CFD Modeling of Pollutants: NOx SOx and Soot

How to model Pollutants from Industries like NOx, SOx and Soot Particles ?



Introduction to Pollutants

Basics of combustion and Pollutions

Understanding combustion processes  is important to control pollution formation.  Flame characteristics and maximum temperature of flue gases depend on fuel composition, equivalent ratio,   air- fuel mixing  mechanisms and burners configuration. For non-premixed combustion, pollution is a matter of concern due to incomplete combustion. SOx and  Soots are observed for burning of  heavy hydrocarbon fuels, liquid or solid fuel containing sulfur and ash.

Before going to Pollutants modeling, CFD users  or Engineers need to understand the following subjects

  • Basic of Combustion Selection of fuels, Thermodynamics, Chemical Kinetics, Fluid mad Heat Transfer, Species Transport, Slow or fast chemistry compared to flow time, Ait fuel mixing (Premixed or non-premixed flames)
  •  Formation and controlling of Pollutants: Identification of harmful pollutants like NO, SOx and Soots, Reasons for formation of pollutants,Design Burners
  • Combustion Modeling: Turbulence models, mechanism of chemical kinetic, Modeling of turbulent -chemistry interaction  (TCI) models
  • Turbulent Multiphase Combustion: Majority of pollutions (NOx, SOx and soots)  due to combustion of liquid and solid fuels which contains high carbon to hydrogen (C/H) ration compared gaseous fuels. For, gaseous fuels, air fuel mixing is  in single phase which is more fast compared that for liquid or solid of multiphase combustion.

Major Pollutants from Combustion 

Basic of pollution and reason for formation of NOx, SOx and Soots are explained the previous post. These three pollutants cause serious detrimental effects to environments. Emission norms are becoming more strict in many countries.

  • Nitrogen Oxide (NOx)
    • Nitrogen oxide comprises majorly NO (nitric oxide). But Two other oxide of nitrogen such as Nitrogen Peroxide and N2O (Nitrous oxide) can be formed
    • Nitric oxide (NO) reacts with oxygen or excess air to form NO2
    • NOx is Highly regulated pollutant Which can results photochemical smog, This pollutant contributes ozone depletion and acid rain
    • There are four different mechanisms to form NOx: Thermal, Prompt, Fuel and N2O route
  • Soot Particles
    • Soot particles are generally formed due to incomplete combustion or pyrolysis in rich mixture of hydrocarbon fuel with strong temperature gradients in combustion chamber
    • Aggregates of Spherical carbon particles are observed within flames. Soot observed in domestic fires or chimneys contains few aggregates but large amounts of particulate fragments of coke or char are found.
    • Formation of soot particle is a complex phenomenon: nucleation, surface growth, coalescence, aggregation
  • Sulphur Oxide (Sox)
    • Sulphur oxides (SOx) is a colourless compounds of sulphur and oxygen molecules
    • Sox compounds consist of SO2, SO, SO3
    • Example: The smoke containing sulphur oxides emitted due to combustion of marine fuel. This smoke will further react with oxygen to form  NO2 and can lead to sulphuric acid as a major cause of acid rain

Steps for CFD Modelings of Pollutants in  Solver

  • As the reaction pathways are extremely complicated, pollutants are modeled by semi-empirical mechanisms
  • CFD results are sensitive to model inputs. Unless a detailed validation is performed, pollutant modeling can be used and parametric study or scaling analysis
  • After complete convergence flow and temperature, NO-model solves species transport equations as a post-processing simulation. NO typically appears in low concentrations
  • NO chemistry does not have significant influence on the predicted velocity, pressure, temperatures and concentrations of major combustion products
  • Correct NO modeling depends on accurate combustion products
  • Pollutants can be modeled based on selection of variables and turbulent chemistry interaction (TCI)
  • Post-processing
    • Transport equation of pollutants (like NOx and Sox) are solved without solving flow velocity, turbulent variables and composition fields
    • In some cases, radicals such as H, O, can be needed in pollutant formation and they are calculated based on equilibrium or partial equilibrium assumptions
    • ANSYS FLUENT and Star CCM have NOx, SOx and Soot formation models
  • Fully coupled Simulation
    • Detailed chemistry contains the sub-mechanism of pollutant formation
    • Transport equations of pollutant species solved together with those of major species
    • Computationally more expensive than post-processing
  • Decoupled detailed chemistry
    • Pollutant Post-processing using a Chemical Kinetic Finite Rate Mechanism
  • NOx Module in CFD Solver
    • Solve NO-model transport equations as a post-processing step
    • NO typically appears in low concentrations
    • Thus, NO chemistry will have a negligible influence on the predicted flow field, temperatures and major combustion product concentrations
    • An accurate combustion solution is a necessary prerequisite to correctly predict NOx

Overview of NOx Formation Mechanism

Thermal NOx

    • Oxidation of atmospheric nitrogen
    • Formed at high temperatures by the Zeldovich mechanism
    • User chooses [O] model as equilibrium or partial equilibrium (recommended)
    • Thermal NO formation proposed by Zeldovich Mechanism is given as

