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Hydrodynamic and thermodiffusive instability effects on the evolution of laminar planar lean premixed hydrogen flames

Published online by Cambridge University Press:  18 May 2012

C. Altantzis ,
C. E. Frouzakis ,
A. G. Tomboulides ,
M. Matalon  and
K. Boulouchos
C. Altantzis
Affiliation:
Aerothermochemistry and Combustion Systems Laboratory, Swiss Federal Institute of Technology, Zurich, CH-8092, Switzerland
C. E. Frouzakis*
Affiliation:
Aerothermochemistry and Combustion Systems Laboratory, Swiss Federal Institute of Technology, Zurich, CH-8092, Switzerland
A. G. Tomboulides
Affiliation:
Department of Mechanical Engineering, University of Western Macedonia, 50100 Kozani, Greece
M. Matalon
Affiliation:
Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana IL 61801, USA
K. Boulouchos
Affiliation:
Aerothermochemistry and Combustion Systems Laboratory, Swiss Federal Institute of Technology, Zurich, CH-8092, Switzerland
*
†Email address for correspondence: frouzakis@lav.mavt.ethz.ch
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Abstract

Numerical simulations with single-step chemistry and detailed transport are used to study premixed hydrogen/air flames in two-dimensional channel-like domains with periodic boundary conditions along the horizontal boundaries as a function of the domain height. Both unity Lewis number, where only hydrodynamic instability appears, and subunity Lewis number, where the flame propagation is strongly affected by the combined effect of hydrodynamic and thermodiffusive instabilities are considered. The simulations aim at studying the initial linear growth of perturbations superimposed on the planar flame front as well as the long-term nonlinear evolution. The dispersion relation between the growth rate and the wavelength of the perturbation characterizing the linear regime is extracted from the simulations and compared with linear stability theory. The dynamics observed during the nonlinear evolution depend strongly on the domain size and on the Lewis number. As predicted by the theory, unity Lewis number flames are found to form a single cusp structure which propagates unchanged with constant speed. The long-term dynamics of the subunity Lewis number flames include steady cell propagation, lateral flame movement, oscillations and regular as well as chaotic cell splitting and merging.

JFM classification

Reacting Flows: Laminar reacting flows Reacting Flows: Flames Reacting Flows: Combustion Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 700 , 10 June 2012 , pp. 329 - 361
Copyright
Copyright © Cambridge University Press 2012

