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Diffusion-flame ignition by shock-wave impingement on a supersonic mixing layer

Published online by Cambridge University Press:  30 October 2015

César Huete
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
Antonio L. Sánchez*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
Forman A. Williams
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
Javier Urzay
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305-3024, USA
*
Email address for correspondence: als@ucsd.edu

Abstract

Ignition in a supersonic mixing layer interacting with an oblique shock wave is investigated analytically and numerically under conditions such that the post-shock flow remains supersonic. The study requires consideration of the structure of the post-shock ignition kernel that is found to exist around the point of maximum temperature, which may be located either near the edge of the mixing layer or in its interior, depending on the profiles of the fuel concentration, temperature and Mach number across the mixing layer. The ignition kernel displays a balance between the rates of chemical reaction and of post-shock flow expansion, including the acoustic interactions of the chemical heat release with the shock wave, leading to increased front curvature. The analysis, which adopts a one-step chemistry model with large activation energy, indicates that ignition develops as a fold bifurcation, the turning point in the diagram of the peak perturbation induced by the chemical reaction as a function of the Damköhler number providing the critical conditions for ignition. While an explicit formula for the critical Damköhler number for ignition is derived when ignition occurs in the interior of the mixing layer, under which condition the ignition kernel is narrow in the streamwise direction, numerical integration is required for determining ignition when it occurs at the edge, under which condition the kernel is no longer slender. Subsequent to ignition, for the Arrhenius chemistry addressed, the lead shock will rapidly be transformed into a thin detonation on the fuel side of the ignition kernel, and, under suitable conditions, a deflagration may extend far downstream, along with the diffusion flame that must separate the rich and lean reaction products. The results can be helpful in describing supersonic combustion for high-speed propulsion.

