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Combustion Modeling
in
FLUENT
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Outline
Applications
Overview of Combustion Modeling Capabilities
Chemical Kinetics
Gas Phase Combustion Models
Discrete Phase Models
Pollutant Models
Combustion Simulation Guidelines
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Applications
Wide range of homogeneous
and heterogeneous reacting
flows
Furnaces
Boilers
Process heaters
Gas turbines
Rocket engines
Predictions of:
Flow field and mixing
characteristics
Temperature field
Species concentrations
Particulates and pollutants
Temperature in a gas furnace
CO
2
mass fraction
Stream function
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Aspects of Combustion Modeling
Dispersed Phase Models
Droplet/particle dynamics
Heterogeneous reaction
Devolatilization
Evaporation
Governing Transport Equations
Mass
Momentum (turbulence)
Energy
Chemical Species
Combustion Models
Premixed
Partially premixed
Nonpremixed
Pollutant Models
Radiative Heat Transfer Models
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Gas phase combustion
Generalized finite rate formulation (Magnussen model)
Conserved scalar PDF model (one and two mixture fractions)
Laminar flamelet model (
V5
)
Zimont model (
V5
)
Discrete phase model
Turbulent particle dispersion
Stochastic tracking
Particle cloud model (
V5
)
Pulverized coal and oil spray combustion submodels
Radiation models: DTRM, P

1, Rosseland and Discrete Ordinates (
V5
)
Turbulence models:
k

, RNG
k

, RSM, Realizable
k

(
V5
) and LES (
V5
)
Pollutant models: NO
x
with reburn chemistry (
V5
) and soot
Combustion Models Available in
FLUENT
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Modeling Chemical Kinetics in Combustion
Challenging
Most practical combustion processes are turbulent
Rate expressions are highly nonlinear; turbulence

chemistry interactions
are important
Realistic chemical mechanisms have tens of species, hundreds of reactions
and stiff kinetics (widely disparate time scales)
Practical approaches
Reduced chemical mechanisms
Finite rate combustion model
Decouple reaction chemistry from turbulent flow and mixing
Mixture fraction approaches
Equilibrium chemistry PDF model
Laminar flamelet
Progress variable
Zimont model
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Generalized Finite Rate Model
Chemical reaction process described using global mechanism.
Transport equations for species are solved.
These equations predict local time

averaged mass fraction,
m
j
, of each
species.
Source term (production or consumption) for species
j
is net reaction
rate over all
k
reactions in mechanism:
R
jk
(rate of production/consumption of species
j
in reaction
k
) is
computed to be the
smaller
of the Arrhenius rate and the mixing or
“eddy breakup” rate.
Mixing rate related to eddy lifetime,
k /
.
Physical meaning is that reaction is limited by the rate at which turbulence
can mix species (nonpremixed) and heat (premixed).
R
R
j
jk
k
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Setup of Finite Rate Chemistry Models
Requires:
List of species and their properties
List of reactions and reaction rates
FLUENT V5
provides this info in a mixture material database.
Chemical mechanisms and physical properties for the most common
fuels are provided in database.
If you have different chemistry, you can:
Create new mixtures.
Modify properties/reactions of existing mixtures.
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Generalized Finite Rate Model: Summary
Advantages:
Applicable to nonpremixed, partially premixed, and premixed combustion
Simple and intuitive
Widely used
Disadvantages:
Unreliable when mixing and kinetic time scales are comparable (requires
Da >>1).
No rigorous accounting for turbulence

chemistry interactions
Difficulty in predicting intermediate species and accounting for
dissociation effects.
Uncertainty in model constants, especially when applied to multiple
reactions.
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Conserved Scalar (Mixture Fraction)
Approach: The PDF Model
Applies to nonpremixed (diffusion) flames only
Assumes that reaction is mixing

limited
Local chemical equilibrium conditions prevail.
Composition and properties in each cell defined by extent of turbulent
mixing of fuel and oxidizer streams.
Reaction mechanism is not explicitly defined by you.
Reacting system treated using chemical equilibrium calculations (
prePDF
).
Solves transport equations for mixture fraction and its variance, rather
than species transport equations.
Rigorous accounting of turbulence

