Separacao Areia Ar em um Ciclone

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

m p Particle mass; V p 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;

C D Drag coefficient; u

Fluid velocity;

ρ

Specific mass;

U

Velocity vector;

φ

Generic variable; Pressure force correlation



Diffusive term;

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

2

Constant factor for each type of cyclone;

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 quartz as 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 insoluble in 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 contained therein. 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 aggregating carbonates. 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, the fundamental 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 gassolid and comparing the results with those obtained experimentally, validating the simulations. Besides the possibility of develop news methods for fluid dynamic studies of cyclones and 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 the software Fluent Ansys 14.0 to prove the veracity of the obtained data.

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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.

Measurement

DC

BC

De

HC

LC

SC

JC

ZC

7.95

1.99

3.97

3.97

15.9

0.99

1.99

15.9

(cm) 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.

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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. Border

Specifications

Wall

Wall

Inlet

Velocity inlet

Outlet (overflow) Pressure outlet Internal edges

Interior

Axis

Axis

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

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component of the fluid velocity is a vector quantity, it can be accompanied by a minus sign, according to the layout of the y-axis (VIEIRA, 2006).

Vr 

Q  Di De

(1)

Referring to exits, overflow and underflow, it is assumed that both were at atmospheric pressure.

4.3

METHODOLOGY APPLIED

The table 3 represent of an abstract way the dates applied to the simulation.

Type of particle

Inert

Material

Sand and Cal

Swirl-velocity

7.14 m.s-1

Radial-velocity

-0.7166 m.s-1

Axial-velocity

0

Spatial discretization Pressure

PRESTO

Pressure-Velocity Coupling Scheme

SIMPLE

Momentum

FIRST ORDER UPWIND K-ε REYNOLDS STRESS

Turbulence model

MODEL

Table 3- Dates applied to the simulation. SOURCE: Authors

About the turbulence models, was chosen the model RSM (Reynolds Stress Model), because the flow on cyclone’s interior can occur in a complex way. Related to interpolation pressure, the scheme PRESTO was chosen. As for the pressure-velocity coupling pair, was used the algorithm SIMPLE. For other fluid dynamic variables, the choice of interpolation schemes was the UPWIND type of first order (VIEIRA, 2006).

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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.



Wsu Ws

(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. 𝑋 =1− 𝑒

(−(

𝑑𝑝 𝑛 ) ) 𝑑∗

(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*): 𝑋=

1 1+(

4.3.1.3

𝑑𝑝 𝑛 ) 𝑑∗

(4)

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 Equation 6, using the court diameter.

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 ( D)    ( D) 

dX U dX A

(5)

1 d  1   50   d 

2

(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. mp

I

mp

dv    s    VP b  I dt

(7)

1 2 (u  v) A CD u  v 2 u v

(8)

dv 1    s    VP b  A CD u  v (u  v ) dt 2

(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.

A

 d P2 4

(10)

b  w2 r

(11)

24 Re

(12)

cD 

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 the cyclone 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 9 Bc d50     2 N eu (  s   ) 

(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)): ∆𝑃 = 𝜉

𝜌𝑉𝑒2 2

(14)

Where ξ is a constant factor for each type of cyclone, Ve 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: 𝜉=

16𝑎𝑏 𝐷𝑒2

(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 results completely 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 (𝜇 𝑇 ) and does not 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 k 2  vi v j ____ ____ [(   Cs  ) ]  vi v j  (vk  vi v j ) 3  xk 2   Pij  i j    ij  p y xk xk 3

(16)

16

Where, 𝜑𝑖𝑗 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. ___

___

P    (v.v(V )T  (V ) v.v)

(17)

The turbulent dissipation equation is given by 18.

 1    k2  ( V  )  (C 1 P  C 2  )  .  (    C RS ).  t k     RS 

(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 a discretization (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.

17

5

RESULTS AND DISCUSSION

The purpose of the present paper is the correct simulation of a recyclable cyclone using CFD 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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100.00. 80.00. 60.00. 40.00. 20.00. 0.00E+00 1.00E-06 2.00E-06 3.00E-06 4.00E-06 5.00E-06 6.00E-06 7.00E-06

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.



1.11n 0.118  n D 1.81  0.322n  D50

.

D D50

(21)

η̅

19

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

2

4

6

8

10

n=2

n=4

12

D/D50 1=0.5

n=1

n=1.5

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

p

η̅

 D   D50  p    D50   D     . dD   D 2    D50  p 2 1     D     1   D50     D  

(22)

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

10

20

30

40

50

60

70

𝐷′/𝐷50 p = 0,5

p=1

p = 1,5

p=2

Figure 6 – Global collecting efficiency for Sigmoid model. Source: Author.

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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.

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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.

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.

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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.

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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

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