2D Direct Numerical Simulation of methane/air turbulent premixed flames under high turbulence intensity Julien Savre 04/13/2011

Transcription

1 1 2D Direct Numerical Simulation of methane/air turbulent premixed flames under high turbulence intensity Julien Savre 04/13/2011

2 2 Outline 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 Characteristics

3 3 Outline 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 Characteristics

4 4 Turbulent premixed flames at high Ka Combustion regimes and diagrams (Poinsot & Veynante, 2001): Ka 100 Karlovitz number: or

5 5 Turbulent premixed flames at high Ka Combustion regimes and diagrams (Poinsot & Veynante, 2001): (Kolmogorov scale smaller than the inner reaction zone thickness) Local/global extinction Combustion instabilities (blow-off)

6 6 Turbulent 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 effectively quench the flame (importance of unsteadiness) Several mechanisms are involved and their respective contribution is still unclear (thermo-diffusive instabilities, differential diffusion, heat losses, flame strain, flame wrinkling...)

7 6 Turbulent 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 effectively quench the flame (importance of unsteadiness) Several mechanisms are involved and their respective contribution is still unclear (thermo-diffusive instabilities, differential diffusion, heat losses, flame strain, flame wrinkling...)

8 7 Turbulent 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 (stability issues) 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)

9 7 Turbulent 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 (stability issues) 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., 1996

10 7 Turbulent 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 (stability issues) 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 the inner reaction layer of the flame The time history of flame/turbulence interactions have to be accounted for (importance of transient phenomena)

11 8 Objectives The distributed reaction zone regime is relevant in various practical applications where quenching/reignition may occur No turbulent combustion model is really efficient to predict those phenomena At present, flamelet models are widely used, even under conditions for which they were not designed There is a real need in further improving our knowledge of this regime and in developing dedicated models

12 8 Objectives The distributed reaction zone regime is relevant in various practical applications where quenching/reignition may occur No turbulent combustion model is really efficient to predict those phenomena At present, flamelet models are widely used, even under conditions for which they were not designed There is a real need in further improving our knowledge of this regime and in developing dedicated models 2D DNS cases are designed here to study methane/air premixed flames in the distributed reaction zone regime

13 9 Outline 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 Characteristics

14 10 What is the pencil-code? The pencil-code is a free, open-source, fully-compressible, high-order DNS code (available at 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 instantaneous physical 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 SVN

15 11 Numerics 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 (as opposed 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 4th order)

16 12 Numerics 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, nonreflecting inflow/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 flux splitting procedure) The time step can either be chosen constant or set by limitations on the convective, diffusive or reaction terms: Compressible code: CFL based on acoustic waves

17 13 Physical 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 modules are 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., JCP 2011)

18 14 Chemistry module Evaluation of the chemical reaction rates as well as the transport and thermodynamic properties: 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 can be found on the net) Transport properties: three possibilities available CHEMKIN format: species diffusion coefficients evaluated as mixture averages of simplified binary diffusion coefficients (Hirschfelder and Curtiss formalism) + flux expressed in terms of molar fraction gradient 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 law

19 15 Outline 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 Characteristics

20 16 Intro 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&F 2010), Aspden et al. x2 (33rd Symp., 2011) Remarks: the simulations reported are not DNSs (low-order schemes were used), Aspden et al. are underresolved, P&O use a 1-step irreversible chemistry Conclusion: Even with huge computational resources, DNSs of flames under high intensity turbulence are still out of reach unless stringent simplifications are made Considering the existing works on the topic, we don t have to be afraid of simplifying the simulations

21 17 Cases description Computational domain: 2D: in the flamelet regime, the flame is most likely to take a cylindrical shape (2D) rather than a spheroidal 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 field

22 18 Cases 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 a power of temperature) For all cases, the turbulence decays over a time equivalent to 1 eddy turnover-time Cases L (cm) u (cm/s) eta (µm) Re Ka Case Case Case

23 19 Outline 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 Characteristics

24 20 2D decaying homogeneous turbulence Properties of decaying turbulence are crucial in those simulations. We have to be carefull that: The simulation is sufficiently well resolved (in our case, the flame front being much larger than the Kolmogorov 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:

25 20 2D decaying homogeneous turbulence Properties of decaying turbulence are crucial in those simulations. We have to be carefull that: The simulation is sufficiently well resolved (in our case, the flame front being much larger than the Kolmogorov 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 the decay : physically inconsistent but hard to avoid

26 21 2D decaying homogeneous turbulence L=0.209, 1024 L=0.209, 2048 L=0.209, L=0.209, 1024 L=0.209, 2048 L=0.126, Ka=7000 L=0.209, Ka=820 k Ka x10 7 n = n = n = x10-7 1x Ka=7000, 1024 Ka=7000, 2048 Ka=820, 1024 Ka=7000, L=0.126 t t/tau To characterize the overall resolution: nu_e Fluid Mechanics seminar series t/tau 04/13/2011