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References

1. Altantzis, C., Frouzakis, C. E., Tomboulides, A. G., Kerkemeier, S. G. & Boulouchos, K. 2011 Detailed numerical simulations of intrinsically unstable two-dimensional planar lean premixed hydrogen/air flames. Proc. Combust. Inst. 33, 1261–1268.CrossRefGoogle Scholar
2. Barenblatt, G. I., Zeldovich, Y. B. & Istratov, A. G. 1962 On diffusional-thermal stability of a laminar flame. J. Appl. Mech. Tech. 4, 21–26.Google Scholar
3. Bradley, D., Cresswell, T. M. & Puttock, J. S. 2001 Flame acceleration due to flame-induced instabilities in large scale explosions. Combust. Flame 124, 551–559.CrossRefGoogle Scholar
4. Bradley, D., Sheppard, C. G. W., Woolley, R., Greenhalgh, D. A. & Lockett, R. D. 2000 The development and structure of flame instabilities and cellularity at low Markstein numbers in explosions. Combust. Flame 122, 195–209.CrossRefGoogle Scholar
5. Bychkov, V. V. 1998 Nonlinear equation for a curved stationary flame and the flame velocity. Phys. Fluids 10, 2091–2098.CrossRefGoogle Scholar
6. Bychkov, V. V. & Liberman, M. A. 2000 Dynamics and stability of premixed flames. Phys. Rep. 325, 115–237.CrossRefGoogle Scholar
7. Byrne, G. D. & Hindmarsh, A. C. 1999 PVODE, an ODE solver for parallel computers. Intl J. High Perform. Comput. Appl. 13, 354–365.CrossRefGoogle Scholar
8. Candel, S. M. & Poinsot, T. J. 1990 Flame stretch and the balance equation for the flame area. Combust. Sci. Technol. 70 (1–3), 1–15.CrossRefGoogle Scholar
9. Chakraborty, N. & Cant, R. S. 2004 Unsteady effects of strain rate and curvature on turbulent premixed flames in an inflow-outflow configuration. Combust. Flame 137, 129–147.CrossRefGoogle Scholar
10. Chen, J. H. & Im, H. G. 1998 Correlation of flame speed with stretch in turbulent premixed methane/air flames. Proc. Combust. Inst. 27, 819–826.CrossRefGoogle Scholar
11. Chu, B. T. & Kovasznay, X. 1958 Non-linear interactions in a viscous heat conducting compressible gas. J. Fluid Mech. 3 (5), 494–514.CrossRefGoogle Scholar
12. Chung, S. H. & Law, C. K. 1984 An invrariant derivation of flame stretch. Combust. Flame 55, 1984.CrossRefGoogle Scholar
13. Clavin, P. 1985 Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Prog. Energy Combust. Sci. 11, 1–59.CrossRefGoogle Scholar
14. Creta, F., Fogla, N. & Matalon, M. 2011 Turbulent propagation of premixed fames in the presence of Darrieus–Landau instability. Combust. Theor. Model. 15, 267–298.CrossRefGoogle Scholar
15. Creta, F. & Matalon, M. 2011 Strain rate effects on the nonlinear development of hydrodynamically unstable flames. Proc. Combust. Inst. 33, 1087–1094.CrossRefGoogle Scholar
16. Darrieus, G. 1946 Propagation d’un front de flamme. Sixth International Congress of Applied Mathematics.Google Scholar
17. Day, M., Bell, J., Bremer, P.-T., Pascucci, V., Becknera, V. & Lijewski, M. 2009 Turbulence effects on cellular burning structures in lean premixed hydrogen flames. Combust. Flame 156 (5), 1035–1045.CrossRefGoogle Scholar
18. Denet, B. & Haldenwang, P. 1992 Numerical study of thermal-diffusive instability of premixed flames. Combust. Sci. Technol. 86, 199–221.CrossRefGoogle Scholar
19. Denet, B. & Haldenwang, P. 1995 A numerical study of premixed flames Darrieus-Landau instability. Combust. Sci. Technol. 104, 143–167.CrossRefGoogle Scholar
20. Deville, M. O., Fischer, P. F. & Mund, E. H. 2002 High-order Methods for Incompressible Fluid Flows. Cambridge University Press.CrossRefGoogle Scholar
21. Fischer, P. F., Lottes, J. W. & Kerkemeier, S. G. 2008 nek5000 Web page. http://nek5000.mcs.anl.gov.Google Scholar
22. Frankel, M. L. & Sivashinsky, G. I. 1982 The effect of viscosity on hydrodynamic stability of a plane flame front. Combust. Sci. Technol. 29, 207–224.CrossRefGoogle Scholar
