Computational Fluid Dynamics (CFD) - American Chemical Society

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Ind. Eng. Chem. Res. 2008, 47, 192-200

Computational Fluid Dynamics (CFD) Analysis of Cyclone Separators Connected in Series Atilano Antoˆ nio Vegini and Henry Franç a Meier Department of Chemical Engineering, UniVersity of Blumenau (FURB), Blumenau, Santa Catarina SC 89010-971, Brazil

Joa˜ o Jaime Iess Votorantim Cement Industry, Curitiba, Parana´ PR 82130-570, Brazil

Milton Mori* Department of Chemical Processes, School of Chemical Engineering, State UniVersity of Campinas, Campinas, Sa˜ o Paulo SP 13081-970, Brazil

Cyclone separators are very useful equipment for particle removal from gaseous streams. Their simple design and low capital and maintenance costs have made cyclones one of the most widely used gas-solid separators. Their dynamic behavior includes several phenomena, such as vortex breakdown, reversal of flow, and high turbulence intensity. Prediction of pressure drop and collection efficiency over a temperature range of several hundred degrees with a high solids loading flow and different cyclone dimensions is very difficult with simplified models. In this work, a model that is based on computational fluid dynamics (CFD) techniques is used to verify the performance of cyclone separators connected in series; this collection of separators is called a cyclone tower. The model is based on the Eulerian-Eulerian approach, and it is composed of several time differential equations in a two-dimensional (2-D) space domain with a three-dimensional (3-D) symmetric cyclone inlet. The model is solved using the finite volume method with staggered grids. The results on collection efficiency and pressure drop of an experimental study were used to validate the proposed model. After validation of the model, it was possible to examine the performance of the cyclone separators through a comparison of the numerical results and information obtained in the cement industry. 1. Introduction Cyclones are extensively used in the cement industry for the heating of raw material (raw meal), which is of basic importance to the thermal performance of the entire system of cement production. Figure 1 shows a typical design of a cyclone tower (cyclone separators that have been connected in series), which is composed of two streams, each having four cyclones connected in series. The raw meal is heated in all the cyclones with the raw meal fed into the system at cyclone C1. The hot gas from the kiln enters cyclone C4 in a countercurrent flow and goes through the other cyclone, heating the raw meal. It can be observed that, in cyclone C4, the phenomena of chemical reactions and combustion are predominant (calcination region). The solid material collected in cyclone C4 goes to the kiln. The exact mechanisms of gas-particle separation in cyclones still are not completely understood, even though the equipment has used for a long time. The dynamic behavior includes several phenomena, such as vortex breakdown, reversal of flow, and high turbulence intensity.1 In addition, different operating conditions such as temperature, pressure, and flow rate create even more difficulties in the already-complicated problem. The typical models had been developed on the basis of experimental data collected at room temperature to calculate the main design parameters of cyclones (i.e., pressure drop and collection efficiency).2-6 These models give acceptable results only under certain limitations or for certain types of cyclones. The prediction of results over a temperature range of several hundred * To whom correspondence should be addressed. Fax: +55 19 35213963. E-mail address: [email protected].

Figure 1. Cyclone tower.

degrees with a high solids loading flow and different cyclone dimensions is very difficult with these simplified models. In this work, a model based on computational fluid dynamics (CFD) techniques was used to predict the design parameters

10.1021/ie061501h CCC: $40.75 © 2008 American Chemical Society Published on Web 11/28/2007

