MASTER’S THESIS
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Numerical Methods for Simulating Separation in a Vacuum Cleaner Cyclone Page 1 (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
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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
Stockholm, Sweden, 2016
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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
Stockholm, Sweden, 2016
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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
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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
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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].
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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.
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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
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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.
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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
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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.
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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
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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.
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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
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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
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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.
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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.
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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.
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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.
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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.
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Figure 22: Histogram of cell quality.
Figure 23: Histogram of skewness angle of neighbouring cells.
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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+.
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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.
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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.
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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.
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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
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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
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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
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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.
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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.
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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
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+ 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
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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 %
Particle size (microns)
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 %
Particle size (microns)
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 %
Particle size (microns)
Dolomite Non-disp
Arizona Non-disp
Arizona
Dolomite
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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 %
Particle size (microns)
Dolomite non-
disp+removed
parcels
Arizona non-disp +
removed parcels
Dolomite non-disp
Arizona non-disp
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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
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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
Date: 08/07/2016 Numerical Methods for Simulating Separation in a Vacuum Cleaner Cyclone Page 56 (58)
- 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
Date: 08/07/2016 Numerical Methods for Simulating Separation in a Vacuum Cleaner Cyclone Page 57 (58)
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
Date: 08/07/2016 Numerical Methods for Simulating Separation in a Vacuum Cleaner Cyclone Page 58 (58)
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