indicates

that the steady state solution of the SST k-ω model is probably due to high diffusivity

independent of mesh resolution.

Figure 33: Comparison of pressure drop between different models and mesh setups. Observe the broken y-axis scale and that the pressure drop is here predicted by the average pressure at the air outlet.

It is here difficult to determine which mesh used for the SST k-ω that is physically

most correct. The margin to the experimental value is almost the same. Consequently,

the coarse mesh is considered sufficient for further studies regarding multiphase

simulations. From Figure 28 and Figure 29, it is easy to conclude that the velocity

distribution is similar which motivates the use of the coarse mesh for multiphase

simulations.

As mentioned in Section 4.2.2, the significance of the radial pressure dependency at

the outlet probe is considered to be important to evaluate. Since rotation is present in

the flow field in the cyclone body, the tangential velocity component will probably be

large enough to affect the local static pressure across a surface.

MASTER’S THESIS


Figure 34: Comparison in prediction of the static pressure at the location of the outlet probe between the two meshes for k-ω.

As seen in Figure 34, the static pressure varies a lot across the surface where the

outlet probe is located. The static pressure at the wall is slightly higher for the fine

mesh, about 50 Pa. It can be concluded that the mesh refinement does not give a

significant difference, meaning that the coarse mesh is sufficient for predicting the

pressure drop.

Figure 35: Cross-sectional variation of static pressure where the outlet probe was located for coarse mesh (left) and fine mesh (right).

In Figure 35, the importance of the variation of static pressure is evident. As stated in

Section 4.2.2, due to large rotational motion in the cyclone, it will still have an impact

on the static pressure. By using the static pressure at the wall instead of the average

pressure over the cross-section, the estimate of the numerical pressure drop will differ

17 %. This number is almost the same for both meshes. From Figure 34 and Figure

35, it can be concluded that the use of the static pressure at the wall is more correct

when comparing to the experimental value of the pressure drop. Table 13 shows the

pressure drop based on the static pressure at the wall.

MASTER’S THESIS


Table 13: Pressure drops and elapsed times.

Model Pressure drop (coarse mesh)

Elapsed time (h)

Pressure drop (fine mesh)

Elapsed time (h)

Experimental pressure drop

SST k-ω 1430 ~ 8 1620 Pa ~ 45 1520 Pa RSM N/A N/A N/A N/A N/A k-ε RSM N/A N/A N/A N/A N/A

A general conclusion is that the pressure drop is fairly well predicted by the SST k-ω

model where the coarse mesh tends to be sufficient. The confirmed instability of the

RSM is also a conclusion worth to mention.

5.4 Multiphase

All multiphase simulations are done by including the dust bin. All one-way coupled

simulations use flow field from the converged SST k-ω single-phase simulations on the

coarse mesh. That means that the solvers for wall distance, segregated flow and k-ω

are frozen.

The main goal of this section is to investigate how well different modeling approaches

predict the overall separation efficiency and how much these models actually affect the

grade efficiency curves. The prediction is made by injecting particles according to the

method described in Section 4.2.4.3. Moreover some aspects are investigated, namely

the need of turbulent dispersion model and two-way coupling.

Figure 36: Tracks showing the motion of parcel streams.

In Figure 36 the typical motion of parcels is shown, where the lower image shows

parcel streams exiting through the air outlet. It is here apparent that only smaller

particles exit via the air outlet as previously stated in Section 2.4.

Table 14: Separation efficiency and elapsed times for both dusts.