Ind. Eng. Chem. Res., Vol. 47, No. 1, 2008 193

for cyclones in a cement industry. The cyclones have different shapes and are operated at high temperatures with a high solids loading flow. The model used is based on the Eulerian-Eulerian approach, and it is composed of several time differential equations in a two-dimensional (2-D) space domain with a threedimensional (3-D) symmetric cyclone inlet. The transformation of a 3-D asymmetric inlet to a 3-D symmetric inlet was validated in previous work,7,13 as suggested by several researchers.1,8-10 This transformation was also validated with the experimental data from Patterson and Munz11 with the numerical simulation obtained with the CYCLO code that was developed by Meier7 and with the commercial code CFX 4.4 of ANSYS,12 which is based on an anisotropic model of the Reynolds stress. Both models provided a successful representation of the behavior of gas and gas-solid turbulent swirling flow in cyclones with industrial characteristics.12 The mathematical model is completed using a hybrid turbulence model composed of a combination of the k- standard model and Prandtl’s longitudinal mixing model to represent the turbulence of the gas phase. Our research group has studied turbulence models for swirling gas-solid flow in cyclones since 1994, and the main conclusion obtained shows that the anisotropy behavior of the Reynolds stress can be introduced very well using this hybrid turbulence model. Comparisons between experimental and numerical profiles of tangential velocity for several experimental cases have shown good agreement.13 The model is solved using the finite volume method with staggered grids. Experimental data on the collection efficiency and pressure drop obtained by Zhao et al.14 are compared with the numerical results to validate the code. The numerical results allowed prediction of pressure drop and collection efficiency, as well as the complete fluid dynamics behavior of the gas-solid flow for the cyclones. By analyzing and comparing the information from the cement industry with the results obtained by the model, we are able to verify the performance of the cyclone tower. 2. Mathematical Modeling Cyclones in the cement industry are operated at very high temperatures (in the range of 450-900 °C) with an inlet dust loading from 250 g/m3 to 500 g/m3. This type of problem can be modeled using a multifluid concept where a phase interacts with one or more other phases by means of drag forces and mass and energy fluxes between phases. The main assumption of this model is that the phases interpenetrate where all phases have fluid dynamics properties at the same point in the timespace domain (i.e., continuous properties, such as density, viscosity, thermal conductivity, etc.). Only the molecular behavior of the material is neglected. More detailed information on multifluid modeling can be obtained in the work of Gidaspow15 and Meier and Mori.13 2.1. The Two-Phase Model. The development of a multifluid model for gas-solid flow in cyclones requires some assumptions: (i) the solid phase can be represented by a mean diameter; (ii) the turbulence in the gas phase is anisotropic and can be represented by means of a hybrid turbulence model that is composed of a combination of the k- standard model and Prandtl’s longitudinal mixing model; and (iii) disturbances in the flow near the inlet region due to asymmetry of the tangential or involute gas inlet to the cyclone quickly disappear, which makes it possible to use axial symmetry and apply the 3-D symmetry model. The flow is incompressible and the pressure force acts only on the gas phase, which is a hypothesis of the mathematical modeling used in this work. 2.1.1. Conservation Equations. The conservations equations involved in this study are given as follows.

Mass ConserVation in the Gas Phase ∂ (f F ) + ∇‚(fgFgvg) ) 0 ∂t g g

(1)

Mass ConserVation in the Solid Phase ∂ (f F ) + ∇‚(fsFsvs) ) 0 ∂t s s

(2)

Momentum ConserVation in the Gas Phase ∂ (f F v ) + ∇‚(fgFgvgvg) ) -fg∇‚(Tef g ) + fgFgg - ∇p + Fres ∂t g g g (3) Momentum ConserVation in the Solid Phase ∂ (f F v ) + ∇‚(fsFsvsvs) ) fsFsg - Fres ∂t s s s

(4)

Energy ConserVation in the Gas Phase ∂ (f F C T ) + ∇‚(fgFgvgCpgTg) ) -fg∇.(qef g ) - fgqgs ∂t g g pg g

(5)

Energy ConserVation in the Solid Phase ∂ (f F C T ) + ∇‚(fsFsvsCpsTs) ) fsqgs ∂t s s ps s

(6)

2.1.2. Constitutive Equations. The model adopted for the effective shear stress is based on the Boussinesq approximation, where the relation of shear stress to deformation rate is similar to that in the general Newtonian fluid model. In this case, the tensor is directly proportional to the deformation rate: ef Tef g ) -2µ Dg

(7)

where the deformation rate is 1 Dg ) [∇vg + (∇vg)T] 2

(8)

and the effective viscosity (µef) is a combination of molecular viscosity (µg) and turbulent viscosity (µ(t)): µef ) µg + µ(t)

(9)

In eq 9, the turbulent viscosity (µ(t)) can be obtained from an anisotropic model,7 from a combination of the k- standard turbulence model and Prandtl’s mixing length theory. In the cylindrical coordinate system, for example, Prandtl’s model can be written as follows:

