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    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;

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    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

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    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.

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    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:

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    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).

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    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.

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    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.

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    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,

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    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

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    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   

      (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.

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    ( )   U 

     A

    dX  D

    dX   

      (5)

    250

    1

    ( )1

     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

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    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

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    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.

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    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)

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    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.

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    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.

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    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

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    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

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    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.

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    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

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