Cyclone as a sugar cane bagasse dryer

CYCLONE AS A SUGAR CANE BAGASSE DRYER

Jefferson L. G. Corrêa1, Daniel R. Graminho1, Maria A. Silva2 and Silvia A. Nebra3 1. Faculty of Mechanical Engineering, State University of Campinas, P.O. Box 6122, Campinas/SP, 13083-970 Brazil E-mail: [email protected] 2. Faculty of Chemical Engineering, State University of Campinas, P.O. Box 6066, Campinas/SP, 13083-970 Brazil E-mail: [email protected] 3. Faculty of Mechanical Engineering, State University of Campinas, P.O. Box 6122, Campinas/SP, 13083-970 Brazil E-mail: [email protected]

Keywords: cyclone, cyclonic dryer, sugar cane bagasse, particle residence time, dryer, energy

ABSTRACT Drying of sugar cane bagasse was theoretical and experimentally studied in a cyclone. The experiments were carried out using hot air as drying agent. The influence of the cyclone conical part was studied. It was shown that the conical part has a great influence on particle residence time and, consequently, on moisture reduction. Experimental results were better than industrial ones. CFX 4.4 from AEA Technology was used to simulate some experiments. Simulated and experimental results were close and showed that the presented model leads to a good prediction. INTRODUCTION Cyclone has been used as a gas cleaner for more than a century. Not only it is a dust collector but also it provides a good contact between solid and gas phases. Some authors reported cyclone as a heat or heat and mass transfer device (Szekely and Carr, 1966, Silva, 1991, Nebra et al., 2000, Corrêa et al., 2001). Particle residence time (PRT) is an important variable to be studied in these cases because the results obtained in the process strongly depend on it. Corrêa et al. (2002a) studied the influence of the conical part of the cyclone in PRT. They observed that cyclone conical part is relevant on PRT. In this work, drying of sugar cane bagasse was experimentally and theoretically studied in a cyclone. Experimental results were compared to a cyclonic chamber and to an industrial cyclone results. The simulations were carried out by the use of CFX 4.4 with a model that considers gas phase as a continuum and a Lagrangean scheme for particulate.

EXPERIMENTAL PROCEDURE Figure 1a shows a scheme of the cyclonic device discussed here. The different dimensions between cyclone and cyclonic chamber are the particulate outlet, B, and consequently, conical part angle, α. B is equal to 0.69m for the cyclonic chamber and equal to 0.10m for the cyclone. The dryer system is shown in Figure 1b.

0.15

1.00

α

8 B

2 Feeder 4 Electrical Conveyor Belt 5 Heater 6 Orifice Plate 8 Cotton Cloth

Figure 1a. Cyclonic Device

Figure 1b. Dryer System

Airflow rate was measured from the pressure drop across a calibrated orifice plate. An electrical heater, with controllable temperature, heated the air. Solid flow was varied using an electrical conveyor belt. Solid flow rate was measured by collecting a sample of material over a known time interval. Temperature was measured using thermocouples located before the Venturi feeder, before the cyclone inlet and at the top and at the bottom outlets of the cyclone. Thermocouples were also used to measure solid temperature before and after the experiment. Measurements of local dry bulb and wet bulb temperatures were done with a psicrometer at ambient conditions. Solid mass flow rate/gas mass flow rate was about 0.02 to 0.07. Gas inlet temperatures were between 35°C and 211°C. The studied sugar cane bagasse particles had diameter in the range 0.15mm < dp < 6.35 mm. This range was obtained with a sample that presented moisture content (d.b.) equal to 0,1236 kg/kg. The method used to measure bagasse residence time was discussed in Lede et al. (1987) and is defined as the ratio between a remaining mass of bagasse when solid and gas flows were simultaneously cut and solid mass flow rate. It is expressed by Eq. (1). PRT =

mr Wpw

(1)

Moisture reduction was calculated by Eq. (2). MR = X i - X o

(2)

MATHEMATICAL MODEL Mathematical model is composed by Eqs. (3) to (17). Conservation Equations Continuity Equation ∂ρ + ∇ ⋅ (ρu) = 0 ∂t

(3)

Momentum Equation

(

)

