Fluent Ansys- Advanced Combustion Systems 1 Intro
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Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Advanced Combustion Modeling in FLUENT
1 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Course Agenda 8:00- 8:30 8:30-10:00 10:00-11:00 11:00-12:00 12:00-1:00 1:00-1:45 1:45-2:30
2:30-3:00
3:00-5:00
Introduction to Combustion Modeling Combustion Models I Hands-on Exercise Session I Combustion Models II Lunch Additional Physical Models – Discrete Phase Modeling and Spray Models Additional Physical Models – Radiation Modeling – Pollutant Modeling Combustion Modeling – Case Studies – Strategies Hands-on Exercise Session II 2 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
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
3 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Applications of Combustion Modeling
Wide range of homogeneous and heterogeneous reacting flows: z z z z z
Furnaces Boilers Process heaters Gas turbines Rocket engines
Temperature in a Gas Furnace
Predictions of: z
z z z
CO2 Mass Fraction
Flow field and mixing characteristics Temperature field Species concentrations Particulates and pollutants
Stream Function 4 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Overview of Combustion Modeling
FLUENT 6 provides an extensive array of physical models for combustion simulations. Zone-based definition of volumetric and surface reaction mechanisms z z
Reactions can be turned off/on in different fluid zones Allow different reaction mechanisms in different zones
FLUENT 6 provides maximum mesh flexibility, and GAMBIT 2 makes it easy to generate hybrid meshes.
Additional distinctive capabilities include: z z z z z z
Materials database Robust and accurate solver Solution-adaptive mesh refinement (conformal and hanging-node) Industry-leading parallel performance User-friendly GUI, post-processing and reporting Highly customizable through user defined functions
5 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Aspects of Reaction Modeling Reaction Models Dispersed Phase Models Droplet/particle dynamics Heterogeneous reaction Devolatilization Evaporation
Infinitely Fast Chemistry Finite Rate Chemistry
Combustion
Governing Transport Equations Mass Momentum (turbulence) Energy Chemical Species
Premixed, Partially premixed and Non-premixed
Surface Reactions
Radiative Heat Transfer Models
Pollutant Models
6 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Reaction Models in Fluent Flow config.
Premixed Combustion
Non-Premixed Combustion
Partially Premixed Combustion
Premixed Combustion Model (Reaction Progress Variable)*
Non-Premixed Equilibrium Model (Mixture Fraction)
Partially Premixed Model
Chemistry
Infinitely Fast Chemistry
(Reaction Progress Variable + Mixture Fraction)
Eddy Dissipation Model Non-Premixed Laminar Flamelet Model
Finite-Rate Chemistry
Laminar Finite-Rate Model Eddy-Dissipation Concept (EDC) Model Composition PDF transport Model * Rate classification not truly applicable since species mass fraction is not determined. 7 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Other Models in FLUENT 6
Surface Combustion Discrete phase model z
Turbulent particle dispersion
z
Stochastic tracking Particle cloud model
Pulverized coal and spray models
Radiation models: DTRM, P-1, Rosseland, S2S and Discrete Ordinates Turbulence models: k-ε, RNG k-ε, Realizable k-ε, κ−ω, RSM and LES and DES Pollutant models: NOx with reburn chemistry and soot
8 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Meshes for Combustion Simulations
For convergence and accuracy, a quality mesh is critical ... z z z z z
Low skew (<0.9 everywhere) Moderate aspect ratios (<10) Sufficient but not excessive resolution Gradual cell volume changes (<30%) Orthogonality at boundaries
In FLUENT 6, unstructured mesh technology allows ... z z z
Complex geometries GAMBIT provides rapid and powerful unstructured mesh generation Local resolution of flow features
Hybrid mesh (hexes, tets, prisms, pyramids) Hanging node adaption Non-conformal interfaces
9 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Complicated Geometry-Tetrahedral Mesh
Burner has several complicated parts Flow is not aligned in any particular direction High gradients at sonic inlets Use a tetrahedral mesh
10 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Complicated Geometry-Tetrahedral Mesh
Tetrahedral mesh allows for a fine mesh on the small inlet holes with larger cells in the furnace domain.
11 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Hybrid Mesh - Boiler
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
hexes pyramids tets
12 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Semi-Automatic Hex/Hybrid Meshing
Typical Burner
Nuclear Reactor Head 13 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
FLUENT 6: Arbitrary Mesh Interfaces
Mesh flexibility, parts-based meshing and model building
14 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Mesh Adaption
Dynamic hanging node adaption to resolve temperature gradients more accurately.
