Experimental Study and Advances in 3-D Simulation of Gas Flow in a Cyclone Using CFD

European Symposium on Computer Aided Process Engineering - 12 J. Grievink and J. van Schijndel (Editors) ® 2002 Elsevier Science B.V. All rights reserved.

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Experimental Study and Advances in 3-D Simulation of Gas Flow in a Cyclone Using CFD A.P. Peres\ H.F. Meier^ W.K. Huziwara\ M. Mori^ ^ School of Chemical Engineering, UNICAMP, P.O. Box 6066, 13081-970, Campinas-SP, Brazil, E-mail: [email protected] ^ Department of Chemical Engineering, FURB, P.O. Box 1507, 89010-971, Blumenau-SC, Brazil. E-mail: [email protected] ^ PETROBRAS, CENPES, Rio de Janeiro-RJ, Brazil.

Abstract Experimental results and a 3-D simulation of gas flow in a cyclone are presented in this work. Inlet gas velocities of 11.0 m/s and 12.5 m/s and measurements of local pressures were used to determine radial distributions of the tangential velocity component at five axial positions throughout the equipment. The aim of this work was to analyze an anisotropic turbulence model, the Differential Stress Model (DSM). First and higher order interpolation schemes and a numerical strategy were used to assure stability and convergence of the numerical solutions carried out using the computational fluiddynamics code CFX 4.4. The models showed a satisfactory capability to predict fluid dynamics behavior since the calculated distribution of velocity components match the experimental results very well.

1. Introduction Cyclones, such as those in FCC units, have been used as solid particle separators in large-scale chemical processes, due to their low building and maintenance costs and the fact that they can be used under severe temperature and pressure conditions. The design of new cyclones and the analysis of the actual equipment can be achieved using computational fluid dynamics (CFD) techniques in order to obtain higher collection efficiency and a lower pressure drop. In our recent studies, Meier and Mori (1999) and Meier et al. (2000), the models analyzed were the standard k-e, RNG k-e and the Differential Stress Model (DSM) and it was observed that turbulence models based on the assumption of isotropy, such as standard k-e and RNG k-e, were inapplicable to the complex swirling flow in cyclones. On the other hand, whenever a turbulence model that considers the effect of the anisotropy of the Reynolds stress is used, such as DSM, an adequate interpolation scheme must also be considered for the prediction of flow in cyclones. In this work, a 3-D simulation of the turbulent gas flow in the cyclone was carried out using the computational fluid-dynamics code CFX 4.4 by AEA Technology. The numerical solutions were obtained with a fmite-volume method and body fitted grid generation aiming at the analysis of an anisotropic turbulence model (DSM) using first and higher order interpolation schemes. The numerical strategy adopted assured stability and convergence of the numerical solutions.

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2. Mathematical Modeling The time-averaged mathematical models along with the Reynolds decomposition governing mass and momentum transfers can be written as follows:

V. (pv) = 0

at

a(pv) -

^

—

(1)

_ (2)

+ V.(pvv) = pg + V. ( a - p v V )

The last term of Equation (2), pv'v', is a time-averaged dyadic product of velocity fluctuations and is called Reynolds stress or turbulent stress. Some difficulties are faced in relating the dyadic product of velocity fluctuations with the time-averaged velocities. In the literature this kind of problem is known as "turbulence closure," and it is still considered an open problem in physics. 2.1 Turbulence Model In engineering applications, there are two types of turbulence models. One is known as the eddy viscosity model, which assumes the Boussinesq hypothesis. Reynolds stress is related to time-averaged properties as strain tensor is related to laminar Newtonian flow. This model neglects all second-order correlations between fluctuating properties that appear during the application of the Reynolds decomposition procedure. The other is known as second-order closure, whereby Reynolds stress is assumed to have anisotropic behavior and also needs to predict the second-order correlation. The model used in this work, the Differential Stress Model (DSM), is known as secondorder closure and has one differential equation, or transport equation, for each component of Reynolds stress. These can generally be expressed by the following differential equation:

a(pvv) at

[

^

1

-T-

V.(pvVv) = V. p - ^ - v ' v ' ( V v V )

