Upload
bruno-felipe-oliveira
View
218
Download
0
Embed Size (px)
Citation preview
8/18/2019 Separação Areia-Ar Em Um Ciclone
1/22
STUDY OF THE SEPARATION OF LIMESTONE AND SAND
PARTICLES IN A GAS MIXTURE INSIDE A CYCLONE
Arthur de Souza OLIVEIRA¹, Bruno Felipe OLIVEIRA¹, Murilo Melo MINARɹ, Kássia
Graciele dos SANTOS¹.
¹Federal University of the Mineiro Triangle, Chemical Engineering Department
Key words: CFD, cyclone, separation process, sand, limestone, chemical engineering
ABSTRACT: The chemical industry has several applications for cyclones, from
environmental issues to essential unit operation processes. Filtering cyclones are
equipment used in the separation of solids in suspension present in gas flows. In this work,
it was studied the behavior of sand and limestone particles inside a didactic model build by
TAVARES et al.
1 NOMENCLATURE
pm Particle mass;
pV Particle volume;
v Particle center of mass velocity;
b Intensity of external field; I Resistive force that the fluid exerts on the particle;
A Particle area projected on the normal plane in the flow direction;
DC Drag coefficient;
u Fluid velocity;
ρ Specific mass;
U Velocity vector;
φ Generic variable; Pressure force correlation Diffusive term;
8/18/2019 Separação Areia-Ar Em Um Ciclone
2/22
2
i,j,k Direction indices;
t Time;
P Production term;
µ Dynamic viscosity;
k Turbulent kinetic energy;
ε Energy dissipation rate;
V Average speed;
C Integration constants;
S Source term;
Vr Radial velocity;
Q Volumetric flow rate at inlet;Di, De Diameters, internal and external respectively;
ξ Constant factor for each type of cyclone;
2 INTRODUCTION
The objective of this project is to simulate the behavior of a cyclone built for the
laboratory of Unit Operations of the University of the Mineiro Triangle and validate the
results obtained with previous studies about cyclones.
2.1 SAND
Sand grains are mainly composed of quartz, but may also be composed of other minerals,
depending on the mother-rock and the amount of transport and change they have undergone.
The sand is classified into three categories of granularity: fine, medium and coarse sand,
with diameters range respectively from 1/1 and 16 mm / 4 mm; 1/4 mm and 1 mm; and 1mm
and 2mm.
The mineral composition of the sand may vary once any existing rock in surface of the
earth's crust can form it. The most common sands are quartz sand, light color, which have quartzas the predominant component, which is explained by higher resistance of this mineral to the
8/18/2019 Separação Areia-Ar Em Um Ciclone
3/22
3
actions of external agents. In some, other minerals can coexist as more or less altered feldspars,
micas and other minerals. However, there are sands that are mainly constituted by iron and
magnesium oxides minerals (olivine, pyroxenes, amphiboles), or lytic components (fragments
limestone, basalt, etc.).
Sands of properties - The color that the sands have relates too much about its
mineralogical composition. Thus, the silica sands are white when pure, as well as calcareous
sands. When basaltic sand, they are black as well as those that are rich in organic matter or
compounds magnesium. Iron compounds give the sands a yellowish or a greenish color.
The sand is mainly composed of quartz grains, due to the hardness given by this mineral,
capable of scratch glass and steel. They are unassailable by acids and are practically insolublein water.
Calcareous sands, as well as those in which in its constitution comes from shells or
fragments, make effervescence with acids and their calcareous materials are easily dissolved by
effervescent water. All sands exhibit a high degree of permeability.
It has several sorts, being the most common the fluvial, marine and dune.
Fluvial Sand – It contains quartz and other sorts of grain (mica, feldspar, pyroxene,grenades, olivines). The grains from this environment are very angular for their little transport,
little rolling, and little impacts. They have some glow by the fact of being transported by water
(washed by it). Sometimes they have diverse colors, for the oxidation process.
