1
A MULTI

FLUID MODEL FOR SIMULATING TURBULENT GAS

PARTICLE
FLOW AND PULVERIZED COAL COMBUSTION
Y
. C.
Guo
Department of Engineering Mechanics, Tsinghua University
Beijing, 100084, China
C. K. Chan
Department of
Applied Mathematics, The Hong K
ong Polytechnic University
Hung Kom, Kowloon, Hong Kong
ABSTRACT:
B
as
ed on
the pure two

fluid model for turbulent reacting gas

particle flows
with combusting pulverized coal particles, a new comprehensive model for pulverized coal
combustion was develop
ed by incorporating a modified k


kp model, a general model of
pulverized coal devolatilization and a general model of char combustion. Both gas

phase and
particle

phase conservation equations are described
using
Eulerian coordinates, and these
equations
are
discretised and
integrated in the computational cell. As the first stage of
numerical modeling of pulverized coal combustion in the cyclone furnace, three dimensional
simulation of turbulent gas combustion and gas

particle flows have been made.
P
red
icted
results show that there is a near wall recirculating zone at the bottom of the cyclone furnace,
and the recirculating zone
enhances
ignition and flame stabilization. The predicted tangential
velocity distribution of both
the
gas phase and
the
partic
le phase similar to
those of the
Rankine vortex.
Keywords:
coal combustion, modeling,
two

phase flow
2
NOMENCLATURE
A
E
=
superficial area of a coal particle
a
g
, a
k
=
absorption coefficient for gas phase and particle phase,
1
m
B
=
pre

ex
ponential factor,
1
s
B
k
=
transfer number
d
C
=
drag coefficient between gas and one particle
C
C
C
,
,
2
1
=
empirical constant of gas phase

k
turbulence model
p
C
=
empiri
cal constant of particle phase turbulence model
C
Y
=
empirical constant of second

order moment closure model
D
=
diffusivity,
1
2
s
m
E
b
=
emissivity of black body,
2
m
J
F
=
turbulence effect on reaction rate
h
=
enthalpy,
1
kg
J
K
0
=
pre

exponential factor of
devolatilization
,
1
s
k
=
gas phase turbulent kinetic energy,
2
2
s
m
L
W
=
latent heat of water evaporation,
1
kg
J
M
=
Molecular weight,
1
mol
k
kg
g
n
=
particle phase number density,
3
m
V
=
volatile content
W
=
reaction rate,
1
s
kg
Greek symbols
N
=
fuel nitrogen content of coal particles
3
k
=
gas

particle flow drag coefficient,
1
3
s
m
kg
=
viscosity,
1
1
s
m
kg
=
gas phase kinematic viscosity,
1
2
s
m
k
=
Particle phase turbulent
kinematic viscosity,
1
2
s
m
=
generalized dependent variable
p
=
turbulent Schmidt number for particle phase
Subscripts
Arr
=
Arrhenius reaction model
ck
=
char of k

group coal particle phase
d
af
=
daf coal
dk
=
daf coal of k

group particle phase
EBU
=
EBU turbulent combustion model
g
=
gas phase
k
j
i
,
,
=
coordinate direction
k
=
k

group particle phase
p
=
particle phase
r
=
radiation heat transfer
s
=
ga
s phase species
T
=
turbulence
wk
=
moisture of k

group particle phase
4
INTRODUCTION
Simulation of pulverized coal combustion process involves modeling a number of complex
simultaneous interdependent processes. The comprehensive model must account fo
r
turbulent gas

particle flow, gas phase combustion, coal particle mass change due to moisture
evaporation, devolatilization and char combustion, NOx formation and radiation heat
transfer.
However, i
t is most difficult to model the reacting coal particles
and their effect on
the gas phase. In treating the particle phase for modeling pulverized coal combustion, most
of currently models adopt
a
Lagrangian treatment of
the
particles
[1