+ P-(t)—pel

(3)

in which P is a shear stress production tensor and is modeled as

p = -p r r v'v'(vv)%(vv)v'v'] 1

^^^

and (^ is the pressure-strain correlation given for incompressible flow defined as 0 = (^,+(^2

(5)

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i=-pC,s- v'v'—kl k 3

2 = - C ,

2 ^ P—PI ' 3

(6)

(7)

P in this case is the trace of P tensor and Cs(0.22), ODSCIO), CIS(1.8) and C2s(0.6) are the model's constants (Lauder et al., 1975). It is also necessary to include an additional equation for the dissipation rate of turbulent kinetic energy that appears in Equation (3), and this is written:

a(pe) + V.(pve) = V. p - ^ - ~ ( v ' v ' ) V e + Q - P - C 2 P — a' e ^ ^ at

(8)

in which Ci(1.44), C2(1.92) and k are obtained direcdy from its definition (k = l/2 v ' ' ) . 2.2 Numerical Methods In a general form, the numerical methods used to solve the models were the finite volume methods with a structured multiblock grid, generated by the body fitted on a generalized coordinate and collocated system. The pressure velocity couplings were the SIMPLEC (Simple Consistent) and PISO algorithms with interpolation schemes of first order, upwind and higher order, QUICK, Van Leer, CCCT and higher upwind. The Rhie Chow algorithm with the AMG solver procedure was also used to improve the solution and to avoid numerical errors like check-boarding and zigzag due to the use of collocated grids and numerical errors caused by no generation of orthogonal cells during the construction of structured grids, for more details on methodologies see Maliska(1995). The boundary conditions were uniform profiles at the inlet for all variables; no slip conditions at the walls; continuity conditions for all variables at the outlet, except for pressure where an open circuit condition with atmospheric pressure conditions were assumed. A laminar shear layer condition was also assumed for the wall with default models from the CFX 4.4 code.

3. Results The experimental study was conducted in an acrylic cyclone settled in a pilot unit belonging to Six/Petrobras in Sao Mateus do Sul, Brazil. The inlet velocities of clean air were 11.0 m/s and 12.5 m/s and the measurements of local pressures obtained with a Pitot tube were used to determine the radial distributions of the tangential velocity component at five axial positions throughout the equipment (two in the cylindrical section, 0.90D and 1.35D from the cyclone roof, and three in the conical section, 2.39D, 3.36D and 4.32D from the cyclone roof). The peak of the tangential velocity like a

946 Rankine curve typical of flows in cyclones was obtained. The grid used in the numerical simulations had about 72,500 cells. The experimental cyclone configuration and a typical 3-D grid are shown in Figure 1. Initially, the numerical solutions were obtained applying the upwind scheme for all variables to guarantee stability of the solution (one of the criteria adopted was a value of less than 10' for the euclidean norm of the source mass in the pressure-velocity coupling), but the results exhibited high numerical diffusion, as previously reported in the literature (Meier et al., 2000, Witt et al., 1999). The first solutions with upwind scheme were used as initial conditions. A higher order interpolation scheme was then introduced for the velocity components using a transient procedure. This has been found useful to overcome the difficulties of convergence presented by the DSM with higher order interpolation schemes. Nevertheless, it was observed that the steady state was achieved after about 1 second of real time. Numerical solutions were obtained for the inlet gas velocities (11.0 m/s and 12.5m/s) at five different heights and the behavior of the higher order schemes were all similar (higher upwind, QUICK, CCCT and Van Leer). More details of the interpolation schemes can be seen in Guidelines of CFX 4.4 (2001). Figure 2 shows the numerical solutions obtained for the inlet gas velocities of 11.0 m/s and 12.5 m/s and using the higher upwind scheme to illustrate the experimental data and the numerical results. Data obtained on the capability of the turbulence model to represent the radial distributions of tangential velocities throughout the cyclone was compared with the experimental data, and it was possible to verify a good agreement, especially for the velocity in the cylindrical section of the cyclone. In the conical section, the numerical results of tangential velocity were overpredicted, probably because of the imperfections in the acrylic surface of the conical section of the cyclone, which became evident during the experiments.