Marine Sand – Usually, it is homogenous (all the particles have the same dimension),
once the energy of the waves is constant. The sand grains are shiny and most of the times
polished, due to the constant transport by the waves. Their characteristics varies with the
mother-rock and the energy of the waves.
Dune Sand – The grains are very light (transported by the wind), homogeneous (the same
dimension) and well rounded. Presents rounded edges and dull surfaces due to the friction
between them. Also presents quartz grains once they are easily transported by the wind.
8/18/2019 Separação Areia-Ar Em Um Ciclone
4/22
4
2.2
LIMESTONE
Limestone is a sedimentary rock composed of calcite – type of crystalline calcium
carbonate (CaCO3) - in proportions greater than fifty percent, with impurities variable rates.
In its broadest sense, it is called the set of limestone calcareous materials that are part
marble, chalk, travertine, coral and marl. The classified as commercial calcareous rocks contain
amounts of magnesium carbonate variables: when the ratio is less than five percent, it is called
rich in calcium lime; when it is between five and thirty percent, magnesian; and when it contains
30-45%, is called dolomite. Rich in calcium and dolomitic limestones are white in its pure state.
The natural tones, however, fluctuate in a wide range due to the many impurities containedtherein. For example, iron oxide gives them yellow, red, or brown coloring, and pyrite,
marcasite and siderite to change the surface color when oxidized.
The differentiation of different species of limestone has been a source of disagreement
among researchers dedicated to the systematization of minerals. Generally speaking, the
limestones are distributed into two main groups: the alien rocks and indigenous. The first are
those are formed from previous existing rocks by transport and deposition of carbonates by the
water currents. Indigenous, by the other hand, originate from ex novo by aggregatingcarbonates. About their origin, limestones use chemical combination of mechanisms, processes
induced by the activity of marine organisms (pelagic rocks) and the buildup of calcareous shell
debris from various animals (detrital rocks).
2.3
CYCLONES
Currently, there are a major concern about environmental aspects. For which,
according to the 3rd resolution of CONAMA, 28/06/1990, the emission limits of inhalable
particles must be less than 10 µm (LACERDA et al., 2012). An equipment widely used in the
process of air purification is the cyclone (for solid particles).
Cyclones are equipment used in processes of separation. It contains a tangential
entrance: the feed of components mixture, usually gas-solid. In addition, two exits Underflow
and Overflow entrance. At the bottom exit (Underflow) is where the denser fluid is excluded,
usually a solid. At the upper exit (Overflow) is where the lighter fluid is excluded, usually a
gas. Figure 1 is a draft of how a cyclone works:
8/18/2019 Separação Areia-Ar Em Um Ciclone
5/22
5
Figure 1 – Draft of a cyclone. SOURCE: (MEIER, 1998)
Cyclones have been used in industry as solid-gas separators since the final os the 19th
century, due its high efficiency of separation for particles with the diameter from 5 to 100 µm,
and the small pressure drop caused by the equipment (MÉIER et al ., 2000).
This equipment can be used in chemical, metallurgic and nutritional industries, and in
the environmental area where it has the most importance. Cyclones, currently, are being used
in new processes, such as dryers, reactors and catalytic retrievers where there is high aggregate
value (LACERDA et al., 2012).
In comparison with other equipment used for this process, cyclones are preferred for
simple design, inexpensiveness to manufacture, low maintenance costs, and adaptability to a
wide range of operating conditions. Against their apparent simplicity, flow and collocation
characteristics of cyclones are complicated and the performance of a cyclone is highly sensitive
to any change in geometrical design and operating conditions (AZADI et al., 2010).
The particle separation inside cyclone separators manages two swirling motions of the
fluid flow in vertically opposed directions (double vortex phenomenon). Centrifugal forces
acquired in the particles due to these swirling motions directly separate particles (BOGODADE;LEUNG, 2015).
