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Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: a chemical explosive mode analysis

  • T. F. LU (a1), C. S. YOO (a2), J. H. CHEN (a2) and C. K. LAW (a1)


A chemical explosive mode analysis (CEMA) was developed as a new diagnostic to identify flame and ignition structure in complex flows. CEMA was then used to analyse the near-field structure of the stabilization region of a turbulent lifted hydrogen–air slot jet flame in a heated air coflow computed with three-dimensional direct numerical simulation. The simulation was performed with a detailed hydrogen–air mechanism and mixture-averaged transport properties at a jet Reynolds number of 11000 with over 900 million grid points. Explosive chemical modes and their characteristic time scales, as well as the species involved, were identified from the Jacobian matrix of the chemical source terms for species and temperature. An explosion index was defined for explosive modes, indicating the contribution of species and temperature in the explosion process. Radical and thermal runaway can consequently be distinguished. CEMA of the lifted flame shows the existence of two premixed flame fronts, which are difficult to detect with conventional methods. The upstream fork preceding the two flame fronts thereby identifies the stabilization point. A Damköhler number was defined based on the time scale of the chemical explosive mode and the local instantaneous scalar dissipation rate to highlight the role of auto-ignition in affecting the stabilization points in the lifted jet flame.


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Current address: Department of Mechanical Engineering, University of Connecticut, CT 06269-3139, USA

Current address: School of Mechanical and Advanced Materials Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Republic of Korea