5
].
In using
particle
trajectory model
, it
is easy to simulate the combu
sting coal particle history
.
However
, in
order to
obtain a
detailed distribution of particle velocity and concentration
for comparison
with experimental data, a large amount of particle trajectories
are required
. Fiveland and
Wessel
[
6
] developed an Eule
rian model for modeling pulverized coal combustion, whi
le
neglecting the velocity slip between the gas phase and coal particle phase, and assuming that
the temperature of coal particle phase is equal to the temperature of gas phase, the
temperature
distrib
ution
of the gas

particle mixture can be obtained by solving the overall
energy equation.
In this paper, a pure two

fluid model for reacting gas

particle flows is developed, using
a
comprehensive
Eulerian treatment for both gas phase and particle phase.
Both velocity slip
and temperature slip between coal particles and gas phase
are
calculated by solving
the
momentum equations and energy equations of gas phase and particle phase respectively.
In
addition
, a modified k


kp two

phase turbulence model, a
second

order moment turbulence

chemistry model for NOx formation, a general model of pulverized coal devolatilization and
a general model of char combustion were incorporated into the comprehensive model. For
5
volatile and CO combustion
as well as
radiatio
n heat transfer,
the
conventional EBU

Arrhenius model and
the
six heat

flux model were used.
GOVERNING EQUATIONS AND CLOSURE MODELS
The basic idea of the pure two

fluid model is to consider the particle phase as a pseudo

fluid
inter
acting
with the gas pha
se. The basic assumptions are:
(1)
At each location of the flow field, particle phase and gas phase co

exist and
interpenetrate
with
each other, each having its own velocity and temperature.
(2)
Each particle phase is identified by its initial size distribution w
hich has its own
continuous velocity and temperature distribution in space.
(3)
Apart from
the mass, momentum and energy interaction with the gas phase, each particle
phase has its own turbulent fluctuation resulting in particle turbulent transport of mass,
mo
mentum and energy
.
Such
particle fluctuation
s
are determined by convection,
diffusion, production and interaction with gas phase turbulence.
(4)
E
ffect
of
particle

particle collision are neglected, as only dilute particulate suspensions
are considered.
Based
on the above assumptions, adopting a modified k


kp two

phase turbulence model,
the time

averaged equations of gas phase and particle phase in Eulerian coordinate
s
are
obtained as follows
Gas phase continuity equation
k
k
j
j
m
k
n
v
x
)
(
(1)
6
The te
rm on the right

hand side of Eq.(1) expresses the coal particle mass change due to
moisture evaporation
,
daf
(dry and free) coal devolatilization and char combustion.
Gas phase momentum equation
k
k
k
i
k
ki
i
k
i
j
i
e
j
i
j
e
j
i
i
j
j
m
n
v
v
v
g
x
v
x
x
v
x
x
p
v
v
x
)
(
)
(
(2)
The last two terms on the right

hand side of Eq.(2) are source terms due to interaction
between the gas phase and particle phase, the fifth term is volume

averaged particle drag
force, where
k
is drag coefficient
between gas and coal particles,
which can be expressed a
s
follows
k
k
D
k
d
v
v
C
4
3
(3)
where
D
C
is drag coefficient based on different Reynolds number given by
,
1000
Re
for
;
44
,
Re
for
;
C
k
k
k
k
D
.
0
1000
6
Re
1
Re
24
6667
.
0
(4)
k
d
is the diameter of k

group coal particles, and
k
Re
is the R
eynolds number of particle

gas
relative motion, defined as
k
k
k
d
v
v
Re
.
(5)
Gas phase turbulent kinetic energy equation
R
p
k
j
k
e
j
j
j
G
G
G
x
k
x
k
v
x
)
(
(6)
where
k
G
is the production term, which can be expressed as:
7
k
k
ij
j
i
i
j
j
i
T
k
x
v
x
v
x
v
x
v
G
3
2
.
(
7
)
T
e
is the effective viscosity
, where
2
k
C
T
is the gas phase turbulence
viscosity determined by the
k

turbulence model
[7]
. The last two terms on the right

hand
side of Eq.(6) are source terms due to interaction
between the gas phase and particle phase,
k
k
k
p
rk
k
p
k
kk
C
G
)
(
2
, where
k
k
is k

group particle phase turbulent kinetic energy, and
k
p
C
is empirical constant which
take
s the value of 0.75, the last term
k
k
k
R
m
n
k
G
is the
production term due to mass change of coal particles
.
Gas phase turbulent kinetic energy dissipation rate equation
)
(
)
1
(
)
(
1
2
1
R
p
igs
gs
k
j
e
j
j
j
G
G
C
k
R
C
C
G
C
k
x
x
v
x
(
8
)
For strongly swirling flows, it is necessary to modify the

equation by using a m
odified
source term, adopting the treatment suggested by Launder et al.[
8].
Gas phase thermal enthalpy equation
k
k
pk
k
k
k
k
k
j
bj
rj
g
S
S
j
h
e
j
j
j
T
C
m
n
Q
n
E
q
a
Q
W
x
h
x
h
v
x
)
3
(
2
)
(
(
9
)
In the right

