Numerical Modeling of Laminar, Reactive Flows with Detailed Kinetic Mechanisms

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1 Department of Chemistry, Materials, and Chemical Engineering G. Natta Politecnico di Milano (Italy) A. Cuoci, A. Frassoldati, T. Faravelli and E. Ranzi Numerical Modeling of Laminar, Reactive Flows with Detailed Kinetic Mechanisms 14 th International Conference on Numerical Combustion April 8-10, 2013 San Antonio (TX), USA

2 Motivation (I) 2 numerical simulation of multidimensional laminar reacting flows with realistic chemical mechanisms (~100 species) is a challenging problem and places severe demands on computational resources Detailed kinetic schemes Multi-dimensional, complex domains ~ 100 species ~ 1,000 reactions thousands of computational cells Several codes were developed to model laminar reacting flows. However: some of them are developed for specific applications (i.e. laminar coflow flames, structured meshes, only 2D cases, etc.) many of them are home-made and the source code is not available some of them cannot manage very large kinetic schemes

3 Motivation (II) 3 We developed a numerical solver for OpenFOAM, called laminarsmoke to simulate laminar reacting flows Complex kinetic mechanisms (CHEMKIN format) MPI-Parallel (domain decomposition method) Unsteady solver Structured/Unstructured meshes Complex 3D domains Free and open-source The code is freely available for OpenFOAM 2.x at the following address:

4 Outline 4 Numerical model Mathematical model Numerical methodology Examples Steady-state coflow diffusion flame Transient coflow diffusion flame Heterogeneous reactions: CPO of methane Discussion Computational cost Parallel performances Conclusions

5 Mathematical model 5 mesh T ρ + = 0 t Mass ( ρv) Momentum t Governing Equations ( ) ( p ) ρv + ρvv + I = τ+ ρg Energy Species NC NC T ρc + ρc v T = q q ρ C, ω V h Ω t t P P rad P k k k k k k= 1 k= 1 ( ρω ) ( ρω v) ( ρω V ) + = + Ω k k k k k k = 1,..., NC air fuel air Laminar conditions Ideal gas Fick and thermal diffusion Optically-thin radiation model Smooke, Proceedings of The Combustion Institute, 34 (2013), pp

6 Numerical methodology 6 Navier-Stokes Eqs. 1. Reactions Uncoupled, stiff ODE systems dψ dd = S Ψ + M(Ψ, t) Ψ: dependent variables (ω i and T) S(Ψ): is the rate of change of Ψ due to reactions M(Ψ,t): the rate of change of Ψ due to transport Properties evaluation 2. Transport Properties evaluation 3. Reactions Pressure Eqn. Velocity correction Uncoupled, stiff ODE systems Sub-step 1. The reaction terms are integrated over Δt/2 through the solution of an ODE system: dψ a = S Ψ a dd Sub-step 2. The transport terms (convection and diffusion) are integrated over Δt by solving: dψ b = M Ψ b, t dd Sub-step 3. identical to Sub-step 1 t i+1 = t i + t Strang, G. On the construction and comparison of difference schemes, SIAM Journal of Numerical Analysis, 5 (1968), p Ren, Z. and Pope S.B. Second-order splitting schemes for a class of reactive systems, Journal of Computational Physics, 227 (2008), p

7 laminarsmoke solver 7 Pre-Processing OpenFOAM BlockMesh GAMBIT, etc. OpenFOAM Framework Convection + Diffusion segregated approach discretization on unstructured meshes Multidimensional, finite-volume code Structured and unstructured meshes Unsteady solutions Kinetics in CHEMKIN format Several ODE solvers (BzzMath, CVODE, DVODE, RADAU, LSODE, LSODA) Freely available (open-source) OpenSMOKE Framework Reactions coupled approach stiff ODE solvers The code is freely available for OpenFOAM 2.x at the following address: Post-processing Paraview Cuoci et al., A computational tool for the detailed kinetic modeling of laminar flames: Application to C 2 H 4 /CH 4 coflow flames, Combustion and Flame, 160(5), p (2013). DOI: /j.combustflame

8 Outline 8 Numerical model Mathematical model Numerical methodology Examples Steady-state coflow diffusion flame Transient coflow diffusion flame Heterogeneous reactions: CPO of methane Discussion Computational cost Parallel performances Conclusions