Dust Case Separation efficiency (%)

Cut size (µm)

Removed parcels (%)

Elapsed time (h)

Dolomite Turbulent dispersion

96.4 1.27 0.8 ~ 1.5

No turbulent dispersion

93.6 2.13 14.3 ~ 3.5

2-way coupled 97.2 1.28 2.8 ~ 20

MASTER’S THESIS


+ turbulent

dispersion Experiment 96 ± 0.4 1.93 - 2.33 -----

-----

Arizona Turbulent dispersion

89.7 1.33 1.2 ~ 1.1

No turbulent dispersion

82.0 1.82 5.8 ~ 3.3

2-way coupled + turbulent dispersion

90.3 1.35 1.1 ~ 31.5

Experiment 84 ± 6

1.5 - 2.7

-----

-----

As seen in Table 14, with the exclusion of the turbulent dispersion model, the solver

seems to underestimate the degree of separation compared to experimental data.

Clearly, the interaction of turbulent eddies and particles have an impact on the

separation process. A qualitative conclusion is that by disabling the turbulent

dispersion model, the prediction seems to be too far from the experimental value.

Grade efficiency curves for both dusts are given below. The separation efficiency,

predicted by the numerical simulations, is calculated by means of the mass fraction of

a discrete particle diameter according to the distribution functions given in Section 3.1,

and then summed over all particle sizes.

𝜂(𝑥) =𝑚 𝑥𝜂𝑥

𝑚𝑖𝑛

25 where x represents a particle diameter.

However the actual mass fraction injected does not need to be included when

computing the overall separation efficiency for one-way coupled simulations. In that

case, it is sufficient to compute how many parcels that are separated for particular

particle size and then multiply with the mass fraction given by the CDF for a discrete

particle size divided by number of parcels injected.

Figure 37: Grade efficiency curve for both bust, dispersion and one-way coupled.

As seen Figure 37, the Dolomite has a slightly better separation due to higher particle

density as stated in Section 3 [2]. As seen in Figure 38 and Figure 39, it can be

concluded that the need of running a two-way coupled flow is unnecessary for both the

overall separation efficiency and the cut size independent of examined dust.

Additionally, the computational time is more than doubled, see Table 14, since the

solver for the bulk flow must be activated in order to be able to proceed the

00.10.20.30.40.50.60.70.80.9

1

0.00E+00 2.00E-06 4.00E-06

Sep %

Particle size (microns)

Arizona

Dolomite

MASTER’S THESIS


simulations. Depending on how the iteration frequency between the bulk flow and

particle flow is set, the accuracy can be increased however the elapsed solver time

increases at the same time. For these simulations, the iteration frequency is set to ten,

meaning after ten iterations for the bulk flow, the Lagrangian solver takes over and

iterates according to the number of substeps specified. Decreasing the iteration

frequency means better results but to a higher degree of computational cost.

Figure 38: Grade efficiency curve for Dolomite.

Figure 39: Grade efficiency curve for Arizona.

Figure 40: Comparison of each dust with and without dispersion model activated (one-way coupled).

00.10.20.30.40.50.60.70.80.9

1

0.00E+00 2.00E-06 4.00E-06

Sep %


Dispersion 1-way

Dispersion 2-way

00.10.20.30.40.50.60.70.80.9

1

0.00E+00 2.00E-06 4.00E-06

Sep %


Dispersion 1-way

Dispersion 2-way

00.10.20.30.40.50.60.70.80.9

1

0.00E+00 2.00E-06 4.00E-06

Sep %


Dolomite Non-disp

Arizona Non-disp

Arizona

Dolomite

MASTER’S THESIS


As seen in Figure 40, the turbulent dispersion model clearly affects the trajectories of

the particles and hence both the overall separation efficiency and the grade efficiency

curve. The interaction, between the turbulent eddies and the particles, seems to be

significant. By enabling the turbulent dispersion model, the numerical value comes

closer to the experimental value and the graph looks more like the classical s-shaped

grade efficiency curve as stated in Section 2.4.3. Besides the simulation converges

faster by use of this model, i.e. all facts confirm that the turbulent dispersion should

be enabled.

Another important conclusion is that the number of removed parcels is relatively high

for both dusts when the turbulent dispersion model is off, which results in a larger

uncertainty when calculating the separation efficiency since it is unclear how to treat

these particles as separated or not. As seen in Figure 41, the cut size is sharper when

considering removed parcels as separated which could be explained by the fact that

the majority of removed parcels are close to the cut size.

