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Ask the Experts: Combustion Simulation
 

Ask the Experts: Combustion Simulation

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Combustion and chemical reactions are all around us! Combustion modeling has become crucial to design clean powerplants, low emissions engines, etc. Join the ANSYS experts to learn about combustion ...

Combustion and chemical reactions are all around us! Combustion modeling has become crucial to design clean powerplants, low emissions engines, etc. Join the ANSYS experts to learn about combustion simulation. Full webinar and Q&A available at: http://bit.ly/1vQIDk6

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Ask the Experts: Combustion Simulation Ask the Experts: Combustion Simulation Presentation Transcript

  • © 2011 ANSYS, Inc. June 18, 20141 Ask The Expert - Everything You Always Wanted To Know About Combustion Simulation ANSYS Technical Engineers Team
  • © 2011 ANSYS, Inc. June 18, 20142 Welcome! 1st Presentation of 5 on Simulation of Combustion 1) Fundamental concepts of reacting flows and models in ANSYS CFD 2) Modeling fast chemistry – Premixed, non-premixed and partially premixed models 3) Modeling detailed chemistry – Concepts, applications and best practices 4) Modeling pollutants and surface chemistry 5) Modeling heterogeneous reactions – Solid and liquid fuels Find all “Ask the Experts” Webinars on ANSYS.COM Follow SUPPORT -> RESOURCE LIBRARY
  • © 2011 ANSYS, Inc. June 18, 20143 Reacting flows are all around us! Did you drive to work? Gasoline + O2  H2O + CO2 OR Diesel + O2  H2O + CO2 Ahh, but I have an electric car! • Battery – Electro-chemical reaction Li  Li+ + e • Charging – ~85% of world-wide electricity generation is from combustion Introduction
  • © 2011 ANSYS, Inc. June 18, 20144 Introduction Ahh, but I rode my bicycle! Did you breath? C6H12O6 (glucose) + 6O2 → 6CO2 + 6H2O No, I held my breath the whole way! Did you partake in the greatest reaction ever? 2 Gamete + Nutrients  Baby No? Permission to leave is granted!
  • © 2011 ANSYS, Inc. June 18, 20145 • Basic definitions and concepts • Gas mixtures • Reacting gas mixtures • Types of flames and related phenomenon • Solid and liquid burning and other reactions • Role of turbulence in reacting flows • Reacting flow modeling Outline
  • © 2011 ANSYS, Inc. June 18, 20146 • Basic definitions and concepts • Gas mixtures • Reacting gas mixtures • Types of flames and related phenomenon • Solid and liquid burning and other reactions • Role of turbulence in reacting flows • Reacting flow modeling Outline
  • © 2011 ANSYS, Inc. June 18, 20147 Basic definitions • Chemical reaction – A process involving changes in the structure and energy content of atoms, molecules, or ions • Exothermic reaction – Chemical reaction that releases energy in the form of light or heat • Endothermic reaction – Chemical reaction that absorbs energy from its surroundings • Basic types of reaction A B A B A BA B BA C A B C BA C A B CD D Synthesis reaction Decomposition reaction Single replacement reaction Double replacement reaction
  • © 2011 ANSYS, Inc. June 18, 20148 Basic definitions (cont…) • Combustion reaction – Sequence of exothermic chemical reactions between a fuel and an oxidizer accompanied by the production of heat and conversion of chemical species – Combustion dominated flows form main part of reacting flows • Stoichiometry – Amount of oxidizer needed to completely burn a given quantity of fuel – CH4 + O2  CO2 + H2O • Stoichiometric fuel-air ratio – Ratio of mass of fuel to the mass of air at stoichiometry • Excess air – Fraction of air (oxidizer) supplied in excess of stoichiometric requirement • Equivalence ratio () – Ratio of actual fuel-air ratio to stoichiometric fuel-air ratio –  > 1  Rich mixture in fuel;  < 1  lean mixture in fuel CH4 + 2O2  CO2 + 2H2O