23. Grcar, J. F., Bell, J. B. & Day, M. S. 2009 The soret effect in naturally propagating, premixed, lean, hydrogen air flames. Proc. Combust. Inst. 32, 1173–1180.CrossRefGoogle Scholar
24. Groff, E. G. 1982 The cellular nature of confined spherical propane-air flames. Combust. Flame 48, 51.CrossRefGoogle Scholar
25. Haworth, D. C. & Poinsot, T. J. 1992 Numerical simulations of Lewis number effects in turbulent premixed flames. J. Fluid Mech. 244, 405–436.CrossRefGoogle Scholar
26. Kadowaki, S. 1997 Numerical study on lateral movement of cellular flames. Phys. Rev. E 56, 2966–2971.CrossRefGoogle Scholar
27. Kadowaki, S. & Hasegawa, T. 2005 Numerical simulation of dynamics of premixed flames: flame instability and vortex–flame interaction. Prog. Energy Combust. Sci. 31, 193–241.CrossRefGoogle Scholar
28. Kadowaki, S., Suzuki, H. & Kobayashi, H. 2005 The unstable behavior of cellular premixed flames induced by intrinsic instability. Proc. Combust. Inst. 30, 169–176.CrossRefGoogle Scholar
29. Kang, S. H., Baek, S. W. & Im, H. G. 2006 Effects of heat and momentum losses on the stability of premixed flames in a narrow channel. Combust. Theor. Model. 10, 659–681.CrossRefGoogle Scholar
30. Karlin, V. 2002 Celular flames may exhibit a nonmodal transient instability. Proc. Combust. Inst. 29 (2), 1537–1542.CrossRefGoogle Scholar
31. Kee, R. J., Dixon-Lewis, G., Warnatz, J., Coltrin, M. E. & Miller, J. A. 1996 a A Fortran computer code package for the evaluation of gas-phase multicomponent transport properties. Tech. Rep. SAND86-8246. Sandia National Laboratories.Google Scholar
32. Kee, R. J., Rupley, F. M. & Miller, J. A. 1996 b Chemkin II: a Fortran chemical kinetics package for the analysis of gas-phase chemical kinetics. Tech. Rep. SAND89-8009B. Sandia National Laboratories.CrossRefGoogle Scholar
33. Kurdyumov, V. N., Pizza, G., Frouzakis, C. E. & Mantzaras, J. 2009 Dynamics of premixed flames in a narrow channel with a step-wise wall temperature. Combust. Flame 156, 2190–2200.CrossRefGoogle Scholar
34. Landau, L. 1944 On the theory of slow combustion. Acta Physicochim. USSR 19, 77–85.Google Scholar
35. Law, C. K. 2006 Propagation, structure, and limit phenomena of laminar flames at elevated pressures. Combust. Sci. Technol. 178, 335–360.CrossRefGoogle Scholar
36. Li, J., Zhao, Z., Kazakov, A. & Dryer, F. L. 2004 An updated comprehensive kinetic model of hydrogen combustion. Intl J. Chem. Kinet. 36, 566–575.CrossRefGoogle Scholar
37. Markstein, G. H. 1951 Experimental and theoretical studies of flame front stability. J. Aeronaut. Sci. 18, 199–220.CrossRefGoogle Scholar
38. Markstein, G. H. 1964 Nonsteady Flame Propagation. The Macmillan Company.Google Scholar
39. Matalon, M. 1983 On flame stretch. Combust. Sci. Technol. 31, 169–181.CrossRefGoogle Scholar
40. Matalon, M. 2007 Intrinsic flame instabilities in premixed and nonpremixed combustion. Annu. Rev. Fluid Mech. 39 (1), 163–191.CrossRefGoogle Scholar
41. Matalon, M., Cui, C. & Bechtold, J. K. 2003 Hydrodynamic theory of premixed flames: effects of stoichiometry, variable transport coefficients and arbitrary reaction orders. J. Fluid Mech. 487, 179–210.CrossRefGoogle Scholar
42. Matalon, M. & Matkowsky, B. J. 1982 Flames as gasdynamic discontinuities. J. Fluid Mech. 124, 239–259.CrossRefGoogle Scholar
43. Michelson, D. M. & Sivashinsky, G. I. 1977 Nonlinear analysis of hydrodynamic instability in laminar flames - II. Numerical experiments. Acta Astronaut. 4, 1207–1221.CrossRefGoogle Scholar
44. Michelson, D. M. & Sivashinsky, G. I. 1982 Thermal-expansion induced cellular flames. Combust. Flame 48, 211–217.CrossRefGoogle Scholar
45. Palm-Lewis, A. & Strehlow, R. A. 1969 On the propagation of turbulent flames. Combust. Flame 13, 111–119.CrossRefGoogle Scholar
46. Patera, A. T. 1984 A spectral element method or fluid dynamics: laminar low in a channel expansion. J. Comput. Phys. 58, 468–488.CrossRefGoogle Scholar
