What is the pencil-code?

12D Direct Numerical Simulation ofmethane/air turbulent premixed flames underhigh turbulence intensityJulien Savre04/13/2011Fluid Mechanics seminar series 04/13/2011

2Outline• Why studying turbulent premixed flames under high turbulent intensity?• A free, open-source compressible DNS code for combustion applications: The pencil-code• What is the pencil-code?• Numerics (brief)• Physical modules• Description of the cases and related issues• Results• Computational domain• Initialization• CharacteristicsFluid Mechanics seminar series 04/13/2011

3Outline• Why studying turbulent premixed flames under high turbulent intensity?• A free, open-source compressible DNS code for combustion applications: The pencil-code• What is the pencil-code?• Numerics (brief)• Physical modules• Description of the cases and related issues• Results• Computational domain• Initialization and homogeneous turbulence• CharacteristicsFluid Mechanics seminar series 04/13/2011

4Turbulent premixed flames at high Ka• Combustion regimes and diagrams (Poinsot & Veynante, 2001):Ka ≈ 100Karlovitz number:orFluid Mechanics seminar series 04/13/2011

5Turbulent premixed flames at high Ka• Combustion regimes and diagrams (Poinsot & Veynante, 2001):(Kolmogorov scale smaller thanthe inner reaction zone thickness)• Local/global extinction• Combustion instabilities(blow-off)Fluid Mechanics seminar series 04/13/2011

6Turbulent premixed flames at high Ka• There is not a good understanding of what happens in that regime• A good example: quenching/reignition phenomena• A clear, comprehensive definition of “quenching phenomena” has yet to be given• Several theories have been proposed and reviewed:– Peters’ theory: the smallest turbulent eddies are able to penetrate the reaction zone and quench it– Poinsot’s suggestion: those small eddies are too weak and do not survive long enough to effectivelyquench the flame (importance of unsteadiness)• Several mechanisms are involved and their respective contribution is still unclear (thermo-diffusiveinstabilities, differential diffusion, heat losses, flame strain, flame wrinkling...)Fluid Mechanics seminar series 04/13/2011

6Turbulent premixed flames at high Ka• There is not a good understanding of what happens in that regime• A good example: quenching/reignition phenomena• A clear, comprehensive definition of “quenching phenomena” has yet to be given• Several theories have been proposed and reviewed:– Peters’ theory: the smallest turbulent eddies are able to penetrate the reaction zone and quench it– Poinsot’s suggestion: those small eddies are too weak and do not survive long enough to effectivelyquench the flame (importance of unsteadiness)• Several mechanisms are involved and their respective contribution is still unclear (thermo-diffusiveinstabilities, differential diffusion, heat losses, flame strain, flame wrinkling...)Fluid Mechanics seminar series 04/13/2011

7Turbulent premixed flames at high Ka• Studies of flames in the distributed reaction zone regime and limits:• Few publications:– Experimentally, the conditions required to create a flame in that regime are difficult to sustain (stabilityissues)– Numerically, several obstacles must be overcome (size, memory, accuracy...)• The existing investigations rely mainly on laminar flame/vortex interactions (f.i. Poinsot et al., JFM 1991)Fluid Mechanics seminar series 04/13/2011

7Turbulent premixed flames at high Ka• Studies of flames in the distributed reaction zone regime and limits:• Few publications:– Experimentally, the conditions required to create a flame in that regime are difficult to sustain (stabilityissues)– Numerically, several obstacles must be overcome (size, memory, accuracy...)• The existing investigations rely mainly on laminar flame/vortex interactions (f.i. Poinsot et al., JFM 1991)Mueller et al.26th Symp., 1996Fluid Mechanics seminar series 04/13/2011

7Turbulent premixed flames at high Ka• Studies of flames in the distributed reaction zone regime and limits:• Few publications:– Experimentally, the conditions required to create a flame in that regime are difficult to sustain (stabilityissues)– Numerically, several obstacles must be overcome (size, memory, accuracy...)• The existing investigations rely mainly on laminar flame/vortex interactions (f.i. Poinsot et al., JFM 1991)• Numerical issues:• Finite chemistry phenomena require the use of relatively detailed kinetic mechanisms• The grid resolution must be very small as the small dissipative turbulent scales are smaller than theinner reaction layer of the flame• The time history of flame/turbulence interactions have to be accounted for (importance of transientphenomena)Fluid Mechanics seminar series 04/13/2011