hand side of Eq.(
9
), there are diffusion term of thermal enthalpy, heat release
from gas phase turbule
nt combustion, radiation heat transfer of gas phase, convective heat
transfer between coal particles and gas phase, and energy source term of phase change due to
evaporation, devolatilization and char combustion.
where
1
)
exp(
)
(
k
k
k
s
k
k
k
B
B
T
T
Nu
d
Q
,
(1
0
)
8
s
k
k
ps
k
k
Nu
d
C
m
B
,
(1
1
)
5
.
0
Re
5
.
0
2
k
k
Nu
.
(1
2
)
In the case
where the
coal particle temperature is different from that of
the
gas phase, the so

called 1/3 Law is used for calculating the thermal

conductivity
s
and specific heat
ps
C
near
the boundary layer of coal particles. As for radiation heat transfer,
the
six heat

flux
model
[9]
is used
.
T
he governing equation
for
the radiation heat flux
r
q
in the
i

th direction
is given as
)
(
)
2
(
3
)
(
1
bk
ri
k
rk
rj
ri
bg
ri
g
i
ri
i
E
q
a
q
q
q
s
E
q
a
dx
dq
s
a
dx
d
,
(
1
3
)
where
2
2
4
,
4
,
,
k
k
sk
k
k
k
ak
k
k
g
k
g
d
n
Q
s
d
n
Q
a
s
s
s
a
a
a
;
g
a
and
k
a
are absorption
coefficient for gas phase and particle phase respectively,
g
s
and
k
s
are scattering coefficient
of the gas phase and
particle phase,
ak
Q
is efficiency factor for absorption of particle
radiation,
sk
Q
is efficiency factor for scattering of particles.
Gas phase species mass fraction equation
k
k
k
s
s
j
s
Y
e
j
s
j
j
m
n
W
x
Y
x
Y
v
x
)
(
(
1
4
)
For
CH
4
volatile a
nd CO combustion, the conventional EBU

Arrhenius
model
[10]
is used,
and
)
,
min(
,
,
Arr
s
EBU
s
s
W
W
W
, where
ox
F
R
EBU
s
Y
Y
k
C
W
,
min
,
,
(1
5
)
RT
E
Y
Y
B
W
s
ox
F
s
Arr
s
exp
,
.
(16)
9
The last term on the right

hand side of Eq.(
1
4
) is the source term due to mass change of coa
l
particles,
s
is the
mass
fraction of contribution of s

species in
the
phase change.
As for NO
X
formation, most of the nitrogen oxides emitted to the atmosphere by combustion
are in
the
form of nitric oxide(NO). Two mechanisms of nitr
ic oxide formation are
considered,
i.e.
thermal NO and fuel NO
.
Thermal NO is predicted using the Zeldovich
mechanism
whereas
fuel NO formation is described by a global mechanism
[11], which
is
explicit only in HCN, NO, and N
2
. The fuel NO formation mecha
nism is shown as
Coal Nitrogen
HCN
O
2
NO
N
2
Char surface reaction
NO
The reaction rate for HCN is
HCN
HCN
M
W
W
W
W
)
(
2
1
0
, and the source term for NO can be
written as
4
3
2
1
)
(
W
M
W
W
W
W
NO
NO
, where
N
k
N
M
m
W
0
,
(1
7
)
)
1
(
0
.
67
exp
)
10
1
(
1
11
1
2
2
F
RT
kcal
M
M
Y
M
M
Y
W
b
O
M
O
HCN
M
HCN
,
(1
8
)
)
1
(
0
.
60
exp
)
10
3
(
2
12
2
F
RT
kcal
M
M
Y
M
M
Y
W
NO
M
NO
HCN
M
HCN
,
(
19
)
RT
kcal
P
A
m
n
W
NO
E
k
k
7
.
34
exp
10
18
.
4
3
,
(
2
0
)
)
1
(
9
.
134
exp
10
39
.
8
3
5
.
0
5
.
0
5
.
1
16
4
2
2
F
RT
kcal
Y
Y
T
W
O
N
.
(2
1
)
10
Using a second

