7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
CFD ANALYSIS OF A LARGE SCALE ENTRAINED
FLOW GASIFIER FOR IGCC POWER PLANTS
Hilseyin Yilmaz, Solairaj Perumalsamy, Gerd Oeljeklaus, Klaus Garner*
,Thomas Klasen** Ali Cemal Benimi, Tino Just and Achim MoserS
LUAT (Environmental Process Engineering and Plant Design), University of DuisburgEssen,
45141 Essen, Germany
**InProConsult GmbH, 45145 Essen, Germany
SDepartment of Mechanical and Process Engineering, Diisseldorf University of Applied Sciences,
40474 Diisseldorf, Germany
9 Siemens Fuel G.silk~.is l I Technology GmbH, 09599 Freiberg, Germany
hueseyin.yilmaz ~unidue.de and klaus.goemner ~unidue.de
Keywords: CFD, entrainedflow gasifier, EulerianLagrangian simulations and gasification reactions
Abstract
In the gasification process, carbonaceous materials such as coal or biomass react into carbon monoxide and hydrogen
at high temperature and pressure (1). There is a broad range of reactor types, which can be classified into three gasifier
categories: Movingbed, fluidizedbed and entrainedflow (1). The focus of this paper is the entrainedflow gasifier
which operates at high temperature and pressure, and typically demands a HO/O, mixture for the gasification
process. The commercial CFD code Fluent is used to simulate an entrainedflow gasifier. The continuous gas and the
dispersed particle phases, which interact mechanically, thermally and chemically, are described by the Eulerian and
Lagrangian formulations respectively. The gas turbulence is described by the realizable k e model. The influence
of the gas phase turbulence on particle dispersion is taken into account by a randomwalk model and a particle size
distribution. For modeling the radiative heat transfer, the P1 method is used. The gasification process is described by
a set of chemical reactions that includes homogeneous and heterogeneous reactions. Available literature information
is used to formulate the reaction mechanism and their related kinetic data [(2), (3), (4), (5)]. In the first part of the
present work, two cases have been analyzed and compared: combustion reactions only, simultaneous combustion and
gasification reactions. The results demonstrate the substantial influence of the gasification reactions. In the second
part of the study, the burner swirl number has been examined.
1 Introduction
Around 41% of the world's electricity is provided by
coal and an increase to 44% is expected until 2030. Coal
is the only fossil fuel with a reserve of more than 100
years at current production. Compared to coal, oil and
gas reserves are in the order of 40 and 60 years. There
fore, it is expected that coal will remain a primary en
ergy source in the next years. One opportunity to use the
coal more efficiently in power stations is to apply gasi
fication technology. In an Integrated GI.silk~.lil al Com
bined Cycle (IGCC) an upstream gasifier produces syn
gas from coal, which drives a high efficient combined
cycle. Furthermore, when it comes to reducing CO,
emissions from power plants, the IGCC technology of
fers favorable conditions for the implementation of Car
bon Capture Storage (CCS) by means of COshift and
CO,separation in front of the syngas combustion. Be
yond this, the syngas can be used as feedstock to substi
tute natural gas and liquid fuels as well as for hydrogen
production.
The research work in this paper is focused on mod
eling and simulating a high pressurized entrainedflow
coal gasifier using the commercial CFD code FLUENT
6.3.26. In the gasification process coal is gasified at high
temperature and pressure with Og and HO. For a bet
ter understanding of the flow pattern and the gasifica
tion process a reaction mechanism have been used for
the volatile pyrolysis, heterogeneous and gas phase re
actions .
The first step of the work is to simulate an entrained
flow gasifier in a combustion environment. For this pur
pose the coal input has been reduced and the amount of
H,0OIO mixture has been adapted to reach hyperstoi
chiometric conditions. In the second step the simulation
of the gasifier has been switched to substoichiometric
conditions. The main results of this study will be shown
and discussed.
Based on this, the influence of the swirl number on the
species concentrations within the gasifier has been ex
amined. In this work the swirl number S is defined as the
ratio of the tangential component to the axial component
of the velocity. The influence of the mixing intensity on
the gasification behavior has been analized with varia
tion of the swirl number. This takes also an effect on the
heat transfer in the reactor and therefore on the gas out
let temperature and the cooling capacity of the reactor.