8/18/2019 Separação Areia-Ar Em Um Ciclone
6/22
6
Many works were made about cyclones, for the cited motives and there are many
cyclone families that are widely used. Some works studied the relation between the different
geometries existent and its efficiency in the particle collection; another ones aimed to evaluate
the relation between the different velocities used and the cargo loss, along with the collection
efficiency (LACERDA et al., 2012).
Over the last decade, CFD simulations have been promoted in fluid mechanics as a
design tool, providing results that are more reliable while minimizing time and cost compared
to experimental investigations (BOGODADE; LEUNG, 2015).
In an attendant and alternative way, along with the technological development, aiming
to solve the high dependency of empirical information, it has been used in studies the technique
of computational fluid dynamics (CFD – Computational Fluid Dynamics). In this endeavor, thefundamental causes of turbulence phenomena became comprehended (VIEIRA, 2006).
The purpose of this work is the development of a cyclone simulation previously
constructed. Such simulation was built in two dimensions. The equipment is from laboratorial
level and has the function of separation particles from gases.
The main objective of this work is study the efficiency of a separation process gas-
solid and comparing the results with those obtained experimentally, validating the simulations.
Besides the possibility of develop news methods for fluid dynamic studies of cyclonesand provide to students a better understanding of unit cyclones operations.
The Project has the objective of a cyclone’s simulation and check its efficiency. It is
intended too making a switchover of the particles used in the separation process. Comparison
of the simulation results with those obtained in an experimental process using recyclables. The
cyclones mentioned were built by TAVARES, et al (2015). For this, was realized a
experimental project that allows the better development of meshes and simulation with thesoftware Fluent Ansys 14.0 to prove the veracity of the obtained data.
3 EXPERIMENTAL PROCEDURES
The experimental procedure, described by Tavares et al. (2015), consist of two parts,
the first one is the sizing and construction of a cyclone and the second is the study of the
collection efficiency of sand and a mixture of sand and limestone.
8/18/2019 Separação Areia-Ar Em Um Ciclone
7/22
7
The cyclone size was calculate using some particular correlations, in Table 1 we have
the dimensions of each part of the equipment, which is show at Figure 2. The equipment was
building using only recyclables like, for example, a glass bottle. In Figure 3, we have the built
cyclone.
Source: SANTOS (2013).
Figure 2. View of each part of the equipment.
DC BC De HC LC SC JC ZC
Measurement
(cm)
7.95 1.99 3.97 3.97 15.9 0.99 1.99 15.9
Source: TAVARES (2015).
Table 1. Cyclone sizes calculated using correlations.
8/18/2019 Separação Areia-Ar Em Um Ciclone
8/22
8
Figure 3. Representation of the cyclone built.
At the Figure 3, we can see the tube where the air get in the cyclone, in orthogonal
with that tube we had the entrance where the injection of the solids occur. So the procedure
consist in insert the air and the solids in the cyclone, where will occur the separation, the solids
will left in the underflow and the air will left in the overflow.
After the construction of the cyclone, the study of the collection efficiency started.
First was made the particle size distribution of each materials used, before the injection in the
cyclone. Then the equipment get started and the gas-liquid separation took place. After the
separation, was necessary another particle size distribution, using the material collected in the
underflow. With the values before and after the separation, was possible to calculate the
collection efficiency.
4 METHODOLOGY SIMULATION
This article aimed at the two-dimensional simulation of cyclones in order to obtain
data for particulars flows, which experimental data were previously determined. Generally,
8/18/2019 Separação Areia-Ar Em Um Ciclone
9/22
9
cyclones have a symmetry axis, this particularly, considerably reduced the number of cells in
the two-dimensional computational simulations. This fact is plausible, because during operation
of a cyclone, a part of the flow is practically identical to that found for other (VIEIRA, 2006).
Two-dimensional mesh construction for cyclones was oriented in the positive xy axis.