  • © 2011 ANSYS, Inc. June 18, 20149 Equation of state • Relation between pressure, temperature and volume of gaseous substance • Ideal gas equation of state: 𝑷 𝝆 = 𝑹 𝒖 𝑴 𝒘 𝑻 – Ru = Universal gas constant = 8314.46 𝑱 𝒌𝒎𝒐𝒍 𝑲 • For devices operating at relatively constant pressure – Overall variation in pressure is not substantial – Idea gas law based on operating pressure can be used – Incompressible ideal gas law: 𝑷 𝒐𝒑 𝝆 = 𝑹 𝒖 𝑴 𝒘 𝑻 • Supercritical pressure systems – Ideal gas law is not accurate – Real gas equation of state is required: e.g. cubic equations of states
  • © 2011 ANSYS, Inc. June 18, 201410 • For ideal gas 𝑪𝒑 ≡ 𝝏𝒉 𝝏𝑻 𝑷 • Energy of molecule – Translational, rotational and vibrational – Rotational and vibrational energy storage are increasingly active at higher temperature – Diatomic molecules have higher Cp than monoatomic molecules • Rotational and translational modes • 𝒉 𝑻 = 𝒉 𝒓𝒆𝒇 + 𝑻 𝒓𝒆𝒇 𝑻 𝑪𝒑(𝑻) 𝒅𝑻 • Enthalpy of a species, h(T) – Reference enthalpy (standard state enthalpy) at Tref = 298.15 K – Specific heat as a function of temperature Specific heat (Cp) Image adapted from Stephen Turns, “An introduction to combustion”
  • © 2011 ANSYS, Inc. June 18, 201411 • Basic definitions and concepts • Gas mixtures • Reacting gas mixtures • Types of flames and related phenomenon • Solid and liquid burning and other reactions • Role of turbulence in reacting flows • Reacting flow modeling Outline
  • © 2011 ANSYS, Inc. June 18, 201412 Gas mixtures • Mole fraction (Xi) – Fraction of total number of moles of a given species in a mixture – 𝑿𝒊 = 𝑵 𝒊 𝑵 𝑻𝒐𝒕 • Mass fraction (Yi) – Fraction of mass of a given species in a mixture, 𝒀𝒊 = 𝒎 𝒊 𝒎 𝑻𝒐𝒕 • Relation between Yi and Xi – 𝒀𝒊 = 𝑿𝒊 𝑴𝒘 𝒊 𝑴𝒘 𝑴𝒊𝒙 • Mixture molecular weight – 𝑴𝒘 𝑴𝒊𝒙 = 𝒊 𝑿𝒊 𝑴𝒘𝒊 = 𝒊 𝒀𝒊 𝑴𝒘 𝒊 −𝟏
  • © 2011 ANSYS, Inc. June 18, 201413 Diffusion mass transfer (binary diffusion) • Species mass transfer in a mixture (1D) – 𝒎′′ 𝑨 = 𝒀 𝑨 × 𝒎′′ 𝒎𝒊𝒙 − 𝝆𝑫 𝑨𝑩 𝒅𝒀 𝑨 𝒅𝑿 – Two components: 1. Convection and 2. Diffusion – Diffusion takes place from high concentration region to low concentration region – DAB is binary diffusion coefficient (m2/s) • For gases: DAB ~1e-5; for liquids: DAB ~1e-9 • Thermal Diffusion – Diffusion due to temperature gradient – Thermal diffusion in liquids is called the Soret diffusion • Baro diffusion – Diffusion due to pressure gradient • Thermal and baro diffusion are usually small • Schmidt number – Ratio of viscous diffusion rate to molecular diffusion rate, 𝑺𝒄 = 𝝁 𝝆𝑫 • Lewis number – Ratio of thermal diffusion rate to molecular diffusion rate, 𝑳𝒆 = 𝜶 𝑫
  • © 2011 ANSYS, Inc. June 18, 201414 Diffusion mass transfer (Multicomponent) • Individual species diffuse in the mixture • Diffusion coefficient of species in mixture (Dim) is required • Different approaches to calculate Dim – Constant: Suitable for dilute mixtures – Computed from binary Dij and mole fractions – Kinetic theory of gases • Diffusion calculated using Maxwell-Stefan equations – Important for diffusion-dominated laminar flows • Diffusion in turbulent flows – 𝒎′′ 𝒊 = − 𝝆𝑫 𝑨𝑩 + 𝝁 𝒕 𝑺𝒄 𝒕 𝒅𝒀𝒊 𝒅𝑿𝒊 – In turbulent flows, diffusion due to turbulence normally overwhelms the laminar diffusion