In the simulation the wall temperature of the reactor is
kept constant which is a simplification of the real pro
cess. However, first tendencies of the interactions have
been identified. Future work will focus on the extension
of the simulation model for example by a slag formation
submodel.
2 Mathematical Modeling
The steadystate Reynolds average NavierStokes
(R,4NS) equations are used to model the entrained
flow gasifier. The continuous gas phase conservation
equations include the equations for continuity, momen
tum and energy.
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
to close the equations. This turbulence model is a recent
development and differs from the standard k t model
in two important ways. First, it contains a new formu
lation for the turbulent viscosity by computing the value
C,,. Second, a new transport equation for the dissipa
tion rate has been derived from an exact equation for the
transport of the meansquare vorticity fluctuation. The
following equations are used to calculate the reynolds
stresses:
"(p i)3 [( p,I <0 r +~
(pu; = p are } zr A (4)
(Pe i) ui
ri
(~ dz + + pC'Se
kC~ + ~tCltb
The turbulent viscosity is calculated by
pt = pC,,k /t. (6)
The terms SI, and S, are user defined functions. The
values of aex, a,, C1, C2, C1e, Cse and the equation for
C,, are given in (7).
GA and ab represent the generation of turbulence kinetic
energy due to the mean velocity gradients and to buoy
ancy.
a~b */
?) _i~ =
2.1 Particle transport equation
The coal particles are assumed to be spherical and de
scribed with the Lagrangian equations. The governing
equation for a particle trajectory (in xdirection) is:
The first term on the right side is the drag force and
the second term is the buoyancy force per unit particle
mass. Fx is an additional acceleration (force unit par
ticle mass) term, e.g. thermophoretic force, Brownian
force, and Saffma's lift force. The drag force FD iS Cal
culated as:
FD (10)
Pr cl 24
where Re, is the Reynolds number and CD is the drag
coefficient of the particles. The random walk model is
applied to consider the effects of turbulent fluctuation.
?) _
J)
3)r 7lb
itryd 0, b)ZX + Sn,,, + S;'
The signs and in equations 1 to 3 represent the
time average and the Reynolds average of a scalar. The
terms p, u, g and b are density, velocity, gravity and en
thalpy of the gas mixture while Sc, Smon,, Sradc and Sht
are the source terms of particle mass, momentum, radia
tion and enthalpy respectively. The only unknown term
is the Reynolds stress '' Because this set of equa
tions is not closed the realizable k t model is used
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
2.2 Heat Transfer
In this work the conductive, convective and radiative
heat transfer are taken into account between the gas, par
ticles and walls. The isotropic scattering properties of
the particles to radiation are assumed and the P1 radia
tion model is used to describe the radiative heat transfer
as:
Q V (11)
3 (ag + ap + os )
where a, and a, are absorption coefficients of gas and
particle and os the scattering coefficient respectivley.
2.3 Reaction Mechanisms
In this study three reactions are included for the gasifica
tion process: (i) coal devolatilization and volatile pyrol
ysis, (ii) heterogeneous char particle surface reactions
and (iii) homogenous gas reactions.
2.3.1 Coal devolatilization and volatile
pyrolysis
The coal devolatilization process is calculated by the two
competing rates (Kobayashi) model:
x? y z O
:CO + H20+ aN,
2 2
CO + 1/2 O, CO,
2.3.2 Heterogeneous char particle surface
reactions
Three global heterogeneous reactions according to (4)
are used for the char gasification process:
C(s)+ +O, CO,
C(s) + CO, a 2CO
C(s) + HO 4 CO + H,
For each reaction the total reaction rate is determined
by diffusion and the intrinsic chemical reaction rate. The
reaction rate Ri of ith reaction can be expressed as:
4 R ,4, (20)
Di + Ri,rc ,
where Rossi, is the kinetic rate of reaction and Di is
the diffusion rate coefficient of the reaction. The diffu
sion rate Di is calculated by
D= ,:lT 0 :)30 7 (21)
where C, is the diffusion rate coefficient of the its
reactant, T, the absolute particle temperature, T, the ab
solute gas temperature and d, the particle diameter.
The apparent chemical reaction rate Rigs, is calculated
by the new empirical reaction model.
Ri,rcin = Agexp RT 10 6 (22)
The preexponential factor A and the activation energy
E for each reaction are taken from Chen (2) and is listed
in table 1.