Thus, only part of the mesh was built.
4.1 BOUNDARY CONDITIONS
The boundary conditions applied in the mesh are in table 2.
Table 2 – Boundary Conditions used in the mesh. SOURCE: Authors.
After meshing and applications of boundary conditions, the mesh was exported and
then open on Fluent Inc. 14. Using values for the materials already contained in the software
database. The materials used were the air, sand and lime.
4.2
PARTICLE INJECTION
Is chosen the type of injection, type and number of particles, the particle size
distribution model, the start coordinates and end of injection, the mass feed, the maximum and
minimum particle diameters, parameters of the model and the values of the velocity of the fluid
components (axial, radial and tangential) (LACERDA et al., 2012). In this case, the axial
component of the fluid velocity in the cyclone inlet is null because air is introduced into the
separator in the direction of its diameter and not on its symmetry axis. Regarding the radial
velocity component of the fluid, this is calculated based on the theoretical conversion of
cyclones input in a symmetric two-dimensional input, as described by (Boysan, Ayers,
Swithenbank; 1982). This is calculated by the equation 1. It is noteworthy that, as the radial
Border Specifications
Wall Wall
Inlet Velocity inlet
Outlet (overflow) Pressure outlet
Internal edges Interior
Axis Axis
8/18/2019 Separação Areia-Ar Em Um Ciclone
10/22
8/18/2019 Separação Areia-Ar Em Um Ciclone
11/22
11
4.3.1
COLLECT EFFICIENCY
The collect efficiency is a variable subordinate to equipment geometry, physical
properties, of air and particles, and the operating conditions. We had two kinds of efficiency,
the global efficiency and individual efficiency.
4.3.1.1 GLOBAL EFFICIENCY
The global efficiency is a relation between the mass of solids collect in the underflow
and the total mass of solids in the feed flow, as it’s possible to see in Equation 2.
su
s
W
W
(2)
4.3.1.2
SIGMOID AND RRB MODELS
The RRB model is characterized for having two adjustable parameters (n,d*). It is a
simple function, that relates directly the particle diameter (dp) with the mass fraction of particles
with diameters smaller than dp.
= 1 (−∗
) 3
Where X is the mass fraction, dp is the particle diameter (μm), n is the defining
parameter of the curve form of granular distribution, d* is the parameter that quantifies the
particle diameter for X=0,632.
The Sigmoid adjustment presents also two adjustment parameters (n,d*):
= +∗ (4)
4.3.1.3 INDIVIDUAL EFFICIENCY
The individual efficiency is the efficiency to collect particles with diameter equal or
beneath D. We two ways to calculate this efficiency, the first one is experimental, using the
Equation 5, and the second was introduce by MASSARANI (1997), as we can see in Equation6, using the court diameter.
8/18/2019 Separação Areia-Ar Em Um Ciclone
12/22
12
( ) U
A
dX D
dX
(5)
250
1
( )1
D d
d
(6)
4.3.2 LAPPLE MODEL
The LAPPLE model (1951) is one of the first models used to predict the particle size
efficiency, or individual efficiency. This model is based in a force balance for a almost
stationary particle, where, in accord to RODRIGUES (2001), the residence time can be express
up to the number of spins that the gas realize inside the cyclone.
LAPPLE (1951), using Newton’s second law, equation 7, and making some
considerations, equation 7, deduced a relation between the resistive force in a fluid with the
rigid particle movement flow, that are represented by equation 9.
p s P dv
m V b I dt
(7)
21 ( )
2
D
u v I A C u v
u v
(8)
1
( )2
p s P D
dvm V b A C u v u v
dt
(9)
In equation 6 we had two tree variables that are given by equations 10, 11 e 12, the
projected area of the equal volume sphere to the particle, the centrifugal field intensity and the
Stokes drag coefficient.
