Combustion involves chemical reactions converting fuel and oxygen to combustion products with light and heat energy. It involves fluid flow, consumption and generation of species by chemical kinetics and heat transfer ( convection and radiation).
Combustion becomes more complex because of phenomena of flame propagation, slow or fast ignition, explosions, slow ignition, correct fuel to oxidizer ratios, phase change for liquid fuel,and so forth depend in subtle ways on the conditions under which combustion takes place.
Modeling Chemical Kinetics in Combustion, the user must be familiar with the problems of fast or slow chemistry problems
Basic subjects for Combustion Modeling
Basics of combsution are explained in the previous post. CFD user has to brush up the following subject before going to combustion modeling
Thermodynamics : Laws of thermodynamics action, thermodynamics states (T, u, V, h, s) and mixture properties ( mass or mole basis) in reactive flows, Heat release rate (HHV/LHV)
Fluid mechanics: Governing equations in Laminar and turbulent flow
Heat and mass transfer: Governing equations for conduction, convection and radiative heat transfer, Species transport equations.
Chemical Kinetics:Reaction rate (forward and backward), consumption and production of species, chemical equilibrium
Numerical Methods/Basic of CFD Modeling:Discretization method or scheme of governing equations for convection, diffusion and source terms. Pressure-velocity coupling and Solution Procedure
Application of Combustion Modeling
Burners: LPG gas stoves,Furnaces, Boilers, Gasifier etc.
Engine : Petrol and diesel engines
Gas turbine combustor: Power plant steam turbine, air-craft gas turbine combustor etc.
Safety: protection fromfires, explosions or blast etc.
Emission controls: Design and development of low NOx/SOx burner or combustor
Examples of Combustion for premixed and non-premixed are given below
IC Engine examples premixed and non-premixed are given below: the combustion mechanism is changed due to change in mixing and type of fuel
Example of burner for steam generation (for demo only)
Typical burner: major components of burners are given as
Fuel (gas) inlet can me more for low NOx fuel staged burner
Governing Equation for non-premixed turbulent combustion:
For more details of combustion modeling, refer combustion books given in the reference section
Chemical kinetics are also important for combustion modelings
Classification of Combustion Modeling
The Damköhler number (Da) is dimensionless numbers used in reactive flow to relate the chemical reaction timescale (reaction rate) to the transport phenomena rate (flow time scale) occurring in a system. This number is named after German chemist Gerhard Damköhler.
Damkohler number, Da = Turbulent flow time/chemistry time
Da ~ 1: Slow chemistry , Da >> 1 : Fast Chemistry
Example of Fast and Slow Chemistry
Example of fast chemistry combustion from burner
Example of slow chemistry combustion from the plume flow from chimney
Classification of Combustion Model based on Da
Da is an important parameter for selection of reaction models and turbulent chemistry interaction (TCI) models
As per type of combustion, species transport model is selected
Before selecting the models , CFD user must study the basic theory of combustion and assumption for combustion models given in ANSYS FLUENT Theory Guide
Overview of Combustion Models in Star CCM+
In star CCM+, based on chemistry and type of phase combustion models are selected
The basic idea of CFD modeling is same irrespective of CFD solvers
In Star CCM, the multi-component gas combustion is classified based on type of fuel and air mixing and emissions
Classification Based on Mixing Mechanism of Fuel and Oxidizer:
Premixed combustion
In the mixing chamber, fuel and oxidizer (air) are already mixed at the molecular level before ignition or combustion
Cold reactants propagate into hot products
Rate of propagation (flame speed) depends on the internal flame structure
Much more difficult to model than non-premixed combustion problems
Turbulence distorts the laminar
Examples: SI enginer, LPG gas stove etc.
Schematic of premixed combustion
Non-premixed combustion
Separate inlet/ streams for Fuel and oxidizer (air) to the combustion chamber
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
Examples: Burner for boiler /furnaces, coal combustion, candle flame, wood fire etc.
Schematic of non-premixed combustion
Partially premixed combustion
In some applications, primary air (oxidizer) is mixed with fuel to form the unburnt mixture before combustion such cases are treated as partially premixed combustion.
Premixed fuel/oxidizer inlet streams
Schematic of partially-premixed combustion
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Modeling of Premixed Combustion Model
Premixed Flame Structure
The structure of premixed combustion is given as below
There are four major zones: unburnt mixture, prehated zones, reaction zones, burned mixture
The flame is defined within the preheated and reaction zones
Schematic of Premixed combustion Structure: Local velocity (without the effect wrinkles)
Turbulent Premixed Combustion Models
• In this case, a reaction progress variable is used to tracks the position of the flame front (e.g. Zimont model).