(( ) ( ) ) ( ) })

∂ug 2 ug 2 + + ∂r r 2 ∂ug ∂wg 2 ∂Vg 2 1/2 + + (10) + ∂z ∂r ∂z

(µ(t))θ,θ ) (µ(t))r,θ ) (µ(t))z,θ ) (µ(t))in + Fgr2l2

( ) {[ ( )] ( ∂wg ∂z

2

+

1 2

r

∂ Vg ∂r r

where the first term on the right side of eq 10, (µ(t))in, physically represents an additional turbulence contribution due to inlet effects11 and l is the mixing length, by analogy with the kinetic theory of gases. A correlation for (µ(t))in, as suggested by Pericleous,16 is given as (µ(t))in ) Fg(kg)1/2

Dh 10

(11)

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Ind. Eng. Chem. Res., Vol. 47, No. 1, 2008

The other component of the anisotropic turbulent viscosity with the application of the k- standard model is

()

(µ(t))r,z ) (µ(t))r,r ) (µ(t))z,z ) CµFg

kg2 g

The rate of heat transfer between the phases can be calculated using the equation

( )

qgs ) hgs

(12)

where Cµ is a constant, kg the turbulent kinetic energy, and g the dissipation rate of turbulent kinetic energy. There are also two additional conservation equations:

( )

∂ µef (fgFgkg) + ∇‚(fgFgvgkg) ) fg∇‚ k ∇kg + fg(Gg - Fgg) (13) ∂t σ

3 (T - Ts) 2dp g

(23)

where the convective heat-transfer coefficient can be predicted by the following equation:18 hgs ) 175

( )( ) ( ) ( ) kg d p d p Dc

0.93

Fs -1 Fg

0.82

Qs Qg

0.64

Re00.14Pr1/3

(24)

with

and

( )

∂ µef (fgFgg) + ∇‚(fgFgvgg) ) fg∇‚ ∇g + ∂t σ

Re0 )

g fg(C1Gg - C2Fgg) (14) kg

where σk, σ, C1, and C2 are constants of the model and Gg is a source of turbulence that can be predicted using the following equation: Gg ) -T(t) g :∇vg

(15)

Now the resistive or drag forces between phases can be modeled by a standard expression: Fres ) βg,s(vg - vs)

(16)

where βg,s is the interface coefficient and can be predicted for concentrated flows (fg < 0.8) by means of the Ergun equation:8

( )

βg,s ) 150µg

fs fgdpφp

2

+ 1.75

Fgfs|vg - vs| dpφp

(17)

where dp is the particle diameter, φp the spherical shape coefficient, and |vg - vs| the relative velocity between phases. For diluted flows where fg > 0.8, a model that has been proposed15 relates the interface coefficient with the drag coefficient, CD, by the following equation: βg,s )

() (

)

fgFg|vg - vs|fs 3 C 4 D dpφp

(18)

In the literature, there is a large number of empirical correlations for drag coefficient calculation, as a function of the Reynolds number for the particles. One that establishes equations for all flow regimes was published by Coelho and Massarani:17 CD )

[( ) 24 K1Rep

0.85

]

- K20.85

1.18

(19)

FgVendp µg

(25)

where Q is the volumetric flow rate and Ven is the inlet mean velocity. 2.2. Boundary and Initial Conditions. The initial conditions used for numerical simulation of the single-phase dynamic flow were start-up conditions, where all velocity components were considered to be equal to zero and the pressure field was the atmospheric field. For the gas-solid flow, profiles for the gas were obtained from the steady state of single-phase flow with an abrupt entry of the solid phase. The boundary conditions used were a uniform profile at the inlet, no-slip conditions on the wall, axial symmetry conditions at the symmetry axis, and continuity conditions at the exits. More details can be found in the work reported by Meier.7 2.3. Numerical Methods. The software used to solve the model was the CYCLO code using CFD techniques; this model was developed by Meier.7 This program is composed of three moduli: the preprocessor modulus, the processor modulus, and the postprocessor modulus. The preprocessor modulus is responsible for generating the grid, which was developed in a cylindrical coordinate system with a multiblock scheme and staggered grids. The numerical solutions were obtained through the processor modulus, which uses the finite volume method to discretize the partial differential equations of the model. For the pressurevelocity coupling, the program uses the SIMPLEC algorithm. After discretization by the finite volume method, a traditional line-by-line algorithm with TDMA is applied to solve the system of nonlinear equations. The time solution is obtained from an implicit first-order procedure. Details about this solution strategy can be found in the work of Patankar,19 Maliska,20 and Meier.7 Animation techniques generated with the postprocessor modulus are applied to visualize the behavior of the flow in the cyclone. 3. Results and Discussion