order moment to account for turbulence

chemistry interaction for NOx
formation, the time

averaged reaction
3
F
,
similar to
thermal NO, can be modeled as
suggested by Khalil [9]
2
2
2
2
2
2
2
2
2
1
1
2
1
2
1
2
3
N
N
O
O
O
N
O
N
Y
T
Y
T
Y
T
Y
T
T
T
RT
E
RT
E
Y
Y
Y
Y
F
.
(2
2
)
The correlations are modeled using gradient assumption
s
. The algebraic expressions can be
written as
j
O
j
N
Y
O
N
x
Y
x
Y
k
C
Y
Y
=
2
2
2
2
2
3
,
(2
3
)
j
O
j
Y
O
x
Y
x
T
k
C
Y
T
2
2
2
3
,
(2
4
)
j
N
j
Y
N
x
Y
x
T
k
C
Y
T
2
2
2
3
,
(2
5
)
2
2
3
2
j
Y
x
T
k
C
T
.
(2
6
)
The terms
1
F
and
2
F
can
also
be modeled in a similar
manner as
HCN
HCN
O
O
O
HCN
O
HCN
Y
T
Y
T
Y
T
Y
T
b
T
T
RT
E
RT
E
Y
Y
Y
Y
b
F
1
2
1
2
2
2
2
2
1
,
(2
7
)
HCN
HCN
NO
NO
NO
HCN
NO
HCN
Y
T
Y
T
Y
T
Y
T
T
T
RT
E
RT
E
Y
Y
Y
Y
F
1
2
1
2
2
.
(2
8
)
11
As t
he heterogeneous char/NO reaction rate is not fast,
turbulence eff
ect on the char surface
reaction rate
is
neglected.
This reaction rate is given by Levy et al.[12]. Smith et al.[13] used
this model to predict the NO formation in coal flames.
Particle phase number density equation
j
k
p
k
j
kj
k
j
x
n
x
v
n
x
)
(
(29)
Particle pha
se (raw coal) bulk density equation
k
k
j
k
p
k
j
kj
k
j
m
n
x
x
v
x
)
(
(
3
0
)
Daf coal bulk density equation
dk
k
j
dk
p
k
j
kj
dk
j
m
n
x
x
v
x
)
(
(
3
1
)
Coal particle moisture bulk density equation
wk
k
j
wk
p
k
j
kj
wk
j
m
n
x
x
v
x
)
(
(
3
2
)
As the bulk density of coal particle phase,
k
k
k
m
n
, the mass
k
m
of
a
single coal particle
can be obtained
by solving Eq.(29) and Eq.(
3
0
). Similarly, by solving Eq.(
3
1
) and Eq.(
3
2
),
the daf coal mass and moisture content can be calculated.
Therefore
, Eq.(29) to Eq.(
3
2
)
describe
the mas
s change due to moisture evaporation, daf coal devolatilization and char
combustion. The total
rate of
chang
e of mass
is the sum of the
devolatilization rate
, the
char
reaction rate and
the
moisture evaporation rate
and
can be expressed as
wk
ck
dk
k
m
m
m
m
,
(
3
3
)
12
where
wk
m
is moisture evaporation rate, which can be determined as
ws
wg
ws
k
k
wk
Y
Y
Y
D
Nu
d
m
1
1
ln
,
(3
4
)
with
ws
Y
being
mass fraction of vapor at the surface of coal particles,
given by
k
w
w
ws
RT
E
B
Y
exp
, and
wg
Y
is mass fraction of vapor in the calculation grid.
Using the general model of pulverized coal devolatilization suggested by Fu et al.[
14
], the
devolatilization rate of daf coal can be obtained as
k
V
daf
daf
daf
daf
dk
RT
E
m
m
m
V
K
m
m
exp
0
,
0
,
0
0
,
.
(
3
5
)
The general
devolatilization model assume
s
that the kinetic parameters,
V
E
and
0
K
are
independent of coal type and depend only on the final temperature of coal particles
.
With the
final temperature taken as the gas phase temperatu
re
,
V
is expressed as
2
0
6
8
.
0
)
(
10
2
exp
2
.
1
T
T
R
V
V
g
daf
.
(
3
6
)
The heterogeneous reaction rate of char can
also
be determined
using the
general model
developed by Fu and Zhang
[
15
]. The overall rate of char combustion is
given as
)
exp(
,
,
0
2
2
k
s
O
s
ch
k
ck
RT
E
Y
K
d
m
,
(
3
7
)
i
n which the activation energy
E
, is independent of coal properties and
depends only
on the
temperature of the char particle
.
However, the
frequency factor of char oxidation
ch
K
,
0
, is
dependent on coal pro
perties during its burning in air. A value of
mol
kJ
E
180
, a constant in
the oxidation of coal char in air
[15], is used
.
Particle phase momentum equation
13
i
k
k
k
i
j
k
p
k
ki
i
k
p
k
kj
j
ki
i
k
j
ki
k
j
i
kj
k
j
ki
kj
k
j
g
m
n
v
x
v
x
v
x
v
v
x
v
x
x
v
x
v
v
x
)
(
)
(
(
3
8
)
Particle phase thermal enthalpy equation
k
k
k
k
k
ck
k
rk
j
k
p
k
j
k
kj
k
j
m
n
h
Q
n
Q
n
Q
x
h
x
h
v
x
)
(
(
39
)
w
here
k
pk
k
T
C
h
,
)
3
(
2
bk
j
rj
k
rk
E
q
a
Q
is the radiation heat transfer,
ck
Q
is the heat
released by heterogeneous reaction on the coal particle surface ( including char combustion,
evaporation and devolatilization)
.
P
article phase turbulent kinetic energy equation
gk
pk
j
k
p
k
k
j
j
k
p
k
j
k
kj
k
j
G
G
x
k
x
x
k
x
k
v
x
)
(
(4
0
)
The particle phase turbulent kinetic energy is determined by convection, diffusion,
production and interaction with gas phase turbulence
.
pk
G
is the production t
erm of particle
phase, which can be expressed as
k
kk
ij
j
ki
i
kj
j
ki
k
pk
x
v
x
v
x
v
x
v
G
3
2
.
(4
1
)
U
sing the kp model
[16]
to model particle phase turbulence, the turbulent viscosity is
determined as
5
.
1
5
.
0
k
k
C
k
k
p
k
.
(4
2
)
The last term on the right

