Lecture 5: Species Transport Model 15.0 Release
Advanced Combustion Modeling
Outline •
Diffusion flame & premixed flames – Introduction & background
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Species transport – Properties & material
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Eddy dissipation Model – Theory – Model set up and solution strategies
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Reacting channel model Detailed chemistry models – Laminar, EDC and PDF transport – Chemistry acceleration tools
Non-premixed Vs Premixed Combustion •
Non-Premixed Combustion – Separate streams for Fuel and oxidizer
Fuel Oxidizer
Combustion chamber Non-Premixed
– Convection or diffusion of reactants from either side
into a flame sheet – Turbulent eddies distort the laminar flame shape and
enhance mixing – May be simplified to a mixing problem •
Premixed combustion – Fuel and oxidizer are already mixed at the molecular
level prior to ignition – Flame propagation from hot products to cold reactants – Rate of propagation (flame speed) depends on the internal flame structure – Turbulence distorts the laminar flame shape and thus accelerates flame propagation
Fuel +
Oxidizer
Combustion chamber Premixed
Turbulent Reacting Flows •
Most of the engineering engineering reacting problems are turbulent furna ces, rocket engines….. – IC Engines, gas turbines, boilers, furnaces,
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Modeling challenges – Accurately represent three interconnected phenomena
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Inhomogeneous turbulent flow
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The chemistry of combustion
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Turbulent fluctuations of temperature, species and density
Approaches – Direct Numerical Solution (DNS) •
Most accurate approach
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Not possible because of wide range of time and l ength scales involved
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So far, DNS efforts are limited to laboratory flames for research purpose
– Mean flow closure Reynolds Average Navier-Stokes (RANS) •
Most commonly used for practical purposes
– Large Eddy Simulation (LES) •
Stands in between DNS and RANS
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Larger energy scales are resolved and sub-grid energy scales are modeled
Turbulent Reacting Flows (Cont…) •
Favre averaged species equation for turbulent reacting flows
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+
=
" "
+
Involves additional term combining velocity and species fluctuations – Requires modeling
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is mean source from chemical reactions – Coupled with temperature – Can fluctuate significantly about its mean value if evaluated from mean
) temperature as ≠ ( – This term is considered to be the main challenge while using moment methods in
turbulent combustion •
Therefore, alternate closures are suggested in literature Turbulent combustion models
Modeling Turbulent Reacting Flows •
Simplify the chemistry – Use finite rate/eddy dissipation approach •
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Considers global chemical reaction mechanisms
Decouple chemistry from flow – Use mixture fraction approach •
Equilibrium chemistry PDF model
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Laminar flamelet model
– Progress variable (premixed model) – Mixture fraction and progress variable (partially premixed model) •
Model detailed chemistry (stiff chemistry) – CPU intensive – Typically requires use of very small time steps to achieve numerical stability
and convergence •
Can be impractical
use d – Use of the stiff chemistry sol ver will allow larger time steps to be used
Reacting Flow Models in Fluent 15.0 Flow Configuration Premixed Combustion
Non-Premixed Combustion
Partially Premixed Combustion
Finite Rate/Eddy Dissipation Model (Species Tr Transport) ansport)
y r t s i m e h C
Fast Chemistry Closures
Premixed Combustion Premixed Model
Non-Premixed Equilibrium Non-Premixed Model
Reaction Progress Variable
Mixture Fraction
Partially Premixed Model Reaction Progress Variable + Mixture Fraction
Steady Laminar Flamelet Model
Finite Chemistry Closures
Flamelet Generated Generated Manifold Model (Premixe (Premixed/Diffusion) d/Diffusion)
Finite Rate
Laminar Finite Rate Model
Chemistry Models
Eddy-Dissipation Concept (EDC) Model
Unsteady Laminar Flamelet Model
Composition PDF Transport Model
Species Transport Model Properties & Materials
15.0 Release
Advanced Combustion Modeling
Setting-up Mixture and Properties •
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Mixture of reacting species is defined as type “Mixture” Required species can be included as a part of mixture – Transport equations are solved for (N-1) species – Maximum 500 species can be included
Species in a mixture are defined as type “Fluid” Three types of species – Gaseous – Site CVD application – Solid e.g. Solid carbon •
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Mixture material name
Species included in a mixture
Parent mixture
Mixture properties Fluid properties
Mixture Material Properties •
Density
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Incompressible ideal gas (default) – Ideal gas law with constant operating pressure – Thus, density as a function of temperature only
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Ideal gas – Density as a function of temperature and pressure both
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Real gas equation of state – Thumb rule: Use when P/Pc > 1 and T/Tc < 2
P Pressure, T Temperature, Pc Critical pressure, Tc Critical temperature – Redlich-Kwong (RK), Aungier-Redlich-Kwong (ARK), Soave- Redlich-Kwong (SRK), PengRobinson (PR) equation of states are available •
