19.0 Release Lecture 2: Species Transport Model ANSYS Fluent Combustion Modeling 1 © ANSYS, Inc. Outline • Diffusion flames & premixed flames – Introduction & background • Species transport – Properties & material • Eddy dissipation model – Theory – Model set up and solution strategies • Relax to chemical equilibrium model • Detailed chemistry models (covered in another lecture) – Laminar, eddy dissipation concept and PDF transport – Chemistry acceleration tools 2 © ANSYS, Inc. Non-Premixed vs Premixed Combustion Fuel • Non-Premixed Combustion – Separate streams for fuel and oxidizer – 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 Fuel ο Combustion chamber Oxidizer ο 3 © ANSYS, Inc. Stoichiometric Surface Non-Premixed Premixed Flame Front • Premixed combustion – Fuel and oxidizer are already mixed at the molecular level prior to ignition – Flame propagation from hot products to cold reactants – Turbulence distorts the laminar flame shape and thus accelerates flame propagation Air Fuel + ο burned Combustion chamber Oxidizer Premixed St St unburned Turbulent Reacting Flows • Most engineering reacting flow problems are turbulent – IC engines, gas turbines, boilers, furnaces, rocket engines….. • Modeling challenges – Accurately represent three interconnected phenomena: • Inhomogeneous turbulent flow • Chemistry of combustion • Turbulent fluctuations of temperature, species and density 4 © ANSYS, Inc. Turbulent Reacting Flows (cont’d) • Approaches – Direct Numerical Solution (DNS) • Most accurate approach • Not practical for engineering applications because of wide range of time and length scales involved • So far, DNS efforts are limited to laboratory flames for research purposes – Mean flow closure Reynolds Averaged Navier-Stokes (RANS) • Most commonly used for practical purposes – Large Eddy Simulation (LES) • Stands in between DNS and RANS • Larger energy scales are resolved and sub-grid energy scales are modeled – Hybrid models (DES, SAS or ELES) 5 © ANSYS, Inc. Turbulent Reacting Flows (cont’d) • Favre averaged species equation for turbulent reacting flows ΰ·ͺπ ΰ·ͺπ ΰ·ͺπ ππ ππ ππ π π ΰ·« " " ΰ·© ΰ·ͺ ΰ΄₯ ΰ΄₯ πΌπ ΰ΄₯πΌ π +π = ππ« − π π ππ + πΊ ππ ππΏπ ππΏπ ππΏπ ππΏπ • Involves additional term combining velocity and species fluctuations – Requires modeling • πΊΰ·¨ is mean source from chemical reactions – Coupled with temperature – Can fluctuate significantly about its mean value if evaluated from mean temperature as πΊΰ·« π» ≠ ΰ·©) πΊ(π» • Therefore, alternate closure models are suggested in the literature – Turbulent combustion models 6 © ANSYS, Inc. Approaches for Modeling Reacting Flows • Simplify the chemistry – Considers global chemical reaction mechanism • Finite Rate/Eddy Dissipation model • Decouple chemistry from flow (Fast Chemistry models – Da >> 1)* – Use progress variable (C) approach • Premixed model – Use mixture fraction (Z) approach • Non-Premixed model – Use progress variable and mixture fraction approach • Partially Premixed model • Model detailed chemistry (Finite Rate Chemistry models – Da ~ 1 )* – – – – 7 CPU intensive (large number of transport equations + stiff kinetics) Stiff chemistry solvers allow larger time steps to be used Chemistry Acceleration tools help to speed up the calculation This includes : • Laminar Finite Rate model • Eddy Dissipation Concept model • Composition PDF Transport model * covered in other lectures © ANSYS, Inc. Reacting Flow Models in Fluent Flow Configuration Premixed Combustion Non-Premixed Combustion Partially Premixed Combustion Chemistry Finite-Rate/Eddy-Dissipation Model (Species Transport) 8 Fast Chemistry Closures Premixed Combustion Model Reaction Progress Variable Non-Premixed Model Mixture Fraction Partially Premixed Model Reaction Progress Variable + Mixture Fraction Chemical Equilibrium Steady Laminar Flamelet Model Finite Chemistry Closures Flamelet Generated Manifold Model (Premixed/Diffusion) Finite Rate Chemistry Models Laminar Finite-Rate Model (Species Transport) © ANSYS, Inc. Unsteady Laminar Flamelet Model Eddy-Dissipation Concept (EDC) Model (Species