CFD Modeling of Turbulent Combustion

Table of Contents

Turbulent Combustion Modeling

(Introduction to Combustion Models in FLUENT, Star CCM+ and OpenFOAM)


Dr. Sharad N. Pachpute (Ph.D.)

Modeling of Multiphysics in Reactive Flows


Introduction to Combustion Modeling

  • 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 from fires, 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


  • 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
    • Air inlet can be more for low NOx  air staged burners
    • Ignition tube (Pilot) is provided to provide ignition energy
    • Combustion chamber
    • Oil inlet if the burner is multiple fuel based

Governing Equations and Classification of Combustion Models

 Governing Equations for combustion

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

Overview of Models for Combustion

  • The overview of combustion models :
    • Transport equations
    • Turbulence models
    • Chemistry of solution
    • Type of chemistry: fast/slow chemistry models
    • Multi-phase models; solid or liquid fuel
    • Radiation models
    • Pollutants models

Outline of Combustion Models  in ANSYS FLUENT

  • 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
Non premixed combustion schematics
Non-premixed combustion schematics

 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

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)


Flame Velocity of premixed combustion schematics
Flame Velocity of premixed combustion schematics

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:
    1. laminar flame speed, which is capitulated  by the fuel concentration, temperature, and molecular diffusion properties, 
    2.  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, DDissipation 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.
  •   Applicability of ECFM-3Z model
    •  Flow Regime: Turbulent flow (high Re)
    • Chemistry: Fast Chemistry
    • Configuration: Premixed and Non-premixed 
For more detail of ECFM-3Z model click here: 

Use CFD Solver for Combustion Modeling:

a) ANSYS FLUENT for Premixed Flame Models:

b) Star CCM+ for Premixed Flame Models:
1) Star CCM video :  Star CCM for IC Engine
c) Open FOAM Solvers  for Premixed Flame Models:

Modeling of Non-Premixed Combustion Model

Mixture fraction for non-premixed flames

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).


    • 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 the maximum number of reaction steps
  • Use of CHEMKIN GRI-Mech 3 of turbulent diffusion flame modeling;
GRI Mech 3 Mechanism for chemical kinetics in combustion
GRI Mech 3 Mechanism for chemical kinetics in combustion

How to get more details of CHEMKIN:

ANSYS FLUENT- Non-premixed Combustion Modeling 


Star CCM+ Non-premixed Combustion Modeling 


OpenFOAM Non-premixed Combustion Modeling




  1. Thierry Poinsot,  Denis Veynate,Theoretical and Numerical Combustion, 2nd Edn., R T Edwards Inc., Click here to Theoretical_and_Numerical_Combustion_PDF
  2. 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. Echekki, Tarek, Mastorakos, Epaminondas (Eds.), Turbulent Combustion Modeling, Advances,New Trends and Perspectives, Springer Pub.,2011
  4.  Kenneth K. Kuo, Ragini Acharya,  Fundamentals of Turbulent and Multiphase Combustion, Wiley Pub., 2012
  5. Masayuki Taniguchi, Fundamental Experiments of Coal Ignition for Engineering Design of Coal Power Plants,
  6. Zhao F. Tian, Peter J. Witt, Mark P. Schwarz, and William Yang, Numerical_Modelling_of_Pulverised_Coal_Combustion ,Springer (2016)
Lecture Slides
  1. Modeling Turbulent Combustion Slides by Prof. Dr.-Ing. Heinz Pitsch :Slides_Turb_Comb_Model_Prof_Pitsch_Princeton
  2. Modeling Turbulent Combustion by Prof.X.S. Bai: Modeling_TC_Bai_PDF

Video Lectures: 


4 thoughts on “CFD Modeling of Turbulent Combustion”

  1. 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.

  2. 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


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