Table 1: Reaction rate constants of the char gasification
constant C + O, C + CO, C + HO
A 0.052 0.0732 0.0782
E [J/kmol] 6.1 107 1.125 10s 1.15 10s
R1 = Ale(E1/(RTp))
where R1 and R, are competing rates that may
control the devolatilization over different temperature
ranges. The two kinetic rates are weighted to yield an
expression for the devolatilization as:
m, (t) _
(1 fw,o) mp,o me
t (0121 + agR,,,, ~i,,~) ep R +2)dii
o a (14)
where m,(t) is the volatile yield up to time t, mp,o
is the initial particle mass at injection and m, is the ash
content in coal particle. The variables at and as are
yield factors.
A two step reaction mechanism is used for the volatile
pyrolysis. The term OxHOzN, is calculated with the
proximate analysis, ultimate analysis. The enthalpy of
formation of the volatiles is based on their lower heating
value. The two step reaction mechanism can be written
according to (6) as:
2.3.3 Homogenous gas phase reactions
The following reaction mechanism is used to describe
the gas phase chemistry.
C,He, a + O,~ nOO + (n + 1) He
H, + 1/202 > HO
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
The source term in the conservation equation for the
mean species i is modeled as:
P y2
Ri = (Y,* Ye) (30)
where Y, is the species mass fraction and Y,* the fine
scale species mass fraction after reacting over the time
In FLUENT, combustion at fine scales is assumed to oc
cur as a constant pressure reactor with initial conditions
taken as the current species and temperature in the cell
(7). Reactions proceed over the calculated time scales
governed by Arrhenius rates and are integrated numeri
cally using the In Situ Adaptive Tabulation (ISAT) algo
rithm (12). ISAT is a powerful tool that enables realistic
chemistry to be incorporated in multidimensional flow
simulations by accelerating chemistry calculations. In
full, the method is: in situ, unstructured, adaptive tab
ulation of the accessed region with control of retrieval
errors (12). In order to use a tabulation method for a
particular flow, it is sufficient to tabulate the accessed
region, rather than the whole of the realizable region
which is much larger. Since the access region depends
on many aspects of the flow, it is not known prior to the
performance of the calculation. Hence the table is built
up during the reactive flow calculation. Each entry in
the table corresponds to a composition that occurs in the
calculation. This is referred to as in situ tabulation.
3 Problem description and numerical settings
In this paper a 2D axisymmetric model is used due to
the symmetry of the gasifier. A cross section of the
entrainedflow gasifier is given in Figure 1. Coal will be
gasified under high temperature and pressure with Og
and He O. Molten slag builds a protection layer for the
cooled wall. The temperature of the liquid slag should
be controlled in a small range. The CFD simulation
of combustion processes is well studied and a lot of
research work is published (13). In the past years only
a few CFD simulations of gasification processes were
performed and a great need for theoretical studies is
required. In the gasification process a valuable and
usable syngas will be generated. A usable syngas
means a high amount of CO and Hg and less CO,.
By innovative conversion processes the syngas can
be converted to a product gas which can be used in
different ways. The purpose of a combustion process is
to burn solid fuels to make use of the heat only.
In the first part an entrainedflow gasifier is calculated at
hyperstoichiometric condition by means a combustion
process. For this an adopted amount of HO/O, is
fed in the gasifier to reach combustion conditions. This
C,H2, 2 + nHO nOO + (2n + 1) H, (25)
CO + HO CO, + H, (26)
The reactions 23 to 26 are based on the fourstep re
action mechanism by Jones and Lindstedt (3) with the
following modifications: for the reactions 23 and 25 the
equations are build for n 1 a backward reaction for
24 is not used, but for the reaction 25. These modifi
cations are made to reach a similar reaction mechanism
like (1) who describe gas phase reactions which is typ
ical for gasification processes. This fourstep reaction
mechanism is also usually used by simulation gasifica
tion processes [(8), (9), (10)].
The kinetic rate k is computed using the Arrhenius ex
pression:
k = ATnexp (E/RT) (27)
where A is the preexponential factor, n the tempera
ture exponent, E is the activation energy and R is the uni
versal constant. For equations 23 to 26 the kinetic data
are based on the reaction scheme by Jones and Lindstedt
(3). For the backward reactions of the equations 25 and
26 the kinetic data are calculated by equilibrium con
stants. The kinetic data for the reaction of the equation
16 is taken from Westbrook and Dryer (5).