Applicability of Models
Flow Regime: Turbulent flow (high Re)
Chemistry: Fast Chemistry
Configuration: Premixed only
Premixed CFD Models available in FLUENT
Progress variable (C) equation (RANS based)
Extended Coherent Flame Model (RANS based)
cLevel Set (G) Equation (Not RANS based)
Limitations of Premixed CFD Models:
Cannot realistically model phenomena which depend on detailed kinetics (such as ignition, extinction).
Progress Variable (C-equation)
The premixed flame is modeled as a Progress Variable (Progress of Fuel Consumption) propagating at SL
On the product side, the progress variable is 1
On the reactant side, the progress variable (c) is equal to 0
The flame has no thickness and is represented by the progress variable discontinuity
Governing Equation for Premixed Combustion
Concept of Progress Variable for Premixed flame flame front capturing
Turbulent Flame Speed Model for Premixed Combustion
The important part of premixed combustion model is the prediction of turbulent flame speed (St),which is normal to the mean surface of the flame.
The turbulent flame speed is influenced by the following:
laminar flame speed, which is capitulated by the fuel concentration, temperature, and molecular diffusion properties,
detailed chemical kinetics flame front wrinkling and stretching by large eddies, and flame thickening by small eddies
Summary of Turbulent flame Speed for Premixed Flames
Depends upon the thermo-chemical state of the mixture
Depends upon the turbulence intensity
Depends upon the turbulence length scale
Zimont Flame Speed Model
The turbulent flame speed is determined
The turbulent flame speed can be written in terms of flow and chemistry time scales
St = A * ( Turbulent time scale/chemical time scale)^0.25 = A* (Da)^0.25
where A (0.52) is the model constant and Da is Damokohler number
Extended Coherent Flame Model (ECFM)
The turbulent flame area (At) is of critical importance. The ECFM tracks an additional parameter, the flame area density (Σ) along with the progress variable C.
where, P1= Source due to turbulence interaction,P2 =Source due to dilatation in the flame,P3 = Source due to expansion of burned gas, D = Dissipation of flame area
Applicability of ECFM:
Model valid in the wrinkled regime
Widely used in Internal Combustion Engine
The range of applicability of the ECFM model is shown on the Borghi diagram in the following fifure, where the wrinkled flamelets regime is indicated below the line. Typical Internal Combustion (IC) engines typically operate in this wrinkled flamelet range.
Borghi diagram for turbulent combustion
ECFM-3Z (Extended Coherent Flame Model – Three Zones) model:
This model is widely used combustion model for in-cylinder simulations.
The model is provide a sub-grid description of the mixing and combustion processes, where the turbulence timescale enters the equations describing mixing and combustion, and that is important when modeling turbulent combustion in engines.
In non-premixed combustion, fuel and oxidizer (air) enter the reaction zone in separate streams. Solves transport equations for mixture fraction (Z or f) and mixture fraction variance (instead of the individual species equations).
Applicability of Non_premixed Combustion Models
Flow Regime: Turbulent flow (high Re)
Chemistry: Equilibrium or moderately non-equilibrium (flamelet)
Configuration: Non-Premixed
Applications of Diffusion Flame Models:
Gas reaction (furnaces, burners). This is usually the model of choice if assumptions are valid for gas phase combustion problems.
Accurate tracking of intermediate species concentration and dissociation effects without requiring knowledge of detailed reaction rates (equilibrium).
Limitations of Models
• Unreliable when mixing and kinetic time scales are comparable
• Cannot realistically model phenomena which depend on detailed kinetics (such as ignition, extinction).
Flamelets
A turbulent flame brush as an ensemble of discrete, steady laminar flames, called flamelets.
The individual flamelets are assumed to have the same structure as laminar flames in simple configurations, and are obtained by experiments or calculations.
Diffusion Flame Models
In this approach, the pre-calculated table of mixture fraction based on probability density function using thermodynamic data is used to calculate the flame brush for diffusion flame.
Use of mixture fraction to decouple the chemical kinetics from the flow dynamics and reduces the burden of solving a large number of species transport equations.