300 kW BERL Combustor
15 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Gas Phase Combustion
Spatio-temporal conservation equations (Navier-Stokes) for z Mass (ρ) z Momentum (ρυ) z Energy (ρh) z Chemical Species (ρYk) The conservation equations have the general form … ∂ (φ) + ∂ (φ ui ) = ∂ Dφ ∂φ + Sφ ∂xi ∂xi ∂xi ∂t rate of change
convection
diffusion
source
It is useful to quantify energy in terms of enthalpy, defined as ….
h=
∑
species
T
Yk ( h + ∫ cpk dT) o k
chemical 16 / 26
To
thermal © Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Chemical Kinetics
The k th species mass fraction transport equation is: ∂ (ρ Yk ) + ∂t
∂ (ρ u i Yk ) = ∂x i
∂ Yk ρ D k ∂x i
∂ ∂x i
+
Rk
Nomenclature: chemical species, denoted Sk , react as: N
∑ ν' k =1
Example:
k
Sk →
N
∑ ν" k =1
k
Sk
CH 4 + 2O 2 → CO 2 + 2H 2 O
S1 = CH 4
S2 = O 2
S3 = CO 2
S4 = H 2 O
ν'1 = 1 ν"1 = 0
ν '2 = 2 ν"2 = 0
ν'3 = 0 ν"3 = 1
ν '4 = 0 ν"4 = 2
17 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Chemical Kinetics
The calculated reaction rate is proportional to the products of the reactant concentrations raised to the power of their respective stoichiometric coefficients. k th species reaction rate (for a single reaction): E − N ν '*k β RT ∏ Cj R k = M k ( ν " k − ν ' k ) AT e j =1 where
A = pre-exponential factor Cj = molar concentration = ρ Yj / Mj Mk = molecular weight of species k E = activation energy R = universal gas constant = 8313 J / kgmol K β = temperature exponent
Note that for global reactions, ν ' k* ≠ ν ' k , and may be noninteger 18 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Practical Combustion Processes are Turbulent Flames Gas turbine combustor Fire
Length scale (m) 0.1
Velocity Reynolds scale (m/s) number 50 250,000
5
2
500,000
After-burner
0.5
100
2,500,000
Utility Furnace
10
10
5,000,000
Smallest length scale in turbulent flow (called the Kolmogorov scale) η ∼ L / Re3/4, where L is the combustor characteristic dimension Number of grid points required for Direct Numerical Simulation (DNS) 3 9/4 (resolving all flow scales) ~ (L/ η) = Re
Example: Re ~ 10 4, number of grid points ~ 10 9
DNS is computationally intractable, and will remain so indefinitely 19 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Necessity for Combustion Modeling
Governing reacting Navier-Stokes equations are accurate, but DNS is prohibitive ... Turbulence z z
Large range of time and length scales Model by time (Reynolds) averaging
Imagine a long exposure photograph of the visualized flow Introduces terms (the Reynolds stresses) which must be modeled
Chemistry z
Realistic chemical mechanisms have tens of species, hundreds of reactions, and stiff kinetics (widely disparate time scales)
Determined for a limited number of fuels
20 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Reynolds (Time) Averaged Species Equation
(
∂ ∂ (ρ u i Yk ) + ∂ ρ u "i Y "k (ρ Yk ) + ∂x i ∂x i ∂t {unsteady term} (zero for steady flows)
convection by mean velocity
)
=
convection by turbulent velocity fluctuations
∂ ∂x i
∂ Yk ρ D k + R k ∂x i
molecular diffusion
mean chemical source term
Yk , Dk , Rk are the k th species mass fraction, diffusion coefficient and
chemical source term respectively
Turbulent flux term modeled by mean gradient diffusion as, ρ u" i Y" k = µ t /Sc t ⋅ ∂ Yk /∂ xi , which is consistent in the k-ε context Gas phase combustion modeling focuses on Rk z
Arguably more difficult to model than the Reynolds stresses (turbulence) 21 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Turbulence Chemistry Coupling in Flames
Arrhenius reaction rate terms are highly nonlinear
Rk = AT β ∏ C j j exp (− E RT ) ν
j
Cannot neglect the effects of turbulence fluctuations on chemical production rates
Rk ≠ Rk ( T )
22 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Turbulence-Chemistry Interaction Demonstration: single step methane reaction (A=2*1011, E=2*108) CH 4 + 2O 2 → CO 2 + 2H 2 O R CH 4 =
1
2
R O 2 = − R CO 2 = − 1 2 R H 2O = − A exp( − E / RT ) [CH 4 ]0.2 [O 2 ]0.3