2
4
P d A
(10)2b w r (11)
24
Re Dc
(12)
It is adopted that the tangential velocity of the particle is equal to the fluid and the
particle radial velocity is equal to the terminal velocity in a centrifugal field.
To calculate the efficiency we need the court diameter, which is the diameter of the
particle collected with 50% of efficiency. If we consider the smaller particle that get in thecyclone at the dimension Bc and is collect with 100% of efficiency, the court diameter is the
8/18/2019 Separação Areia-Ar Em Um Ciclone
13/22
13
diameter of the particle that get in the cyclone at the dimension Bc/2 an is collected with 100%
of efficiency (RODRIGUES, 2001).
Using all this concepts we get to the equation 13, which represents the court diameter
of the particle. With this diameter, it is possible to calculate the individual efficiency.1
2
50
9
2 ( )
c
e s
Bd
N u
(13)
4.3.3 PRESSURE DROP IN CYCLONES
Another important parameter in cyclones is the pressure drop, which diminishes when
the particles are injected in the flow. The phenomena was attributed to the particle inertia, which
would tend to be equal to the gas momentum in the adjacent layers in the gas flow direction
(FASSANI and GOLDSTEIN, 2000).
The knowledge of the cargo loss of the cyclone is one of the necessary items to the
calculation of the energy consumption and optimization of the cyclone parameters. The pressure
drop consists in the entrance, exit and inside losses of the cyclone. The main part of the pressure
drop is attributed to the inside losses of the cyclone due to the dissipation of energy by the
viscosity tensor of the rotational turbulent flux (OGAWA, 1997 apud SILVA (2006)):
∆ =
2 14
Where ξ is a constant factor for each type of cyclone, V e is the entrance velocity and ρ
is the density of the gas with the powder.
SHEPERD and LAPPLE (1939) also were the first to approach the effect of the
concentration of solids in the pressure drop, observing that it diminished with the concentration
of solids. SHEPERD and LAPPLE (1939) also the pioneers in a equation to evaluate ξ:
= 6 (15)
Suppling the pressure drop in N/m², being a, b, De, the dimensions of the cyclone.
LINTTLEJOHN, ((1978 apud BERNARDO (2005)), affirms that if the gas flow is
constant, when started the solid feed, it will occur a big momentum transference from the gas
to the solids, producing drag forces. So, the gas velocity reduces causing pressure drop. The
8/18/2019 Separação Areia-Ar Em Um Ciclone
14/22
14
deposited particles in the wall are the cause to the reduction in the pressure drop (YUU et al
(1978) apud BERNARDO (2055)).
4.3.4
TURBULENCE
SILVEIRA-NETO (2001) defines turbulence as a regime of operation of any dynamic
system, which a number of degrees of freedom sufficiently high can characterize its operation.
As applications, it is cited some more familiar examples. In the chemical processes, it
is interesting to accelerate the reactions through turbulence. It is interesting to maximize a heat
exchange process, for the turbulent diffusion is many times more important than the molecular
diffusion. In termohydraulic problems, the mechanic devices inserted to rise the heat exchange
implies also in a cargo log (SILVEIRA-NETO, 2001).
According to SILVEIRA-NETO(2011), some characteristics of the turbulence
phenomena are:
Irregularity: the turbulent flow are difficult to predict deterministically, and the use of
statistic tools is currently the only form of analysis. In this way, it is considered a random
process. A more realistic vision considers an half random and an half deterministic process.
High diffusivity: The mixture process of all properties tied to a flow (movement
quantity, energy, contaminants, etc.) many magnitude orders are bigger in the turbulent regime
than in the laminar. This happens due to the fact that, in the turbulent regime, there are thermal
and concentration fluctuations, that creates strong and numerous local gradients, making the
process more efficient in the molecular diffusion. For engineering processes, this is perhaps the
most important characteristic of turbulence, for it implies in: combustion process and heat
exchange acceleration, strong influence in the velocity control along with the submerged wall.
