Hostname: page-component-7bb8b95d7b-w7rtg Total loading time: 0 Render date: 2024-09-15T08:13:48.276Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of finite-rate chemistry and detailed transport on the instability of jet diffusion flames

Published online by Cambridge University Press:  25 March 2014

Yee Chee See  and
Matthias Ihme
Yee Chee See
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Matthias Ihme*
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Local linear stability analysis has been shown to provide valuable information about the response of jet diffusion flames to flow-field perturbations. However, this analysis commonly relies on several modelling assumptions about the mean flow prescription, the thermo-viscous-diffusive transport properties, and the complexity and representation of the chemical reaction mechanisms. In this work, the effects of these modelling assumptions on the stability behaviour of a jet diffusion flame are systematically investigated. A flamelet formulation is combined with linear stability theory to fully account for the effects of complex transport properties and the detailed reaction chemistry on the perturbation dynamics. The model is applied to a methane–air jet diffusion flame that was experimentally investigated by Füri et al. (Proc. Combust. Inst., vol. 29, 2002, pp. 1653–1661). Detailed simulations are performed to obtain mean flow quantities, about which the stability analysis is performed. Simulation results show that the growth rate of the inviscid instability mode is insensitive to the representation of the transport properties at low frequencies, and exhibits a stronger dependence on the mean flow representation. The effects of the complexity of the reaction chemistry on the stability behaviour are investigated in the context of an adiabatic jet flame configuration. Comparisons with a detailed chemical-kinetics model show that the use of a one-step chemistry representation in combination with a simplified viscous-diffusive transport model can affect the mean flow representation and heat release location, thereby modifying the instability behaviour. This is attributed to the shift in the flame structure predicted by the one-step chemistry model, and is further exacerbated by the representation of the transport properties. A pinch-point analysis is performed to investigate the stability behaviour; it is shown that the shear-layer instability is convectively unstable, while the outer buoyancy-driven instability mode transitions from absolutely to convectively unstable in the nozzle near field, and this transition point is dependent on the Froude number.

JFM classification

Instability: Absolute/convective instability Reacting Flows: Combustion Reacting Flows: Laminar reacting flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 745 , 25 April 2014 , pp. 647 - 681
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Becker, H. A. & Yamazaki, S. 1978 Entrainment, momentum flux and temperature in vertical free turbulent diffusion flames. Combust. Flame 33 (2), 123–149.Google Scholar
Bergmann, M., Bruneau, C.-H. & Iollo, A. 2009 Enablers for robust POD models. J. Comput. Phys. 228, 516–538.Google Scholar
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 2007 Transport Phenomena. rev. 2nd edn. John Wiley & Sons.Google Scholar
Bowman, C. T., Hanson, R. K., Davidson, D. F., Gardiner, W. C., Lissianski, V., Smith, G. P., Golden, D. M., Frenklach, M. & Goldenberg, M.1997 GRI-Mech 2.11. Available at: http://www.me.berkeley.edu/gri-mech/.Google Scholar
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. MIT Press.Google Scholar
Buckmaster, J. & Peters, N. 1988 The infinite candle and its stability—a paradigm for flickering diffusion flames. Proc. Combust. Inst. 21 (1), 1829–1836.Google Scholar
Chamberlin, D. S. & Rose, A. 1948 The flicker of luminous flames. Proc. Combust. Inst. 1–2, 27–32.Google Scholar