  • © 2011 ANSYS, Inc. June 18, 201415 • Basic definitions and concepts • Gas mixtures • Reacting gas mixtures • Types of flames and related phenomenon • Solid and liquid burning and other reactions • Role of turbulence in reacting flows • Reacting flow modeling Outline: part-I
  • © 2011 ANSYS, Inc. June 18, 201416 Reacting gas mixtures Reactor Reactants (Stoichiometric mixture at standard condition) Products at temp, T (Complete combustion) Heat removed = 0 T = Tad (Adiabatic flame temp) h T hreact Tref hprod Heat of reaction Reactants Products Products Tad Reactor Reactants (Stoichiometric mixture at standard condition) Products (Complete combustion at standard condition) Heat removed Practical state of products 𝑯 𝒓 = ∆𝒉 𝒇 𝒑𝒓𝒐𝒅 − ∆𝒉 𝒇 𝒓𝒆𝒂𝒄𝒕 = Heat of reaction (Hr)
  • © 2011 ANSYS, Inc. June 18, 201417 Global reaction • Overall reaction where fuel and oxidizer reacts to form product – Fuel + a Ox  b Prod • Fuel consumption rate: 𝒅 𝑪 𝒇 𝒅𝒕 = −𝒌(𝑻) 𝑪 𝒇 𝒎 𝑪 𝒐𝒙 𝒏 – Ci  Molar concentrations (kmol/m3); i = f or ox – K(T)  Rate constant; Strong function of temperature – m and n  Reaction order; Not necessarily integers for global reactions • In reality, many reactions involving many intermediate species take place to form products – Individual reactions are called elementary reactions – Some elementary reactions may produce some intermediate species – Some elementary reactions may involve free radicals like O, OH, H, etc. – Collection of elementary reactions is called reaction mechanism
  • © 2011 ANSYS, Inc. June 18, 201418 Reaction mechanism • Tens of species and hundreds of reactions • Each species participate in a series of reaction steps – Produced in some steps and destroyed in some other steps • Chain reactions – Produce radical species – For global reaction: A2 + B2 2AB – Chain initiation: Starts forming radicals – Chain propagation: Forming other radicals – Chain branching: Forming two radicals – Chain termination: Forming products A2+ M  A + A + M A + B2  AB + B A2 + B  AB + A AB + B  A + 2B A + B + M AB + M 10 1 10 2 10 3 10 4 10 2 10 3 10 4 before 2000 2000 to 2005 after 2005 iso-ocatane (LLNL) iso-ocatane (ENSIC-CNRS) n-butane (LLNL) CH4 (Konnov) neo-pentane (LLNL) C2H4 (San Diego) CH4 (Leeds) Methyl Decanoate (LLNL) C16 (LLNL) C14 (LLNL) C12 (LLNL) C10 (LLNL) USC C1-C4 USC C2H4 PRF n-heptane (LLNL) skeletal iso-octane (Lu & Law) skeletal n-heptane (Lu & Law) 1,3-Butadiene DME (Curran)C1-C3 (Qin et al) GRI3.0 Numberofreactions Number of species GRI1.2 pre-2000 2000 – 2005 post-2005 Number of Species NumberofReactions nC7H16 C11H22O2
  • © 2011 ANSYS, Inc. June 18, 201419 Arrhenius reaction rate • Reaction rate for elementary reactions is derived from molecular collision theory • Elementary reaction: A + B  C + D – Reaction rate, 𝑹 = 𝒌 𝑻 𝑻 𝜷 𝑪 𝑨 𝑪 𝑩 – Rate coefficient, 𝒌 𝑻 = 𝑨 𝒆𝒙𝒑 −𝑬 𝒂 𝑹 𝒖 𝑻 – A  Pre exponential factor – Ea  Activation energy • This form of reaction rate is called Arrhenius form – Originally proposed by Jacobus Henricus van 't Hoff – Svante Arrhenius provided the physical justification and interpretation – Term T is added later by other researchers Jacobus Henricus van 't Hoff Svante Arrhenius
  • © 2011 ANSYS, Inc. June 18, 201420 • Reaction will take place when the kinetic energy of the colliding molecules is larger than a threshold energy • This threshold energy is called Activation energy • Effect of catalyst – Catalyst is not consumed in reactions – Increases the frequency of successful collisions – Changes the relative orientation of the reactant molecules – Reduces the intra-molecular bonding within the reactant molecules – Provides an alternate pathway Activation energy Activation Energy ProductsEnergy Time Heat of Reaction Without catalyst With catalyst Reactants