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Volume weighted mixing law – Density of liquid mixtures should be defined as volume weighted mixing law
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User defined – DEFINE_PROPERTY UDF – Need to specify speed of sound
Mixture Material Properties (cont…) •
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Specific heat –
Mixing law (recommended option for reacting flow cases)
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Constant, Piecewise-linear, Piecewise-polynomial, Polynomial
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User defined
Thermal conductivity and Viscosity –
Several options are available
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Constant is recommended for highly turbulent flow
Absorption coefficient –
If radiation is included
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Constant; Piecewise-linear; Piecewise-polynomial; Piecewise-polynomial; Polynomial; various WSGGM options
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WSGGM-domain-based is recommended
Mass Diffusivity –
Dilute approximation (recommended for highly turbulent flow)
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Multi-component
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Unity Le diffusivity option
Species (Fluid) Material Properties •
Specific heat – Constant (default) – Piecewise-linear – Piecewise-polynomial – Polynomial
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Thermal conductivity and viscosity – Constant (default) – Piecewise-linear – Piecewise-polynomial – Polynomial
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Diffusivity – Kinetic theory (L-J parameters) – Dij coefficient
Eddy Dissipation Model 15.0 Release
Advanced Combustion Modeling
Eddy Dissipation Model •
Remove the influence of chemistry reactin g fuels ( Da >> 1) – A good assumption for fast reacting – Most of the useful fuels are fast burning
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D Brian Spalding (1971) suggested eddy break-up (EBU) model – Introduced eddy lifetime, k /
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Bjorn F Magnussen and B. H. Hjertager (1976) adapted EBU and generalized it for non-premixed and partially premixed combustion – Eddy dissipation model (EDM)
D. B. Spalding, Chemical Eng. Sci. 26-1 (1971), 95-107 th
B. F. Magnussen and B. H. Hjertager, 16 Symposium (Int.) on Combustion (1976) p. 719
Eddy Dissipation Model (Cont…) •
Reaction is mixing limited
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Chemistry is described by a global g lobal reaction mechanism – 1 or 2 steps
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Reaction rate is governed by large-eddy mixing time scale – Eddy break-up (EBU) or turbulence time scale, k / – Rate of production of a species, i due due to reaction, r •
= () , ()
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() =
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() =
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A and B are constants
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A = 4.0 and B = 0.5 suggested suggested by Magnussen
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Works fine for most of the problems
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Sometimes needs tuning to get required temperature distribution
The rates are not function of temperature
Eddy Dissipation Model (Cont…) •
Remove the influence of chemistry (Da >> 1) – Rates are mixing limited and depend on Turbulence time scale Reactants/Products mass fractions Model constants – Advantages Simple and physically based Applicable to every flow configuration – Disadvantages Rates are temperature independent React towards complete products • • •
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– – – •
Cannot capture detailed chemistry effects Does not predict intermediate species and dissociation effects Temperature over predicted
Model constants require sometimes calibration
Finite Rate/Eddy Dissipation Model •
The source term for species “i ” is the sum of sources in all participating reactions N R
Ri M i
R ˆ
i , k
k 1
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The rate of production or consumption of species “ i ” in reaction k, Rik – Computed from both •
Arrhenius rate (kinetics) Reaction rate, =
– – – •
A Ea
−
Pre exponential factor Activation energy
C f and C ox
Concentrations
The “eddy breakup” rate (mixing dependent rate)
c alculate production or consumption – Smaller of these two is used to calculate
Model Set-up • • • • •
Switch on turbulence model Switch on species transport model Enable volumetric reaction Select eddy dissipation model Mixture materials – Some default reacting mixture mixture materials
are available – Can be customized •
Material properties – Mixture
Species, reactions, density, transport properties… – Individual species Specific heat, molecular weight, standard state enthalpy and entropy… •
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Set up boundary conditions – Species mass/mole fraction
Some Tips & Tricks •
Fluent solves for ( N -1) -1) included species –
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Keep the species with abundant mass fraction as the last species
Use temperature dependent specific heat for included species –
To avoid unrealistic high temperature field
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Global reaction mechanisms •
Dissociated species are neglected. In high-temperature flames, may cause the temperature to be over-predicted
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IFRF C p polynomials (Rose and Cooper, 1977) give more realistic temperature field
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RP var for some common species like CH 4, CO2, CO, H2O, O2 , N2 … (set-ifrf-cp-polynomials ‘methane-air)