Figure 41: Graph showing the difference when removed parcels are included in the calculation of separation efficiency or not.

5.4.1 Calculation of Euler number and Stokes number

As mentioned in Section 2.4.4, cyclones can be characterized by non-dimensional

numbers. By using Equation 4 and inserting the pressure drop given in Table 13, the

mean diameter of the separation space, density of air, and the volumetric flow rate,

the experimental and numerical Euler numbers are computed to,

𝐸𝑢𝑒𝑥𝑝 ~ 174

𝐸𝑢𝑛𝑢𝑚 ~ 164

Stokes number is calculated by use of Equation 11.

𝑆𝑡𝑘50,𝑒𝑥𝑝 ~2 ∗ 10−3

𝑆𝑡𝑘50,𝑛𝑢𝑚 ~ 5.9 ∗ 10−4

Intended for guidance only, most well designed cyclones are located along the

correlation line given in Figure 42. The line in Figure 42 represents Svarovsky’s

empirical relationship for cyclones of conventional design and low solid loading, see

Equation 12.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00E+00 2.00E-06 4.00E-06

Sep %


Dolomite non-

disp+removed

parcels

Arizona non-disp +

removed parcels

Dolomite non-disp

Arizona non-disp

MASTER’S THESIS


Figure 42: Svarosky’s correlation line with experimental and numerical points. Note the logarithmic scale.

The numerical point is located above the Svarosky’s line which is understandable since

the vortex finder is not modeled. By importing the vortex finder in the model, the

pressure drop will increase, as stated in Section 2.4.1, since major losses occur in the

vortex finder. Additionally, it is consistent that the experimental point is located more

to the right since the experimental cut size is higher than the numerical one.

1.00E+01

1.00E+02

1.00E+03

1.00E+04

1.00E-05 1.00E-04 1.00E-03 1.00E-02

Eub

Stkb,50

Svaroksky's

correlation line

Experimental point

Numerical point

MASTER’S THESIS


6 Conclusions - Dust bin boundary condition

Selecting an appropriate boundary condition seems to be less cost-effective than just

importing the entire dust bin into the computational domain. As concluded the flow

properties differ significantly depending on which boundary condition used.

Additionally, by use of pressure outlet, the elapsed time to reach convergence is

drastically increased. That can partially be due to a high degree of reversed flow at the

boundary and a bad initial guess of the static pressure of the dust outlet. Even though

an additional amount of cells must be generated when including the dust bin, it is

preferable since the computational time is reduced.

- Average pressure versus wall pressure at outlet probe

It is confirmed that if using the average pressure instead of the static pressure at the

wall, the difference is determined to roughly 17 %. To obtain a pressure drop closer to

what is measured in the experiments, the static pressure at the wall, where the outlet

probe is located, should be used instead.

- Comparison of pressure drop

The conclusion is that the pressure drop seems to be relatively well predicted

independent of turbulence model and mesh resolution. The difference of predicted

pressure drops between the coarse and the fine mesh for SST k-ω model is about 13

%. Since the results from both meshes deviate equally from the experimental value it

is considered that the coarse mesh is sufficient in further simulations of cyclones with

similar geometry. Concerning the RSM simulations some diverge completely, but when

starting the RSM simulations with a two equation model the pressure drop for the fine

mesh oscillates within a range of 200 Pa.

- Comparison of overall separation efficiency

The experiments and the numerical simulations predict similar values of the overall

separation efficiency when the turbulent dispersion model is activated. When this is

deactivated the prediction differs more and especially for the Arizona dust. Another

advantage is that the computational time is also reduced than the turbulent dispersion

model is activated. Besides the total number of removed parcels, i.e. parcels that are

depleted due to very long residence times, is heavily reduced. Consequently it results

in higher accuracy when computing the grade efficiency curve.