hand side of Eq.(
4
0
)
is
the
source term due to interaction between
the gas phase and particle phase
and is expressed as
14
j
k
kj
j
p
k
k
k
rk
k
k
k
k
k
p
k
k
k
p
rk
k
gk
x
v
v
m
m
m
n
k
kk
C
k
kk
C
G
)
(
1
)
2
(
)
(
2
.
(4
3
)
For the pure two

fluid model, the gas phase and particle phase have
separate
momentum
equation
s,
thermal enthalpy equation
s
a
nd turbulent kinetic energy equation
s.
V
elocity slip
and temperature slip between the gas phase and particle phase
can be predicted
. Each particle
phase has a set of governing equations
describing
particle mass, momentum and energy
turbulent diffusion.
NUMERICAL SOLUTION PROCEDURE
Both gas

phase and particle

phase conservation equations in the Eulerian coordinates are
integrated in the computational cell to obtain finite

difference equations.
The generalized
finite

difference equation can be written as
b
a
a
a
a
a
a
a
T
T
B
B
S
S
N
N
W
W
E
E
P
P
(4
4
)
where
is generalized dependent variable of the gas phase and the particle phase.
The gas
phase equations are solved by means of
the SIMPLE algorithm
[17],
i.e. p

v corrections with
TDMA line

by

line it
erations and under

relaxation
.
A s
imilar procedure is used for
the
particle phase, but without p

v corrections.
In addiation,
multiple iteration
s
between gas
phase and particle phase have been adopted based on a two

way coupling (Eulerian gas

Eulerian pa
rticle).
PREDICTED RESULT AND DISCUSSION
As the first stage of numerical modeling of pulverized coal combustion in
a typical
cyclone
furnace, three