Chen, L.-D., Seaba, J. P., Roquemore, W. M. & Goss, L. P. 1989 Buoyant diffusion flames. Proc. Combust. Inst. 22 (1), 677–684.Google Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37 (1), 357–392.Google Scholar
Chomaz, J. M., Huerre, P. & Redekopp, L. G. 1988 Bifurcations to local and global modes in spatially developing flows. Phys. Rev. Lett. 60 (1), 25–28.Google Scholar
Coenen, W. & Sevilla, A. 2012 The structure of the absolutely unstable regions in the near field of low-density jets. J. Fluid Mech. 713, 123–149.Google Scholar
Coenen, W., Sevilla, A. & Sánchez, A. L. 2008 Absolute instability of light jets emerging from circular injector tubes. Phys. Fluids 20, 074104.Google Scholar
Crighton, D. G., Dowling, A. P., Ffowcs Williams, J. E., Heckl, M. & Leppington, F. G. 1992 Modern Methods in Analytical Acoustics: Lecture Notes. Springer.Google Scholar
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77, 397–413.Google Scholar
Day, M. J., Reynolds, W. C. & Mansour, N. N. 1998 The structure of the compressible reacting mixing layer: insights from linear stability analysis. Phys. Fluids 10 (4), 993–1007.Google Scholar
Füri, M.2001 Non-premixed jet flame instabilities. Thèse No. 2468 (2001), École Polytechnique Fédérale de Lausanne.Google Scholar
Füri, M., Papas, P. & Monkewitz, P. A. 2000 Non-premixed jet flame pulsations near extinction. Proc. Combust. Inst. 28, 831–838.Google Scholar
Füri, M., Papas, P., Rais, R. M. & Monkewitz, P. A. 2002 The effect of flame position on the Kelvin–Helmholtz instability in non-premixed jet flames. Proc. Combust. Inst. 29, 1653–1661.CrossRefGoogle Scholar
Han, D. & Mungal, M. G. 2001 Direct measurement of entrainment in reacting/non-reacting turbulent jets. Combust. Flame 124 (3), 370–386.Google Scholar
Hirschfelder, J. O. & Curtiss, C. F. 1949 Theory of propagation of flames. Part I: General equations. Symp. Combust. Flame Explos. Phenom. 3 (1), 121–127.Google Scholar
Holmes, P., Lumley, J. L. & Berkooz, G. 1998 Turbulence, Coherent Structures, Dynamical Systems, and Symmetry. Cambridge University Press.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.Google Scholar
Ihme, M., Cha, C. M. & Pitsch, H. 2005 Prediction of local extinction and re-ignition effects in non-premixed turbulent combustion using a flamelet/progress variable approach. Proc. Combust. Inst. 30, 793–800.Google Scholar
Ihme, M., Shunn, L. & Zhang, J. 2012 Regularization of reaction progress variable for application to flamelet-based combustion models. J. Comput. Phys. 231 (23), 7715–7721.Google Scholar
Juniper, M. P., Li, L. K. B. & Nichols, J. W. 2009 Forcing of self-excited round jet diffusion flames. Proc. Combust. Inst. 32, 1191–1198.Google Scholar
Katta, V. R., Goss, L. P. & Roquemore, W. M. 1994 Effect of non-unity Lewis number and finite-rate chemistry on the dynamics of a hydrogen–air jet diffusion flame. Combust. Flame 96, 60–74.Google Scholar
Katta, V. R. & Roquemore, W. M. 1993 Role of inner and outer structures in transitional jet diffusion flame. Combust. Flame 92, 274–282.CrossRefGoogle Scholar
Kortschik, C., Honnet, S. & Peters, N. 2005 Influence of curvature on the onset of autoignition in a corrugated counterflow mixing field. Combust. Flame 1142, 140–152.Google Scholar
Kreiss, H.-O., Lorenz, J. & Naughton, M. J. 1991 Convergence of the solutions of the compressible to the solutions of the incompressible Navier–Stokes equations. Adv. Appl. Math. 12, 187–214.Google Scholar
Kurdyumov, V. N. & Matalon, M. 2002 Radiation losses as a driving mechanism for flame oscillations. Proc. Combust. Inst. 29, 45–52.Google Scholar
Lee, D. J., Thakur, S., Wright, J., Ihme, M. & Shyy, W.2011 Characterization of flow field structure and species composition in a shear coaxial rocket GH2/GO2 injector: modeling of wall heat losses. AIAA Paper 2011-6125.Google Scholar
Lesshafft, L. & Marquet, O. 2010 Optimal velocity and density profiles for the onset of absolute instability in jets. J. Fluid Mech. 662, 398–408.Google Scholar