Type
Papers
Copyright
© 2015 Cambridge University Press 

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References

Brummund, U. & Nuding, J. R. 1997 Interaction of a compressible shear layer with shock waves – an experimental study. AIAA Paper 0392.Google Scholar
Buttsworth, D. R. 1996 Interaction of oblique shock waves and planar mixing regions. J. Fluid Mech. 306, 4357.CrossRefGoogle Scholar
Calhoon, W. H. & Sinha, N. 2005 Detonation wave propagation in concentration gradients. AIAA Paper 1167.Google Scholar
Dolvin, D. 2008 Hypersonic international flight research and experimentation (HiFiRE). AIAA Paper 2581.Google Scholar
Frank-Kamenetskii, D. A. 1969 Diffusion and Heat Transfer in Chemical Kinetics, 2nd edn. Plenum.Google Scholar
Génin, F. & Menon, S. 2010 Studies of shock/turbulent shear layer interaction using large-eddy simulation. Comput. Fluids 39, 800819.Google Scholar
Grosch, C. E. & Jackson, T. L. 1991 Ignition and structure of a laminar diffusion flame in a compressible mixing layer with finite rate chemistry. Phys. Fluids 3, 30873097.Google Scholar
Hayes, W. D. & Probstein, R. F. 2004 Hypersonic Inviscid Flow, 2nd edn. pp. 480484. Dover.Google Scholar
Huete, C., Sánchez, A. L. & Williams, F. A. 2013 Theory of interactions of thin strong detonations with turbulent gases. Phys. Fluids 25, 076105.Google Scholar
Huete, C., Sánchez, A. L. & Williams, F. A. 2014 Linear theory for the interaction of small-scale turbulence with overdriven detonations. Phys. Fluids 26, 116101.Google Scholar
Huete, C., Urzay, J., Sánchez, A. L. & Williams, F. A. 2015 Weak-shock interactions with transonic laminar mixing layers of fuels for high-speed propulsion. AIAA J. (to appear).Google Scholar
Jackson, T. L. & Hussaini, M. Y. 1988 An asymptotic analysis of supersonic reacting mixing layers. Combust. Sci. Technol. 57, 129140.CrossRefGoogle Scholar
Kessler, D. A., Gamezo, V. N. & Oran, E.  S. 2012 Gas-phase detonation propagation in mixture composition gradients. Phil. Trans. R. Soc. Lond. A 370, 567596.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics, 2nd edn. pp. 422423. Pergamon.Google Scholar
Laurence, S. J., Karl, S., Schramm, J., Martínez, J. & Hannemann, K. 2013 Transient fluid-combustion phenomena in a model scramjet. J. Fluid Mech. 722, 85120.Google Scholar
Libby, P. A. & Williams, F. A. 1980 Turbulent Reacting Flows. pp. 3233. Springer.Google Scholar
Lighthill, M. J. 1950 Reflection at a laminar boundary layer of a weak steady disturbance to a supersonic stream, neglecting viscosity and heat conduction. Q. J. Mech. Appl. Maths 3, 303325.CrossRefGoogle Scholar
Lighthill, M. J. 1953 On boundary layers and upstream influence. II. Supersonic flows without separation. Proc. R. Soc. Lond. A 213, 478507.Google Scholar
Liñán, A. & Crespo, A. 1976 An asymptotic analysis of unsteady diffusion flames for large activation energies. Combust. Sci. Technol. 14, 95117.CrossRefGoogle Scholar
Lu, P. J. & Wu, K. C. 1991 On the shock enhancement of confined supersonic mixing flows. Phys. Fluids A 3, 30463062.CrossRefGoogle Scholar
Marble, F. E. 1994 Gasdynamic enhancement of nonpremixed combustion. Proc. Combust. Inst. 25, 112.CrossRefGoogle Scholar
Marble, F. E., Hendricks, G. J. & Zukoski, E. E. 1987 Progress toward shock enhancement of supersonic combustion processes. AIAA Paper 1880.Google Scholar
Menon, S. 1989 Shock-wave-induced mixing enhancement in scramjet combustors. AIAA Paper 0104.Google Scholar
Moeckel, W. E. 1952 Interaction of oblique shock waves with regions of variable pressure, entropy, and energy. NACA Tech. Rep. 2725.Google Scholar
Nuding, J. R. 1996 Interaction of compressible shear layers with shock waves: an experimental study, part I. AIAA Paper 4515.Google Scholar
O’Brien, J., Urzay, J., Ihme, M., Moin, P. & Saghafian, A. 2014 Subgrid-scale backscatter in reacting and inert supersonic hydrogen–air turbulent mixing layers. J. Fluid Mech. 743, 554584.CrossRefGoogle Scholar
Riley, N. 1960 Interaction of a shock wave with a mixing region. J. Fluid Mech. 7, 321339.CrossRefGoogle Scholar
Sánchez, A. L. & Williams, F. A. 2014 Recent advances in understanding of flammability characteristics of hydrogen. Prog. Energy Combust. Sci. 41, 155.Google Scholar
Vázquez-Espí, C. & Liñán, A. 2001 Fast, non-diffusive ignition of a gaseous reacting mixture subject to a point energy source. Combust. Theor. Model. 5, 485498.Google Scholar
Waidmann, W., Alff, F., Brummund, U., Böhm, M., Clauss, W. & Oschwald, M. 1994 Experimental investigation of the combustion process in a supersonic combustion ramjet (SCRAMJET). DGLR Jahrestagung, Rep. 94-E3-084, pp. 629638.Google Scholar
Whitham, G. B. 1958 On the propagation of shock waves through regions of non-uniform area or flow. J. Fluid Mech. 4, 337360.Google Scholar
Williams, F. A. 1985 Combustion Theory, 2nd edn. pp. 576581. Benjamin Cummings.Google Scholar
Zhang, Y., Wang, B., Zhang, H. & Xue, S. 2015 Mixing enhancement of compressible planar mixing layer impinged by oblique shock waves. J. Propul. Power 31, 156169.Google Scholar