QM)

A afl)

Figure 1 - 3-D grid and geometrical dimensions of the cyclone.

947 ,.

30-

f'*

•

. -

\

25-

•-V

- •--

20-

15 -

•

•

*

.

.

.

,

h r 0 90D experimental simulated V|j=11m/s

/

25-

•

•

- - - - simulated v^=12 5m/8

/

35-

-

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30-

25-

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20-

/-

15-

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20-

i

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• " " ' • • • - - . , . . - . .

•;

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h = 1.35D • experimental . . . . . . . . simulated

.1

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h X 0 90D

-

,-^..,

30-

,''

-V "

«i

m'

V|j=11 m/s

h = 1.35D • experimental -••—•- simulated v^=12 5 m / s

5-

—

_

_

,

• — ^

J

_J

,

_

0-

^

,

1

3

/ h = 2.39D • experimental ——— simulated

•

-

h = 2.39D experimental

:

v„=12 5 m / s

,

_ .....--

35 -

25-

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,.

30• • • - . ,

25-

• • . . .

• .

"

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•

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1510-

h = 3.36D • experimental -—•-•- simulated v^= 11 m/s

5-

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• h = 3 36D • experimental . . . . . . . . simulated v ^ = 12.5m/8

]

30-

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20-

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15-

10-

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h = 4 32D experimental - simulated v^=1 i m / s

....

.,

i-, ,

. •

Figure 2 - Distributions of tangential velocity in the cyclone.

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4. Conclusions The Differential Stress Model (DSM) with higher order interpolation schemes (higher upwind, QUICK, CCCT and Van Leer) showed great capability to represent the swirling flow in the cyclone, and no significant difference was observed between the higher order schemes used. Higher order schemes avoid numerical diffusion but introduce instability and convergence difficulties that can be minimized by using appropriate solution procedures. Transient procedure used in this work had been found useful to overcome these difficulties.

5. References Guidelines of CFX 4.4 User Guide, 2001, AEA Technology. Lauder, D.E., Reece, GJ., Rodi, W., 1975, Progress in the Development of a ReynoldsStress Turbulence Closure, J. Fluid Mech., 68, 537-566. Maliska, C , 1995, Transferencia de Calor e Mecanica dos Fluidos Computacional. LTC Editora, Rio de Janeiro, Brasil, 424p. Meier H.F., Mori M., 1999, Anisotropic Behavior of the Reynolds Stress in Gas and Gas-Solid Flows in Cyclones, Powder Technology, 101, 108-119. Meier H.F., Kasper, F.S., Peres, A.P., Huziwara, W.K., Mori, M., 2000, Comparison Between Turbulence Models for 3-D Turbulent Flows in Cyclones, Proceedings of XXI CILAMCE, 18p., Rio de Janeiro, Brasil. Witt, P. J., Mittoni, L.J., Wu, J. and Shepherd, I.C. 1999, Validation of a CFD Model for Predicting Gas Flow in a Cyclone, Proceedings of CHEMECA99, Australia. Acknowledgments The authors are grateful to PETROBRAS for the financial support that makes this work possible and to Eng. Alexandre Trentin from Trentin Engenharia for his help in the experimental study in the cyclone at SIX/PETROBRAS. Nomenclature D diameter of the cyclone g gravity acceleration I identity tensor k kinetic turbulent energy p pressure P shear stress production tensor P trace of the tensor P t time V velocity vector w tangential velocity component e dissipation rate of turbulent kinetic energy ({) pressure strain correlation ^ viscosity p density a stress tensor Superscripts mean time-averaged property fluctuation property T transpose tensor or matrix