  • © 2011 ANSYS, Inc. June 18, 201421 • Time required for concentration of a reactant to fall from its initial value to a value 1/e times the initial value during a reaction • Important for analysis of combustion process • Represented with respect to convective or mixing time scale of the flow by some non dimensional number • Uni-molecular reaction – A  B + C – 𝝉 𝒄𝒉𝒆𝒎 = 𝟏 𝑲(𝑻) • Bi-molecular reaction – A + B  C + D – 𝝉 𝒄𝒉𝒆𝒎 ≈ 𝟏 𝑪 𝒍𝒂𝒓𝒈𝒆 𝑲(𝑻) – Clarge Concentration of abundant reactant (CA or CB) Chemical time scales
  • © 2011 ANSYS, Inc. June 18, 201422 Chemical equilibrium • State at which both reactants and products are present at concentrations with no further tendency to change with time • Example: CO + 0.5 O2  CO2 • CO + 0.5 O2 (1-)CO2 + CO + 0.5O2 • According to second law – dS ≥ 𝟎 OR dG ≤ 𝟎 – G is Gibbs free energy; G ≡ 𝑯 − 𝑻𝑺 • At Equilibrium – CO, O2 and CO2 will be present – Forward and reverse reaction rates are in equilibrium Reactor Fixed volume Fixed mass and Adiabatic reactor Image adapted from Stephen Turns, “An introduction to combustion”
  • © 2011 ANSYS, Inc. June 18, 201423 • Equilibrium constant can be obtained as – 𝒌 𝒆 = 𝒆𝒙𝒑 −∆𝑮 𝑻 𝒐 𝑹 𝒖 𝑻 = 𝒆𝒙𝒑 −∆𝑯 𝒐 𝑹 𝒖 𝑻 × 𝒆𝒙𝒑 ∆𝑺 𝒐 𝑹 𝒖 – GT o Change in standard state Gibbs function • Reversible reaction – A reaction resulting in equilibrium mixture of reactants and products CO + H2O CO2 + H2 • At equilibrium, ratio of forward and backward reactions constants is equal to equilibrium constant – 𝒌 𝒆 = 𝒌 𝒇 𝒌 𝒃 Chemical equilibrium (cont…) kf kb
  • © 2011 ANSYS, Inc. June 18, 201424 • Basic definitions and concepts • Gas mixtures • Reacting gas mixtures • Types of flames and related phenomenon • Solid and liquid burning and other reactions • Role of turbulence in reacting flows • Reacting flow modeling Outline
  • © 2011 ANSYS, Inc. June 18, 201425 Types of flames Air Hole Opening Close Open Diffusion Premixed Diffusion flames • Separate streams for fuel and oxidizer • Convection or diffusion of reactants from either side into a flame sheet Premixed flames • Fuel and oxidizer are already mixed at the molecular level prior to ignition • Cold reactants propagate into hot products • Rate of propagation (flame speed) depends on the internal flame structure Fuel  Diffusion flame Oxidizer  Premixed flame Fuel +  Oxidizer
  • © 2011 ANSYS, Inc. June 18, 201426 Tad Diffusion flames • Mixture fraction (Z) • 𝒁 = 𝒎 𝒇𝒖𝒆𝒍 𝒎 𝒇𝒖𝒆𝒍 + 𝒎 𝒐𝒙 – Z = 1 at fuel inlet – Z = 0 at oxidizer inlet – In other region • Z represents fraction of fuel stream • (1 - Z) represents fraction of oxidizer stream • Fuel-air ratio = 𝒁 (𝟏−𝒁) • Equivalence ratio = 𝒁 (𝟏−𝒁) × (𝟏−𝒁 𝒔𝒕) 𝒁 𝒔𝒕 • For methane-air reaction: CH4+2(O2+3.76N2) CO2+2H2O+7.52N2 – ZSt = 𝑴𝒂𝒔𝒔 𝒐𝒇 𝒎𝒆𝒕𝒉𝒂𝒏𝒆 𝑴𝒂𝒔𝒔 𝒐𝒇 𝒎𝒊𝒙𝒕𝒖𝒓𝒆 = 𝟏𝟔 𝟏𝟔+𝟐(𝟑𝟐+𝟑.𝟕𝟔×𝟐𝟖) = 𝟎. 𝟎𝟓𝟓 Mass fraction Temperature
  • © 2011 ANSYS, Inc. June 18, 201427 Premixed flames Flame Preheatzone Perfectly mixed mixture of unburned reactants – Unburned Temperature – Unburned density Perfectly mixed mixture of burned products – Adiabatic flame temperature – Product density Reactionzone Diffusion of Heat + Radicals Temperature Fuel mass fraction Oxidizer mass fraction Product mass fraction Tub Tad