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Bilger, R. W. 1988 The structure of turbulent nonpremixed flames. Proc. Combust. Inst. 22, 475488.
Bongers, H., Van Oijen, J. A. & De Goey, L. P. H. 2002 Intrinsic low-dimensional manifold method extended with diffusion. Proc. Combust. Inst. 29, 13711378.
Cabra, R., Myhrvold, T., Chen, J. Y., Dibble, R. W., Karpetis, A. N. & Barlow, R. S. 2002 Simultaneous laser Raman-Rayleigh-LIF measurements and numerical modelling results of a lifted turbulent H2/N2 jet flame in a vitiated coflow. Proc. Combust. Inst. 29, 18811888.
Chen, J. H., Choudhary, A., de Supinski, B., DeVries, M., Hawkes, E. R., Lasky, S., Liao, W. K., Ma, K. L., Mellor-Crummey, J., Podhorszki, N., Sankaran, R., Shende, S. & Yoo, C. S. 2009 Terascale direct numerical simulations of turbulent combustion using S3D. Comput. Sci. Disc. 2, 015001.
Chung, S. H. 2007 Stabilization, propagation and instability of tribrachial triple flames. Proc. Combust. Inst. 31, 877892.
Davis, M. J. 2006 Low-dimensional manifolds in reaction–diffusion equations. Part I. Fundamental aspects. J. Phys. Chem. A 110, 52355256.
Davis, M. J. & Tomlin, A. S. 2008 Spatial dynamics of steady flames. Part I. Phase space structure and the dynamics of individual trajectories. J. Phys. Chem. A 112, 77687783.
Fotache, C. G., Kreutz, T. G. & Law, C. K. 1997 Ignition of counterflowing methane versus heated air under reduced and elevated pressures. Combust. Flame 108, 442470.
Gordon, R. L., Masri, A. R., Pope, S. B. & Goldin, G. M. 2007 A numerical study of auto-ignition in turbulent lifted flames issuing into a vitiated co-flow. Combust. Theory Model. 11, 351376.
Goussis, D. A. 1996 On the construction and use of reduced chemical kinetic mechanisms produced on the basis of given algebraic relations. J. Comput. Phys. 128, 261273.
Goussis, D. A. & Najm, H. N. 2006 Model reduction and physical understanding of slowly oscillating processes: the circadian cycle. Multiscale Model. Simul. 5, 12971332.
Goussis, D. A. & Valorani, M. 2006 An efficient iterative algorithm for the approximation of the fast and slow dynamics of stiff systems. J. Comput. Phys. 214, 316346.
Hadjinicolaou, M. & Goussis, D. A. 1998 Asymptotic solution of stiff PDEs with the CSP method: the reaction–diffusion equation. SIAM J. Sci. Comput. 20, 781810.
Jimenez, C. & Cuenot, B. 2007 DNS study of stabilization of turbulent triple flames by hot gases. Proc. Combust. Inst. 31, 16491656.
Joedicke, A., Peters, N. & Mansour, M. 2005 The stabilization mechanism and structure of turbulent hydrocarbon lifted flames. Proc. Combust. Inst. 30, 901909.
Kalghatgi, G. T. 1984 Lift-off heights and visible lengths of vertical turbulent jet diffusion flames in still air. Combust. Sci. Technol. 41, 1719.
Kaper, H. G. & Kaper, T. J. 2002 Asymptotic analysis of two reduction methods for systems of chemical reactions. Physica D 165, 6693.
Kazakov, A., Chaos, M., Zhao, Z. W. & Dryer, F. L. 2006 Computational singular perturbation analysis of two-stage ignition of large hydrocarbons. J. Phys. Chem. A 110, 70037009.
Lam, S. H. 1985 Singular perturbation for stiff equations using numerical methods. In Recent Advances in the Aerospace Sciences (ed. Casci, Corrado, in honor of Luigi Crocco). Plenum.
Lam, S. H. 1992 The effects of fast chemical reactions on mass diffusion. MAE Rep. T1953, Princeton University, New Jersey.
Lam, S. H. 1993 Using CSP to understand complex chemical kinetics. Combust. Sci. Technol. 89, 375404.
Lam, S. H. 2007 Reduced chemistry-diffusion coupling. Combust. Sci. Technol. 179, 767786.
Lam, S. H. & Goussis, D. A. 1994 The CSP method for simplifying kinetics. Intl J. Chem. Kinet. 26, 461486.
Lee, J. C., Najm, H. N., Lefantzi, S., Ray, J., Frenklach, M., Valorani, M. & Goussis, D. A. 2007 A CSP and tabulation-based adaptive chemistry model. Combust. Theory Model. 11, 73102.
Li, J., Zhao, Z. W., Kazakov, A. & Dryer, F. L. 2004 An updated comprehensive kinetic model of hydrogen combustion. Intl J. Chem. Kinet. 36, 566575.
Lu, T. F., Ju, Y. G. & Law, C. K. 2001 Complex CSP for chemistry reduction and analysis. Combust. Flame 126, 14451455.
Lu, T. F. & Law, C. K. 2008 A CSP-based criterion for the identification of QSS species: a reduced mechanism for methane oxidation with no chemistry. Combust. Flame 154, 761774.
Lu, T. F., Law, C. K. & Ju, Y. G. 2003 Some aspects of chemical kinetics in Chapman-Jouguet detonation: induction length analysis. J. Propul. Power 19, 901907.
Maas, U. & Pope, S. B. 1992 Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space. Combust. Flame 88, 239264.
Markides, C. N. & Mastorakos, E. 2005 An experimental study of hydrogen autoignition in a turbulent co-flow of heated air. Proc. Combust. Inst. 30, 883891.
Massias, A., Diamantis, D., Mastorakos, E. & Goussis, D. A. 1999 a Global reduced mechanisms for methane and hydrogen combustion with nitric oxide formation constructed with CSP data. Combust. Theory Model. 3, 233257.
Massias, A., Diamantis, D., Mastorakos, E. & Goussis, D. A. 1999 b An algorithm for the construction of global reduced mechanisms with CSP data. Combust. Flame 117, 685708.
Mizobuchi, Y., Shinjo, J., Ogawa, S. & Takeno, T. 2005 A numerical study on the formation of diffusion flame islands in a turbulent hydrogen jet lifted flame. Proc. Combust. Inst. 30, 611619.
Peters, N. & Williams, F. A. 1983 Liftoff characteristics of turbulent jet diffusion flames. AIAA J. 21, 423429.
Pitts, W. M. 1988 Assessment of theories for the behaviour and blowout of lifted turbulent jet diffusion flames. Proc. Combust. Inst. 22, 809816.
Ren, Z. & Pope, S. B. 2006 The use of slow manifolds in reactive flows. Combust. Flame 147, 243261.
Ren, Z. & Pope, S. B. 2007 a Transport-chemistry coupling in the reduced description of reactive flows. Combust. Theory Model. 11, 715739.
Ren, Z. & Pope, S. B. 2007 b Reduced description of complex dynamics in reactive systems. J. Phys. Chem. A 111, 84648474.
Singh, S., Powers, J. M. & Paolucci, S. 2002 On slow manifolds of chemically reactive systems. J. Chem. Phys. 117, 14821496.
Su, L. K., Sun, O. S. & Mungal, M. G. 2006 Experimental investigation of stabilization mechanisms in turbulent, lifted jet diffusion flames. Combust. Flame 144, 494512.
Tacke, M. M., Geyer, D., Hassel, E. P. & Janicka, J. 1998 A detailed investigation of the stabilization point of lifted turbulent diffusion flames. Proc. Combust. Inst. 27, 11571165.
Upatnieks, A., Driscoll, J. F., Rasmussen, C. C. & Ceccio, S. L. 2004 Liftoff of turbulent jet flames: assessment of edge flame and other concepts using cinema-PIV. Combust. Flame 138, 259272.
Valorani, M., Creta, F., Goussis, D. A., Lee, J. C. & Najm, H. N. 2006 An automatic procedure for the simplification of chemical kinetic mechanisms based on CSP. Combust. Flame 146, 2951.
Valorani, M., Goussis, D. A., Creta, F. & Najm, H. N. 2005 Higher order corrections in the approximation of low-dimensional manifolds and the construction of simplified problems with the CSP method. J. Comput. Phys. 209, 754786.
Valorani, M., Najm, H. N. & Goussis, D. A. 2003 CSP analysis of a transient flame-vortex interaction: time scales and manifolds. Combust. Flame 134, 3553.
Vanquickenborne, L. & van Tiggelen, A. 1966 Stabilization mechanism of lifted diffusion flames. Combust. Flame 10, 5969.
Yamashita, H., Shimada, M. & Takeno, T. 1996 A numerical study on flame stability at the transition point of jet diffusion flames. Proc. Combust. Inst. 26, 2734.
Yoo, C. S., Sankaran, R. & Chen, J. H. 2009 Three-dimensional direct numerical simulation of a turbulent lifted hydrogen/air jet flame in heated coflow: flame stabilization and structure. J. Fluid Mech. 460, 453481.
Zagaris, A., Kaper, H. G. & Kaper, T. J. 2004 a Analysis of the computational singular perturbation reduction method for chemical kinetics. J. Nonlinear Sci. 14, 5991.
Zagaris, A., Kaper, H. G. & Kaper, T. J. 2004 b Fast and slow dynamics for the computational singular perturbation method. Multiscale Model. Simul. 2, 613638.
Zagaris, A., Kaper, H. G. & Kaper, T. J. 2005 Two perspectives on reduction of ordinary differential equations. Math. Nachr. 278, 16291642.
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Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: a chemical explosive mode analysis

  • T. F. LU (a1), C. S. YOO (a2), J. H. CHEN (a2) and C. K. LAW (a1)


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