D. VEYNANTE. Introduction à la Combustion Turbulente. Dimanche 30 Mai 2010, 09h00 10h30

D. VEYNANTE Introduction à la Combustion Turbulente Dimanche 30 Mai 2010, 09h00 10h30

Introduction to turbulent combustion D. Veynante Laboratoire E.M2.C. CNRS - Ecole Centrale Paris Châtenay-Malabry France

Scope Introduction Flame and turbulence Numerical simulations DNS / RANS / LES Averaging Tools for combustion modeling A example: BML analysis Turbulent transport («counter-gradient diffusion») Turbulence / intermittency Large Eddy Simulations

Practical applications LAMINAR TURBULENT Small Power Large Power

Introduction TURBULENCE COMBUSTION Velocity fluctuations Strong and irreversible heat release Large range of scales Integral length scale Kolmogorov length scale Large temperature gradients Non-linear reaction rate

Premixed laminar flames Thermal flame thickness Reaction rate thickness Progress variable

Premixed turbulent flames S T Flame Fresh gases Burnt gases δ T Damköhler (1940)

Non-premixed flames No flame propagation (no flame speed) No characteristic flame thickness Strong dependence on flow conditions

Non-premixed flames Hottel and Hawthorne (1949) Turbulence increases combustion rates

DNS / LES / RANS Model DNS LES model RANS temps Time

DNS / LES / RANS E(k) Modeled in RANS Computed in DNS Computed in LES Modeled in LES kc k

Large eddy simulation Filtering F 1 / Δ box -Δ / 2 0 Δ / 2 x F 1 F Gaussian 0 kc Spectral space k Δ / 2 0 Δ / 2 Physical space x

Experimental analysis Flame holder (blockage ratio 50 %) propane/air flow 5 cm 32 cm Burner Flame

Planar OH laser induced fluorescence

Comparison DNS/LES/RANS Experimental data Flame visualization using PLIF on OH radical Extracted flame front Instantaneous filtered flame front (LES) Mean flame front (RANS)

Comparison RANS/LES Instantaneous flame front Mean flame front (RANS) α P(c) β c Mean temperature = probability to be in burnt gases! time

Comparison RANS/LES Instantaneous flame front Local (weighted) average over a small volume Fresh and burnt gas instantaneous locations identified at the resolved scale level Turbulence Pollutant formation Radiative heat transfers Instantaneous filtered flame front (LES)

Comparison DNS/LES/RANS

Comparison DNS/LES/RANS Industrial simulations : Practical simulations: one night restitution time Today: almost only RANS LES is developing for: Combustion instabilities Internal combustion engines (cycle-to-cycle variations Physical analysis of unsteady phenomena Future: more and more LES (possible coupled computations RANS + LES) BUT: RANS is sufficient for some applications Efficiency of industrial codes Engineer experience more important than simulations

LES : To combine RANS and LES (Schlüter et al, 2004)

Averaging / Filtering Mass balance equation: Conventional Reynolds averaging / filtering: Correlations Density / velocity To be modelled!

Averaging / Filtering: Favre (mass weighted) Objective: Favre (mass weighted) averaging: (RANS) Mass balance equation:

Balance equations are formally the same Mass: Momentum: Species mass fractions: Unknown Formally identical to classical Reynolds averaged equations

BUT only a mathematical formalism!!!!! No simple relation between Reynolds and Favre averages ρ Q = ρq = ρq + ρ Q ρ Q correlations remain hidden in Favre averaged quantities Comparison with experimental data? «Favre turbulent fluxes» remain to be modelled (ũ ) i u j, ũ i Y k,... Usual turbulence models!!!

BUT only a mathematical formalism!!!!!

Modelling Species mass fractions balance equation: Three inclosed terms: Turbulent transport: gradient assumption! Reaction rate: to be modelled Counter gradient transport? Molecular diffusion: negligible (high Reynolds number assumption)

Modelling A simple irreversible chemical reaction Arrhenius law Averaging

Modelling: Taylor expansion

Modelling: Taylor expansion Unclosed quantities Truncature errors (very low convergence speed, alternate series) Valid only for a simple irreversible reaction Physical analysis!

