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Advanced Combustion
Modelingin FLUENT
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Course Agenda8:00- 8:30 Introduction to Combustion Modeling
8:30-10:00 Combustion Models I
10:00-11:00 Hands-on Exercise Session I
11:00-12:00 Combustion Models II
12:00-1:00 Lunch
1:00-1:45 Additional Physical ModelsDiscrete Phase Modeling and Spray Models
1:45-2:30 Additional Physical Models
Radiation Modeling
Pollutant Modeling
2:30-3:00 Combustion Modeling
Case Studies
Strategies
3:00-5:00 Hands-on Exercise Session II
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Introduction to Combustion Modeling
Applications of Combustion Modeling
Overview of Capabilities in FLUENT 6
Meshes for Combustion Simulations
Kinetics and Turbulence-Chemistry Interaction
Scaling Analysis
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Applications of Combustion Modeling Wide range of homogeneous
and heterogeneous reacting
flows:z Furnaces
z Boilers
z Process heaters
z Gas turbines
z Rocket engines
Predictions of:
z Flow field and mixingcharacteristics
z Temperature field
z Species concentrations
z Particulates and pollutants
Temperature in a Gas Furnace
CO2 Mass Fraction
Stream Function
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Overview of Combustion Modeling FLUENT 6provides an extensive array of physical models for combustion
simulations.
Zone-based definition of volumetric and surface reaction mechanisms
z Reactions can be turned off/on in different fluid zones
z Allow different reaction mechanisms in different zones
FLUENT 6provides maximum mesh flexibility, and GAMBIT 2
makes it easy to generate hybrid meshes.
Additional distinctive capabilities include:
z Materials database
z Robust and accurate solver
z Solution-adaptive mesh refinement (conformal and hanging-node)
z Industry-leading parallel performance
z User-friendly GUI, post-processing and reporting
z Highly customizable through user defined functions
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Aspects of Reaction Modeling
Dispersed Phase Models
Droplet/particle dynamics
Heterogeneous reaction
Devolatilization
Evaporation Governing Transport
Equations
Mass
Momentum (turbulence)
Energy
Chemical Species
Pollutant Models Radiative Heat
Transfer Models
Reaction Models
Combustion
Premixed, Partially premixed
andNon-premixed
Infinitely Fast Chemistry
Finite Rate Chemistry
Surface Reactions
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Reaction Models in Fluent
Laminar Finite-Rate Model
Eddy-Dissipation Concept (EDC) Model
Composition PDF transport Model
Non-Premixed
Laminar Flamelet
ModelFinite-RateChemistry
Eddy Dissipation Model
Partially
Premixed Model
(Reaction Progress
Variable + Mixture
Fraction)
Non-Premixed
Equilibrium
Model
(Mixture Fraction)
Premixed
Combustion
Model
(Reaction Progress
Variable)*
Infinitely Fast
Chemistry
Partially
Premixed
Combustion
Non-Premixed
Combustion
Premixed
Combustion
* Rate classification not truly applicable since species mass fraction is not determined.
Flow config.
Chemistry
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Surface Combustion
Discrete phase modelz Turbulent particle dispersion
Stochastic tracking
Particle cloud model
z Pulverized coal and spray models
Radiation models: DTRM, P-1, Rosseland, S2S and Discrete Ordinates
Turbulence models: k-, RNG k-, Realizable k-, , RSM and LES and
DES
Pollutant models: NOx with reburn chemistry and soot
Other Models in FLUENT 6
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Meshes for Combustion Simulations For convergence and accuracy, a quality mesh is critical ...
z Low skew (
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Complicated Geometry-Tetrahedral Mesh
Burner has several
complicated parts Flow is not aligned
in any particular
direction
High gradients atsonic inlets
Use a tetrahedral
mesh
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Complicated Geometry-Tetrahedral Mesh
Tetrahedral mesh
allows for a finemesh on the small
inlet holes with
larger cells in the
furnace domain.
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Hybrid Mesh - Boiler
hexes
pyramids
tets
Conical section at bottom
favors a tetrahedral mesh
Heat exchanger plates at top
are suited for a hex mesh
Prisms can be extruded off
the triangular surface at the
corner inlet planes to model
the windbox - get better jet
penetration
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Semi-Automatic Hex/Hybrid Meshing
Nuclear Reactor HeadTypical Burner
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FLUENT 6: Arbitrary Mesh Interfaces Mesh flexibility,
parts-based meshing
and model building
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Mesh Adaption Dynamic hanging node adaption to resolve temperature gradients more accurately.