27 21 2D decaying homogeneous turbulence L=0.209, 1024 L=0.209, 2048 L=0.209, L=0.209, 1024 L=0.209, 2048 L=0.126, Ka=7000 L=0.209, Ka=820 k Ka x10 7 n = n = n = x10-7 1x Ka=7000, 1024 Ka=7000, 2048 Ka=820, 1024 Ka=7000, L=0.126 t t/tau To characterize the overall resolution: nu_e Numerical dissipation Fluid Mechanics seminar series t/tau 04/13/2011

28 22 Instantaneous snapshots L=0.209, Ka=820 Progress variable contours: L=0.126, Ka=7000 Reaction zone: 0.75 < c < 0.95 L=0.209, Ka=7000 Vorticity iso-lines Fluid Mechanics seminar series 04/13/2011

29 23 Instantaneous snapshots Heat release contours and vorticity lines L=0.209, Ka=7000 L=0.209, Ka=820

30 23 Instantaneous snapshots Heat release contours and vorticity lines L=0.209, Ka=7000 L=0.209, Ka=820 Presence of small vortices within the reaction zone at Ka=7000

31 23 Instantaneous snapshots Heat release contours and vorticity lines L=0.209, Ka=7000 L=0.209, Ka=820 Presence of small vortices within the reaction zone at Ka=7000 Existence of low HR regions: local quenching in progress

32 24 Curvature 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)

33 25 Remarks 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 100

34 26 Remarks The limit Ka=100 is largely exceeded mainly because the definition of Ka doesn t account for thermal expansion as temperature increases Previous studies of laminar flame/vortex interactions have shown that the vortex surface in the burnt gases is multiplied by The vortex rotation velocity is divided by the same factor

35 26 Remarks The limit Ka=100 is largely exceeded mainly because the definition of Ka doesn t account for thermal expansion as temperature increases Previous studies of laminar flame/vortex interactions have shown that the vortex surface in the 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=6.2

36 27 Remarks Corrected Ka estimates: Cases L (cm) Ka Ka* Cases Case Ka* is still a rough estimate but is coherent with the observations According to this new definition, Case 3 no longer belongs to the distributed flame regime, as suggested by the snapshots

37 27 Remarks Corrected Ka estimates: Cases L (cm) Ka Ka* Cases Case Ka* is still a rough estimate but is coherent with the observations According to this new definition, Case 3 no longer belongs to the distributed flame regime, as suggested 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)

38 28 Turbulent flame structure (case 2) Scatter plots of temperature and species mass fractions accross the flame with respect to the progress variable: Quasi linear response of T and major species mass fractions: consistent with the results of Aspden et al. (PCI 2011) with various fuels

39 29 Turbulent flame structure (case 2) Radical peaks (here H) are dramatically increased in the turbulent flame: chain branching reactions 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 experiments

40 30 Turbulent flame structure (case 2) CH2O becomes significant early in the preheat zone suggesting flame broadening (in agreement with recent experimental observations) Unlike other radicals, CH3 formation is mainly decreased accross the flame

41 30 Turbulent flame structure (case 2) Overestimated levels of CH3 in the preheat zone: effects of reduced chemistry CH2O becomes significant early in the preheat zone suggesting flame broadening (in agreement with recent experimental observations) Unlike other radicals, CH3 formation is mainly decreased accross the flame

42 31 Conclusion 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 chemistry and 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 better than 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 CPU µs ns 4.45 µs 3840 h

43 32 Conclusion Conclusions: Local quenching was observed along the inner reaction layer, but no global extinction (that seems far more 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 in the definition of Ka seems to provide a better evaluation of this limit The inner flame structure and species distributions seem consistent with experimental observations and 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 which raises one crucial issue:

44 32 Conclusion Conclusions: Local quenching was observed along the inner reaction layer, but no global extinction (that seems far more 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 in the definition of Ka seems to provide a better evaluation of this limit The inner flame structure and species distributions seem consistent with experimental observations and 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 which raises one crucial issue: Is it appropriate to use a reduced kinetic mechanism to predict small scale turbulence/flame interactions; & how accurate must be the CH3 reaction path?

45 33 Conclusion 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. differential diffusion (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 accuracy of the simulations (3D, better resolution, more detailed chemistry...)

46 34 Overview of the chemical structure Carbon chain: Importance of reaction R13: Contribution of 2 reactions to the consumption of CH3: comparison between a positively curved region and a hole

47 34 Overview of the chemical structure Carbon chain: Importance of reaction R13: Contribution of 2 reactions to the consumption of CH3: comparison between a positively curved region and a hole Clear change in the chemical path: R11 becomes dominant to the expense of R13

48 34 Overview of the chemical structure Carbon chain: Importance of reaction R13: Contribution of 2 reactions to the consumption of CH3: comparison between a positively curved region and a hole Clear change in the chemical path: R11 becomes dominant to the expense of R13 The carbon chain is broken by a default of formaldehyde production