with

( )

K1 ) 0.843 log10

φp 0.065

(20)

K2 ) 5.31 - 4.88φp

(21)

Fg|vg - vp|dp µg

(22)

and Rep )

3.1. Validation of the Model. This model was compared with data obtained under the experimental conditions presented by Zhao et al.14 Experiments were performed with air under ambient conditions, as a function of flow rate and with a dust load of 5.0 g/m3. The solid particles were talcum powder with a skeletal density of 2700 kg/m3 and a mass median particle diameter of 5.97 µm. The cyclone with a conventional tangential inlet and a body diameter of 0.3 m was studied. Because of the main purpose of the article, it is not necessary to give the full


Figure 2. Comparison of experimental grade efficiency with numerical results at different velocities.

geometries of the test cyclone here; however, complete information can be found in the reported work of Zhao et al.14 and Vegini et al.21 In our previous work, the global collection efficiency of the high solids flux inlet in the cement industry cyclone was validated with CYCLO code, which showed a deviation of 20%, and for the pressure drop, a relative error of ∼13.3% was observed. This difference seems to be caused by irregularly shaped particles and a particle size distribution, which prevents an accurate modeling of the interaction between particles of different diameters (see Meier et al.26,27). Figure 2 compares the grade collection efficiency of the numerical results obtained with the CYCLO code to that of the experimental data for different inlet velocities. As expected, the experimental and predicted efficiency of all cases increase as the particle size and entrance velocity increase. Good agreement is observed between the numerical calculation of the two-phase model and the experimental data. As can be observed, generally, the predicted results are lower than the experimental values, probably because of the model adopted for interaction between the phases, which considers only the gas-solid interaction. The influence of the solid-solid interaction in the performance of cyclones is being studied by the authors. Figure 3 shows the comparison of pressure drop as a function of inlet velocity obtained by experiments to that obtained by numerical prediction. The pressure drop is obtained with the CYCLO code, by integrating the pressure field into the inlet and outlet sections, followed by subtraction of the integrated values (in this way, calculating a macroscopic property (pressure

Figure 3. Pressure drop, as a function of inlet velocity.

drop) from a microscopic property (pressure field as a function of spatial domain)). The results are generally in good agreement, with the prediction being within 13%-25% of the experimental value. As expected, the pressure drop increases as the inlet velocity increases. In conclusion, it can be said that the CYCLO code is able to predict the performance parameters of cyclones.

196


Figure 4. Definition of cyclone dimensions.

3.2. Application of the Cyclone Tower in the Cement Industry. The cyclone dimensions used in this case study are listed in Table 1. Cyclones C4A and C4B could not be used in this study, because the CYCLO code is not prepared to predict results in situations where reactions such as calcinations occur. A schematic diagram that represents the definition of cyclone dimensions is shown in Figure 4. The cyclone dimensions are the same at each stage, for streams A and B (see Tables 2 and 3). It was assumed that all particles have the same average diameter. The average diameter of the particle was calculated using the values given in Table 4. The average diameter of the particle is given as average particle diameter )

∑ (particle diameter) ×

(% under size)

