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CFD MODELLING OF FLUIDIZED BED SYSTEMS

Kari Myöhänen, Vesa Tanskanen, Timo Hyppänen, Riitta Kyrki-Rajamäki

Lappeenranta University of Technology, P.O.Box 20,

FI-53851 Lappeenranta, Finland

kari.myohanen@lut.fi, vesa.tanskanen@lut.fi, timo.hyppanen@lut.fi, riitta.kyrki-rajamaki@lut.fi

Abstract: Gas-solid fluidized bed systems are used for various purposes, such as for

energy production and in petrochemical processes. Because of the high volume

fraction of the solid phase, the fluid dynamics of the solids have a major effect on

mixing of reactants and the performance of the overall processes. The fluidized bed

systems can be simulated by computational fluid dynamics (CFD), but the

complicated processes set limits for the modelling. This paper presents the current

status of CFD modelling capabilities and modelling examples.

Keywords: modelling, multiphase, computational fluid dynamics, FCC, CFB

1 INTRODUCTION

The advantages of gas-solid fluidized beds are

numerous, for example: fluidization of particles

enables controlled handling of solids; good solids

mixing and the large thermal inertia of solids produce

nearly isothermal conditions; heat flow and reaction

rates between gas and solids are high due to large

gas-particle contact area; heat transfer from

suspension to heat exchanger surfaces is enhanced by

the solids; constant movement of particles and the

large interparticle forces enable operation close to

melting temperature of solids. Hence, the fluidized

beds are used for gasification, combustion, catalytic

cracking and various other chemical and

metallurgical processes.

The fluid dynamics of solids have a large effect on

various phenomena, such as the mixing of different

reactants and heat transfer. Thus, as a starting point

for a more comprehensive model, first the fluid

dynamics of the solids would have to be modelled

correctly. Because of large volume fraction of solids,

the best alternative is usually the Eulerian approach,

in which different gas and solid phases are treated as

interpenetrating continua and momentum and

continuity equations are defined for each phase.

Bubbling fluidized beds have been modelled with

relatively good results, but modelling of circulating

fluidized bed (CFB) applications remains to be a

challenge (Arastoopour, 1999; van Wachem et al.,

2001; Cruz et al., 2002). The following article

concentrates on hydrodynamic modelling of CFB

applications. The paper presents the theories and

software for multiphase modelling. Modelling

examples are presented, which show the challenges

and possibilities of the CFD modelling.

2 FLUIDIZED BED APPLICATIONS

The following presents two examples representing

circulating fluidized beds: fluid catalytic cracking

and circulating fluidized bed combustion.

The fluid catalytic cracking (FCC) is used for

converting crude oil into a variety of higher-value

light products, such as gasoline (Fig. 1). Hot catalyst

(650 – 700 °C) flows from the regenerator to the

3 EULERIAN MULTIPHASE MODELLING bottom of the riser and meets the liquid feed, which

is vaporized. The mean size of the FCC particles is

about 40 – 80 µm and particle density 1100 – 1700

kg/m3, representing Geldart group A. Inside the riser,

the feed vapor is cracked by the catalyst. Fluidization

velocity in the riser is 6 – 28 m/s, increasing towards

top due to molar expansion. The net solids flow is

400 – 1200 kg/m

3.1 Modelling theories

Substantial development of multiphase CFD

techniques occurred in late 1970’s. In 1975, Harlow

and Amsden introduced a numerical method called

IMF – Implicit MultiField solution method (Witt,

1997). On the other field, Spalding (1981) proposed

an extension to the SIMPLE (Semi-Implicit Method

for Pressure-Linked Equations) algorithm of Patankar

and Spalding (1972). This method is called IPSA

(Inter-Phase Slip algorithm) and is used in many

multiphase codes like Phoenics and CFX (Witt,

1997). Also, some other SIMPLE modifications have

been used, such as PC-SIMPLE in Fluent (Fluent

manual 2001) Table 1 lists properties of different

solution methods.