8Objectives• The distributed reaction zone regime is relevant in various practical applications wherequenching/reignition may occur• No turbulent combustion model is really efficient to predict those phenomenaAt present, flamelet models are widely used, even underconditions for which they were not designedThere is a real need in further improving our knowledge of thisregime and in developing dedicated modelsFluid Mechanics seminar series 04/13/2011

8Objectives• The distributed reaction zone regime is relevant in various practical applications wherequenching/reignition may occur• No turbulent combustion model is really efficient to predict those phenomenaAt present, flamelet models are widely used, even underconditions for which they were not designedThere is a real need in further improving our knowledge of thisregime and in developing dedicated models2D DNS cases are designed here to study methane/air premixed flames in the distributedreaction zone regimeFluid Mechanics seminar series 04/13/2011

9Outline• Why studying turbulent premixed flames under high turbulent intensity?• A free, open-source compressible DNS code for combustion applications: The pencil-code• What is the pencil-code?• Numerics (brief)• Physical modules• Description of the cases and related issues• Results• Computational domain• Initialization• CharacteristicsFluid Mechanics seminar series 04/13/2011

10What is the pencil-code?• The pencil-code is a free, open-source, fully-compressible, high-order DNS code(available at http://code.google.com/p/pencil-code/)• Developed since 2001, originally for magnetohydrodynamics/astrophysics applications (A.Brandenburg, Stockholm and W. Dobler, Potsdam)• Main characteristics:• The code is accessible via SVN• Systematic reproducibility auto-tests for troubleshooting• The equations are solved along pencils in order to optimize the cash memory: all the instantaneousphysical quantities are stored in 1D vectors in the x direction• The code benefits from the contribution of several research groups around the world: very mature code• Written in fortran 90/95• Easy to program and share its developments with the community via SVNFluid Mechanics seminar series 04/13/2011

11Numerics• Compressible balance equations (solved under a non-conservative form):• continuity equation• equation of motion (for the velocity)• entropy equation (temperature)• species equations• perfect gas law• The equations are solved using a centered sixth-order explicit finite difference scheme (asopposed to compact schemes):• facilitates parallelization (compact schemes require the resolution of a tridiagonal system)• to avoid wiggles, upwind schemes are also available for entropy and density equations (5th or 4thorder)Fluid Mechanics seminar series 04/13/2011

12Numerics• Domain, grids and BCs:• Cartesian, cylindrical or spherical referential• Cartesian grids (preferably in a power of 2 for FFTs)• Non regular grids with local stretching (but no adaptive refinement)• Available BCs: periodicity, walls (heated or not), symmetry (no-slip walls), regular inflow/outflow, nonreflectinginflow/outflow (characteristic boundary conditions)• Time-stepping:• A 3rd order 2N-Runge Kutta scheme is commonly used• Possibility to use an implicit solver for stiff ODEs in combustion applications (LSODE, symmetric fluxsplitting procedure)• The time step can either be chosen constant or set by limitations on the convective, diffusive or reactionterms:Compressible code: CFL based on acoustic wavesFluid Mechanics seminar series 04/13/2011

13Physical modules• Great modularity of the code: each physical process has its own module• Great transparency as a lot of unnecessary modules remain black boxes (only the required modulesare compiled)• Easy to understand and to contribute• Easy to debug• For combustion applications, the main required modules are:• NSCBC (non-reflecting boundary conditions)• Entropy (resolution of the temperature equation)• Equation of state• Time-step• Chemistry (for the implementation and validation of chemistry in pencil, see Babkovskaia et al., JCP2011)Fluid Mechanics seminar series 04/13/2011

14Chemistry module• Evaluation of the chemical reaction rates as well as the transport and thermodynamicproperties:• The CHEMKIN formalism is employed• All the input files are taken from CHEMKIN (chem.inp, tran.dat)• This enables the use of generic detailed as well as reduced kinetics (ready-to-use CHEMKIN files canbe found on the net)• Transport properties: three possibilities available• CHEMKIN format: species diffusion coefficients evaluated as mixture averages of simplified binarydiffusion coefficients (Hirschfelder and Curtiss formalism) + flux expressed in terms of molar fractiongradient with the possibility to add Dufour and Soret effects• Constant Lewis numbers for each species + Fick’s law• Simplified diffusion coefficients (power law of T) + Fick’s lawFluid Mechanics seminar series 04/13/2011