9 Examples 9 Methane/Ethylene coflow flames Counter-flow diffusion flame Buoyancy-driven coflow flames* Partially premixed CH4 and C2H4 flames Low-temperature burner Transient flame fed with methane CPO of methane on Pt gauze Tubular reactor with catalytic Raschig rings * In cooperation with Technical University of Ostrava and J. Heyrovský Institute of Physical Chemistry (Czech Republic)

10 Examples 10 Methane/Ethylene coflow flames Counter-flow diffusion flame Buoyancy-driven coflow flames* Partially premixed CH4 and C2H4 flames Low-temperature burner Transient flame fed with methane CPO of methane on Pt gauze Tubular reactor with catalytic Raschig rings * In cooperation with Technical University of Ostrava and J. Heyrovský Institute of Physical Chemistry (Czech Republic)

11 Kinetic mechanisms nc7-ic8 C6 C3 NOx Kinetic mechanism includes hydrocarbons up to Diesel and jet fuels as well as several pollutants - Hierarchy - Modularity Oxygenated species C2 CH4 - Generality Soot CO H2-O2 ~ 450 chemical species ~ 14,000 reactions PAH The kinetic mechanism is freely available in CHEMKIN format at this web address: SOx Frassoldati, A. et al., Combustion and Flame 157(2010), pp Ranzi, E. at al., Progress in Energy and Combustion Science 38 (2012), pp

12 Outline 12 Numerical model Mathematical model Numerical methodology Examples Steady-state coflow diffusion flame Transient coflow diffusion flame Heterogeneous reactions: CPO of methane Discussion Computational cost Parallel performances Conclusions

13 C 2 H 4 /CH 4 /N 2 coflow flames (I) 13 T [K] β=0 C 6 H 6 β=0 100% C 2 H 4 C 6 H 6 β=0.5 33% C 2 H 4 66% CH 4 C 6 H 6 β=1 100% CH 4 Flame details Fuel: CH 4 /C 2 H 4 Air: O 2 /N 2 (23.2%, 76.8% mass) V fuel : cm/s V air : cm/s Fuel nozzle diameter: 11.1 mm Chamber diameter: 110 mm Computational details Domain: 2D axisymmetric (55 x 200 mm) Computational grid: ~25,000 cells Discretization: second order centered Kinetic scheme POLIMI_HT1212: 198 species, 6307 reactions The concentrations of C 2 H 4 and CH 4 are identified by the mixture parameter β: J.F. Roesler, M. Martinot, C.S. McEnally, L.D. Pfefferle, J.L. Delfau, C. Vovelle, Combustion and Flame, 134 (2003) β = X X CH 4 + 2X CH 4 C2H 4

14 C 2 H 4 /CH 4 /N 2 coflow flames (II) 14 The peak values (along the center-line) of mole fractions of several species are reported versus the the β parameter and compared with the experimental measurements (points). C6H6 C3H4 (x50) amount of CH 4 C2H2 pure C 2 H 4 pure CH 4 C4H2 C6H5C2H C4H4 C7H8

15 Outline 15 Numerical model Mathematical model Numerical methodology Examples Steady-state coflow diffusion flame Transient coflow diffusion flame Heterogeneous reactions: CPO of methane Discussion Computational cost Parallel performances Conclusions

16 Transient flame fed with CH 4 (I) 16 Mohammed, R.H., et al., Computational and experimental study of a forced, timevarying, axisymmetric, laminar diffusion flame. Proceedings of the Combustion Institute, : p Fuel mixture: 65% CH4, 35% N2 Coflow stream: 21% O2, 79% N2 The transient behavior is induced by a 20 Hz perturbation in the fuel velocity profile: ( ) 2 r v r = v + ε ( π ) max 1 1 sin 2 ft 2 R Temperature ( K) CO2 mass fraction (0-0.16) POLIMI_C1C31212 kinetic scheme: 82 species, 1485 reactions 2D computational domain with lengths of 51.2 mm and mm in the radial and axial directions (16,000 cells). The calculated flame lift-off is 4 mm. Mohammed et al. report an experimental lift-off between 1.6 and 2.2 mm HO 2 mass fraction Possibility to locally refine the mesh to improve the accuracy of the solution (in this case to better capture the flame lift-off)