47. Patnaik, G., Kailasanath, K., Oran, E. S. & Laskey, K. J. 1988 Detailed numerical simulations of cellular flames. Proc. Combust. Inst. 22, 1517–1526.CrossRefGoogle Scholar
48. Pelce, P. & Clavin, P. 1982 Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames. J. Fluid Mech. 124, 219–237.CrossRefGoogle Scholar
49. Peters, N., Terhoeven, P., Chen, J. H. & Echekki, T. 1998 Statistics of flame displacement speeds from computations of 2-D unsteady methane-air flames. Proc. Combust. Inst. 27, 833–839.CrossRefGoogle Scholar
50. Poinsot, T. & Veynante, D. 2005 Theoretical and Numerical Combustion. R.T. Edwards, Inc.Google Scholar
51. Rastigejev, Y. & Matalon, M. 2006a Nonlinear evolution of hydrodynamically unstable premixed flames. J. Fluid Mech. 554, 371–392.CrossRefGoogle Scholar
52. Rastigejev, Y. & Matalon, M. 2006b Numerical simulation of flames as gas-dynamic discontinuities. Combust. Theor. Model. 10, 459–481.CrossRefGoogle Scholar
53. Rehm, R. G. & Baum, H. R. 1978 Equations of motion for thermally driven, buoyant flows. J. Res. Natl Bur. Stand. 83 (3), 97–308.CrossRefGoogle ScholarPubMed
54. Rupley, F. M., Kee, R. J. & Miller, J. A. 1995 PREMIX: a Fortran program for modeling steady laminar one-dimensional premixed flames. Tech. Rep. SAND85-8240. Sandia National Laboratories.Google Scholar
55. Sharpe, G. J. 2003 Linear stability of planar premixed flames: reactive Navier–Stokes equations with finite activation energy and arbitrary lewis number. Combust. Theor. Model. 7, 45–65.CrossRefGoogle Scholar
56. Sharpe, G. J. & Falle, S. A. E. G. 2006 Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the reactive Navier–Stokes equations. Combust. Theor. Model. 10, 483–514.CrossRefGoogle Scholar
57. Sharpe, G. J. & Falle, S. A. E. G. 2011 Numerical simulations of premixed flame cellular instability for a simple chain-branching model. Combust. Flame 158, 925–934.CrossRefGoogle Scholar
58. Sivashinsky, G. I. 1977a Nonlinear analysis of hydrodynamic instability in laminar flames: I-derivation of basic equations. Acta Astronaut. 4, 1177–1206.CrossRefGoogle Scholar
59. Sivashinsky, G. I. 1977b Diffusional-thermal theory of cellular flames. Combust. Sci. Technol. 15, 137–146.CrossRefGoogle Scholar
60. Sivashinsky, G. I. 1983 Instabilities, pattern formation, and turbulence in flames. Annu. Rev. Fluid Mech. 15, 179–199.CrossRefGoogle Scholar
61. Sun, C. J., Sung, C. J., He, L. & Law, C. K. 1999 Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters. Combust. Flame 118, 108–128.CrossRefGoogle Scholar
62. Tomboulides, A. G., Lee, J. C. Y. & Orszag, S. A. 1997 Numerical simulation of low Mach number reactive flows. J. Sci. Comput. 12, 139–167.CrossRefGoogle Scholar
63. Tomboulides, A. G. & Orszag, S. A. 1998 A quasi-two-dimensional benchmark problem for low Mach number compressible codes. J. Comput. Phys. 146, 691–706.CrossRefGoogle Scholar
64. Vaynblat, D. & Matalon, M. 2000a Stability of pole solutions for planar propagating flames. I. Exact eigenvalues and eigenfunctions. SIAM J. Appl. Math. 60 (2), 679–702.CrossRefGoogle Scholar
65. Vaynblat, D. & Matalon, M. 2000b Stability of pole solutions for planar propagating flames. II. Properties of the eigenvalues and eigenfunctions with implications to flame stability. SIAM J. Appl. Maths 60 (2), 703–728.CrossRefGoogle Scholar
66. Williams, F. A. 1985 Combustion Theory, 2nd edn. Benjamin Cummins.Google Scholar
67. Yuan, J., Ju, Y. & Law, C. K. 2005 Coupled hydrodynamic and diffusional-thermal instabilities in flame propagation at subunity Lewis numbers. Phys. Fluids 17, 1063–1072.CrossRefGoogle Scholar
68. Yuan, J., Ju, Y. & Law, C. K. 2007 On flame-front instability at elevated pressures. Proc. Combust. Inst. 31, 1267–1274.CrossRefGoogle Scholar