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 1700 1000 300
T P(T)
time trace
PDF
t
T [K] R [kgm-3s-1]
300 10-25
1000 1
300 1000 1700
1700 105
23 / 26
T
R (T ) = 1 kg ⋅ m −3 s −1 R = 3 ⋅10 4 kg ⋅ m −3 s −1
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Modeling Chemical Kinetics in Combustion Practical Approaches: Reduced chemical mechanisms z
Finite rate/Eddy Dissipation model
Decouple chemistry from turbulent flow and mixing z
z
z
Mixture fraction approaches Equilibrium chemistry PDF model Laminar flamelet model Progress variable Zimont model Mixture fraction and progress variable Partially premixed combustion model
24 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Scaling Analysis
Reynolds number ρUL inertial force ~ Re = µ viscous force
ρ, U, L, µ are characteristic (e.g. inlet) density, velocity, length and dynamic viscosity, respectively Turbulence models valid at high Re
Damkohler Number Da =
L/U k/ε mixing time scale ~ ~ ρ ad / R slow ρ ad / R slow chemical time scale
ρ ad adiabatic flame density Rslow slowest reaction rate at Tad and stoichiometric concentrations
Gas phase turbulent combustion models valid at high Da 25 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Scaling Analysis
Mach number Ma =
U convection speed ~ c acoustic speed
Mixture fraction model valid at Ma < 0.3 (incompressible)
Boltzman number Bo =
(ρUc p T ) inlet σTad4
~
convection heat flux radiation heat flux
σ Stefan-Boltzman constant (5.672 10-8 W/m2K4) (assumes convection overwhelms conduction) Radiation important at Bo < 10 26 / 26
© Fluent Inc. 6/23/2005
Fluent Software Training Combustion Apr 2005
Advanced Combustion Modeling in FLUENT
1 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Course Agenda 8:00- 8:30 8:30-10:00 10:00-11:00 11:00-12:00 12:00-1:00 1:00-1:45 1:45-2:30
2:30-3:00
3:00-5:00
Introduction to Combustion Modeling Combustion Models I Hands-on Exercise Session I Combustion Models II Lunch Additional Physical Models – Discrete Phase Modeling and Spray Models Additional Physical Models – Radiation Modeling – Pollutant Modeling Combustion Modeling – Case Studies – Strategies Hands-on Exercise Session II 2 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
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
3 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Applications of Combustion Modeling
Wide range of homogeneous and heterogeneous reacting flows: z z z z z
Furnaces Boilers Process heaters Gas turbines Rocket engines
Temperature in a Gas Furnace
Predictions of: z
z z z
CO2 Mass Fraction
Flow field and mixing characteristics Temperature field Species concentrations Particulates and pollutants
Stream Function 4 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Overview of Combustion Modeling
FLUENT 6 provides an extensive array of physical models for combustion simulations. Zone-based definition of volumetric and surface reaction mechanisms z z
Reactions can be turned off/on in different fluid zones Allow different reaction mechanisms in different zones
FLUENT 6 provides maximum mesh flexibility, and GAMBIT 2 makes it easy to generate hybrid meshes.
Additional distinctive capabilities include: z z z z z z
Materials database Robust and accurate solver Solution-adaptive mesh refinement (conformal and hanging-node) Industry-leading parallel performance User-friendly GUI, post-processing and reporting Highly customizable through user defined functions
5 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Aspects of Reaction Modeling Reaction Models Dispersed Phase Models Droplet/particle dynamics Heterogeneous reaction Devolatilization Evaporation
Infinitely Fast Chemistry Finite Rate Chemistry
Combustion
Governing Transport Equations Mass Momentum (turbulence) Energy Chemical Species
Premixed, Partially premixed and Non-premixed
Surface Reactions
Radiative Heat Transfer Models
Pollutant Models
6 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Reaction Models in Fluent Flow config.