∂ρu + ∇ ⋅ (ρuu ) = ∇ ⋅ τ + ρu ′u ′ + ρg ∂t

(4)

where u is velocity vector, t is time, ρ is density, g is gravity acceleration, τ stress tensor and ρu ′u ′ is Reynolds tensor. Turbulence Model In this work, k-ε model (CFX Documentation, 2000) was used. Lagrangean Particle Transport Model The total flow of the particulate phase is modeled by tracking a small number of particles through the continuum fluid. Particles are treated individually. Particle-particle interactions are not considered. Momentum Equation: The equations for the change of velocity of the particle come directly from Newton 2nd Law. m

du =F dt

(5)

where F is a force acting on the particle and m is particle mass. The standard particle transport and heat and mass transfer equations are based on a totally spherical particle. All bagasse particles were considered as cylindrical ones (Corrêa et al., 2000 and Nebra, 1985) to adapt these equations to bagasse particles. Two ratio factors: cross-section factor, CSF, and surface factor, SF (Eqs. 6 and 7, respectively) were used. These two ratios relate dimensions of same volume particle and sphere.  Ap   CSF =   Asp  V 

(6)

 SA p   SF =   SA sp   V

(7)

The major component of F is the drag exerted on the particle by the continuous phase, given by:

1 FD = πd 2CSFρC D v R v R 8

(8)

where CD is given by Eq (9). CD =

(

24 1 + 0,15 Re 0,687 Re

)

(9)

Particle Reynolds number is defined by: Re =

ρ vR d µSF

(10)

where d is a sphere diameter, ρ and µ are the density and viscosity in the continuum and vR is the relative velocity of the two phases. Heat Transfer Two physical processes govern the rate of change of temperature: convective heat transfer and latent heat transfer associated with mass transfer The convective heat transfer Qc is given by: Qc =

(

πdλNu Tg − Tp

)

(11)

SF

where λ is thermal conductivity and Nu, Nusselt number, is given by 1/ 3

Nu = 2 + 0.6 Re

 C pg   µ  λ   

0.5 

(12)

The heat transfer associated with mass transfer QM is given by the relation: QM = ∑

dm Cl dt

(13)

where the sum is taken over the components of the particle (bagasse and water). The latent heat of vaporization Cl is temperature dependent through: T

(

)

Cl = Cl 0 + ∫ C p g − C p p dT T0

(14)

The rate of temperature change for the particle is then obtained from:

(

∑ mC p p

)dTdt = Q

c + QM

This sum is also taken over the components of the particle (bagasse and water).

(15)

Mass Transfer Mass transfer depends on the water vapor pressure. This is determined by the Antoine equation If the particle temperature is above the boiling point, the convective heat transfer determines mass transfer: dm Q =− c dt Cl

(16)

If the particle temperature is bellow the boiling point, mass transfer is given by: dm πdSh M vap 1− X  = log  2 dt (SF ) M g 1− Y 

(17)

The rate of mass transfer is set to zero when all the water in the particle has evaporated. NUMERICAL METHOD AND BOUNDARY CONDITIONS The numerical method used on partial differential equations calculation is finite volume co-located, coupling pressure-velocity (SIMPLE Consistent), with interpolation scheme upwind and relaxation factors. Algebraic equations are solved by AMG algorithm (Algebraic Multi-Grid) and grid generation is done with multi-blocks technique (CFX Documentation, 2000). The Boundary Conditions are: a) Uniform velocity field on Venturi feeder inlet. It is more coherent than a uniform velocity field consideration in the cyclone inlet because of the divergent pipe located before the cyclone inlet, as showed by Corrêa et al. (2002b). b) No-slip conditions to continuous phase and slip condition to particulate phase. For particulate particles, the interaction between particles and wall was a restitution coefficient. This coefficient was taken here equal to one. Griffiths and Boysan (1996) also used these considerations in a Lagrangean model; c) Null inlet particle velocity (at Venturi inlet); and d) Outlet conditions defined by pressure condition. Ambient pressure was defined and mass flux was calculed based on inner-out pressure differences. Such condition should be used when outlet velocity value is not known. There are two outlets in a cyclone and it is not interesting to fix a value in any of them. RESULTS AND DISCUSSION Experimental Results The experimental results obtained in the cyclone are shown in Table 1. In a previous work, sugar cane bagasse drying was carried out in a cyclonic chamber (Table 2). This apparatus was called in this way because it was projected to be a cyclone that provides a large particle residence time, as proposed by Dibb and Silva (1997), but the used geometry resulted in a different device. Particle residence time (PRT) was not as large as expected. Corrêa et al. (2002a) verified theoretical and experimentally that it was a consequence of the kind of gas flow. The major part of gas that enters the chamber leaves it at the bottom