Turbulence occurs at high number of Reynolds: The transition of a flow to the
turbulent regime, as well as its maintenance depends on the relative importance between the
convective and diffusive effects. The convective effects highly non-linear are amplifying effects
of perturbations and generators of instability. On the other hand, the diffusive effects are
inhibitors of the formation of instabilities.
8/18/2019 Separação Areia-Ar Em Um Ciclone
15/22
15
Turbulence is a phenomena highly dissipative: The process of viscous dissipation of
turbulent kinetic energy generates the rise in the internal energy at high frequencies.
Turbulence is a continuous phenomena: Any Newtonian fluid flows can be modulated
using Navier-Stokes equations. If the fluid is non-newtonian this equations have to be modified
in its viscous term. It is important to emphasize that this equations modulate any flow,
regardless turbulent or laminar.
Turbulence is an essential phenomena: This is the relative characteristic to our
inability to reproduce or repeat a given experiment. Even in the laboratory, under extreme
conditions of control, it is not possible to develop two identical results. Turbulent flow, for its
non-linear effects, has a high capacity of amplification of little error, conduction resultscompletely differents.
4.3.5 TURBULENCE MODEL
Turbulence model is classified according with the existence or not of turbulent
viscosity. The turbulent viscosity is a property of the flow and not the fluid.
4.3.6 REYNOLD STRESS MODEL (RSM)
It is a model to six transport equations, depends of turbulent viscosity () and doesnot admit to be isotropic (LACERDA, 2007). This was the model used in this paper to describe
the turbulence in the cyclone.
RSM is based in transport equations for all Reynolds tensor components and for the
dissipation rate.
There differential equations for each Reynolds tensioners and their solution provides
the tensor components. An equation that represent this statement is presented in equation 16.
_____ 2
____ ____ 2
[( ) ]( ) 3 2
3
i j
si j k i j k
ij i j ij
k k
v vk C
v v v v v x P p
y x x
(16)
8/18/2019 Separação Areia-Ar Em Um Ciclone
16/22
16
Where, it is the correlation of the pressing force, k it is the turbulent kinetic energy,ε is the dissipation rate of turbulent kinetic energy, V the average speed and P is the produce
term, which is in the equation 17.
___ ___
( . ( ) ( ) . )T P v v V V v v (17)
The turbulent dissipation equation is given by 18.
2
1 2
1( ) ( ) . ( ) . RS
RS
k V C P C C
t k
(18)
4.3.7
NUMERICAL METHODS
With ease, the complexity of physical and mathematical problems encompassing
engineering is highly necessary to use numerical methods (MALISKA, 2004).
The numerical method consists in solving one or more differential equations, derived
by replacing the algebraic expressions involving the unknown function.
In deciding the numerical solution rather than analytical, the obtained solution is for a
discrete set of points, with a particular error.
For the finite volume method (method for discretization of a set of partial differential
equations) has a physical basis. This method is applied implicitly in meshing using the Gambit
software, in case this article.
In this method, the calculation domain is divided into control volumes, which contain
nodes, each node being represented by a volume control. The variables are defined in the center
of the volume control, and the equations are integrated on these volumes, thus leading to adiscretization (LACERDA, 2007).
The equations solved by the method have generally given by the equation 19.
__
.( ) .( )U S t
(19)
Where, ρ is the specific mass, φ is the generic variable, Г is the term diffusive, U is the
velocity vector and S is the source term.
8/18/2019 Separação Areia-Ar Em Um Ciclone
17/22
17
5 RESULTS AND DISCUSSION
The purpose of the present paper is the correct simulation of a recyclable cyclone usingCFD techniques. The results were collect by measured of collecting efficiencies and
comparison using correlations of simulation’s values and experimental ones.