Prompt NOx

    • Produced in lower temperature, fuel rich regions
    • Formed predominantly through the intermediate HCN

Fuel NOx

      • Oxidation of volatile nitrogen to HCN and/or NH3
      • Oxidation of char nitrogen to NO, HCN and/or NH3
      • FLUENT solves an additional transport equation for HCN and/or NH3 mass fraction

NOx from intermediate N2O

    • Favorable under elevated pressure and oxygen rich conditions
    • Additional transport equation for N2O is solved if steady state approximation is not used


Method to reduce NOx in power plant

  • Ammonia or Urea is injected over flue gas to reduce NOx.
  • The ammonia reacts with NO.  N2 and H20 are formed at the outlet


  • Ammonia injection is placed after furnace

BD Heat Recovery Division, Inc. - SNCR (Selective Non Catalytic Reduction)

Transport Equations for NOx Modeling

Species transport for NOx and NH3

  • For thermal and prompt NO predictions, only the NO mass fraction transport equation is solved
  • For fuel NO mechanisms, transport equations for NO and HCN and/or NH3 are necessary


  • In above equation species j can be NO, HCN, NH3
  • The mean reaction rate terms need to be modelled
  • Modelling Turbulence chemistry interactions: PDF approach for turbulence chemistry interaction
  • Reaction expressions may be functions of species concentrations which are not calculated in the combustion simulation (O and OH radicals)
  • Customized User-Defined Kinetics can be used for NOx Rate using UDF in ANSYS FLUENT

Modeling  of Turbulent-Chemistry Interaction (TCI)

  • The relationship of NOx formation rate with temperature and species concentrations is highly nonlinear
  • Temperature and composition fluctuations are considered using the probability density functions (PDF) which considers their statistical fluctuations in the turbulent flow of flue gases after combustion
  • The PDF approach is used for obtaining the mean turbulent reaction rates (ω) after the integration over suitable parametric range:


  • where ω is the NOx formation rate and V1, V2, … are temperature and/or the various species concentrations present
  • P is the probability density function

Calculation of Mean NO Production rate by the PDF Approach

Single Variable Approach


  • For a single variable approach, the variable V1 can be mixture fraction or temperature
    • Mixture fraction is recommended for non-premixed (diffusion flame) and partially premixed model
    • Temperature is recommended for species transport model

Two variable PDF


  • For a two variable PDF, choices for V1 and V2 include
    • Fuel Mass Fraction, temperature
    • Temperature, O2 Mass Fraction
    • Fuel Mass Fraction, O2 Mass Fraction

The PDF Approach for NOx Calculation

  • PDF’s comprises mean and variance of species variables which are assumed to be two-moment beta functions


  • During simulation, mean values are computed from the data of initial combustion
  • For species transport model, the variance of variable V is calculated in either of two ways
  • The transport equation of variance for any variable V is given as follows

  • By approximating same production and dissipation rate in the above transport equation, the following algebraic expression is presented

NO Reburn Model

  • NO can be reduced in fuel rich zones by reaction with hydrocarbons

Modeling of NO Reduction 

  • 10% – 20% reburn fuel added above the main combustion zone
  • After reburn zone, additional air added to complete combustion
  • Significant reductions possible (> 50%) when flue gas consists of high initial NO
  • Reburn rate is the sink term NO transport equation. It is a strong function of temperature and concentrations of NO, CH, CH2, CH3, O2 and HCN. Reburning of NO occurs for when temperature of flue in the range of 1600K – 2100K
  • The reburn rate of NO can be computed with Eddy dissipation model (EDM) considering partial equilibrium for hydrocarbon (CH) radicals

NO Reduction by Selective Non-Catalytic Reduction (SNCR)

  • NH3 or Urea is the reductant injected to convert NO to N2
  • Simplified pathway for NH3 – SNCR
  • Reductant are oxidized to NO and selectivity of reduction reactions decreases with an increase in flue gas temperature
  • If NH3 is added as an intermediate species for fuel N. Natural SNCR can be observed if the SNCR model is not activated
  • The temperature range for SNCR: 1073 K < T < 1373 K


NO Reduction by  SNCR with UREA injection

  • Simplified seven steps reaction mechanism can be used for modelling of SNCR with Urea injection

  • Additional species transport equations need to be solved for Urea, HNCO and NCO are solved
  • Urea injection is defined as a multi component mixture droplet. Urea will be released in the gas phase based on the Arrhenius reaction with devolatilization law
  • Two methods for the Urea decompositions are set to NH3 and HNCO
    • Rate limiting reaction
    • User specified decomposition
  • For simplified modelling Urea injection (CO(NH2)2), droplets are considered as combusting particle or wet combustion
  • For wet combustion, initially water will be released following phase change with evaporation or boiling law

Numerical Solution Strategy in CFD solver

  • Steady state Solver
    • Ensure the convergence of the combustion solution with high resolution of solid angles for radiative heat transfer
    • Disable all other equations like momentum, turbulent variables, energy, multiphase and combustion
    • Solve only for NOx equations
    • Set pollutant models for with NO mechanism
    • Refer ANSYS FLUENT User guide for NOx set up
    • with unit value as under relaxation factor (URF = 1) and solve NOx equation