As expected, we can see that the particle diameter becomes smaller with increasing temperature (see Table 4); this is due to the volatilization of some components. The main purpose of the present study is to examine the performance of a cyclone tower (cyclone separators connected in series) in a cement industry. The performance variables of greatest concern are usually pressure drop and solid collection efficiency. The study here was conducted to present a methodology for detection of process deviation, which can be done by comparing the pressure drop obtained in the cement plant with the results of prediction with the CYCLO code. 3.2.1. Fluid Dynamic Behavior of the Two-Phase Flow. The prediction of two-phase flow with CFD techniques can be used to identify the main phenomenological characteristics of the swirling flow in cyclones. Using the numerical results obtained with the cyclone C1A for an average particle diameter of 30 µm, it is possible to visualize some microscopic information. For example, by means of visualizing the pressure field on the symmetrical r-z plane, as shown in Figure 5, it is possible to identify a low-pressure center that is responsible for the stability of the high swirling flows, which attracts the fluid in its vicinity, preventing dispersion of the swirl. Reversal of the axial flow of the gas phase in the cyclone, for the same case, can be observed in Figure 6. It is possible to

conclude that the reversal occurs within practically the entire conical section of the cyclone. This means that the natural length was respected, ensuring the flexibility and the good performance of the cyclone. In the same way, Figure 7 shows the tangential velocity field for the same conditions. Velocities close to twice the inlet tangential velocity can be found near the inlet of the vortex finder, which produces stability of the swirling flow and a large centrifugal field, hwhich is responsible for the high collection efficiency of the cyclone. Finally, all of the previously mentioned analyses were made possible only through the use of the microscopic properties of the two-phase flow predicted by CFD techniques developed in this work. 3.2.2. Pressure Drop and Collection Efficiency in the Pressure and Volumetric Fraction Fields. Figures 8-13 were obtained by numerical simulation, using the CYCLO code, and have the purpose of verifying the consistency of the results with practical knowledge, whereas the case under study represents an industrial situation with specific process conditions. For example, Figures 8 and 9 show the collection efficiency curves for cyclones for streams A and B. As expected, the collection efficiency increases as the particle size increases, and particles with a diameter of >50 µm have a collection efficiency of 100%. It can be verified that the collection efficiency of cyclone C1 is greater than those of cyclones C2 and C3, although the inlet velocity is lower for this cyclone. This type of behavior is expected in practice, because cyclone C1 is responsible for the efficiency of the process (i.e., the solid material that is lost in this cyclone will not return to the process, which causes a reduction in the efficiency of the process). The results can be explained, because other effects beyond inlet velocity (such as solid loading, temperature, and cyclone shape) also influence the efficiency of cyclones. Hoffmann et al.22 reported the effects of shape, and solids loading on the performance of cyclones, while the effect of high temperatures was studied by Patterson and Munz23 and Shi et al.24 Analyzing this information, and because the experimental results follow the same trend, it can be said that the results are qualitatively consistent. In Figures 10 and 11, the results of the effect of pressure drop for various particle diameters are presented. A reduction in pressure drop, as a function of particle size, can be observed, and the same behavior can also be observed for particles larger than ∼40 µm. The phenomenon could be due to a reduction in tangential gas velocity in the axial position near the entrance of the vortex finder, which can be seen in Figures 12 and 13. The tangential velocity is mostly responsible for the pressure drop in the cyclone, and its reduction, as a function of particle size, is due to the larger consumption of energy in the drag of larger particles. As a consequence, there is a decrease in the centrifugal field and, therefore, a decrease in the pressure drop. The primary purpose of the present study was to examine the performance of a cyclone tower in a cement industry to detect process deviation by comparing the pressure drop

Table 1. Cyclone Dimensions dimension

cyclone C1A-C1B

cyclone C2A-C2B

cyclone C3A-C3B

length of the inlet, Le (mm) length of the vortex finder, Ls (mm) length of the cylinder, Lc (mm) length of the conical section, Lco (mm) diameter of the vortex finder, DS (mm) diameter of the cyclone, DC (mm) diameter of the underflow, DL (mm) width of the inlet, b (mm)