Turbulencechemistry interactions are taken into ac
count by using the Eddy Dissipation Concept (EDC)
model (11). EDC is an extension of the Eddy Dissipa
tion model to include detailed chemical mechanisms in
turbulent flows. It assumes that reaction occurs in small
turbulent structures, called the fine scales. The length
fraction of the fine scales, y is modeled as:
? = 2.1337 kB :
00 Re"4'
where the volume fraction constant is 2.1337 and a
represents the kinematic viscosity. Species are assumed
to react in the fine structures over a time scale 7, which
is proportional to the Kolmogorov time scale.
S=0.4082 
00 tKolnzogorov
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
ture of the reactor wall is kept constant.
4 Results and Discussion
4.1 Comparison of combustion and
gasification process
Table 2 shows the calculated average molar gas compo
sitions of selected species at the outlet of the reactor.
In both processes adopted mixtures of H,0OIO have
been assumed to simulate hyperstoichiometric and sub
stoichiometric conditions, respectively.
Table 2: Selected average species cop .. r ] at outlet
of the gasifier
Species combustion process gasification process
CO 3.6: 6~0.9
O, 0.0
As expected the amount of CO, is higher in the com
bustion than in the gasification case, which can be seen
in Figure 2
simulation considers the reactions of equations 15,
16, 23 and 24. In terms of the gasification process at
substiochiometric conditions the reaction mechanisms
has been extended. In this case all reactions listed in
section 2.3 have been taken into account.
The equilibrium of the combustion reactions are clearly
on the right side (CO,, H,0). For a gasification process
the equilibriums of reaction mechanisms are not clearly
on one side as indicated in the equations 25 and 26. This
makes a simulation of a gasifier difficult and therefore
two cases are studied to approach the simulation of an
entrainedflow gasifier.
GI.lsilk~.Ililln as a very complex process is influenced by
many parameters. As a start of a better understanding
of the gasification process the influence of the swirl
number on the gasification behaviour has been studied.
The SIMPLE method is used to couple the pressure and
velocity. For spatial discretization of the convective
term the second order upwind scheme is selected. A
converged result has been obtained when the residuals
of mass are smaller than 103, for energy smaller than
10" and for turbulent momentum, turbulent kinetic
energy and dissipation rate smaller than 10
Fuel
Burner
Pressure. water
outlet t
Cooling screen~
Pressure. water
Inlet )
Quench p
water
I'0.
0.2
Hil
0.0,
Cooling jacket
 Gas outlet
W1~aeter
Figure 2: Comparison of CO2 concentration for gasifi
cation (top) and combustion (bottom)
Figure 3 shows the CO concentration distribution in
side the gasifier for gasification and combustion process.
For gasification the CO, concentration increases near
the burner, but decreases towards the outlet whereas the
CO concentration increases. For the combustion pro
cess the opposite characteristic can be observed.
It is clear that the results of the combustion process are
not realistic and are only made to prove the simulation
for gasification conditions. However, the comparison of
these two cases shows that with reducing the amount of
O, the species distribution and the values at the outlet of
the reactor are reasonable for a gasification process.
1 Granulated slag
Figure 1: Example for an entrainedflow gasifier
In all cases the simulations are in a steadystate con
dition. For the inlet an amount of H, O and O, are given
as a mass flow rate condition and the coal with a particle
size distribution is injected in the gasifier. The tempera
Oxygen, steam
Figure 3: Comparison of CO concentration for gasifi
cation (top) and combustion (bottom)
4.2 Comparison of different values of swirl
number
Two CFD simulations have been carried out for the
entrainedflow gasifier under gasification mode with two
different values of swirl number, even S = 11it I' and
S 17 .' .The swirl number S = 11II I' has been
taken as a reference.
Figure 4 shows the velocity distribution within the gasi
fier for the two swirl numbers. It can be seen that the
velocity near the burner increases from the lower to the
higher swirl number. However, the orientation of the ve
locity jet depends on the swirl number. The smaller the
swirl number the more the velocity jet is orientated to
the centreline. This has a high effect on the temperature
and species concentration distributions. Another effect
is the residence time and with this, the mixing effect of
the gas mixture.
1.0.
I oo
Figure 4: Velocity profile for S 1 ItI I' (top) and S
17 ".' (bottom)
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Figure 5 shows the temperature distribution for the
two swirl numbers. The high temperatures are orien
tated outwards at the upper part for S 17 ".' .~ and for
reference number more to the centreline.