  • © 2011 ANSYS, Inc. June 18, 201428 Laminar flame speed Laminar flame speed (SL) Stationary flame Air-fuel mixture U SL  U  𝑺𝒍 = 𝑼𝒔𝒊𝒏𝜶 • It looks so simple to obtain the flame speed! Is it so? No… • Local heat release rates and non- uniformity in flow cause flame stretching (change in area of flame elements) – Additional complexities for determining flame speed
  • © 2011 ANSYS, Inc. June 18, 201429 Flame extinction Temperature Tub TadWithout heat loss With heat loss Flame • Effect of heat loss – Propagation speed (S) < SL – Reduce flame temperature • Using one dimensional steady analysis – 𝒔 𝟐 𝒍𝒏 𝒔 𝟐 = −𝒒 𝑳 • s = S/SL • qL = Q/(CpTub)  Heat loss • At extinction the flame speed is nearly 60% of the adiabatic flame speed 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 s qL Unstable sext
  • © 2011 ANSYS, Inc. June 18, 201430 Ignition • Ignition will occur – If the energy added in a region of reacting mixture is sufficient to overcome the heat loss by conduction – Required critical region size is of the order of flame thickness – Minimum energy required for ignition, 𝑬 𝒎𝒊𝒏 = 𝒎 𝑪 𝒑 𝑻 𝒃 − 𝑻 𝒖 𝒓 𝒄𝒓 = 𝟔 𝜶 𝑺 𝑳 = 𝟔 𝟐 𝜹 𝜶 = 𝒌 𝝆 𝒖 𝑪 𝒑  = Flame thickness QReleased QCond T r Tb rcr Tu
  • © 2011 ANSYS, Inc. June 18, 201431 Detonation and deflagration • Deflagration – Reaction front at subsonic speed; pressure wave at sonic speed – Disturbances behind the reaction front can propagate ahead and affect the unburned gas before arrival of reaction front • Detonation – Both reaction front and shock wave at supersonic speed – Gas gets compressed through shock, temp. rise is ~ thousands of degrees – Reactions are completed very rapidly in a thin region behind the shock Unburned air-fuel mixture Burned products Unburned air-fuel mixture Burned products Pressure wave Reaction front Detonation Deflagration Shock wave
  • © 2011 ANSYS, Inc. June 18, 201432 • Basic definitions and concepts • Gas mixtures • Reacting gas mixtures • Types of flames and related phenomenon • Solid and liquid burning and other reactions • Role of turbulence in reacting flows • Reacting flow modeling Outline
  • © 2011 ANSYS, Inc. June 18, 201433 Liquid evaporation and burning • Applications – IC engines; Gas turbines; Oil fired boilers, scrubbers; etc. • Combined action of flow dynamics and surface tension causes liquid break up – Unstable liquid sheet  ligaments droplets • Vaporization – Droplet evaporation and boiling • Mixing and reactions in gas phase IC engine Gas turbine combustor
  • © 2011 ANSYS, Inc. June 18, 201434 Heterogeneous reactions (Solids) • Applications – Pulverized coal fired boilers; cement kilns; Soot formation; etc. • Particles get heated up to devolatilization temperature – Released volatiles burn in gas phase • Remaining solid undergoes heterogeneous reactions – Reactant gas molecules transfer to solid surface by convection or diffusion – Adsorbed by solid surface – Surface reaction at solid surface – Desorption of product of reaction – Transport of product by convection or diffusion to surrounding Coal  Air  Ash  Flue gas Coal fired boiler
  • © 2011 ANSYS, Inc. June 18, 201435 Other reactions • Chemical vapor deposition – Involves gas phase as well as surface reactions • Air dissociation at hypersonic flows – Involves gas phase and ion reactions • Exhaust gas treatment is SCR – Involves catalytic reactions • Hydrocarbon capture in carbon canisters – Involve adsorption and desorption reactions • Foam formation – Involves liquid-liquid reactions with release of CO2 • Calcination reaction – Endothermic particle surface reaction • Liquid-liquid reactions – Liquid micro-mixing CVD image adapted from H. O. Pierson “Handbook of Chemical Vapor Deposition” Reentry vehicle Catalytic convertor Carbon canister