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If radiation model is employed –
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Absorption coefficient for mixture as WSGGM-domain-based
For better convergence –
Start with non-reacting flow (disable reactions)
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Patch small values for product species mass fractions in the flame region •
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Also patch higher temperature (>1500 K) for finite rate/eddy dissipation model
Run reacting flow calculation with lower species and energy with under-relaxation factors (URF) ~ 0.9 in the beginning without r adiation Final solution with species and energy URFs of 1 and radiation included
Species Reports report/species-mass-flow •
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Print list of species mass flow rate at inlets and outlets Available after performing 1 iteration
These options are more accurate than surface integrals at boundary zones since no interpolation is used. Report → Fluxes…
Characteristic Time Scale Model-Relax to equilibrium •
Extension of the Eddy Dissipation model – Species react towards chemical equilibrium state over a
characteristic time scale – No complete reaction •
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Reaction source terms for species equations are independent of the reaction mechanism Approach made affordable with ISAT (Discussed later) Relax to equilibrium: Constrained Equilibrium – Equilibrium calculations using species included in the mixture – Non-premixed model
Equilibrium using a set of species from
the thermodynamic file •
Applications – Equilibrium with species transport – To obtain initial solution for detailed kinetic simulations
Characteristic Time Scale Model Relaxation to Chemical Equilibrium model •
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The reaction source term in the i th mean species conservation equation is modeled as
This option is available for LFR, ED and FR/ED Provides more accurate predictions of intermediate intermediate species such as CO and radicals required for NOx modeling such as O and OH
Outline •
Diffusion flame & premixed flames – Introduction & background
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Species transport – Properties & material
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Eddy dissipation Model – Theory – Model set up and solution strategies
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Reacting channel model Detailed chemistry models – Laminar, EDC and PDF transport – Chemistry acceleration tools
1D Reacting Channel Model Model fluids reacting in thin tubes, which exchange exchange heat with an external flow – Flow inside the tubes is simple (pipe profile), but the chemistry is complex – Flow outside the tubes is complex, but the chemistry is usually simple (equilibrium) • Example applications: cracking furnace, fuel reformers, … •
Reacting Channel Model (cont...) •
Must resolve the outerdiameter of the channels
– No mesh inside channels – Channels can be curvilinear Channels with common properties can be grouped Flow direction specified Different chemical mechanism in different groups
1D Reacting Channel Model • • • • •
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No mesh inside the channels Channels can be curvilinear The channel can have variable cross-section Detailed chemistry chemistry in the tube (plug (p lug flow) Ability to define porous medium inside the channel Surface reactions option available
Two reacting channels with different different materials with non reacting outer flow. Results of the channel model are compared with full simulation (mesh inside Channels is resolved)
Bulk Mean Mea n Temperature Temperature
Heat Transfer Calculations Inside the Channels The plug flow equations are solved with a stiff ODE solver using time steps based on the grid size ( size of the channel element) and the local channel channel velocity •
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Convective heat transfer source :
Tw is averaged from the 3D outer flow temperature field on the resolved channel wall The heat transfer coefficient is calculated as : •
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Where: Kc :gas-phase thermal conductivity Dc : channel diameter N can be calculated from empirical correlations • •
Outer Flow in the Domain The energy solution of the outer flow uses a prescribed heat flux boundary condition at the channel walls from the solution of the reacting channel •
Under relaxation parameter
Channel heat gain/loss
Heat flux from previous iteration
Reacting Flow Channel Options Surface chemistry / Porous medium in the channel •
– The reacting channel can be model as porous
medium – Pressure drop will be taken into account – Surface chemistry can be included •
Post-processing – Average quantities from the channel outlet
can be printed out directly – Plot options (one variable can be plot on
multiple channels in the same plot)
Outline •
Diffusion flame & premixed flames – Introduction & background
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Species transport – Properties & material
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Eddy dissipation Model – Theory – Model set up and solution strategies
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Reacting channel model Detailed chemistry models – Laminar, EDC and PDF transport – Chemistry acceleration tools
Summary •
Eddy dissipation Model – Theory – Model set up and solution strategies
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Reacting channel model – Theory and model set up
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Several tutorials available for these models