dimensional simulation of turbulent gas combustion and gas

particle flows
have been made.
A grid system of
7200
15
16
30
had been adopted.
The configuration of
15
cyclone furnace and the inlet conditions are shown in Fig.1. The inlet temperature of primary
air and secondary air is 300K, and the inlet velocity is along the tangential direction of the
f
urnace. A single group
of
coal particles with diameter
s
60
m are calculated. The mass flow
rate of particle phase to gas phase is taken as 0.09. Five species are considered in
the
turbulent gas combustion,
namely
CH
4
, O
2
, CO, CO
2
and H
2
O.
Fig.2 is the
gas phase and particle phase velocity vector distribution
s
under gas phase
combustion
.
It can be seen that both
the
gas phase and
the
particle phase have large axial
velocities in the centre of the furnace
compare with
the near wall region.
On the contra
ry, for
isothermal flow, axial velocities of gas phase and particle phase are all small in the centre of
the furnace. From the distribution
s
of gas phase and particle phase velocity vectors, it can be
seen that there is a large velocity slip between the g
as phase and particle
phase
especially in
the radial direction. Compared with the gas phase radial velocity, the particle phase radial
velocity is much larger due to the centrifugal force. At the bottom of the cyclone furnace,
predicted results show that
there is a recirculating zone near the wall, this recirculating zone
enhances
ignition and flame stabilization. Fig.3 shows the axial velocities of gas phase and
particle phase
.
It can be seen that the particle phase axial velocity distribution is simil
ar to
that of gas phase, in
dicating that t
he velocity slip
in the axial direction
is small.
Fig.4 shows the tangential velocity distribution
s
of gas phase and particle phase
.
P
redicted
results show that tangential velocity distribution
s
of both
the
gas p
hase and particle phase are
similar to
those of the
Rankine vortex. Comparing with the particle phase, the gas phase has
larger values of tangential velocities. Fig.5 shows the bulk density distribution of particle
phase
.
P
redicted results show that the
particle phase concentration is much higher in the
region near the wall of the furnace due to centrifugal force
.
I
n the central upper part of the
16
furnace, the particle concentration is nearly zero,
which is a
character
istic
of swirling gas

particle flows.
Fig.6 shows the gas phase temperature distribution
.
T
he temperature changes rapidly near
the wall of the furnace, at the central region of the furnace, the gas phase temperature is
nearly uniform
at about
1700K. Fig.7 gives the
M
ethane
(CH
4
) concentrat
ion profile
.
A
t the
inlet, the mass fraction of methane concentration is 0.03, and methane is injected into the
furnace only at the primary air inlet located at the bottom of the furnace
.
Velocity of primary
air is 4.2m/s From Fig.7, it can be seen that
methane combustion is rapid
and
complete at the
lower part of the furnace.
Fig.8 shows the carbon monoxide
(CO) concentration distribution
.
A
t the inlet, the mass
fraction of carbon monoxide is 0.03
.
C
arbon monoxide is injected into the furnace at the
primary air inlet located at the bottom of the furnace
as well as
at the upper secondary air
inlets. It can be seen that the carbon monoxide combustion rate is slow
.
A
t the exit of the
furnace, the carbon monoxide
concentration is about
0.005,
indicating
that the
combustion
process is not complete. Fig.9 shows the oxygen
(O
2
) concentration distribution
.
T
he mass
fraction of oxygen in the central region of the furnace
is
reduced due to methane and carbon
monoxide combustion,
whereas it
is nearly uniform
at the exit of the furnace
at
about 0.10.
Fig.10 and Fig.11 show the combustion productions carbon dioxide and water vapor
concentration distribution.
CONCLUSIONS
A comprehensive numerical model for pulverized coal combustion has been developed on the
ba
sic of pure two

fluid model for reacting gas

particle flows, as the first stage of numerical
modeling of pulverized coal combustion. This model has been applied to the simulation of
17
turbulent gas combustion and gas