5.1. Individual collecting particles
Related to individual collecting particles, the values were obtained with CFD
simulation. Particles were injected into inlet surface, according the parameters values
previously informed. The particle was sand with specific mass value of 1100 kg.m-3. The drag
law was nonspherical and shape factor of 0.8. It were injected a particle per cell displayed at
the entrance and total injected 106 particles.
The efficiency individual collecting particles was measured by a simple correlation.
This one is in equation 20.
Ptrapped
Ptotal (20)
Where η is the efficiency individual collecting, Ptrapped is the particles trapped by the
underflow and Ptotal is the total of particles injected into the cyclone.
The particles were injected varying diameters and then calculating the efficiency. In
CFD simulation can appear incomplete and this can’t be measured, therefore must be avoid. In
the present paper was chosen a range of diameters where this problem does not appear.
The table 3 represent the diameters used and its efficiency.
Diameter (m) Trapped Escaped Incomplete Efficiency (%)
6.00E-06 106 0 0 100.00.
4.00E-06 106 0 0 100.00.
3.00E-06 95 11 0 89.62.
2.00E-06 72 34 0 67.92.
1.00E-06 65 41 0 61.32.
9.00E-07 39 67 0 36.79.
Table 4 - Individual collection efficiency
The graph represented particles individual collection is presented in Figure 4.
8/18/2019 Separação Areia-Ar Em Um Ciclone
18/22
18
Figure 4 - Individual collection efficiency. Source: Author.
This data was used to calculate the parameter D50, which were used in sigmoid
correlation for global collection efficiency calculation. The value of this parameter were 0.954
µm.
Comparing the value for D50 found experimentally by TAVARES (2015), 810 µm, and
found in this simulation, it is found that this is not representative for the system and requires
further work and simulation time.
5.2. Global collecting efficiency
The global efficiency was calculated using two models of particles size distribution,
the RRB and the Sigmoid. For the RRB model we use equation 21, for values of n from 0.5
until 4. Than we get the graphic represent in figure 5, where we can see that for D/D50 equal
to 1, the global efficiency is 50 % for n equal to 2, so the global efficiency for RRB model is
better represented by n equal to 2.
1.11
0.118 .50
1.81 0.32250
n Dn
D Dn
D
(21)
-
20.00.
40.00.
60.00.
80.00.
100.00.
0.00E+00 1.00E-06 2.00E-06 3.00E-06 4.00E-06 5.00E-06 6.00E-06 7.00E-06
8/18/2019 Separação Areia-Ar Em Um Ciclone
19/22
19
Figure 5 – Global collecting efficiency for RRB model. Source: Author.
For Sigmoid model we use equation 22, where we integrates using the trapezoidal rule.
In figure 6 we can see the global efficiency for Sigmoid model. In figure 6 we couldn’t find the
value of p that better fit to the case. But, as we saw in figure 5, increasing p or n more fast the
efficiency reaches 1.
2
22
5050
.
501 1
50
p
p
D D p D D
dD D D
D D D
(22)
Figure 6 – Global collecting efficiency for Sigmoid model. Source: Author.
0
0.1
0.2
0.3
0.4
0.50.6
0.7
0.8
0.9
1
0 2 4 6 8 10 12
η
̅
D/D50
1=0.5 n=1 n=1.5 n=2 n=4
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 10 20 30 40 50 60 70
η ̅
′/50
p = 0,5 p = 1 p = 1,5 p = 2
8/18/2019 Separação Areia-Ar Em Um Ciclone
20/22
20
5.3. Fluid-flow contours
In figure 7 we can see the fluid flow contours for axial, radial and swirl velocity’s. It’s
possible to see that the center is the place where we have the highest velocity, for both axial
and swirl. The radial velocity is practically constant in all the equipment.
Figure 7 – Fluid-flow contours for a) Axial velocity, b) Radial velocity and c) Swirl velocity.
Source: Author.
6 CONCLUSION
The only type of particle used in the present simulation was sand, because this one had
experimental database.In this work was done simulation of a cyclone constructed using recyclable materials.