15Outline• Why studying turbulent premixed flames under high turbulent intensity?• A free, open-source compressible DNS code for combustion applications: The pencil-code• What is the pencil-code?• Numerics (brief)• Physical modules• Description of the cases and related issues• Results• Computational domain• Initialization• CharacteristicsFluid Mechanics seminar series 04/13/2011

16Intro• DNS of premixed flame/turbulence interactions at high Karlovitz number (Ka >> 100)• Short litterature review:• Very limited simulations of flames under such conditions were reported: Poludnenko and Oran (C&F2010), Aspden et al. x2 (33rd Symp., 2011)• Remarks: the simulations reported are not DNSs (low-order schemes were used), Aspden et al. areunderresolved, P&O use a 1-step irreversible chemistry• Conclusion:Even with huge computational resources, DNSs of flames under high intensity turbulence arestill out of reach unless stringent simplifications are made• Considering the existing works on the topic, we don’t have to be afraid of simplifying thesimulationsFluid Mechanics seminar series 04/13/2011

17Cases description• Computational domain:• 2D: in the flamelet regime, the flame is most likely to take a cylindrical shape (2D) rather than aspheroidal one (3D)• 0.6x0.6 cm2• 1024x1024 grid• Dx ≈ 5.9 µm• Boundary conditions:• Periodic in y• non-reflecting inflow/outflow in x• Initialization:• A cold turbulent field is first generated using a forcing function in the momentum equation:with:• A laminar premixed flame calculated with FlameMaster is then overimposed to this initial turbulent fieldFluid Mechanics seminar series 04/13/2011

18Cases description• Physics and Chemistry:• We are here interested in methane/air flames• A 16 species, 25 reactions scheme is used, suitable for lean premixed flames (Smooke & Giovangigli,1991)• Simplified transport is employed (constant Le for each species and heat conductivity expressed as apower of temperature)• For all cases, the turbulence decays over a time equivalent to 1 eddy turnover-timeCases L (cm) u’ (cm/s) eta (µm) Re KaCase 1 0.209 5900 2.7 7700 7000Case 2 0.209 940 8 1250 820Case 3 0.126 4850 2.7 3820 7000Fluid Mechanics seminar series 04/13/2011

19Outline• Why studying turbulent premixed flames under high turbulent intensity?• A free, open-source compressible DNS code for combustion applications: The pencil-code• What is the pencil-code?• Numerics (brief)• Physical modules• Description of the cases and related issues• Results• Computational domain• Initialization• CharacteristicsFluid Mechanics seminar series 04/13/2011

202D decaying homogeneous turbulence• Properties of decaying turbulence are crucial in those simulations. We have to be carefullthat:• The simulation is sufficiently well resolved (in our case, the flame front being much larger than theKolmogorov scale, the resolution criterion is imposed by turbulence and not by the flame)• Turbulence does not decay too much• Decay of TKE in power of t after a short transient period:After some manipulations:Fluid Mechanics seminar series 04/13/2011

202D decaying homogeneous turbulence• Properties of decaying turbulence are crucial in those simulations. We have to be carefullthat:• The simulation is sufficiently well resolved (in our case, the flame front being much larger than theKolmogorov scale, the resolution criterion is imposed by turbulence and not by the flame)• Turbulence does not decay too much• Decay of TKE in power of t after a short transient period:After some manipulations:Existence of a threshold at high Re (m=-1) over which viscous effects decrease during thedecay : physically inconsistent but hard to avoidFluid Mechanics seminar series 04/13/2011

212D decaying homogeneous turbulenceL=0.209, 1024L=0.209, 2048L=0.209, 51210000L=0.209, 1024L=0.209, 2048L=0.126, Ka=7000L=0.209, Ka=820kKa10001x10 7n = -0.162n = -0.169n = -0.131001x10 -7 1x10 -6 0.00001Ka=7000, 1024Ka=7000, 2048Ka=820, 1024Ka=7000, L=0.126t0.01 0.1 1t/tauTo characterize the overall resolution:nu_e0.1 1Fluid Mechanics seminar series t/tau04/13/2011

212D decaying homogeneous turbulenceL=0.209, 1024L=0.209, 2048L=0.209, 51210000L=0.209, 1024L=0.209, 2048L=0.126, Ka=7000L=0.209, Ka=820kKa10001x10 7n = -0.162n = -0.169n = -0.131001x10 -7 1x10 -6 0.00001Ka=7000, 1024Ka=7000, 2048Ka=820, 1024Ka=7000, L=0.126t0.01 0.1 1t/tauTo characterize the overall resolution:nu_eNumerical dissipation0.1 1Fluid Mechanics seminar series t/tau04/13/2011

