Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-07T20:28:13.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermal-ignition analysis in boundary-layer flows

Published online by Cambridge University Press:  19 April 2006

C. K. Law  and
H. K. Law
C. K. Law
Affiliation:
Department of Mechanical Engineering and Astronautical Sciences, Northwestern University, Evanston, Illinois 60201
H. K. Law
Affiliation:
Department of Mechanical Engineering and Astronautical Sciences, Northwestern University, Evanston, Illinois 60201
Get access Rights & Permissions [Opens in a new window]

Abstract

The weakly reactive state leading to the ignition of a steady laminar boundary-layer flow of a combustible mixture over a hot, isothermal, non-permeable, non-catalytic flat plate is studied both numerically and using matched asymptotic analysis in the realistic limit of large activation energy. It is shown that the flow consists of a locally similar diffusive-reactive region next to the plate and a non-similar diffusive-convective region outside it; that the analytic solution obtained reproduces the lower half of the S-shaped ignition-extinction response curve such that ignition is expected to occur when a suitably defined Damköhler number, which increases with the streamwise distance, reaches unity; and that at the point of ignition the heat transfer from the wall vanishes identically. An explicit expression for the minimum distance for ignition to occur is also derived.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 92 , Issue 1 , 15 May 1979 , pp. 97 - 108
Copyright
© 1979 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

Berman, V. S. & Ryazantsev, YU. S. 1978 Ignition of a gas in a boundary layer at a heated plate. Fluid Dyn. 12, 758.Google Scholar
Bush, W. B. & Fendell, F. E. 1970 Asymptotic analysis of laminar flame propagation for general Lewis numbers. Combust. Sci. Tech. 1, 421.Google Scholar
Chapman, D. R. & Rubesin, M. W. 1949 Temperature and velocity profiles in the compressible boundary layer with arbitrary distribution of surface temperature. J. Aero. Sci. 16, 547.Google Scholar
Chung, P. M. 1965 Chemically reacting nonequilibrium boundary layers. In Advances in Heat Transfer, vol. 2, pp. 109–270. Academic Press.
Dooley, D. A. 1957 Ignition in the laminar boundary layer of a heated plate. Heat Transfer Fluid Mech. Inst., Stanford Univ. pp. 321–342.Google Scholar
Dorrance, W. H. 1962 Viscous Hypersonic Flow. McGraw-Hill.
Fendell, F. E. 1965 Ignition and combustion of initially unmixed reactants. J. Fluid Mech. 21, 281.Google Scholar
Hayes, W. D. & Probstein, R. F. 1959 Hypersonic Flow Theory. Academic Press.
Law, C. K. 1978 On the stagnation-point ignition of a premixed combustible. Int J. Heat Mass Transfer 21, 1363.Google Scholar
Lees, L. 1958 Convective heat transfer with mass addition and chemical reaction. 3rd Combust. Propulsion Coll. AGARD, pp. 451–497. Pergamon.Google Scholar
Lián, A. & Williams, F. A. 1978 Ignition of a reactive solid exposed to a step in surface temperature. SIAM J. Appl. Math. 21, 1363.Google Scholar
Marble, F. E. & Adamson, T. C. 1954 Ignition and combustion in a laminar mixing zone. Jet Propulsion 24, 85.Google Scholar
Sharma, O. P. & Sirignano, W. A. 1970 On the ignition of a premixed fuel by a hot projectile. Combust. Sci. Tech. 1, 481.Google Scholar
Toong, T. Y. 1957 Ignition and combustion in a laminar boundary layer over a hot surface. 6th Symp. (Int.) Combust. pp. 532–540. Reinhold.Google Scholar
Williams, F. A. 1965 Combustion Theory. Addison-Wesley.
Williams, F. A. 1971 Theory of combustion in laminar flows. Ann. Rev. Fluid Mech. 3, 171.Google Scholar