2

s. At the top of the riser, the

catalyst is separated from reaction products and

returned back to regenerator.

For the continuum equations, following set of

equations is used in most of the models (van

Wachem et al., 2000):

()

()

solidsfor

t

gasfor

t

ss

s

gg

g

0

0

=⋅∇+

∂

∂

=⋅∇+

∂

∂

v

v

α

α

α

α

(1)

, where α is volume fraction and ‘g’ and ‘s’ denotes

gas and solid phases. Moreover, α

g

+ α

s

= 1, has to be

satisfied.

Fig. 1. Side-by-side FCC unit (King, 1992).

The continuity equations are basic physics, but

several different approaches exist for the phase

momentum equations. According to Witt (1997), the

three most common models can be classified as

• Model A: Pressure drop shared between phases

(Ishii, 1975; Harlow and Amsden, 1975)

• Model B: Pressure drop in gas phase only.

(Anderson and Jackson, 1967)

• Model C: Relative velocity model.

(Gidaspow 1978,1994)

In bare form, the model A has been considered as ill-

posed and the model B well-posed. However,

addition of viscosity or extra terms, such as granular

pressure, lift force and virtual mass, can make the

model A well-posed. It is not well known what

combined effects these terms have, and often the

main interest of codes has been in granular pressure

term (Witt, 1997). Confusingly, in the current CFD

models, there are two typical sets of governing

equations; by Jackson (1997) or by Ishii (1975)

(Table 2). The difference is not anymore clearly in

the pressure drop, but in the fluid stress-strain tensor

effect on the granular phase. In Eqs. (2) - (3), β is

drag coefficient, P

Fig. 2. CFB boiler (EC Chorzów Elcho, adapted from

Foster Wheeler reference material).

In a circulating fluidized bed boiler (Fig. 2), the

fluidization velocity is typically about 5 m/s at full

load. The solids are coarser and denser than in FCC,

particle size 100 – 300 µm and particle density 1800

– 2600 kg/m

3

(Geldart group B). The fuels used in

CFB combustion include coal, oil shale, petroleum

coke, lignite, wood, biomass and different wastes.

Typical furnace temperatures are 800 – 900 °C and

net solids flow in furnace 10 – 100 kg/m

2

s.

s

is granular pressure and

τ

is

stress-strain tensor. It seems that most of the codes

use Ishii (1975) type equations, but especially stress

terms may be handled differently.

Table 1. Commonly used solution algorithms.

IMF IPSA Other SIMPLE extensions

Properties -Point-relaxation iterative

technique

-Volume fractions solved from individual

phase mass conservation equations

PC-SIMPLE:

-Volume fractions are obtained from phase

continuity equations.

-Pressure and phase coupling

terms treated implicitly

-Pressure correction equation derived from

global mass conservation

-Velocities are solved coupled by phases,

but in a segregated fashion. Velocities are

solved simultaneously for all phases.

-Convective, viscous and

body force terms treated

explicitly

-PEA (partial elimination algorithm) is

used in implicit solution of interphase

coupling terms.

-Pressure correction equation is based on

total volume continuity. Pressure and

velocities are corrected to satisfy the

continuity constraint.

-As in SIMPLE, convective and diffusive

fluxes are handled implicitly and variables

have to be relaxed.

Software K-FIX CFX,PHOENICS,STAR-CD, FLUENT4 Fluent (PC-SIMPLE),

MFIX (extension)

Table 2. Momentum equations.