chemistry interactions.
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Mixture Fraction Definition
The mixture fraction,
f
, can be written in terms of elemental mass
fractions as:
where
Z
k
is the elemental mass fraction of some element,
k
. Subscripts
F
and
O
denote fuel and oxidizer inlet stream values, respectively.
For simple fuel/oxidizer systems, the mixture fraction represents the fuel
mass fraction in a computational cell.
Mixture fraction is a conserved scalar:
Reaction source terms are eliminated from governing transport equations.
O
k
F
k
O
k
k
Z
Z
Z
Z
f
,
,
,
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Systems That Can be Modeled Using a
Single
Mixture Fraction
Fuel/air diffusion flame:
Diffusion flame with oxygen

enriched inlets:
System using multiple fuel
inlets:
60% CH
4
40% CO
21% O
2
79% N
2
f = 1
f = 0
35% O
2
65% N
2
60% CH
4
40% CO
35% O
2
65% N
2
f = 1
f = 0
f = 0
60% CH
4
20% CO
10% C
3
H
8
10% CO
2
21% O
2
79%
N
2
f = 1
f = 0
f = 1
60% CH
4
20% CO
10% C
3
H
8
10% CO
2
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Equilibrium Approximation of System
Chemistry
Chemistry is assumed to be fast enough to achieve equilibrium.
Intermediate species are included.
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PDF Modeling of Turbulence

Chemistry Interaction
Fluctuating mixture fraction is completely defined by its probability
density function (PDF).
p
(
V
), the PDF, represents fraction of sampling time when variable,
V
,
takes a value between
V
and
V
+
V
.
p
(
f
) can be used to compute time

averaged values of variables that
depend on the mixture fraction,
f
:
Species mole fractions
Temperature, density
p
V
V
T
T
i
i
(
)
lim
1
i
i
p
f
f
df
(
)
(
)
0
1
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PDF Model Flexibility
Nonadiabatic systems:
In real problems, with heat loss or gain, local thermo

chemical state must
be related to mixture fraction,
f
, and enthalpy,
h
.
Average quantities now evaluated as a function of mixture fraction,
enthalpy (normalized heat loss/gain), and the PDF,
p
(
f
).
Second conserved scalar:
With second scalar in
FLUENT
, you can model:
Two fuel streams with different compositions and single oxidizer stream
(visa versa)
Nonreacting stream in addition to a fuel and an oxidizer
Co

firing a gaseous fuel with another gaseous, liquid, or coal fuel
Firing single coal with two off

gases (volatiles and char burnout products)
tracked separately
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Mixture Fraction/PDF Model: Summary
Advantages:
Predicts formation of intermediate species.
Accounts for dissociation effects.
Accounts for coupling between turbulence and chemistry.
Does not require the solution of a large number of species transport
equations
Robust and economical
Disadvantages:
System must be near chemical equilibrium locally.
Cannot be used for compressible or non

turbulent flows.
Not applicable to premixed systems.
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The
Laminar Flamelet Model
Temperature, density and species (for adiabatic)
specified by two parameters, the mixture
fraction and scalar dissipation rate
Recall that for the mixture fraction PDF
model (adiabatic), thermo

chemical state is
function of
f
only
c
can be related to the local rate of strain
Extension of the mixture fraction PDF model to
moderate chemical nonequilibrium
Turbulent flame modeled as an ensemble of
stretched laminar, opposed flow diffusion flames
2
)
/
(
x
f
c
)
,
(
c
f
i
i
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Laminar Flamelet Model (2)
Statistical distribution of flamelet ensemble is specified by the PDF
P(f,
c
)
, which is modeled as
P
f
(f) P
c
(
c
)
, with a Beta function for
P
f
(f)
and a Dirac