1849.00 5490.00 5469.00 6180.00 3500.00 5701.00 865.00 3721.00

1720.00 2060.00 3660.50 5703.50 3190.00 5333.00 952.00 4244.00

1720.00 2060.00 3660.50 5703.50 3190.00 5333.00 952.00 4244.00

Ind. Eng. Chem. Res., Vol. 47, No. 1, 2008 197 Table 2. Operating Conditions: Stream A operating conditions

cyclone C1A

cyclone C2A

cyclone C3A

fluid volumetric flow rate (m3/s) inlet mean velocity (m/s) dust load (g/m3) mean temperature (°C) mean pressure (mbar)

gas with particles 121.78 17.70 471.83 460.42 873.96



Table 3. Operating Conditions: Stream B operating conditions

cyclone C1B

cyclone C2B

cyclone C3B

fluid volumetric flow rate (m3/s) inlet mean velocity (m/s) dust load (g/m3) mean temperature (°C) mean pressure (mbar)




Table 4. Particle Size Distributions % under size (mass) particle diameter (µm)

cyclone C1

cyclone C2

cyclone C3

50.00 40.00 30.00 20.00 10.00

41.59 6.28 7.92 12.36 31.85

39.99 6.56 8.81 13.14 31.50

33.20 7.60 10.40 16.10 32.70

obtained in the cement plant with the results predicted by the CYCLO code. The average pressure drop was calculated using the results obtained for each particle size, and its mass fraction is shown in Table 4. The calculated pressure drop shown in Figures 14 and 15 is the total pressure loss between the inlet and outlet sections of the cyclones studied. The comparison between the calculated and the measured pressure drops for the cyclones is presented in Figures 14 and 15. The results show that pressure drop for gas-solid flow (GasSolid-CYCLO) is higher than that for gas flow (GasCYCLO). This can be explained because the model used is based on a multifluid concept where a phase interacts with one

Figure 5. Pressure field on the r-z symmetrical plane of the C1A cyclone.

or more other phases by means of drag forces. The influence of solids loading on pressure drop has been presented in the literature by various authors.2,22,25 They observed that the pressure drop decreases when solid particles are introduced into the flow. However, the results were obtained with low solids loadings, with a maximum value of 130 g dust/m3 gas. The case under study has values of >300 g dust/m3 gas. One of the most important results obtained in this study was the detection of a process deviation that can be observed by analyzing Figures 14 and 15. The cyclones simulated in this case study are connected in series, as shown in Figure 1. Because of this geometric arrangement (see Figure 1), if one fault is detected in one of the outlet valves in the bottom of one of the cyclones, there will be a false air inlet into the system. This false air inlet will affect the fluid dynamics behavior of the cyclone and could change the conditions of the subsequent cyclone. Figures 14 and 15 show the numerical results obtained with the CYCLO code. The operating conditions were obtained from the industrial control unit system, and they represent the historical average values of unit operation during several days.

Figure 6. Axial velocity field of the gas phase on the r-z symmetrical plane of the C1A cyclone.

198


Figure 9. Collection efficiency for stream B.

Figure 7. Tangential velocity field of the gas phase on the r-z symmetrical plane of the C1A cyclone.

Figure 10. Pressure drop, as a function of particle size (stream A).

Figure 8. Collection efficiency for stream A.

The numerical results show a similar behavior for both towers. In the numerical simulation, the mass flow rate of gas through the cyclones connected in series is the same: only the conditions of temperature (T) and pressure (P) are changed. However, when the pressure decreases in both streams, which is as measured when the system showed an operational deviation with no known cause, one observes that cyclones C1 and C2 in stream B (see Figure 15) exhibit behavior that is different from the numerical results for cyclones C1 and C2 in stream A. A false air inlet causes perturbations in the fluid dynamics behavior by absorbing energy from the centrifugal field and, thus, reduces the tangential velocity profile, which is responsible for most of the pressure drop in cyclones. In addition, the measured pressure drop in cyclone C2 in stream B is smaller than the numerical value, which suggests that the false air inlet occurs in the valve located on the bottom of this cyclone. Thus, cyclone C1 will

Figure 11. Pressure drop as a function of particle size (stream B).

be affected, because it will receive all the gas from cyclone C2 (see Figure 1), and as a consequence, the increase in mass flow rate in cyclone C1 will cause an increase in pressure drop in


Figure 12. Radial profiles of tangential velocity for cyclone C1A. Figure 15. Pressure drop (average) for stream B.

This probable process deviation in the system was discovered in the maintenance of the cyclones for the company. During the inspection, a defect was detected in the valves of the cyclones for stream B. 4. Conclusions

Figure 13. Radial profiles of tangential velocity for cyclone C1B.