Premixed Combustion
Non-Premixed Combustion
Partially Premixed Combustion
Premixed Combustion Model (Reaction Progress Variable)*
Non-Premixed Equilibrium Model (Mixture Fraction)
Partially Premixed Model
Chemistry
Infinitely Fast Chemistry
(Reaction Progress Variable + Mixture Fraction)
Eddy Dissipation Model Non-Premixed Laminar Flamelet Model
Finite-Rate Chemistry
Laminar Finite-Rate Model Eddy-Dissipation Concept (EDC) Model Composition PDF transport Model * Rate classification not truly applicable since species mass fraction is not determined. 7 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Other Models in FLUENT 6
Surface Combustion Discrete phase model z
Turbulent particle dispersion
z
Stochastic tracking Particle cloud model
Pulverized coal and spray models
Radiation models: DTRM, P-1, Rosseland, S2S and Discrete Ordinates Turbulence models: k-ε, RNG k-ε, Realizable k-ε, κ−ω, RSM and LES and DES Pollutant models: NOx with reburn chemistry and soot
8 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Meshes for Combustion Simulations
For convergence and accuracy, a quality mesh is critical ... z z z z z
Low skew (<0.9 everywhere) Moderate aspect ratios (<10) Sufficient but not excessive resolution Gradual cell volume changes (<30%) Orthogonality at boundaries
In FLUENT 6, unstructured mesh technology allows ... z z z
Complex geometries GAMBIT provides rapid and powerful unstructured mesh generation Local resolution of flow features
Hybrid mesh (hexes, tets, prisms, pyramids) Hanging node adaption Non-conformal interfaces
9 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Complicated Geometry-Tetrahedral Mesh
Burner has several complicated parts Flow is not aligned in any particular direction High gradients at sonic inlets Use a tetrahedral mesh
10 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Complicated Geometry-Tetrahedral Mesh
Tetrahedral mesh allows for a fine mesh on the small inlet holes with larger cells in the furnace domain.
11 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Hybrid Mesh - Boiler
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
hexes pyramids tets
12 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Semi-Automatic Hex/Hybrid Meshing
Typical Burner
Nuclear Reactor Head 13 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
FLUENT 6: Arbitrary Mesh Interfaces
Mesh flexibility, parts-based meshing and model building
14 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Mesh Adaption
Dynamic hanging node adaption to resolve temperature gradients more accurately.
300 kW BERL Combustor
15 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Gas Phase Combustion
Spatio-temporal conservation equations (Navier-Stokes) for z Mass (ρ) z Momentum (ρυ) z Energy (ρh) z Chemical Species (ρYk) The conservation equations have the general form … ∂ (φ) + ∂ (φ ui ) = ∂ Dφ ∂φ + Sφ ∂xi ∂xi ∂xi ∂t rate of change
convection
diffusion
source
It is useful to quantify energy in terms of enthalpy, defined as ….
h=
∑
species
T
Yk ( h + ∫ cpk dT) o k
chemical 16 / 26
To
thermal © Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Chemical Kinetics
The k th species mass fraction transport equation is: ∂ (ρ Yk ) + ∂t
∂ (ρ u i Yk ) = ∂x i
∂ Yk ρ D k ∂x i
∂ ∂x i
+
Rk
Nomenclature: chemical species, denoted Sk , react as: N
∑ ν' k =1
Example:
k
Sk →
N
∑ ν" k =1
k
Sk
CH 4 + 2O 2 → CO 2 + 2H 2 O
S1 = CH 4
S2 = O 2
S3 = CO 2
S4 = H 2 O
ν'1 = 1 ν"1 = 0
ν '2 = 2 ν"2 = 0
ν'3 = 0 ν"3 = 1
ν '4 = 0 ν"4 = 2
17 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Chemical Kinetics
The calculated reaction rate is proportional to the products of the reactant concentrations raised to the power of their respective stoichiometric coefficients. k th species reaction rate (for a single reaction): E − N ν '*k β RT ∏ Cj R k = M k ( ν " k − ν ' k ) AT e j =1 where
A = pre-exponential factor Cj = molar concentration = ρ Yj / Mj Mk = molecular weight of species k E = activation energy R = universal gas constant = 8313 J / kgmol K β = temperature exponent
Note that for global reactions, ν ' k* ≠ ν ' k , and may be noninteger 18 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Practical Combustion Processes are Turbulent Flames Gas turbine combustor Fire