Transport) Composition PDF Transport Model Species Transport Model Properties & Materials 9 © ANSYS, Inc. Setting-up Mixture and Properties • Mixture of reacting species is defined as type “Mixture” • Required species can be included as a Mixture material name part of mixture Species included in a mixture – Transport equations are solved for (N-1) species – Maximum 500 species can be included • Species in a mixture are defined as type “Fluid” • Three types of species – Gaseous – Site • CVD application – Solid • e.g. Solid carbon 10 © ANSYS, Inc. Parent mixture Mixture Fluid properties properties Mixture Material Properties - Density • Incompressible ideal gas (default) – Ideal gas law with constant operating pressure – Density as a function of temperature only • Ideal gas – Density as a function of both temperature and pressure • Real gas equation of state – Rule of thumb: Use when P/Pc > 1 and T/Tc < 2 • P ο Pressure, T ο Temperature, Pc ο Critical pressure, Tc ο Critical temperature – Redlich-Kwong (RK), Aungier-Redlich-Kwong (ARK), Soave- Redlich-Kwong (SRK), Peng-Robinson (PR) equations of state are available • Volume weighted mixing law – Density of liquid mixtures should be defined as volume weighted mixing law • User defined – DEFINE_PROPERTY UDF – Need to specify speed of sound as well 11 © ANSYS, Inc. Mixture Material Properties (cont’d) • Specific heat – Mixing law (recommended option for reacting flow cases) – Constant, Piecewise-linear, Piecewise-polynomial, Polynomial, User defined • Thermal conductivity and Viscosity – Several options are available – Constant is recommended for highly turbulent flow • Absorption coefficient – If radiation is included – Constant; Piecewise-linear; Piecewise-polynomial; Polynomial; various WSGGM options – WSGGM-domain-based is recommended • Mass Diffusivity – Dilute approximation (recommended for highly turbulent flow) – Multi-component, Kinetic theory – Unity Lewis number diffusivity option 12 © ANSYS, Inc. Species (Fluid) Material Properties • Specific heat – – – – Piecewise-polynomial (default) Piecewise-linear Polynomial Constant • Thermal conductivity and viscosity – – – – Constant (default) Piecewise-linear Piecewise-polynomial Polynomial • Diffusivity – Kinetic theory (L-J parameters) – Dij coefficient 13 © ANSYS, Inc. Eddy Dissipation Model (EDM) 14 © ANSYS, Inc. Eddy Dissipation Model (EDM) • Removes the influence of chemistry – A good assumption for fast reacting fuels (Da >> 1) – Most of useful fuels are fast burning • D Brian Spalding (1971) suggested eddy break-up (EBU) model – Introduced eddy lifetime, k/ο₯ • Bjorn F Magnussen and B. H. Hjertager (1976) adapted EBU and generalized it for non-premixed and partially premixed combustion – Eddy dissipation model (EDM) References: D. B. Spalding, Chemical Eng. Sci. 26-1 (1971), 95-107. B. F. Magnussen and B. H. Hjertager, 16th Symposium (Int.) on Combustion (1976) p. 719. 15 © ANSYS, Inc. Eddy Dissipation Model (cont’d) • Reaction is mixing limited • Chemistry is described by a global reaction mechanism – 1 or 2 steps • Reaction rate is governed by large-eddy mixing time scale – Eddy break-up (EBU) or turbulence time scale, k/ο₯ – Rate of production of a species, i due to reaction, r • πΉππ = π΄π°π΅ πΉππ (πΉππππ) , πΉππ (π·πππ ) • πΉππ (πΉππππ) = πππ π΄πΎπ π¨ π π πππ π • πΉππ (π·πππ ) = πππ π΄πΎπ π¨ π© π π π ππ π ππ π΄ πΎπ σπ π π σπ΅ π πππ π΄πΎπ • A and B are constants ο A = 4.0 and B = 0.5 suggested by Magnussen – Works fine for most of the problems – Sometimes needs tuning to get required temperature distribution • The rates are not functions of temperature 16 © ANSYS, Inc. Eddy Dissipation Model (cont’d) • Rates are mixing limited and depend on – Turbulence time scale – Reactants/Products mass fractions – Model constants • Advantages – Simple and physically based – Applicable to every flow configuration • Disadvantages • Rates are not temperature-dependent • React towards complete products – Cannot capture detailed chemistry effects – Does not predict intermediate species and dissociation effects – Temperature over predicted • Model constants sometimes require calibration 17 © ANSYS, Inc. Finite Rate/Eddy Dissipation Model • The source term for species “i” is the sum of sources in all participating reactions NR ˆ Ri ο½ M i ο₯ R i, k k ο½1 • The rate of production or consumption of species “i” in reaction k, Rik – Computed from both 1) Arrhenius rate (kinetics) Reaction rate, πΉ = π¨ πππ – – – −π¬π πΉπ π» π»π· πͺπ π πͺππ π A ο Pre exponential factor Ea ο Activation energy Cf and Cox ο Concentrations 2) The “eddy breakup” rate (mixing dependent rate), explained in EDM section • Smaller of these two is used to calculate production or consumption 18 © ANSYS, Inc. Model Set-up • Switch on turbulence model • Switch on species transport model • Enable volumetric reaction • Select eddy dissipation model • Mixture materials – Some default reacting mixture materials are available – Can be customized • Material properties – Mixture • Species, reactions, density, transport properties… – Individual species • Specific heat, molecular weight, standard state enthalpy and entropy… • Set up boundary conditions – Species mass/mole fraction 19 © ANSYS, Inc. Tips & Tricks for Solution Setup • Fluent solves for (N-1) included species – Keep the species with abundant mass fraction as the last species • Use temperature dependent specific heat for included species – To avoid unrealistic high temperature field – In global reaction mechanisms: • Dissociated species are neglected. In high-temperature flames, may cause the temperature to be over-predicted • IFRF Cp polynomials (Rose and Cooper, 1977) give more realistic temperature field • RP var for some common species like CH4, CO2, CO, H2O, O2 , N2 …, type (set-ifrf-cp-polynomials ‘methane-air) • If radiation model is employed – Absorption coefficient for mixture as “WSGGM-domain-based” • For better convergence – Start with non-reacting flow (disable reactions) – Patch small values for product species mass fractions in the flame region (for eddy dissipation) – Alternatively increase B constant to very high values • Also patch higher temperature (>1500 K) for finite rate/eddy dissipation model – Run reacting flow calculation with lower species and energy under-relaxation factors (URF) ~ 0.9 in the beginning without radiation – Final solution with species and energy URFs of 1 and radiation included 20 © ANSYS, Inc. Species Reports • report/species-mass-flow – Print list of species mass flow rate at inlets and outlets – Available after performing 1 iteration • These options are more accurate than surface integrals at boundary zones since no interpolation is used. 21 © ANSYS, Inc. Relax to Chemical Equilibrium - Characteristic Time Scale Model • Extension of the Eddy Dissipation model – Species react towards chemical equilibrium state over a characteristic time scale (πππππ ) – No complete reaction • Reaction source terms for species equations are • • independent of the reaction mechanism Approach made affordable with ISAT (Discussed later) Relax to equilibrium: Constrained Equilibrium – Equilibrium calculations using species included in the mixture • Applications – Equilibrium with species transport – To obtain initial solution for detailed kinetic simulations 22 © ANSYS, Inc. Relax to Chemical Equilibrium Model (cont’d) • The reaction source term in the ith mean species conservation equation is modeled as • This option is available for laminar finite rate, • 23 ED and FR/ED Provides more accurate predictions of intermediate species such as CO and radicals required for NOx modeling such as O and OH © ANSYS, Inc. Outline • Diffusion flames & premixed flames – Introduction & background • Species transport – Properties & material • Eddy dissipation Model – Theory – Model set up and solution strategies • Detailed chemistry models (covered in another lecture) – Laminar, eddy dissipation concept and PDF transport – Chemistry acceleration tools 24 © ANSYS, Inc. Summary • Eddy dissipation model – Theory – Model set up and solution strategies • Relax to Chemical Equilibrium • Several tutorials available for these models 25 © ANSYS, Inc.