part and there is a null velocity core in the cyclonic chamber center. By simulating geometry-modified apparatuses; they got the present cyclone geometry. By observing tests done in comparable Wpw/Wa and Tai in these cyclonic devices (test 2, Table 1 to test 1, Table 2; test 3, Table 1 to tests 2 and 4, Table 2), one can see that the conical part modification resulted in a improved dryer. This modification is responsible by large PRT and large moisture reduction. Particle outlet temperatures (Table 1) are nearby adiabatic saturation temperature of outlet gas. This shows that the removed moisture corresponds to unbounded moisture. Nebra (1985) presented bagasse-drying data obtained in an industrial cyclone using similar conditions to these used here. In the present paper, the achieved moisture reduction is greater than Nebra’s industrial one. Table 1. Experimental results for sugar cane bagasse drying obtained in the cyclone Test Wpw/Wa x102 [-] 1 2.56 2 2.30 3 6.87 4 7.24 5 7.65 6 3.13

Wax102 [kg/s] 7.93 7.78 9.53 9.56 9.54 9.57

Tai [°C] 211 209 216 35 35 36

Tao Yix102 Yox102 [°C] [kg/kg] [kg/kg] 113 2.0 3.4 105 2.1 3.3 98 2.2 4.8 31 2.2 2.6 28 2.2 2.6 30 2.2 2.3

Tpi [°C] 27.9 25.1 30.6 27.3 27.3 27.3

Tpo Xi [kg/kg] [°C] 44.0 3.4471 41.0 3.4471 43.8 3.2000 27.3 2.0474 27.3 2.0474 27.3 2.0474

Xo [kg/kg] 0.9086 0.9373 1.5569 1.8393 1.8809 1.8929

MR [kg/kg] 2.5385 2.5098 1.6431 0.2081 0.1665 0.1545

PRT [s] 20.08 23.44 7.57 7.04 9.51 15.20

Table 2. Experimental results for sugar cane bagasse drying obtained in cyclonic chamber (Correa et al., 2001) Test Wpw/Wa Wax102 Tai Yix102 x102 [-] [kg/s] [°C] [kg/kg] 1 2.2 1.63 7.40 224 2 2.3 5.59 7.56 224 3 74 2.4 3.50 8.18 4 2.3 5.86 7.47 224

Yox102 [kg/kg] 2.9 4.0 2.7 3.9

Wpwx103 [kg/s] 1.21 4.23 2.86 4.38

Tpi [°C] 28.0 27.5 29.0 27.5

Tpo Xi [°C] [kg/kg] 42.0 2.1906 42.0 1.5256 30.0 1.8457 41.0 1.5256

Xo MR PRT [kg/kg] [kg/kg] [s] 0.7611 1.4295 1.92 0.7205 0.8051 0.82 1.6274 0.2183 1.25 0.7857 0.7399 0.84

SIMULATED RESULTS Tests 3, 4 and 6 from Table 1 were also simulated using CFX 4.4. The Lagrangean model used is based in an individual particle treatment and gives each individual particle results. The results of test 3 for each different bagasse size particle are presented in Table 3. Table 4 shows final moisture and temperature average results. The final moisture result of each experiment corresponds to an average based on the inlet mass fraction. The results presented in Table 4 are nearby the experimental ones. Experimental PRT (particle residence time) is certainly a mean measurement. Table 4 presents average simulated PRT based on inlet particle mass fraction and on remained particle mass fraction. Even though the results based on this last consideration fit better experimental results, they are not so different from that based on inlet mass fraction. Because of the individual particle treatment, results of simulated PRT were different from experimental ones. PRT is strongly dependent on solid volumetric concentration and this fact is not taken in account in a Lagrangean model. The present model considers the wall of the equipment as insulated. Because of this, the simulated Tpo were higher than experimental ones (Tables 1, 3 and 4). Figure 1b shows that bagasse particles get in touch with hotted air in the Venturi feeder. Therefore, gas-particle flow was simulated from the Venturi inlet. Table 4 also shows simulated results in the horizontal duct from Venturi feeder to the cyclone. These simulations allow quantifying drying in this distance. Even though there is a great particle velocity gradient in this distance, the correspondent particle

residence time is not so significant and, because of this, almost all the drying seems to occur in the cyclone. Table 3. Drying Simulation Results of Test 3, Table 1 dpx10-3 [m] 6.35 2.75 0.84 0.42