  • Set model formation parameters in ANSYS FLUENT

  • Unsteady Solver
    • Solve the NOx equation at the end of the time step by using the pollutant post- processing option
    • Set pollutant with unit under relaxation factor, URF = 1
  • Turbulence-chemistry interaction
    • Use the mixture fraction option for non-premixed and partially-premixed combustion models
    • Use the temperature option for species transport model

Case study for NOx: CFD Results

  • CFD results are presented with and without urea injection for boiler or furnace
  • Without ammonia or urea injection, the concentration of NO is higher in top portion of boiler


  • The follwoing CFD results show that, NO concentration is less after ammonia injection in boiler


SOx Modeling

  • If fuel contains Sulfur then SOx is formed during or after combustion


Soot Modeling

  • Aircraft engines burning hydrocarbon-based fuels emit Particulate Matter (PM) emissions
  • These fine (PM2.5) particles have a great impact on human health. They affect lungs and are carcinogenic
  • They are also known to affect the climate/ global warming
  • Soot deposition on combustor liners can adversely affect durability, heat transfer and performance of combustor

Main Soot Models in Fluent

  • Soot affects the radiation absorption. Enable Soot-Radiation option in the Soot panel
  • Soot Models: 1) Moss-Brookers Model, 2) Method of Moments

Moss-Brookes model 

  • Solve transport equations for the soot mass fraction and (normalized) number density
  • Moss-Brookes model was originally developed for methene CH4
  • For higher hydrocarbon Moss-Brookes-Hall extension is available
    • Two equation model
    • Soot mass fraction
  • The Nuclei concentration ‒ Constructed and validated for methane flames
  • Soot formation is modelled using the species transport equations solved considering concentration of normalized soot radical nuclei ( bnuc) and mass fraction of soot particles (Ysoot )

  • In above equation, M presents the soot mass concentration and N is the soot particle number density
  • These variables (M and N) are used to model soot formation such as inception, coagulation, growth and oxidation rates

  • The equation for soot mass concentration (M)

  • As per Moss–Brookes model, the inception rate is a linear function of the local concentration of the acetylene (C2H2)

  • The extended model of soot formation, the inception rate considers the rate of formation of two and three-ringed aromatics from radicals of acetylene, benzene, and phenyl

Selection of Moss-Brookes-Hall Model in FLUENT

  • Two equation model:
    • Soot mass fraction
    • The Nuclei concentration
  • Nucleation:
    • Precursors : C6H6, C2H2 , C6H5
  • Surface Growth
    • SGS species: C2H2
  • Oxidation: Lee model: OH radical, O2
  • Moss-Brookes-Hall Model: Setting of Soot model in FLUENT

Method of Moments for Soot Modeling

Governing Equation for Method of Soot Moments 

  • The soot size distribution due to incomplete combustion is defined based on the concentration moment of the particle number density function for a given number of moments and recast as
  • In above equation, Mn presebts soot size distribution for nth moment and Nt is the particle density of the size class “i”.
  • Soot concentrations are calculated in the physical space by solving the following transport equation


  • The source term (Sn) considers the altogether of nucleation, coagulation, surface growth, and oxidation source term.
  • This term is related to soot statistics and can be determined as


  • Nucleation: it is generally called as a coagulation process between two precursor species for soot

  • Coagulation: the assumption is a coalescent coagulation. The particles after the collision will remain a sphere with an increased diameter. The source term related to coagulation for the n = 0th moment

For higher moments of soot particles, n ≥ 2

Where, αi,j is termed as the collision frequency

  • Surface Growth and Oxidation: due to nucleation the soot formation is negligible as compared to the overall soot formation. The major route of the soot formation is driven by surface growth. Simultaneously, the soot particles can lose its mass due to oxidation with O2 or OH species. Mainly, the chemical kinetics controls the overall process of surface growth and oxidation and it is difficult to model higher order of complexities

Setting of Moment Model in ANSYS FLUENT

    • Interpolative closure for soot diameter and surface area
    • 3 to 6 moment transport equations solved in ANSYS FLUENT
    • Source terms consider realistic chemical and physical processes Available with species transport and flamelet models
    • Coupled to the flow through radiation heat transfer
    • Aggregation can be included

Case study for Soot CFD results

  • The follwoing figures shows the concentration of carbon and soot particles for coal fired burners
  • Higher concetration of soot are away from inlet due to  delayed or improper mixing process


  • Understanding combustion process, fuel composition its CFD modeling is important for pollution modeling
  • Before setting the pollution simulation, first ensure numerical convergence of combustion simulation including radiative heat fluxes
  • To save simulation cost, pollutants are solved as species transport in a commercial finite element method (FVM) solver  based on single or two variables PDF functions
  • Selection of NOx mechanism and correct CFD input date like equivalent ration, carbon index, are important
  • SOX and Soot models can simulated for liquid or solid fuels using ANSYS FLUENT


You Tube Video Lecture



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