Jackson (1997)

()

()

gvvvv

v

gvvvv

v

sssgs

s

s

g

sss

s

ss

ggsgg

g

ggg

g

gg

PP

t

P

t

ραβτατααρ

ραβατααρ

+−+∇−⋅∇+∇−⋅∇=

⎥

⎦

⎤

⎢

⎣

⎡

∇+

∂

∂

+−−∇−⋅∇=

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

∇+

∂

∂

(2)

Ishii (1975)

()

()

gvvvv

v

gvvvv

v

sssgs

s

sss

s

ss

ggsgg

g

ggg

g

gg

PP

t

P

t

ραβτααρ

ραβατααρ

+−+∇−⋅∇+∇−=

⎥

⎦

⎤

⎢

⎣

⎡

∇+

∂

∂

+−−∇−⋅∇=

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

∇+

∂

∂

(3)

3.2 Codes for multiphase modelling

Of the dozens of different CFD software packages

only few include possibility for Eulerian multiphase

modelling. The following is a list of codes most

commonly referenced in the literature:

• Phoenics (www.cham.co.uk)

• Fluent (www.fluent.com)

• CFX (www.ansys.com)

• Star-CD (www.cd-adapco.com)

• Estet-Astrid (www.simulog.fr)

• MFIX (www.mfix.org)

It is possible to implement user defined modifications

to any of these codes. The following presents only

the originally programmed features.

Phoenics was released in 1981 and it can be

considered as a prototype code for many of the later

CFD softwares. Phoenics uses IPSA algorithm and

solves type A momentum equations, but IPSA has

been implemented for two phases only. According to

Muehlbauer (2004), Phoenics uses so called drift-flux

method for more than two phases having the same

range of properties.

Fluent was launched in 1983, but the multiphase

models have been more developed in the later

versions only. Eulerian multiphase modelling with

more than two phases, including granular material,

can be calculated. For the pressure-velocity coupling,

Fluent uses Phase Coupled SIMPLE algorithm.

Kinetic theory is applied and the momentum equation

of granular phase is of Ishii (1975) type A, where

viscosity, granular temperature and lift force can be

included. For fluid-solid momentum exchange

coefficient, Fluent offers Syamlal-O’Brien and

Gidaspow models for granular modelling. For dilute

systems, Wen and Yu model can be used as well. For

solid-solid momentum exchange coefficient Syamlal-

O’Brien-symmetric model can be used. Fluid-fluid

momentum transfer can be calculated using Schiller-

Naumann or Morsi-Alexander exchange coefficients.

Granular temperature is an important factor in

calculation of granular viscosities. Differential

equation for granular temperature is possible, but due

to convergence problems, the simplified algebraic

form is useful. For granular kinetic part of viscosity,

Syamlal-O’Brien and Gidaspow models can be used,

and for the frictional part, Schaeffer’s expression is

available. Lun et al. expressions can be used for

granular bulk viscosity, solids pressure and radial

distribution function.

For turbulence modelling Fluent offers, in multiphase

cases, k-ε-models (Standard, RNG, realizable) and

now also Reynolds Stress model. In these k-ε-

models, turbulence can be modelled by ‘mixture’,

‘dispersed’ or ‘k-ε per phase’ models. In the

dispersed model, k-ε-equations are solved for the

primary phase and Tchen’s theory is used for the

dispersed phases. (Fluent manual 2001).

The commercial version of

CFX was published in

1990. The version CFX 5 was based on unstructured

mesh and later, when ANSYS Inc. bought CFX, the

name was changed to ANSYS CFX. CFX uses IPSA

method as solution algorithm. Model A equations

(+additional terms) are solved and kinetic theory is

applied for granular flows. There are no restrictions

in the amount of phases. Furthermore, for the

dispersed phases, a so called MUSIG (Multiple Size

Group) scheme is applicable for bubbly flows.

According to Muehlbauer 2004, the single-phase k-

ε- and Reynolds Stress models are generalized to

multiphase situation (at least in CFX-4). As some

additional implementations; optional Sato’s model is

available for bubble-induced turbulence, turbulent

dispersion force exists for phasic momentum

equations, and optional turbulent diffusion term is

available for phasic continuity equations. In May,

2006, Ansys bought the Fluent Inc., which is likely to

cause changes to these two codes.