Under certain assumptions for non-premixed combustion, the thermochemistry can be reduced to a single parameter: the mixture fraction (f or Z)
The mixture fraction is the mass fraction that originated from the fuel stream
It is a conserved scalar quantity. Hence, its transport equation does not have a source term
Combustion is simplified to a mixing problem, and the difficulties due to the closing non-linear mean reaction rates are avoided.
Once fuel and oxidizer are mixed, the chemistry can be modeled as being in chemical equilibrium with the Equilibrium (chemistry) mode,
Being near chemical equilibrium with the Steady Laminar Flamelet model, or significantly departing from chemical equilibrium with the Unsteady Laminar Flamelet model can be used
Mixture fraction approach for diffusion flame modeling:
Pre-flamelet computing and look up table for diffusion flame modeling
Computing the scalar in terms of mean mixture fraction and variance mixture fraction
Modeling of Chemical Kinetics in Diffusion Flames
The CHEMKIN® software is developed to model the chemically reacting flow configurations due to low computational cost for modeling chemical kinetics
CHEMKIN GRI Mech-3 is widely used for detailed chemical kinetics for diffusion flame modeling due to low computational for maximum number of reaction steps
Use of CHEMKIN GRI-Mech 3 of turbulent diffusion flame modeling;
De, S., Agarwal, A.K., Chaudhuri, S., Sen, S, Modeling and Simulation of Turbulent Combustion, Springer Publication, Click here: Modeling_and_simulation_combustion_PDF
3 thoughts on “CFD Modeling of Turbulent Combustion”
Principles of mathematical models as tools in engineering and science are discussed in relation to turbulent combustion modeling. A model is presented for the rate of combustion which takes into account the intermittent appearance of reacting species in turbulent flames. This model relates the rate of combustion to the rate of dissipation of eddies and expresses the rate of reaction by the mean concentration of a reacting specie, the turbulent kinetic energy and the rate of dissipation of this energy. The essential features of this model are that it does not call for predictions of fluctuations of reacting species and that it is applicable to premixed as well as diffusion flames. The combustion model is tested on both premixed and diffusion flames with good results.
Special attention is given to soot formation and combustion in turbulent flames. Predictions are made for two C2 H2 turbulent diffusion flames by incorporating both the above combustion model and the model for the rate of soot formation developed by Tesner et al., as well as previous observations by Magnussen concerning the behavior of soot in turbulent flames. The predicted results are in close agreement with the experimental data.
All predictions in the present paper have been made by modeling turbulence by the k-? model. Buoyancy is taken into consideration in the momentum equations. Effects of terms containing density fluctuations have not been included.
As per our budget and scope of analysis we can select models for turbulence and chemical kinetics
k-e realizable model is widely used for turbulent combustion modelling under RANS models
For soot formation is modelled explicitly.
Effect buoyancy we can enable in momentum eqn.
ERCOFTAC Course: Best Practice Guidelines for CFD of Turbulent Combustion including an introduction to machine learning tools for chemistry reduction and error estimation, h-h December 2019
Principles of mathematical models as tools in engineering and science are discussed in relation to turbulent combustion modeling. A model is presented for the rate of combustion which takes into account the intermittent appearance of reacting species in turbulent flames. This model relates the rate of combustion to the rate of dissipation of eddies and expresses the rate of reaction by the mean concentration of a reacting specie, the turbulent kinetic energy and the rate of dissipation of this energy. The essential features of this model are that it does not call for predictions of fluctuations of reacting species and that it is applicable to premixed as well as diffusion flames. The combustion model is tested on both premixed and diffusion flames with good results.
Special attention is given to soot formation and combustion in turbulent flames. Predictions are made for two C2 H2 turbulent diffusion flames by incorporating both the above combustion model and the model for the rate of soot formation developed by Tesner et al., as well as previous observations by Magnussen concerning the behavior of soot in turbulent flames. The predicted results are in close agreement with the experimental data.
All predictions in the present paper have been made by modeling turbulence by the k-? model. Buoyancy is taken into consideration in the momentum equations. Effects of terms containing density fluctuations have not been included.
https://www.frostburg.edu/
As per our budget and scope of analysis we can select models for turbulence and chemical kinetics
k-e realizable model is widely used for turbulent combustion modelling under RANS models
For soot formation is modelled explicitly.
Effect buoyancy we can enable in momentum eqn.
ERCOFTAC Course: Best Practice Guidelines for CFD of Turbulent Combustion including an introduction to machine learning tools for chemistry reduction and error estimation, h-h December 2019