Combustion Models

rangebeaverMechanics

Feb 22, 2014 (3 years and 3 months ago)

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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.