delta distribution for
P
c
(
c
)
Only available for adiabatic systems in
V5
Import strained flame calculations
prePDF or Sandia’s OPPDIF code
Single or multiple flamelets
Single:
user specified strain,
a
Multiple:
strained flamelet library,
0 < a < a
extinction
a=0
equilibrium
a= a
extinction
is the maximum strain rate before flame extinguishes
Possible to model local extinction pockets (e.g. lifted flames)
1
0
0
)
(
)
(
)
,
(
df
d
P
f
P
f
f
i
i
c
c
c
c
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The Zimont Model for Premixed Combustion
Thermo

chemistry described by a single progress variable,
Mean reaction rate,
Turbulent flame speed,
U
t
, derived for lean premixed combustion and
accounts for
Equivalence ratio of the premixed fuel
Flame front wrinkling and thickening by turbulence
Flame front quenching by turbulent stretching
Differential molecular diffusion
For adiabatic combustion,
The enthalpy equation must be solved for nonadiabatic combustion
t
c
x
u
c
x
Sc
c
x
R
c
i
i
i
t
t
i
c
0
1
R
U
c
c
unburnt
t
p
ad
p
p
p
Y
Y
c
/
ad
unburnt
T
c
T
c
T
)
1
(
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Discrete Phase Model
Trajectories of particles/droplets/bubbles are
computed in a Lagrangian frame.
Exchange (couple) heat, mass, and
momentum with Eulerian frame gas phase
Discrete phase
volume
fraction must < 10%
Although the
mass
loading can be large
No particle

particle interaction or break up
Turbulent dispersion modeled by
Stochastic tracking
Particle cloud (
V5)
Rosin

Rammler or linear size distribution
Particle tracking in unsteady flows (
V5
)
Model particle separation, spray drying,
liquid fuel or coal combustion, etc.
Continuous phase
flow field calculation
Particle trajectory
calculation
Update continuous
phase source terms
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Turbulent dispersion is modeled by an ensemble of
Monte

Carlo realizations (discrete random walks)
Particles convected by the mean velocity plus a random
direction turbulent velocity fluctuation
Each trajectory represents a
group
of particles with the
same properties (initial diameter, density etc.)
Turbulent dispersion is important because
Physically realistic (but computationally more expensive)
Enhances stability by smoothing source terms and
eliminating local spikes in coupling to the gas phase
Particle Dispersion: The Stochastic Tracking Model
Coal particle tracks in an
industrial boiler
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Particle Dispersion: The Particle Cloud Model
Track mean particle trajectory along mean velocity
Assuming a 3D multi

variate Gaussian distribution about this mean
track, calculate particle loading within three standard deviations
Rigorously accounts for inertial and drift velocities
A particle cloud is required for each particle type (e.g. initial
d,
etc.)
Particles can escape, reflect or trap (release volatiles) at walls
Eliminates (single cloud) or reduces (few clouds) stochastic tracking
Decreased computational expense
Increased stability since distributed source terms in gas phase
BUT decreased accuracy since
Gas phase properties (e.g. temperature) are averaged within cloud
Poor prediction of large recirculation zones
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Particle Tracking in Unsteady Flows
Each particle advanced in time along with the flow
For coupled flows using implicit time stepping, sub

iterations for the particle
tracking are performed within each time step
For non

coupled flows or coupled flows with explicit time stepping, particles
are advanced at the end of each time step
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Coal/Oil Combustion Models
Coal or oil combustion modeled by changing the modeled particle to
Droplet

for oil combustion
Combusting particle

for coal combustion
Several devolatilization and char burnout models provided.
Note
: These models control the rate of evolution of the fuel off

gas from
coal/oil particles. Reactions in the gas (continuous) phase are modeled
with the PDF or finite rate combustion model.
Particle Type
Description
Inert
inert/heating or cooling
Droplet (oil)
heating/evaporation/boiling
Combusting (coal)
heating;
evolution of volatiles/swelling;
heterogeneous surface reaction
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NO
x
Models
NO
x
consists of mostly nitric oxide (NO).
Precursor for smog
Contributes to acid rain
Causes ozone depletion
Three mechanisms included in
FLUENT
for NO
x
production:
Thermal NO
x

