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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 ,
Antonio L. Sánchez ,
Forman A. Williams  and
Javier Urzay
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: [email protected]
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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.

JFM classification

Boundary Layers: Free shear layers Reacting Flows: Laminar reacting flows Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 784 , 10 December 2015 , pp. 74 - 108
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Copyright
© 2015 Cambridge University Press 

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