9 species / 19 reactions scheme for H 2 / O 2 combustion

Modelling: Taylor expansion, applications Atmospheric chemistry Supersonic combustion Segregation factor S perfect mixing S = 0 Full separation S = -1

Rea cting flow parameters (premixed combustion) TURBULENCE COMBUSTION Velocity fluctuations Laminar flame speed Integral length scale Kolmogorov length scale Laminar flame thickness thermal thickness reaction zone thickness

Rea cting flow parameters (premixed combustion) Damköhler number = Turbulent time Chemical time

Diagram (premixed combustion) Well stirred reactor Da 1 Flamelets Da 1 Barrère-Borghi, Peters,

Rea cting flow parameters (premixed combustion) Karlovitz number = Chemical time Kolmogorov time

Diagram (premixed combustion) Well stirred reactor Klimov-Williams criterion Flamelets Barrère-Borghi, Peters,

Rea cting flow parameters (premixed combustion) Comparison with reaction zone thickness

Diagram (premixed combustion) Klimov-Williams criterion Thin flame regime (flamelets) Peters (2000)

Diagram (premixed combustion) Thickened-wrinkled flame regime Klimov-Williams criterion Thin flame regime (flamelets) Peters (2000)

Diagram (premixed combustion) Thickened flame regime Thickened-wrinkled flame regime Klimov-Williams criterion Thin flame regime (flamelets) Peters (2000)

Diagram (premixed combustion) BUT: Only qualitative! Limits? Strong assumptions Homogeneous turbulence Comparison of scales neglecting turbulence / combustion interactions Curvature effects Viscous effects Kolmogorov scales have short lifetime Non unique chemical time scale BE CAREFUL!!!!!

Modelling? Premixed combustion Non premixed combustion Eddy Break Up Bray-Moss-Libby model Flame surface density Probability density functions G-equation Renormalization group theory Zimont s model Eddy Dissipation Concept Infinitely fast chemistry Laminar flame model Flame surface density Probability density functions CMC A large range of approaches

Tools for modelling: definitions Fresh gases (premixed) T u T b Burnt gases (premixed) c = 0 c = 1 Z = 1 Z = 0 Flame Fuel (non premixed) Oxidizer (non premixed)

Tools for modelling Fresh gases (premixed) Burnt gases (premixed) Fuel (non premixed) Turbulent mixing (scalar dissipation rate) Da 1 X Geometrical analysis - Iso-surface (c or Z) -Flame structure analysis (along the normal to the flame surface) One-point statistics (probability density function) Oxidizer (non premixed)

Tools: geometrical analysis S T Fresh gases S T Flame Flame Burnt gases G t + u. G = S T G δ T Empirical relations Turbulent flame speed (to be modeled) Flame located at G = G 0 Renormalization group theory

Tools: geometrical analysis Global description G t + u. G = S T G S T should be modeled! not a well-defined quantity depends on many parameters Numerical difficulties «flame cusps» kinematic description May be of interest for large scale systems no need to resolve the flame structure

Geometrical analysis: flame surface density Fresh gases Burnt gases c = 0 c = 1 Mean reaction rate per unit flame surface Laminar flame studies Flame surface density Flame turbulence interaction Measurements: tomography, LIF (2D, 3D?)

Geometrical analysis: flame surface density

Geometrical analysis: flame surface density c =0 Algebraic expression BML model L y c =1 Fractal approach

Geometrical analysis: flame surface density Balance equation Fresh gases Burnt gases c = 0 c = 1 c = c* Pope (1988)

Geometrical analysis: flame surface density c balance equation balance equation Σ balance equation balance equation n c =0 c =1

Tools for modelling Fresh gases (premixed) Burnt gases (premixed) Fuel (non premixed) Turbulent mixing (scalar dissipation rate) Da 1 Oxidizer (non premixed)

Mixing approach Perfect mixing Perfect segregation Mixing:

Mixing approach Premixed Non premixed Scalar dissipation rate (mixing speed)

Mixing approach Algebraic expression Balance equation Thin front assumption Balance equation Measurements:????? Eddy-Break-Up model (Spalding, 1972)