Zeldovich mechanism (oxidation of atmospheric N)
Most significant at high temperatures
Prompt NO
x

empirical mechanisms by De Soete, Williams, etc.
Contribution is in general small
Significant at fuel rich zones
Fuel NO
x

Empirical mechanisms by De Soete, Williams, etc.
Predominant in coal flames where fuel

bound nitrogen is high and
temperature is generally low.
NO
x
reburn chemistry (
V5
)
NO can be reduced in fuel rich zones by reaction with hydrocarbons
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Soot modeling in
FLUENT
Two soot formation models are available:
One

step model (Khan and Greeves)
Single transport equation for soot mass fraction
Two

Step model (Tesner)
Transport equations for radical nuclei and soot mass fraction
concentrations
Soot formation modeled by empirical rate constants
where,
C
,
p
f
, and
F
are a model constant, fuel partial pressure and
equivalence ratio, respectively
Soot combustion (destruction) modeled by Magnussen model
Soot affects the radiation absorption
Enable Soot

Radiation option in the Soot panel
RT
E
n
f
formation
e
p
C
R
/
F
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Combustion Guidelines and Solution Strategies
Start in 2D
Determine applicability of model physics
Mesh resolution requirements (resolve shear layers)
Solution parameters and convergence settings
Boundary conditions
Combustion is often very sensitive to inlet boundary conditions
Correct velocity and scalar profiles can be critical
Wall heat transfer is challenging to predict; if known, specify wall
temperature instead of external convection/radiation BC
Initial conditions
While steady

state solution is independent of the IC, poor IC may cause
divergence
due to the number and nonlinearity of the transport equations
Cold flow solution, then gas combustion, then particles, then radiation
For strongly swirling flows, increase the swirl gradually
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Combustion Guidelines and Solution Strategies (2)
Underrelaxation Factors
The effect of under

relaxation is highly nonlinear
Decrease the diverging residual URF in increments of 0.1
Underrelax density when using the mixture fraction PDF model (0.5)
Underrelax velocity for high bouyancy flows
Underrelax pressure for high speed flows
Once solution is stable, attempt to increase all URFs to as close to defaults as possible
(and at least 0.9 for
T, P

1
, swirl and species (or mixture fraction statistics))
Discretization
Start with first order accuracy, then converge with second order to improve accuracy
Second order discretization especially important for tri/tet meshes
Discrete Phase Model

to increase stability,
Increase number of stochastic tracks (or use particle cloud model)
Decrease DPM URF and increase number of gas phase iterations per DPM
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Combustion Guidelines and Solution Strategies (3)
Magnussen model
Defaults to finite rate/eddy

dissipation (Arrhenius/Magnussen)
For nonpremixed (diffusion) flames turn off finite rate
Premixed flames require Arrhenius term so that reactants don’t burn
prematurely
May require a high temperature initialization/patch
Use temperature dependent C
p
’s to reduce unrealistically high temperatures
Mixture fraction PDF model
Model of choice if underlying assumptions are valid
Use adequate numbers of discrete points in look up tables to ensure
accurate interpolation (no affect on run

time expense)
Use beta PDF shape
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Combustion Guidelines and Solution Strategies (4)
Turbulence
Start with standard
k

model
Switch to RNG
k

, Realizable
k

or RSM to obtain better agreement
with data and/or to analyze sensitivity to the turbulence model
Judging Convergence
Residuals should be less than 10

3
except for
T
,
P

1 and species
, which
should be less than 10

6
The mass and energy flux reports must balance
Monitor variables of interest (e.g. mean temperature at the outlet)
Ensure contour plots of field variables are smooth, realistic and steady
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Concluding Remarks
FLUENT V5
is the code of choice for combustion modeling.
Outstanding set of physical models
Maximum convenience and ease of use
Built

in database of mechanisms and physical properties
Grid flexibility and solution adaption
A wide range of reacting flow applications can be addressed by the
combustion models in
FLUENT
.
Make sure the physical models you are using are appropriate for your
application.
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