0.604
0 406
0.209
0.011
Figure 5: Temperature profile for S = 1II II' (top) and
S = 17 .'. (bottom)
0.8
0.6
0.4
0.2
0.0
Figure 6: O, profile for S
(bottom)
11 it (top) and S
17 ".'
The mixing intensity can be increased from the lower
to the higher swirl number. The species concentration
distribution within the gasifier for as, CO and He is
confirmed in Figures 6 to 8. The amount of ag for
S 17 ".' .~ is very low at the centreline so that a high
mixing leads to a faster consumption of O,. For the ref
erence swirl number of S 11 II l' the total consumption
of GO is a little bit later. The as distribution has a influ
ence on the species distribution on the top of the gasifier.
The species profiles of CO and He are different near the
burner for the both cases, but they get almost equal to
ward to the outlet.
0.6
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
02 H2 CO Temperature
0.4
Figure 7: CO profile for S
17 .~' (bottom)
11II I' (top) and S
0.6
04
0.2,
Figure 8: H~ profile for S = 11II I' (top) and S=
17 .~ (bottom)
Figure 9 shows the curves of selected species con
centrations and temperature over the centreline of the
gasifier, which are in line with the results from the Fig
ures 6, 7 and 8. For the case of the high swirl num
ber (S 17 l' .' I the almost quasi constant curves of the
species concentrations and temperature toward to outlet
shows that the reactions of the gas mixture reached their
equilibrium. The case for the reference swirl number
shows that the mixing effect is still well appropriate to
guarantee the total consumption of ag within the upper
area of the entrainedflow gasifier. The species concen
trations and temperature have also an almost quasi con
stant curve towards the outlet.
Table 3 shows the average molar concentrations and
temperature of selected species at the outlet of the gasi
fier. The species concentration for the cases are almost
the same. Only the amount of CO differs because of
the higher mixing effect of the gas for S = 1i ".' The
outlet temperature is in both cases different, because the
0,8
c,c
0,4
C,0 '
00 2 D,4 0,6 0,8
Height [%]
1,8
1,4
1.0 
C,G
0,4
0.0
00,2 0,4 0,6 0,8
Height [%]
Figure 9: Selected species concentration over the cen
treline of the gasifier for S 11 II l' (top) and
S 17 ".' (bottom)
heat transfer to the wall is influenced by the swirl num
ber. These results show that the cooling capacity of the
wall changes with the swirl numbers and with this dif
ferent outlet temperatures can be adjusted. The different
Table 3: Selected average molar gas composition
n~..d'.] and temperature at the outlet of the
gasifier
Species S I HI I S
C~O 60.9 (11 1 ) 6.(1.*)
He 21.7 (11 III' .) 21.8 (100. i'.)
T[ 0] 1647 (11 III' ) 1373 (83. i' .)
temperature distribution can also have an influence of
the slag formation on the cooling screen. It can be seen
in Figure 5 that for the case of S = 11 it and S = 17i~~ ".
the temperature profile near the wall are different. Only
the case with the reference swirl number shows the most
even temperature profile near the wall, which is important
for a homogeneous slag flow along the reactor wall.
The results show that the amount of CO is higher for the
11 0
0.8
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
References
[1] Higman C., van der Burgt M., GI.silk~.elis on, Chap
ter 5 pp., New York, GPP, Elsevier, 2003.
[2] Chen, C., Horio, M., and Kojima, T., Numerical
simulation of entrained flow coal gasifiers. Part 1:
modeling of coal gasification in an entrained flow
gasifier, Chemical Engineering Science, 55, 3861
3874, 2000.
[3] W. P. Jones; R. P. Lindstedt, Global Reaction
Schemes for Hydrocarbon Combustion, Combus
tion and Flame, 73, 233249, 1988.
[4] L. D. Smoot, P. J. Smith, Coal Combustion and
GI.silk~.eli lll Plenum Press, 1985.