Eddy-Break-Up (Spalding) Combustion controled by turbulent mixing Very simple and popular model overestimate reaction rates Non-premixed flames: Eddy-Dissipation Concept (Magnussen model) F + so P

Tools for modelling Fresh gases (premixed) Burnt gases (premixed) X One-point statistics (probability density function) Fuel (non premixed) Oxidizer (non premixed)

Statistical approach Thermochemical variable (mass fractions, temperature, ) Normalization relation Averaged quantities are determined as Measurements: statistics on one point data

Statistical approach Averaged quantities are determined as Mass weighted (Favre) pdf

Statistical approach: non-premixed flames assuming infinitely fast chemistry steady laminar flamelet assumption Z =0 Z =1

Statistical approach Arrhenius law (chemical studies) To be determined Presumed pdf (functions of known quantities Balance equation Measurements: statistics on one point data

Statistical approach: presumed pdf β functions P(c) a = 0.1 ; b =10 P(c) a = 10 ; b =0.1 0.0 0.2 0.4 0.6 0.8 1.0 c =0 0.0 0.2 0.4 0.6 0.8 1.0 P(c) a = 0.1 ; b =0.1 c =1 P(c) a = 2 b =5 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Statistical approach: presumed pdf β functions Balance equations for mean and variances

Statistical approach: presumed pdf β functions balance equations In practice: pre-processing tabulation

Statistical approach: pdf balance equation Transport in physical space Evolution in phase (chemical) space

Statistical approach: pdf balance equation To be modeled CLOSED!!!!

Statistical approach: pdf balance equation Numerical solution based on Monte-Carlo formulation Can (theoretically) handle very complex chemical scheme Very expensive approach Coupling with tabulated chemistry ILDM (Mass and Pope) FPI / FGM ISAT May be extended to flow variables no more turbulence model need closure very expensive

Tools for modelling Fresh gases (premixed) Burnt gases (premixed) Turbulent mixing (scalar dissipation rate) Fuel (non premixed) X Geometrical analysis - Iso-surface (c or Z) -Flame structure analysis (along the normal to the flame surface) One-point statistics (probability density function) Oxidizer (non premixed)

Tools for modelling: links Conditional Moment Closure Flame surface density? Probability Density function Scalar dissipation rate Close relations between modelling approaches!!!

Tools for modelling: links Close relations between modelling approaches!!!

Bray-Moss-Libby analysis Premixed combustion Infinitely thin flame front Unity Lewis number Adiabatic and isobaric combustion progress variable bimodal pdf c =0 c =1

Bray-Moss-Libby analysis c =0 P(c) β c c =1 α time

Bray-Moss-Libby analysis is the probability to be in burned gases!!!

Bray-Moss-Libby analysis Pdf fully determined from the mean progress variable

Bray-Moss-Libby analysis Relations between Favre and Reynolds averages

Bray-Moss-Libby analysis

Bray-Moss-Libby analysis Usual model:?

Bray-Moss-Libby analysis Counter gradient transport 0 0 Gradient transport?? x

Bray-Moss-Libby analysis Direct Numerical simulations 3D simulations Two different codes Two different databases - CTR (Trouvé et al.) - C. Rutland

Bray-Moss-Libby analysis Counter gradient transport Gradient transport

Counter gradient transport u b i > u u i Gradient transport u b i < u u i

Gradient / Counter-gradient Counter gradient transport Gradient transport

Counter gradient To include counter-gradient in turbulent combustion modeling 3 balance equations for turbulent scalar fluxes 6 balance equations for turbulent momentum fluxes!!!

Gradient / Counter-gradient Two limiting cases: Low turbulence levels Flow dynamics imposed by thermal expansion Counter gradient transport High turbulence intensities Flow dynamics imposed by turbulence Gradient transport A criterion: the Bray number N B = τs L αu Veynante et al. (1997)

Counter gradient To include counter-gradient in turbulent combustion modeling 3 balance equations for turbulent scalar fluxes 6 balance equations for turbulent momentum fluxes Large Eddy Simulations???!!!