22Instantaneous snapshotsL=0.209, Ka=820• Progress variable contours:L=0.126, Ka=7000• Reaction zone: 0.75 < c < 0.95L=0.209, Ka=7000• Vorticity iso-linesFluid Mechanics seminar series 04/13/2011

23Instantaneous snapshots• Heat release contours and vorticity linesL=0.209, Ka=7000L=0.209, Ka=820Fluid Mechanics seminar series 04/13/2011

23Instantaneous snapshots• Heat release contours and vorticity linesL=0.209, Ka=7000L=0.209, Ka=820Presence of small vortices withinthe reaction zone at Ka=7000Fluid Mechanics seminar series 04/13/2011

23Instantaneous snapshots• Heat release contours and vorticity linesL=0.209, Ka=7000L=0.209, Ka=820Presence of small vortices withinthe reaction zone at Ka=7000Existence of low HR regions:local quenching in progressFluid Mechanics seminar series 04/13/2011

24Curvature correlations• Correlations between local curvature and heat release rate at c=0.8 (inside the reaction zone)• Positive correlation at Ka=820, 0 correlation at Ka=7000• In both cases: low heat release rate regions correspond to negatively curved elements(importance of curvature effects)Fluid Mechanics seminar series 04/13/2011

25Remarks• In cases 1 and 3, at Ka=7000, the flames belong to the distributed flame regime:• Presence of small vortices inside the fuel consumption layer• The reaction layer is quite irregular exhibiting locally stretched elements• In case 2, at Ka=820, the flame seems not to belong to the distributed flame regime:• No vortices are able to penetrate the reaction zone• The reaction layer is very regular, with a constant thickness• In all cases:• The inner reaction layer is locally quenched, showing reduced HR rate• Two important conclusions:• The fuel consumption layer can be quenched even if small scale vortices cannot survive within it• The distributed flame regime is reached for Karlovitz numbers much higher than 100Fluid Mechanics seminar series 04/13/2011

26Remarks• The limit Ka=100 is largely exceeded mainly because the definition of Ka doesn’t account forthermal expansion as temperature increases• Previous studies of laminar flame/vortex interactions have shown that the vortex surface inthe burnt gases is multiplied by• The vortex rotation velocity is divided by the same factorFluid Mechanics seminar series 04/13/2011

26Remarks• The limit Ka=100 is largely exceeded mainly because the definition of Ka doesn’t account forthermal expansion as temperature increases• Previous studies of laminar flame/vortex interactions have shown that the vortex surface inthe burnt gases is multiplied by• The vortex rotation velocity is divided by the same factor• Redifining the Karlovitz number according to gas expansion:• Methane/air at Φ=0.7: τ=6.2Fluid Mechanics seminar series 04/13/2011

27Remarks• Corrected Ka estimates:Cases L (cm) Ka Ka*Cases 1 - 2 0.209 - 0.126 7000 450Case 3 0.209 820 50• Ka* is still a rough estimate but is coherent with the observationsAccording to this new definition, Case 3 no longer belongs to the distributed flame regime, assuggested by the snapshotsFluid Mechanics seminar series 04/13/2011

27Remarks• Corrected Ka estimates:Cases L (cm) Ka Ka*Cases 1 - 2 0.209 - 0.126 7000 450Case 3 0.209 820 50• Ka* is still a rough estimate but is coherent with the observationsAccording to this new definition, Case 3 no longer belongs to the distributed flame regime, assuggested by the snapshots• In the following, another definition of the progress variable will be employed:• Allows a detailed description of the entire flame front (including the oxidation layer)Fluid Mechanics seminar series 04/13/2011

28Turbulent flame structure (case 2)• Scatter plots of temperature and species mass fractions accross the flame with respect to theprogress variable:• Quasi linear response of T and major species mass fractions:consistent with the results of Aspden et al. (PCI 2011) with various fuelsFluid Mechanics seminar series 04/13/2011

29Turbulent flame structure (case 2)• Radical peaks (here H) are dramatically increased in the turbulent flame: chain branchingreactions become dominant to the expense of chain terminating reactions• Direct effect of turbulent mixing within the flame front• Increased CO peak and equilibrium level: consistent with turbulent flame experimentsFluid Mechanics seminar series 04/13/2011