STAR-CD applies IPSA algorithm in multiphase

calculations and the momentum equation for a phase

is according to Ishii (1975). At the moment, the

Eulerian model in STAR-CD allows only two phases,

but the extension to multiple phases is in progress.

According to Muehlbauer (2004), turbulence is

modelled based on high Reynolds number k-ε-model.

Modified k-ε-equations are solved for the continuous

phase and the dispersed phase turbulence is

correlated using semi-empirical models. Particles

effects on turbulence field are taken account by

additional terms.

Simulog/

Estet-Astrid, N3S and many other codes

allow Eulerian multiphase calculations as well, but in

this survey it is not possible to examine these

packages in more details.

MFIX (Multiphase Flow with Interphase

eXchanges), developed at the National Energy

Technology Laboratory (NETL), has been used for

CFB simulations and as a test-stand for multiphase

equations (Benyahia

et al., 2006). The code itself is

based on a generally accepted set of multiphase

equations. In kinetic theory, modified Princeton

model is used.. Syamlal-O’Brien and Gidaspow

models exist for the drag correlation for fluid-solid

momentum transfer. Additionally, Wen-Yu

correlation (dilute case) and Hill-Koch-Ladd

correlation are available. The latter one is valid for

one solid phase only. For solid-solid momentum

exchange coefficient Syamlal-O’Brien-symmetric

can be used. MFIX documentation informs that Yu-

Standish correlation (multi-component) and Fedor-

Landell correlation (binary mixture of powders) are

available for calculation of solids maximum packing

in polydisperse systems. For heat transfer coefficient,

Gunn correlation is applied for Nusselt number in

granular phase. The turbulence model in MFIX is

quite similar to dispersed k-ε-model in Fluent. For

turbulence interaction terms, Simonin’s and

Ahmadi’s models are optional in that model. For

calculation of granular temperature, differential and

algebraic equations are available. However, the

turbulence kinetic energy ‘k’ for granular phase is

replaced by the granular temperature, which forms

still a differential equation. For the granular

quantities like solids pressure, viscosities and

granular conductivity, Simonin and Ahmadi

expressions are optional. For frictional viscosity,

Schaeffer or Princeton models are available.

3.3 Common problems in Eulerian modelling

Axial density or velocity profiles are not realistic

with current drag models.

According to Kallio

(2005), the CFD simulations underpredict the solids

concentration in the bottom region of a CFB. Kallio

mentions, that this is due to underestimation of the

average slip velocity and overestimation of the

average gas-solid drag force. These problems are

results of mismatch between the computational mesh

size and the assumption of homogenous conditions

inside of each control volume. Kallio obtained better

results by using a simple drag model based on Ergun

(1952) and modified Poikolainen (1992) models. In

this model, some empirical correlations are needed to

calculate the ratio of the slip velocity to the terminal

velocity, but this term is not very sensitive.

Ibsen

et al. (2000) noted that two-phase modelling is

not able to capture the hydrodynamic behaviour of

particles with different diameters. Ibsen

et al,

obtained more realistic results, especially in dilute

conditions, by increasing the amount of solid phases

of different particle diameters. In the simulations of

multiple phases, the major drawback is the

simulation time, which increases steeply when the

amount of phases increases.

Simulation times are long, convergence is poor

and stability problems occur when multiple

phases exist.

Convergence problems and long

computing time make large scale simulations with

more than two phases very challenging. At the

beginning of a simulation, some of these problems

can be reduzed by using small under-relaxation factor

for the volume fraction, and trying to avoid zero

volume fractions as an initial condition. In close-to-

symmetrical cases, 2D-results can be used for

initialization of 3D-problems, which may reduce the

required stabilization time. Mixture based models can

be used as initialization tools before starting real

Eulerian calculations, but these mixture models may

not work properly with dense and large particle

phases. A quite clear solution would be to reduce the

time-step size below the characteristic time of flow,

but this makes 3D simulations of large scale units

practically impossible. Furthermore, because of flaws

in current granular models and numerical schemes,

sudden divergences can be possible even with a very

small time-step.