Bray-Moss-Libby analysis Turbulence in fresh gases Turbulence in burnt gases Additional term due to intermittency and Favre averaging

Propane 0.20 0.15 Fully burnt gases Air velocity pdf 0.10 0.05 0.00 0 10 20 30 40 velocity (m/s) 50 60 70 velocity pdf 0.20 0.15 0.10 0.05 Fresh gases velocity pdf 0.12 0.10 0.08 0.06 0.04 0.02 combusting gases u b > u u 0.00 0.00 0 10 20 30 40 velocity (m/s) 50 60 70 0 10 20 30 40 velocity (m/s) 50 60 70

An example

Bray-Moss-Libby reaction rate

Bray-Moss-Libby reaction rate Thin front assumption Proof EBU

Bray-Moss-Libby model: evolutions c time Reaction rate per flame crossing Crossing frequency

Bray-Moss-Libby model: evolutions c =0 L y c =1

Bray-Moss-Libby analysis Flame surface density Probability Density function Scalar dissipation rate

A very powerful tool Large Eddy Simulations

Modelling (RANS) TURBULENCE k - ε model Applied to Favre averaged quantities COMBUSTION Very sophisticated models balance equation for flame surface density balance equation for scalar dissipation rate full pdf transport equation complex chemical schemes sub models (ignition, quenching ) No explicit connection!!!

Large eddy simulations Filtering Variable density flows : Favre or mass-weighted filtering Assumption: filtering and derivative operators exchange

LES : combustion Chemical species: Gradient modeling (assumption!) Negligible? + unresolved momentum transport (modeled by extending usual models for non-reacting flows) To be modeled!

Reaction rate modeling Various possible approaches : ω k Extension of usual RANS models Eddy-Break-Up G-equation Flame surface density concept Probability density function New approaches Artificial flame thickening (to allow flame resolution) To use the knowledge of large scales - Similarity formulation - Dynamic formulation Good results achieved with simple models: better turbulence predictions reduced importance of models

Reaction rate modeling ω k A difficulty : to resolve the flame front flame front LES grid mesh (Δx) Fresh gases Burnt gases Combustion is a subgrid scale phenomenon! Adapted models required (LES filter for combustion implicitly larger than for velocities)

Premixed flames Three main solutions: Flame front tracking technique (G-equation) G t + u. G = S T G Filtered progress variable (filter larger than the mesh size) Flame surface density formalism Turbulent flame speed Thickened flame model (to be modeled) Flame thicker than the original one (Butler and O Rourke) Algebraic expressions Mathematical Flame given formalism by G=G BML-like formulation 0 iso-surface (Boger et al.) Global Properties Fractal description of convection / diffusion / reaction balance equations expression (outer cut-off = filter size) Balance Numerical Arrhenius equation difficulties laws are conserved (cusps, ) (chemical description) Modelled May (Boger be subgrid et of al, Hawkes interest scale and for Cant, wrinkling large Richard scale et al., factor Weller systems (efficiency et al.) function) (Colin et al., Charlette et al., ) One of the most popular approaches (Menon et al., Pitsch et al., )

Non-premixed flames Three main approaches: Linear eddy model (LEM) Stochastic one-dimensional stirring process («triplet map») One-dimensional DNS at subgrid scale Thickened To manage flame exchanges model between (variable grid thickening cells factor) (Kerstein, Menon et al., Smith et al., ) Theoretically not well-sustained But provides successfull results Probability density functions Extension of RANS concept (subgrid scale pdf, Gao and O Brien) Presumed pdf (Cook et al., Reveillon and Vervisch, Pierce and Moin, Pitsch et al., ), Balance equation

Example : turbulent premixed flame Flame stabilised behind a diedra (Boger et Veynante., 2000) (BML-like modeling) Instantaneous resolved temperature field Mean temperature Should be predicted in RANS AVBP code (CERFACS - Oxford Univ.)

Example: Flame stabilized behind a diedra (Boger and Veynante, 2000) Transport due to resolved motions resolved in LES to be modeled in RANS gradient counter-gradient Usual gradient model: Better results than in RANS!!!

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Turbulent transport x Equilibrium in turbulent fluxes balance equation

(Borghi et Destriau, 1998)

Fresh gases Burnt gases Reaction zone Preheat zone

(Borghi et Destriau, 1998)

Fresh gases Burnt gases Reaction zone Preheat zone

(Borghi et Destriau, 1998)