Length scale (m) 0.1
Velocity Reynolds scale (m/s) number 50 250,000
5
2
500,000
After-burner
0.5
100
2,500,000
Utility Furnace
10
10
5,000,000
Smallest length scale in turbulent flow (called the Kolmogorov scale) η ∼ L / Re3/4, where L is the combustor characteristic dimension Number of grid points required for Direct Numerical Simulation (DNS) 3 9/4 (resolving all flow scales) ~ (L/ η) = Re
Example: Re ~ 10 4, number of grid points ~ 10 9
DNS is computationally intractable, and will remain so indefinitely 19 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Necessity for Combustion Modeling
Governing reacting Navier-Stokes equations are accurate, but DNS is prohibitive ... Turbulence z z
Large range of time and length scales Model by time (Reynolds) averaging
Imagine a long exposure photograph of the visualized flow Introduces terms (the Reynolds stresses) which must be modeled
Chemistry z
Realistic chemical mechanisms have tens of species, hundreds of reactions, and stiff kinetics (widely disparate time scales)
Determined for a limited number of fuels
20 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Reynolds (Time) Averaged Species Equation
(
∂ ∂ (ρ u i Yk ) + ∂ ρ u "i Y "k (ρ Yk ) + ∂x i ∂x i ∂t {unsteady term} (zero for steady flows)
convection by mean velocity
)
=
convection by turbulent velocity fluctuations
∂ ∂x i
∂ Yk ρ D k + R k ∂x i
molecular diffusion
mean chemical source term
Yk , Dk , Rk are the k th species mass fraction, diffusion coefficient and
chemical source term respectively
Turbulent flux term modeled by mean gradient diffusion as, ρ u" i Y" k = µ t /Sc t ⋅ ∂ Yk /∂ xi , which is consistent in the k-ε context Gas phase combustion modeling focuses on Rk z
Arguably more difficult to model than the Reynolds stresses (turbulence) 21 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Turbulence Chemistry Coupling in Flames
Arrhenius reaction rate terms are highly nonlinear
Rk = AT β ∏ C j j exp (− E RT ) ν
j
Cannot neglect the effects of turbulence fluctuations on chemical production rates
Rk ≠ Rk ( T )
22 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center
Fluent Software Training Combustion Apr 2005
www.fluentusers.com
Turbulence-Chemistry Interaction Demonstration: single step methane reaction (A=2*1011, E=2*108) CH 4 + 2O 2 → CO 2 + 2H 2 O R CH 4 =
1
2
R O 2 = − R CO 2 = − 1 2 R H 2O = − A exp( − E / RT ) [CH 4 ]0.2 [O 2 ]0.3
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 1700 1000 300
T P(T)
time trace
t
T [K] R [kgm-3s-1]
300 10-25
1000 1
300 1000 1700
1700 105
23 / 26
T
R (T ) = 1 kg ⋅ m −3 s −1 R = 3 ⋅10 4 kg ⋅ m −3 s −1
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Modeling Chemical Kinetics in Combustion Practical Approaches: Reduced chemical mechanisms z
Finite rate/Eddy Dissipation model
Decouple chemistry from turbulent flow and mixing z
z
z
Mixture fraction approaches Equilibrium chemistry PDF model Laminar flamelet model Progress variable Zimont model Mixture fraction and progress variable Partially premixed combustion model
24 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Scaling Analysis
Reynolds number ρUL inertial force ~ Re = µ viscous force
ρ, U, L, µ are characteristic (e.g. inlet) density, velocity, length and dynamic viscosity, respectively Turbulence models valid at high Re
Damkohler Number Da =
L/U k/ε mixing time scale ~ ~ ρ ad / R slow ρ ad / R slow chemical time scale
ρ ad adiabatic flame density Rslow slowest reaction rate at Tad and stoichiometric concentrations
Gas phase turbulent combustion models valid at high Da 25 / 26
© Fluent Inc. 6/23/2005
Fluent User Services Center www.fluentusers.com
Fluent Software Training Combustion Apr 2005
Scaling Analysis
Mach number Ma =
U convection speed ~ c acoustic speed
Mixture fraction model valid at Ma < 0.3 (incompressible)
Boltzman number Bo =
(ρUc p T ) inlet σTad4
~
convection heat flux radiation heat flux
σ Stefan-Boltzman constant (5.672 10-8 W/m2K4) (assumes convection overwhelms conduction) Radiation important at Bo < 10 26 / 26
© Fluent Inc. 6/23/2005
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March 2021 0
Wee Budget
January 2021 0