300 kW BERL Combustor
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Gas Phase Combustion Spatio-temporal conservation equations (Navier-Stokes) for
z Mass ()
z Momentum ()z Energy (h)
z Chemical Species (Yk)
The conservation equations have the general form
rate of change convection diffusion source
It is useful to quantify energy in terms of enthalpy, defined as .
chemical thermal
( ) ( ) +
=
+
Sx
Dx
uxt ii
i
i
+=species
T
T
pk
o
kko
)dTch(Yh
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Chemical Kinetics The kth species mass fraction transport equation is:
Nomenclature: chemical species, denoted Sk, react as:
Example:
( ) ( ) ki
kk
i
ki
i
k RxYD
xYu
xY
t+
=
+
==
N
1k
kk
N
1k
kk S"S'
OH2COO2CH 2224 ++
2"1"0"0"
0'0'2'1'
OHSCOSOSCHS
4321
4321
24232241
====
====
====
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Chemical Kinetics The calculated reaction rate is proportional to the products of the
reactant concentrations raised to the power of their respective
stoichiometric coefficients.
kth species reaction rate (for a single reaction):
where A = pre-exponential factor
Cj = molar concentration =Yj/ MjMk = molecular weight of species k
E= activation energy
R = universal gas constant = 8313 J / kgmol K
= temperature exponent
Note that for global reactions, , and may be noninteger
=
=
N
1j
'
jRT
E
kkkk
*kCeAT)'"(MR
k*k ''
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Flames Length
scale (m)
Velocity
scale (m/s)
Reynolds
number
Gas turbine combustor 0.1 50 250,000
Fire 5 2 500,000
After-burner 0.5 100 2,500,000
Utility Furnace 10 10 5,000,000
Practical Combustion Processes are Turbulent
Smallest length scale in turbulent flow (called the Kolmogorov scale)
L / Re3/4
, whereL is the combustor characteristic dimension
Number of grid points required for Direct Numerical Simulation (DNS)(resolving all flow scales) ~ (L/)
3= Re
9/4
Example:Re ~ 10 4, number of grid points ~ 10 9
DNS is computationally intractable, and will remain so indefinitely
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Necessity for Combustion Modeling Governing reacting Navier-Stokes equations are accurate,
but DNS is prohibitive ...
Turbulence
z Large range of time and length scales
z Model by time (Reynolds) averaging
Imagine a long exposure photograph of the
visualized flow
Introduces terms (the Reynolds stresses) which must be modeled
Chemistryz Realistic chemical mechanisms have tens of species, hundreds of
reactions, and stiff kinetics (widely disparate time scales)
Determined for a limited number of fuels
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Reynolds (Time) Averaged Species Equation
{unsteady term} convection convection molecular mean
(zero for by mean by turbulent diffusion chemical
steady flows) velocity velocity fluctuations source term
are the kth species mass fraction, diffusion coefficient and
chemical source term respectively
Turbulent flux term modeled by mean gradient diffusion as,, which is consistent in the k- context
Gas phase combustion modeling focuses on
z Arguably more difficult to model than the Reynolds stresses (turbulence)
( ) ( ) ( ) ki
kk
i
ki
i
ki
i
k Rx
YD
x"Y"u
xYu
xY
t+
=
+
+
kkk R,D,Y
kR
ikttki x/Y/ScY"u" =
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Turbulence Chemistry Coupling in Flames
( )RTEexpCATRj
jkj =
Arrhenius reaction rate terms are highly nonlinear
Cannot neglect the effects of turbulence fluctuations on chemical
production rates
)T(RR kk
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Turbulence-Chemistry InteractionDemonstration: single step methane reaction (A=2*1011, E=2*108)
Assume turbulent fluid at a point has constant species concentration at all
times, but spends one third its time at T=300K, T=1000K and T=1700K
3.0
2
2.0
4OH21
COO21
CH
2224
]O[]CH[)RT/Eexp(ARRRR
OH2COO2CH
2224====
++
t
T1700
1000
300
time trace
T
P(T)
PDF
300 1000 1700
T [K] 300 1000 1700
R [kgm-3s-1] 10-25 1 105 134
13
smkg103R
smkg1)T(R
=
=
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Modeling Chemical Kinetics in Combustion
Practical Approaches:
Reduced chemical mechanismsz Finite rate/Eddy Dissipation model
Decouple chemistry from turbulent flow and mixing
z Mixture fraction approaches Equilibrium chemistry PDF model
Laminar flamelet model
z Progress variable
Zimont model
z Mixture fraction and progress variable
Partially premixed combustion model
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Scaling Analysis
forceviscous
forceinertial~
ULRe
=
, U, L, are characteristic (e.g. inlet) density, velocity, length and
dynamic viscosity, respectively
Turbulence models valid at highRe
scaletimechemical
scaletimemixing~
R/
/k~
R/
U/LDa
slowadslowad
=
adiabatic flame density
slowest reaction rate at and stoichiometric concentrations
ad
adTslowR
Gas phase turbulent combustion models valid at highDa
Reynolds number
Damkohler Number
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Mach number
Boltzman number
speedacoustic
speedconvection~
c
UMa =
fluxheatradiation
fluxheatconvection~
T
)TUc(Bo
4
ad
inletp
=
Stefan-Boltzman constant (5.672 10-8 W/m2K4)
Radiation important atBo < 10
Mixture fraction model valid atMa < 0.3 (incompressible)
(assumes convection overwhelms conduction)
Scaling Analysis