  • © 2011 ANSYS, Inc. June 18, 201436 • Basic definitions and concepts • Gas mixtures • Reacting gas mixtures • Types of flames and related phenomenon • Solid and liquid burning and other reactions • Role of turbulence in reacting flows • Reacting flow modeling Outline
  • © 2011 ANSYS, Inc. June 18, 201437 Role of turbulence in reacting system • Flows encountered in most of the practical reacting systems are turbulent • Reactions and turbulence affect each other – Turbulence-chemistry interaction • Turbulence is modified by flames – Through flow acceleration, modified kinematic viscosity • Modified turbulence alters the flame structure – Enhanced mixing and chemical reactions (through temp fluctuations) • Mixing time scale (F) relative to chemical time scale (chem) – An important parameter to decide whether the reaction is mixing limited or chemically limited – Mixing time scale in turbulent flows = 𝒌 𝝐 – Damkohlar Number (Da) = 𝝉 𝑭 𝝉 𝑪𝒉𝒆𝒎 – If Da > 1  Fast chemistry and Da ≤ 1  Finite rate chemistry
  • © 2011 ANSYS, Inc. June 18, 201438 • Basic definitions and concepts • Gas mixtures • Reacting gas mixtures • Types of flames and related phenomenon • Solid and liquid burning and other reactions • Role of turbulence in reacting flows • Reacting flow modeling Outline
  • © 2011 ANSYS, Inc. June 18, 201439 • Engines: Gas-turbines, IC, … • Burners: Furnaces, Boilers, Gasifiers, … • Safety: Fires, Explosions, Dispersion, … • Surface chemistry: Catalysis, CVD, … • Materials: Synthesis, Polymerization, … • and many more… What do we want to model? Environment & Emissions control Propulsion & Engines Micros & Nanos Biomedicine & Biochemistry Climate change & Energy sustainability Fire & Fire protection Gas turbine combustors IC Engines
  • © 2011 ANSYS, Inc. June 18, 201440 • Devices are very complex – Complex geometry, complex BCs, complex physics (turbulence, multi-phase, chemistry, radiation,…), complex systems, … • Tool to gain insight and understanding • Reduce expensive experiments • Eventually design! Why to model reacting flows?
  • © 2011 ANSYS, Inc. June 18, 201441 Overview of combustion modeling Transport Equations • Mass • Momentum + Turbulence • Energy • Chemical Species Reaction Models • Eddy Dissipation model • Premixed model • Non-premixed model • Partially premixed model Reaction Models • Laminar Flamelet model • Laminar Finite rate model • EDC • Composition PDF Infinitely fast chemistry Da >> 1 Finite rate chemistry Da ~ 1 Dispersed Phase Model (Solid/liquid fuels) • Droplet/particle dynamics • DEM collisions (New in R14) • Evaporation • Devolatilization • Heterogeneous reaction Turbulence Models • LES, DES, SAS…. • RANS: k-e, k-w, RSM….. Pollutant Models • NOx, Soot, SOx Radiation Models • P1, DO (Gray/Non-gray) Real gas effects • SRK, ARK, RK, PR
  • © 2011 ANSYS, Inc. June 18, 201442 Combustion models in Fluent Premixed Combustion Non-Premixed Combustion Partially Premixed Combustion Fast Chemistry Eddy Dissipation Model (Species Transport) Premixed Combustion Model C equation G equation ECFM Non-Premixed Equilibrium Model Mixture Fraction Partially Premixed Model Reaction Progress Variable + Mixture Fraction Finite Rate Chemistry Laminar Finite-Rate Model Eddy-Dissipation Concept (EDC) Model Composition PDF transport Model Laminar Flamelet model (Steady/Unsteady) Flow Configuration Chemistry