- Numerical grade efficiency curve

Grade efficiency curves have been computed for each dust, where the cut size for each

dust differs a bit from each other. That can probably be explained by the fact that the

particle density between both dusts differs slightly. Since a larger mass concentration

tends to increase the separation efficiency stated previously in Section 3.1, it is logic

that the cut size of the Dolomite dust is lower than that for the Arizona dust. It is also

concluded that the need of two-way coupling is unnecessary.

- Comparison of cut size

Multiphase simulations result in a lower cut size than the experimental data does.

Probably the numerical value is more accurate since the calculation of the

experimental cut size is a rough approximation [2].

MASTER’S THESIS


- Transient simulation

RSM simulations and SST k-ω with curvature correction indicate that the flow field is

transient. The RSM is normally less robust compared to two-equation models and

therefore a stationary solution is hard to obtain. An alternative for further simulations

is to enable a time-stepping solver.

MASTER’S THESIS


7 Further work There are several aspects that could be highlighted in further work. The most

important thing to mention is how the inclusion of the vortex finder would affect the

flow field and how to model it and its interactions with particles.

For the airflow, an alternative modeling approach can be the implementation of Explicit

Algebraic Reynolds Stress model in Star-CCM+ to see how this model could handle the

flow physics. Additionally, the electrostatic interaction with the wall can be interesting

to model in order to observe how large impact the electrostatic field has on the cyclone

performance.

Other possible ways of broadening the analysis could also be to vary the particle

concentration at the inlet surface. One method can be to inject the particles arbitrary

from each other instead of injecting all particles equidistantly.

Turbulent two-way coupling is something that also could be investigated in further

work.

MASTER’S THESIS


References [1] Crowe C T, Schwarzkopf J D, Sommerfeld M, Tsuji Y (2012) Multiphase flows

with droplets and particles, 2nd ed., CRC Press Taylor and Francis Group, USA

[2] Hoffmann A C, Stein L E (2008) Gas cyclone and Swirl Tubes, 2nd ed.,

Springer, USA

[3] Montgomery D C (1997) Design and analysis of experiments, 4th ed., John

Wiley and Sons, USA

[4] Johansson A V, Wallin S (2013) An introduction to turbulence, KTH, Sweden

[5] Sommerfeld M, van Wachem B, Oliemanns R (2008), Best Practice Guidelines

for Computational Fluid Dynamics of Dispersed Multiphase Flows, ERCOFTAC,

European Union

[6] Dakal P, Walters K, Strasser W (2014), Numerical study of gas-cyclone airflow:

an investigation of turbulence modelling approaches, Taylor and Francis Group,

USA

[7] CD-adapco (2014) Modeling Particle and Droplet Flows using the Lagrangian

Multiphase Method, CD-adapco, United Kingdom

[8] CD-adapco (2015) User’s Guide, CD-adapco, USA

[9] Svarovsky L, (2009) Gas Cyclones, Fine Particle Software, United Kingdom

[10] Wilcox C D, (1998) Turbulence Modeling for CFD, 2nd ed., DCW

Industries Inc., USA

[11] http://www.powdertechnologyinc.com/product/iso-12103-1-a2-fine-

test-dust/ [Accessed: Mars 2016]

[12] http://oxfordhouse.com.mt/wp-

content/uploads/2014/10/product_brochures_label_vacuum_cleaners_general.

jpg [Accessed: February 2016]

[13] http://imgc.allpostersimages.com/images/P-473-488-

90/72/7280/RKNT100Z/posters/david-mack-water-air-interface.jpg [Accessed:

July 2016]

[14] https://thumbs.dreamstime.com/z/blue-air-bubbles-water-

8275871.jpg [Accessed: July 2016]

[15] http://www.cfd-online.com/W/images/b/b0/HRNvsLRN.png [Accessed:

April 2016]

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