30Turbulent flame structure (case 2)• CH2O becomes significant early in the preheat zone suggesting flame broadening (in agreementwith recent experimental observations)• Unlike other radicals, CH3 formation is mainly decreased accross the flameFluid Mechanics seminar series 04/13/2011

30Turbulent flame structure (case 2)Overestimated levels ofCH3 in the preheat zone:effects of reducedchemistry• CH2O becomes significant early in the preheat zone suggesting flame broadening (in agreementwith recent experimental observations)• Unlike other radicals, CH3 formation is mainly decreased accross the flameFluid Mechanics seminar series 04/13/2011

31Conclusion• Summary:• 2D DNS of lean premixed turbulent methane/air flames at Ka > 100 were achieved• Use of the pencil-code (evaluation of the code for complexe reactive flows) with reduced chemistryand simplified transport• Investigation of turbulent flame structure and response of the inner reaction zone• Conclusions:• The pencil-code is perfectly adapted to the kind of simulations proposed here, and performed betterthan expected in terms of CPU time: simulation time of 120 h (for case 2)Case Nproc Phys. time N steps mean Δt CPU/Δt/pts total CPU2 32 217 µs 92600 2.3 ns 4.45 µs 3840 hFluid Mechanics seminar series 04/13/2011

32Conclusion• Conclusions:• Local quenching was observed along the inner reaction layer, but no global extinction (that seems farmore difficult to achieve as the burnt gases constantly provide heat)• The distributed flame regime is reached for higher Ka than expected: accounting for flow dilataion inthe definition of Ka seems to provide a better evaluation of this limit• The inner flame structure and species distributions seem consistent with experimental observationsand numerical simulations:» Quasi linear response of temperature with respect to the fuel mass fraction» Broadening of the formaldehyde layer» Increased CO levels• The chemical paths at such high turbulence intensities are highly perturbed:» Chain branching reactions are more dominant» The formation of formaldehyde via CH3 seems pivotal during the quenching process whichraises one crucial issue:Fluid Mechanics seminar series 04/13/2011

32Conclusion• Conclusions:• Local quenching was observed along the inner reaction layer, but no global extinction (that seems farmore difficult to achieve as the burnt gases constantly provide heat)• The distributed flame regime is reached for higher Ka than expected: accounting for flow dilataion inthe definition of Ka seems to provide a better evaluation of this limit• The inner flame structure and species distributions seem consistent with experimental observationsand numerical simulations:» Quasi linear response of temperature with respect to the fuel mass fraction» Broadening of the formaldehyde layer» Increased CO levels• The chemical paths at such high turbulence intensities are highly perturbed:» Chain branching reactions are more dominant» The formation of formaldehyde via CH3 seems pivotal during the quenching process whichraises one crucial issue:Is it appropriate to use a reduced kinetic mechanism to predict small scale turbulence/flameinteractions; & how accurate must be the CH3 reaction path?Fluid Mechanics seminar series 04/13/2011

33Conclusion• Future works:• At least two more simulations could bring additional informations:» Ka=2000 (or Ka*=150): limit of the distributed flame regime in terms of Ka*» Ka=150: limit of the distributed flame regime in terms of Ka• Detailed investigation of transport processes within the flame front: turbulent transport vs. differentialdiffusion (in progress)• Study of time history of the quenching process: how the holes will evolve?• Given the available computational resources, it seems still difficult to increase the accuracyof the simulations (3D, better resolution, more detailed chemistry...)Fluid Mechanics seminar series 04/13/2011

34Overview of the chemical structure• Carbon chain:• Importance of reaction R13:• Contribution of 2 reactions to the consumption of CH3: comparisonbetween a positively curved region and a “hole”Fluid Mechanics seminar series 04/13/2011

34Overview of the chemical structure• Carbon chain:• Importance of reaction R13:• Contribution of 2 reactions to the consumption of CH3: comparisonbetween a positively curved region and a “hole”Clear change in the chemical path:R11 becomes dominant to theexpense of R13Fluid Mechanics seminar series 04/13/2011

34Overview of the chemical structure• Carbon chain:• Importance of reaction R13:• Contribution of 2 reactions to the consumption of CH3: comparisonbetween a positively curved region and a “hole”Clear change in the chemical path:R11 becomes dominant to theexpense of R13The carbon chain is broken by a default offormaldehyde productionFluid Mechanics seminar series 04/13/2011