In the present paper, a model that is based on computational fluid dynamics (CFD) techniques was used to predict the design parameters for cyclones in a cement industry to verify the performance of a cyclone tower (cyclone separators connected in series). The cyclones have different shapes and are operated at high temperatures and with a high solids loading flow. The model was validated with experimental data on pressure drop and collection efficiency. The results obtained in this work have demonstrated the sensitivity of the model to particle size, thereby showing that the CYCLO code has considerable potential for prediction of the collection efficiency. In conclusion, it can be said that the multifluid concept adopted in this study was demonstrated to be a reliable and relatively inexpensive method of detecting process deviation. Nomenclature

Figure 14. Pressure drop (average) for stream A.

this cyclone. This can be observed in Figure 15, which shows that the measured pressure drop in cyclone C1 is larger than the simulated value. Through this investigation, one can conclude that the cyclones in stream B are operating with a false air inlet into the system.

b ) width of the inlet CD ) drag coefficient C1, C2, C, µ ) constants of the k- model D ) deformation rate tensor d ) diameter Dc ) cyclone diameter Dh ) hydraulic diameter of the inlet Dl ) “underflow” diameter Ds ) “vortex finder” diameter Fres ) resistive force f ) volumetric fraction g ) gravitational acceleration G ) source of turbulence generation h ) convective heat-transfer coefficient k ) turbulent kinetic energy l ) mixing length Lc ) cylinder length Lco ) conical length Le ) inlet length Ls ) “vortex finder” length p ) pressure

200


Pr ) Prandtl number Q ) volumetric flow rate q ) heat-transfer rate Re ) Reynolds number r ) radial direction t ) time T ) temperature Tef ) effective shear stress u ) radial velocity component V ) tangential velocity component v ) velocity vector Ven ) inlet mean velocity z ) axial coordinate w ) velocity in the z-direction Greek Letters β ) interface coefficient ) dissipation rate of turbulent kinetic energy φ ) spherical shape coefficient µ ) viscosity F ) density σ ) constant of the k- model θ ) tangential coordinate Superscripts ef ) effective property ) dissipation rate of turbulent kinetic energy k ) turbulent kinetic energy t ) turbulent property T ) shear stress tensor Subscripts g ) gas phase p ) particle r ) radial direction ref ) reference s ) solid phase z ) axial coordinate Acknowledgment The authors are very grateful to Universidade Estadual de Campinas, Universidade Regional de Blumenau, CAPES and to Votorantim Cimentos S. A., which made this work possible. Literature Cited (1) Dyakowski, T.; Williams, R. A. Modelling turbulent flow within a small-diameter hydrocyclone. Chem. Eng. Sci. 1993, 48, 1143. (2) Shepherd, C. B.; Lapple, C. E. Flow pattern and pressure drop. Ind. Eng. Chem. 1939, 31, 972. (3) Lapple, C. E. Processes use many collector types. Chem. Eng. 1951, 58, 144. (4) Barth, W. Berechnung und Auslegung von Zyklonabscheidern auf Grund neuerer Untersuchungen. Brennst. Waerme-Kraft 1956, 8, 1. (5) Leith, D.; Licht, W. The collection efficiency of cyclone type particle collectors: A new theoretical approach. AIChE Symp. 1972, 68, 196. (6) Altmeyer, S; Mathieu, V.; Jullemier, S.; Contal, P.; Midoux, N.; Rode, S.; Leclerc, J. P. Comparison of different models of cyclone prediction