Lingens, A., Neemann, K., Meyer, J. & Schreiber, M. 1996 Instability of diffusion flames. Proc. Combust. Inst. 26 (1), 1053–1061.Google Scholar
Lo Jacono, D. & Monkewitz, P. A. 2007 Scaling of cell size in cellular instabilities of non-premixed jet flames. Combust. Flame 151, 321–332.Google Scholar
Matalon, M. 2007 Intrinsic flame instabilities in premixed and non-premixed combustion. Annu. Rev. Fluid Mech. 39, 163–191.Google Scholar
Maxworthy, T. 1999 The flickering candle: transition to a global oscillation in a thermal plume. J. Fluid Mech. 390, 297–323.CrossRefGoogle Scholar
McBride, B. J., Zehe, M. J. & Gordon, S.2002 NASA Glenn coefficients for calculating thermodynamic properties of individual species. NASA/TP Rep. 2002-211556. NASA.Google Scholar
Michalke, A. 1984 Survey on jet instability theory. Prog. Aerosp. Sci. 21, 159–199.Google Scholar
Monkewitz, P. A. & Sohn, K. D. 1988 Absolute instability in hot jets. AIAA J. 26 (8), 911–916.Google Scholar
Müller, B. 1999 Low Mach number asymptotics of the Navier–Stokes equations and numerical implications. In Proc. 30th Computational Fluid Dynamics Lecture Series. Von Karman Institute for Fluid Dynamics.Google Scholar
Muñiz, L. & Mungal, M. G. 2001 Effects of heat release and buoyancy on flow structure and entrainment in turbulent non-premixed flames. Combust. Flame 126 (1–2), 1402–1420.Google Scholar
Nayfeh, A. H. 2000 Perturbation Methods. Wiley-VCH.CrossRefGoogle Scholar
Nichols, J. W. & Schmid, P. J. 2008 The effect of a lifted flame on the stability of round fuel jets. J. Fluid Mech. 609, 275–284.Google Scholar
Nichols, J. W., Schmid, P. J. & Riley, J. J. 2007 Self-sustained oscillations in variable-density round jets. J. Fluid Mech. 582, 341–376.Google Scholar
Oberleithner, K., Sieber, M., Nayeri, C. N., Paschereit, C. O., Petz, C., Hege, H.-C., Noack, B. R. & Wygnanski, I. 2011 Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction. J. Fluid Mech. 679, 383–414.Google Scholar
Papas, P., Rais, R. M., Monkewitz, P. A. & Tomboulides, A. G. 2003 Instabilities of diffusion flames near extinction. Combust. Theory. Model. 7, 603–633.Google Scholar
Peters, N. 1983 Local quenching due to flame stretch and non-premixed turbulent combustion. Combust. Sci. Technol. 30, 1–17.Google Scholar
Peters, N. 1984 Laminar diffusion flamelet models in non-premixed turbulent combustion. Prog. Energy Combust. Sci. 10 (3), 319–339.Google Scholar
Pier, B. & Huerre, P. 2001 Nonlinear self-sustained structures and fronts in spatially developing wake flows. J. Fluid Mech. 435, 145–174.Google Scholar
Pierce, C. D. & Moin, P. 2004 Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion. J. Fluid Mech. 504, 73–97.Google Scholar
Pitsch, H. & Peters, N. 1998 A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects. Combust. Flame 114 (1–2), 26–40.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Applied Mathematical Sciences. vol. 142. Springer.Google Scholar
Shin, D. S. & Ferziger, J. H. 1991 Linear stability of the reacting mixing layer. AIAA J. 29 (10), 1634–1642.Google Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. 1. Coherent structures. Q. Appl. Maths 45, 561–571.Google Scholar
Srinivasan, V., Hallberg, M. P. & Strykowski, P. J. 2010 Viscous linear stability of axisymmetric low-density jets: parameters influencing absolute instability. Phys. Fluids 22, 024103.Google Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.Google Scholar
Westbrook, C. K. & Dryer, F. L. 1981 Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames. Combust. Sci. Technol. 27, 31–43.Google Scholar
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18 (4), 517–519.Google Scholar
Williams, F. A. 1991 Overview of asymptotics for methane flames. In Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane–Air Flames (ed. Smooke, M. D.), pp. 68–85. Springer.Google Scholar