Mass fraction [kg/kg] Tpo [°C] 0.091 0.022 0.872 0.014

62 62 62 209

PRT [s] 25,60 9,84 1,88 3,05

Xo [kg/kg] 2.3670 1.9940 1.6596 0.0009

Table 4. Average Drying Simulated Results Test 3 4 6 *

Only Horizontal Duct Xo [kg/kg] Tpo [°C] 56 3.0684 31 2.0428 31 2.0428

Tpo [°C] 64 30 30

Xo [kg/kg] 1.7081 2.0125 1.9952

All over the system PRT*[s] PRT**[s] 4,24 4,08 4,36 4,64 5,79

Average value based on inlet particle mass fraction. ** Average value based on remained solid mass fraction

CONCLUSIONS The great difference in moisture reduction (MR) and in particle residence time (PRT) between a drying carried out in the cyclone and in the cyclonic chamber shows that the conical part is very relevant in a cyclone reactor. The present model gives a satisfactory prediction of MR and PRT in a cyclone. Almost all the MR that occurs in the presented drying system happens in the cyclone. Some improvements, as the consideration of heat losses, particle-particle interactions, among others, will be performed in a further work. NOTATION Latin Letters A Projected area B Cyclonic device outlet diameter Cl Vaporization Latent Heat Cp Specific heat d Diameter m Mass M Molar Mass MR Moisture reduction P Pressure PRT Particle residence time SA Superficial area Sh Sherwood number T Temperature V Volume W Mass flow rate X Moisture content (dry basis) Y Gas humidity

m2 m J/K J/kgK m kg kg/kmol kg/kg Pa s m2 °C m3 kg/s kg/kg kg/kg

Greek Letters Cyclone conical part angle α Subscripts a wet air B dried air d Dried i Inlet o Outlet p Particle sp Sphere r Remained solid vap Vapor w Wet

grade

ACKNOWLEDGMENTS The authors wish thank “Usina Ester” Sugar Industry for the given sugar cane bagasse, Profa. Dra. Meuris Gurgel Carlos da Silva and Profa. Dra. Katia Tannous for the lent sieves and CNPq and FAPESP for the financial support. LITERATURE CFX 4.4 Documentation – Solver (2000), AEA Technology – United Kingdom - in CD-rom Corrêa, J. L. G., Chamma, M. O., Godoy, A. L., Silva, M. A., Nebra, S. A. (2001), Experimental Study of Drying and Residence Time of Sugar Cane Bagasse in Cyclonic Devices. Proceedings of the Second Inter-American Drying Conference, 2001, Boca del Rio, Veracruz, México, pp.407-414. Corrêa, J. L. G., Peres, A. P., Graminho, D. R., M. O., Pacífico, A. L., Godoy, A. L., Silva, M. A., Nebra, S. A. (2002), Analysis of flow in a particle Venturi feeder. Submitted to XIV Brazilian Congress of Chemical Engineering (COBEQ 2002) August 25-28, 2002, Natal, RN, Brazil. Corrêa, J. L. G., Rios, M. T. T., Nebra, S. A. (2000), Sugar cane bagasse caracterization and study of feed system. Proceedings of National Conference of Mechanical Engineering (Conem 2000), Mechanical Systems Project Section, p. 251-258 (in Portuguese). Corrêa, J. L.G., Graminho, D. R., Silva, M. A., Nebra, S. A. (2002), Cyclonic Reactor – Analysis of Conical part influence on particle residence time. Submitted to Second International Conference on Computational Fluid Dynamics, July, 15-18, 2002 Sydney, Australia. Dibb, A., Silva, M. A. (1997), Cyclone as a dryer – the optimum geometry, Proceedings of the First InterAmerican Drying Conference (IADC), B, pp. 396-403. Griffiths, W. D., Boysan, F. (1996), Computational fluid dynamics (CFD) and empirical modeling of the performance of a number of cyclone samplers. Journal of Aerosol Science, Vol. 27, no. 2, pp. 281-304. Lede, J., Li, H. Z., Soulignac, F., Villermaux J. (1987), Measurement of solid particle residence time in a cyclone reactor: a comparison of four methods, Chemical Engineering Process, Vol. 22, pp. 215 - 222. Nebra, S. A. (1985) Pneumatic drying of sugar cane bagasse PhD Thesis, FEM/UNICAMP, Campinas (SP). (in portuguese) 121 pp. Nebra, S. A., Silva, M. A., Mujumdar, A.S. (2000), Drying in cyclones - a review, Drying Technology, Vol. 18, no.3, pp.791-832. Silva, M. A. (1991), Study of drying in cyclone. PhD Thesis, FEM/UNICAMP, Campinas (SP). (in portuguese) 146 pp. Szekely, J., Carr, R. (1966), Heat transfer in a cyclone, Chemical Engineering Science, Vol. 21, pp.11191132.