performance for various operating conditions using a general software. Chem. Eng. Process. 2004, 43, 511. (7) Meier, H. F. Modelagem Fenomenolo´gica e Simulaç aõ Bidimensional de Ciclones por Tećnicas da Fluidodinaˆmica Computacional. Ph.D. Dissertation, Universidade Estadual de Campinas, Campinas-SP, Brazil, 1998. (8) Boysan, F.; Ayers, W. H.; Swithenbank, J. A fundamental mathematical modeling approach to cyclone design. Trans. Inst. Chem. Eng. 1982, 60, 222. (9) Zhou, L. X.; Soo, S. L. Gas-solid flow and collection of solids in a cyclone separator. Powder Technol. 1990, 63, 45. (10) Madsen, H. J.; Thorstensen, J. H.; Salimi, P.; Hassing, N. H.; Rusaas, J. Prediction of the performance of gas cyclones. In Proceedings of the Second CFDS International User Conference, 1994; p 211. (11) Patterson, P. A.; Munz, R. J. Gas and particle flow patterns in cyclones at room and elevated temperatures. Can. J. Chem. Eng. 1996, 74, 213. (12) Noriler, D.; Vegini, A. A.; Meier, H. F., Mori, M. Verificaç aõ e validaç aõ em CFD do escoamento girato´rio em ciclones a ga´s. In XXV Iberian Latin-American Congress on Computational Methods in Engineering, 2004. (13) Meier, H. F.; Mori, M. Anisotropic behavior of the Reynolds stress in gas and gas-solid flows in cyclones. Powder Technol. 1999, 101, 108. (14) Zhao, B.; Shen, H.; Kang, Y. Development of a symmetrical spiral inlet to improve cyclone separator performance. Powder Technol. 2004, 145, 47. (15) Gidaspow, D. Multiphase Flow and Fluidization-Continuum and Kinetic Theory Descriptions; Academic Press: London, 1994. (16) Pericleous, K. A. Mathematical simulation of hydrocyclones. Appl. Math. Modell. 1987, 11, 242. (17) Massarani, G. Fluidodinaˆ mica em Sistemas Particulados; Editora UFRJ: Rio de Janeiro, Brazil, 1997. (18) Peres, A. P.; Cremasco, M. A. Proposta de uma correlaç aõ para o coeficiente de transfereˆncia de calor ga´s-partıćula em um cyclone. XXIV ENEMP Ann. 1997, 2, 512. (19) Patankar, S. V. Numerical Heat Transfer and Fluid Flow; Hemisphere Publishing Co.: New York, 1980. (20) Maliska, C. R. Transfereˆ ncia de Calor e Mecaˆ nica dos Fluidos Computacional: Fundamentos e Coordenadas Generalizadas; LTC: Rio de Janeiro, Brazil, 1995. (21) Vegini, A. A.; Meier, H. F.; Mori, M. Four phase Eulerian-Eulerian model for prediction of multiphase flow in cyclones, In XXVI Iberian LatinAmerican Congress on Computational Methods in Engineering, 2005. (22) Hoffmann, A. C.; van Santen, A.; Allen, R. W. K. Effects of geometry and solid loading on the performance of gas cyclones. Powder Technol. 1992, 70, 83. (23) Patterson, P. A.; Munz, R. J. Cyclone collection efficiencies at very high temperatures. Can. J. Chem. Eng. 1989, 67, 321. (24) Shi, L.; Bayless, D. J.; Kremer, G.; Stuart, B. CFD simulation of the influence of temperature and pressure on the flow pattern in cyclones. Ind. Eng. Chem. Res. 2006, 45, 7667. (25) Bernardo, S.; Mori, M.; Peres, A. P.; Dionı´sio, P. D. 3-D computational fluid dynamics for gas and gas-particle flows in a cyclone with different inlet section angles. Powder Technol. 2006, 162, 190. (26) Meier, H. F.; Ropelato, K.; Forster, H.; Iess, J. J.; Mori, M. Computational fluid Dynamics (CFD) zur Berechnung und Auslegung von Zyklonen, Teil 1 (Computational Fluid Dynamics (CFD) for cyclone evaluation and design, Part 1). ZKG Int. 2002, 55 (4), 64. (27) Meier, H. F.; Ropelato, K.; Forster, H.; Iess, J. J.; Mori, M. Computational fluid Dynamics (CFD) zur Berechnung und Auslegung von Zyklonen, Teil 2 (Computational fluid Dynamics (CFD) for cyclone evaluation and design, Part 2). ZKG Int. 2002, 55 (6), 64.

ReceiVed for reView November 24, 2006 ReVised manuscript receiVed September 21, 2007 Accepted October 2, 2007 IE061501H

Computational Fluid Dynamics (CFD) - American Chemical Society

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