particle flows in a cyclone furnace.
P
r
edicted results show
that there is a large velocity slip between the gas phase and particle phase, especially in the
radial direction.
P
article velocities are much large
r
than that of gas
velocities
due to
centrifugal force
.
I
n the annular wall region of
the cyclone furnace, the particle phase
reaches its concentration peak. The predicted results show that there is a near wall
recirculating zone at the bottom of the cyclone furnace and is beneficial to ignition and flame
stabilization.
Acknowledgements
This work was partially supported by the Research Committee of The Hong Kong
Polytechnic University under Grant No.A.63.37.PA81.
18
References
[
1
]
Lockwood, F.C., Papadopoulos,
C.
,
and Abbas,
A.S
.
Comb Sci
&
Tech
1988
,
58
,
5
[2]
Wennerberg
,
D.
Comb Sci
&
Te
ch.
1988
,
58
,
25
[3]
Gorner
,
K
. and
Zinser
,
W.
Comb Sci
&
Tech.
1988
,
58
,
43
[4]
Papadakis, G. and Bergeles,
G.
J of the Institute of Energy
1994
,
6
7
,
156
[5]
Coimbra, C.F.M., Azevedo, J.L.T.
,
and
Carvalho, M.G.
Fuel
1994
,
73
,
1128
[6]
Fiveland, W.A. and W
essel, R.A.
J Eng for Gas Turb and Power
1988
,
110
,
117
[7]
Launder
,
B
.
E
. and
Spalding
,
D
.
B
.
Mathematical Models of Turbulence, Academic Press,
London, England, 1972
[8]
Launder, B.E., Priddin, C.H.
,
and
Sharma, B.I.
J Fluid Eng
ineeri
ng
1979
,
99
,
363
[9]
K
halil
,
E
.
E
.
Modeling of Furnace and Combustors, Abacus Press, 1982
[10]
Magnussen
,
B
.
F
. and
Hjerager
,
B
.
H
.
Sixteenth Symposium (Int.) on Combustion. Pittsburgh, PA
,
The
Combustion Institute, 1976
,
719
[11]
DeSoete
,
G
.
G
.
,
F
ifteenth Symposium (Int.) on Combu
stion. Pittsburgh, PA
,
The
Combustion
Institute, 1975
,
1093
[12]
Levy
,
J
.
M
.
, Chan
,
L
.
K
.
, Sarofim
,
A
.
F
.
,
and
Beer
,
J
.
M
.
Eighteenth Symposium (Int.) on
Combustion. Pittsburgh, PA
,
The Combustion Institute, 1981
,
111
[13]
Smith
,
P
.
J
.
, Hill
,
S
.
C
.
,
and
Smoot
,
L
.
D. Nineteenth Symposium (Int.) on Combustion. Pittsburgh,
PA
,
The Combustion Institute, 1982
,
1263
[14]
Zhou
,
L
.
X
.
Theory and Numerical Modeling of Turbulent Gas

Particle Flows and Combustion,
Science Press and CRC Press Inc, 1993
[15]
Fu,
W
.
,
Zhang,
Y
.
,
Han,
H
.
,
and
Wang, D.
Fuel
,
1989
,
68
,
505
[16]
Fu,
W
. and
Zhang,
B.
J of Combustion Science and Technology
,
1997
,
3
,
1
[17]
Patankar
,
S
.
V.
Numerical Heat Transfer and Fluid Flow, Hemisphere, New York
,
1980
19
Figure Captions
Fig
ure
1
Configuration of cyclon
e furnace
Fig
ure
2
Gas and particle phase velocity vectors
Fig
ure
3
Gas and particle
phase axial velocity
Fig
ure
4
Gas and particle phase tangential velocity
Fig
ure
5
Bulk density of particle phase
Fig
ure
6
Gas phase temperature
Fig
ure
7
CH
4
concentration
Fig
ure
8
CO concentration
Fig
ure
9
O
2
concentration
Fig
ure
10
CO
2
concentration
Figure 11
H
2
O concentration
20
90
180
650
1600
7
7
650
500
115
20
45m/s
45m/s
4.2m/s
v
2
v
1
v
o
160
Fuel / Guo and Chan / Figure 1
21
45m/s
4.2m/s
45m/s
45m/s
45m/s
4.2m/s
8m/s
gas phase
particle phase
Fuel / Guo and Chan / Figure 2
22
4.2m/s
45m/s
45m/s
10m/s
45m/s
45m/s
4.2m/s
particle velocity
gas velocity
Fuel / Guo and Chan / Figure 3
23
45m/s
45m/s
4.2m/s
45m/s
45m/s
4.2m/s
8m/s
particle velocity
gas velocity
Fuel / Guo and Chan / Figure 4
24
45m/s
4.2m/s
45m/s
4.2m/s
45m/s
45m/s
kg/m
3
0.126
Fuel / Guo and Chan / Figure 5
25
45m/s
45m/s
45m/s
4.2m/s
45m/s
4.2m/s
Fuel / Guo an
d Chan / Figure 6
26
45m/s
45m/s
4.2m/s
45m/s
45m/s
4.2m/s
Fuel / Guo and Chan / Figure 7
27
45m/s
4.2m/s
45m/s
45m/s
4.2m/s
45m/s
Fuel / Guo and Chan / Figure 8
28
45m/s
4.2m/s
45m/s
45m/s
45m/s
4.2m/s
Fuel / Guo and Chan / Figure 9
29
45m/s
4.2m/s
45m/s
45m/s
45m/s
4.2m/s
Fuel / Guo and Chan / Figure 10
30
45m/s
45m/s
4.2m/s
4.2m/s
45m/s
45m/s
Fuel / Guo and Chan / Figure 11
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