- Turbulence models: k-?, RNG k-?, RSM, Realizable k-? (V5) and LES (V5)
- Pollutant models: NOx with reburn chemistry (V5) and soot
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
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, mj , 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).
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.
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.
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.
Mixture Fraction Definition
- The mixture fraction, f, can be written in terms of elemental mass fractions as:
where Zk 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.
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:
Equilibrium Approximation of System Chemistry
- Chemistry is assumed to be fast enough to achieve equilibrium.
- Intermediate species are included.
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
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
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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