4

EXAMPLE STUDY

Figure 2 presents a schematic diagram of the studied

furnace and Table 3 lists the main boiler data. The

fuel is fed to four feeding points at the front wall and

three points at the back. Circulating bed is fluidized

by primary air through the grid. Secondary air is

introduced at level 2 – 4 m from grid. From the

furnace, the gas and solids enter the separator, which

separates the solids from flue gas. The separated

solids flow to internal heat exchanger units

(INTREX). Part of the bed material enters the

INTREX units directly from furnace. From the

INTREX units, the bed is returned back to furnace.

Fig. 4. Model geometry in 3D-calculations.

Table 3. Boiler data.

Capacity (electr., thermal) 102 MWe, 250 MWth

Furnace dim.ensions 14.3 m × 6.7 m × 43.8 m (w×d×h)

Fuel Subbituminous coal

In each case, the model was first calculated without

fuel feeding in order to establish stable process

conditions. This could take several days, depending

on the case and the starting point. After the stable

conditions were reached, the fuel feeding was started

and simulated for 5 to 15 seconds. As expected, the

measured vertical solid concentration profile could

not be exactly simulated (Fig. 5 – 7). Because of this,

the results are qualitative.

Total flue gas flow 125 kg/s

Bed temperature 802 °C

Primary air share 60%

The calculations were performed by Fluent version

6.2.16 (Tanskanen, 2005). Table 4 summarizes

essential model options.

Table 3. Model options.

Fluid-solid drag Syamlal-O’Brien

Solid-solid drag Syamlal-O’Brien-symmetric

Granular viscosity Syamlal-O’Brien

Gran. bulk viscosity Lun et al

Frictional viscosity Schaeffer

Granular temperature Algebraic

Solids pressure Lun et al

Phases Flue gas, ρ

g

=0.329 kg/m

3

Bed, dp=175 µm, ρ = 2548 kg/m

3

Fig. 5. Example of volume fraction of bed.

p

Fuel, dp = 32-4000 µm, ρ = 1262 kg/m

3

p

The purpose of the work was to study the penetration

and mixing of fuel and char at the lower part of the

furnace. The model volume was restricted to a 15 m

height section of the furnace. First, the case was

modelled in two dimensions (Fig. 3) and the effect of

different parameters was studied (particle size,

secondary air, etc.). Finally, the case was modelled as

a three-dimensional slice of furnace (Fig. 4).

Fig. 6. Solid concentration profile in 2D-calculations.

Fig. 3. Model geometry in 2D-calculations.

Fig. 7. Solid concentration profile in 3D-calculations.

At the moment, the multiphase CFD codes and

models are not yet developed to their final form.

Especially the physics of granular material is not

completely known and the CFD calculations of more

than two phases in circulating fluidized bed

conditions are quite challenging. Many of the

phenomena in fluidized bed systems are three-

dimensional in nature and include multiple phases,

but modelling these conditions is time-consuming

and the results are unreliable. However, the data of

CFD studies can be utilized for better understanding

of the process, if care is taken and the results

compared with experience and measurements.

Based on calculation results, the particle size of fuel

has relatively small effect on penetration and mixing

of fuel in dense bed zone (Fig. 8). This further

emphasis the need to model the fluid dynamics of

bed correctly. Figure 9 presents the volume fraction

of fuel at 2.5 seconds after start of feeding in 3D-

calculation. The 3D simulation was calculated in a

Linux cluster with 5 x 2 GHz processors. With mesh

of 216200 cells, the simulation of 2.5 seconds took

about two months of calculation time.

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p

=4 mm, b) d

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5

CONCLUSIONS

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