[5] Westbrook, C.K.; Dryer,F.L. Simplified reaction
mechanisms for the oxidation of hydrocarbon fu
els in flames. Combustion Science and Technology,
27, 3143, 1981
[6] F. Brandt, Brenstoffe unf Verbrennungsrechnung,
FDBRFachbuchreihe Band 1, 1991
[7] Fluent Inc., FLUENT 6.3 User's Guide, 2006
[8] P. Carlsson, M. Marklund, H. Wiinikka, R. Gebart,
Gas Phase Reaction Schemes For Black Liquor
GI.lsilk~.llil on Modeling, FinnishSwedish Flame
days, 2009
[9] H. Watanabe; M. Otaka, Numerical simulation of
coal gasification in entrained flow coal gasifier,
Fuel 85, 19351943, 2006
[10] Y. Wu, P. J. Smith, J. Zhang, J. N. Thornock, G.
Yue, Effects of Turbulent Mixing and Controlling
Mechanisms in an Entrained Flow Coal Gasifier,
Energy and Fuels, 2009
[11] B.F. Magnussen; Ninteenth AIAA meeting, (1981)
[12] S.B. Pope, Combust. Theory Modelling 1 (1997)
4163
[13] Klasen, T., Giirner, K., Auel, W., Elkendorf, H.,
Optimierung der Feuerung flir das Kraftwerk In
owroclaw, Konferencja Naukowa, Krak6w, 1999
swirl number of S = 17i ".' which corresponds with the
lower outlet temperature. However, the reference case
has a more even temperature profile near the wall. This
means the chosen design of the Siemens Fuel Gasifica
tion reactor is the optimum of a good gasification pro
cess in combination with minimized wearing and long
operating times.
5 Conclusion
In this paper, the reaction mechanims for the simulation
of an entrainedflow gasifier is confirmed by comparison
of a case where the gasifier is calculated at hyperstoi
chiometric and substoichiometric conditions. The first
case was called as a combustion process because only
combustion reactions was taken into account. An op
posite species concentration distribution within the re
actor and species values at the outlet are the results of
these study. Reasonable results for gasification condi
tions could be shown by the transition from the hyper
to the substoichiometric condition. With this the used
reaction mechanisms for the entrainedflow gasifier was
confirmed.
It could be observed that the swirl number has a high in
fluence on the temperature, species concentration distri
bution, cooling capacity and slag formation on the wall.
The residence time of the gas mixture is high for the case
of S 17 ".'i with the result that the reactions reach a
quasi equilibrium condition immediately. The high tem
perature is orientated outwards at the upper part. For the
reference case the swirl number is appropriate to gener
ate a sufficiently high mixing effect to obtain equlibrium
conditions at the reactor outlet. The high temperature is
orientated more to the centreline. Compared to the case
of S = 17 ".' the temperature profile near the wall is
more even at the case of S = 1II II'. which is important
for a homogeneous slag flow along the reactor wall.
The above results show that the case with the refer
ence swirl number is a optimized design for the gasifier.
The outcomes of the 2D OFD modeling of a Siemens
entrainedflow gasifier have confirmed the quality of the
chosen design, which meets both targets of a good gasi
fication process as well as long standing operation times.
Further analysis should be the cooling capacity and slag
formation on the wall.
Acknowledgements
Nomenclature
The authors would like to thank the German Federal
Ministry of Economics and Technology (BMWi) and
Siemens FGT for the financial support of the project
in the frame of the COORETEC program (Grant No.
0327797C).
Roman symbols
24 preexponential factor (kg m2 s1 Paq
a absorption coefficient (1/m)
cp heat capacity (J/ (kgK())
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
C,,,1,2,le,se value and constants of the
realizable kt model ()
D diffusion rate (11i/s)
E activation energy (J/kinol)
FD drag coefficient ()
y gravitational constant (Ins
b enthalpy (J/kg)
k turbulent kinetic energy (111/s )
ar, ash content (kg)
at, volatile yield (kg)
n temperature exponent ()
p pressure (N111)
Q radiative heat transfer (W)
R universal gas constant (J/ (m1olK())
S swirl number ()
Scnionesid,h SOurce term of the Reynolds average
NavierStokes ()
T temperature (K()
a velocity (11/s)
Y mass fraction ()
.r, y, z spatial coordinate of an coordinate
system ()
Greek symbols
P
r;
asc, we
Subscripts
aJr
9
p
tang
yield factor ()
length fraction ()
turbulent dissipation rate (11i/s3)
thermal conductivity (W/ (11iK))
viscosity (kg/ (nis))
turbulent viscosity (kg/ (nis))
density (kg/m13)
shear stress (kg/ (s2m1))
time scale (s)
scattering factor( )
model constants of the
realizable kt model ()
axial
gas
particle
tangential