17 Transient flame fed with CH 4 (II) 17 maps of CH radical temperature CH mass fraction Steady-state t = 10 ms t = 20 ms t = 30 ms t = 40 ms t = 50 ms Mohammed, R.H., et al., Computational and experimental study of a forced, time-varying, axisymmetric, laminar diffusion flame. Proceedings of the Combustion Institute, : p forcing amplitude of 50%

18 Outline 18 Numerical model Mathematical model Numerical methodology Examples Steady-state coflow diffusion flame Transient coflow diffusion flame Heterogeneous reactions: CPO of methane Discussion Computational cost Parallel performances Conclusions

19 CPO of CH 4 over Pt gauze* (I) 19 Original gauze structure Detail of wire intersections * In cooperation with Matteo Maestri (Department of Energy, Politecnico di Milano) Operating conditions Inlet temperature Inlet velocity Gauze temperature 600 K 10 m/s K 3D computational mesh 140,000 cells 3,500 catalytic faces Inlet CH 4 mole fraction (-) O 2 mole fraction (-) He mole fraction 0.80 (-) Pressure 1.3 bar Pt site density mol/cm 2 Catalytic surf. 5 cm -1 Symmetry planes Heterogeneous kinetics 11 Species, 36 Reactions Outlet Symmetry planes Quiceno R., J. Perez-Ramirez, J. Warnatz, O. Deutschmann, Applied Catalysis A: General 303 (2006) Homogeneous kinetics 82 Species, 1485 Reactions

20 CPO of CH 4 over Pt gauze (II) 20 Comparison with experimental data Quiceno R. et al, Applied Catalysis A: General 303 (2006) CO selectivity O 2 conversion CH 4 conversion CH4 and O2 conversions are not temperature dependent The CO selectivity is strongly influenced by the gauze temperature Mass fraction of main adsorbed species (CO(s), OH(s), etc.) is maximum downstream, where the inlet mixture meet the catalyst wires

21 Outline 21 Numerical model Mathematical model Numerical methodology Examples Steady-state coflow diffusion flame Transient coflow diffusion flame Heterogeneous reactions: CPO of methane Discussion Computational cost Parallel performances Conclusions

22 Computational cost 22 Transport step The reaction step results to be the most consuming part of the code, requiring more than 80-85% of the total computational time. The evaluation of the transport properties and the transport step cover the 5-7% and the 10% of the total time, respectively. Reaction step The CPU time of the reaction steps increases more than quadratically (~2.3) with the number of species, while the transport properties with a power of ~1.8 Increasing the number of species, the relative weight of the reaction step increases.

23 Stiff ODE solvers in laminarsmoke 23 Language Linear system solution Parallel Code available BzzOde C++ Direct No No License Free only for academic use DVODE FORTRAN Direct No Yes Free CVODE C Direct/Iterative Yes Yes Free DLSODE FORTRAN Direct No Yes Free DLSODA FORTRAN Direct No Yes Free RADAU5 FORTRAN Direct No Yes Free Most of the CPU Time (80-90%) is spent for the numerical integration of the ODE systems corresponding to the reaction step The best performances are obtained using the following solvers: BzzOde, DVODE, CVODE 82 species 1,400 reactions 198 species 6307 reactions

24 Weighted domain decomposition 24 When dealing with large mechanisms, the CPU time required by the chemical step is not uniform, and is usually larger in the region where the reactivity is higher. A (static) weighted domain decomposition procedure (based on METIS) was implemented, in order to weight the different cells according to their CPU time for solving the reaction step. The decomposition procedure is designed in order to assign to each processor a number of cells such that the sum of their weights is comparable. The CPU time is normalized on the mean CPU time evaluated with respect to all the computational cells

25 Parallel performances 25 Counter-flow flame simulated using the POLIMI Skeletal kinetic scheme (25 species) on 19,680 cells. Counter-flow flame on 19,680 cells. Infiniband Cluster 192 Intel Xeon processors 3.07 GHz The scaling performances improve with increasing the number of species. By increasing the number of species, the role played by the transport step decreases. Since only the transport step requires inter-processor communication this results in a benefit in terms of speedup and parallel efficiency.

26 Perspectives 26 Storage/retrieval methods (e.g. ISAT) for fast numerical integration of stiff ODE systems Steady-state flows Validation on more complex 3D systems CH 2 O mass fraction H 2 mass fraction K. Zhang, et al., Experimental investigation of partially premixed, highly-diluted dimethyl ether flames at low temperatures, Proceedings of the Combustion Institute 34 (2013)