Although the mesh was made with the correct measurements and have taken all necessary care
in the development of the case, the simulation result was not the expected. There was a great
disparity in value experimentally obtained with the simulation one, there was no way to develop
the simulation using the average size of particulates.
The reason for such errors can be credited for the boundary conditions used in
underflow, where we need to change directly in the program, changing the underflow from
interior to wall, which has not responded well.
8/18/2019 Separação Areia-Ar Em Um Ciclone
21/22
21
The correlations for efficiency global collecting particles presented a good result,
indicating that the simulation has theoretical basis and can be crafted to best represent the
experimental system.
7 REFERENCES
AZADI, M.; AZADI, M.; MOHEBBI, A. A CFD study of the effect of cyclone size on its
performance parameters. Journal of Hazardous Materials, 182, p. 835-841, 2010.
BOGODAGE, S. G., LEUNG, A. Y. T. CFD simulation of cyclone separators to reduce air
pollution. Powder Technology, 286, p. 488-506, 2015.BOYSANT, F.; AYERS, W. H.; SWITHENBANK, J. A fundamental mathematical modelling
approach to cyclone design. Institution of Chemical Engineers, v. 60, p. 222-230, 1982.
CARVALHO, A. T. Otimização de ciclone para a pré-separação de areia na produção de
petróleo. 19 p. Dissertação de mestrado, Escola de Química da Universidade Federal do
Rio de Janeiro, Rio de Janeiro, 2008.
LACERDA, A. F. Estudo dos efeitos das variáveis geométricas no desempenho de ciclones
convencionais e filtrantes. Tese de doutorado, Programa de Pós Graduação em
Engenharia Química – UFU. Uberlândia, 2007.
LACERDA, A. F., LOURENÇO, R. O., CASTRO FILHO, P. R. C. study of cyclone fluid
dynamic behavior. XXIV Encontro do SEMIC, UFMA. São Luiz, 2012.
MALISKA, C. R. Computational Fluid Mechanics and Heat Transfer. 2 Ed., São Paulo,
2004.
MEIER, H. F., KASPER, F. S., PERES, A. P., HUZIWARA, W. K., MORI, M. Comparison
Between Turbulence Models for 3-D Turbulent Flows in Cyclones, Proceedings of
XXI CILAMCE - 21st Iberian Latin-American Congress on Computational
Methods in Engineering, 1-18. Rio de Janeiro, 2000.
MEIER, H. F. Modelagem fenomenológica e simulação bidimensional de ciclones por
Técnicas da Fluidodinâmica computacional. Tese de doutorado, Faculdade de
Engenharia Química – UNICAMP, Campinas, 1998.
SANTOS, K. G. Separação no campo Centrífugo - Ciclones. Universidade Federal do
Triângulo Mineiro. Uberaba, 2013.
8/18/2019 Separação Areia-Ar Em Um Ciclone
22/22
22
TAVARES, F. P., et al . Construção de ciclone a partir de materiais recicláveis. Relatório
para conclusão da disciplina Desenvolvimento de processos químicos II. Departamento
de Engenharia Química da Universidade Federal do Triângulo Mineiro. Uberaba, 2015.
VIEIRA, L. G. M. Otimização dos processos de separação em hidrociclones filtrantes. 7 p.
Tese de doutorado, Programa de Pós Graduação em Engenharia Química – UFU.
Uberlândia, 2006.
CRUZ, O. C., et al. Eficiência granulométrica de um hidrociclone de geometria “rietema”
para pré-filtragem de água para irrigação. Revista Brasileira de agricultura irrigada.
Fortaleza, CE, 2011.
Areias e Ambientes Sedimentares. Ciência Viva, Agência Nacional para a cultura Científica
e Tecnológica. Portugal. Acesso em 04 dez. 2015. Disponível em: <http://www.cienciaviva.pt/img/upload/areiasfinal23jan.pdf>