Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T22:35:18.818Z Has data issue: false hasContentIssue false
  • English
  • Français

Reacting flow as an example of a boundary layer under singular external conditions

Published online by Cambridge University Press:  29 March 2006

Raul Conti  and
Milton Van Dyke
Raul Conti
Affiliation:
Lockheed Palo Alto Research Laboratory, Palo Alto, California
Milton Van Dyke
Affiliation:
Lockheed Palo Alto Research Laboratory, Palo Alto, California
Get access Rights & Permissions [Opens in a new window]

Abstract

An inviscid flow with infinite gradients at the wall poses a problem for the accompanying boundary layer that is fundamentally different from the conventional one of bounded gradients. It turns out that in both cases the external gradients do not affect the first-order boundary layer, but the unbounded gradients generate second-order corrections that are of a lower order in Reynolds number than the conventional ones. The present singularity in stagnation-point reacting flow is of an algebraic type, and the boundary-layer corrections that it generates are proportional to non-integral powers of the Reynolds number, with exponents that vanish with the rate of reaction. The present example clarifies such matters as the matching of boundary layer and singular inviscid flow, the structure and decay of the new corrections, and their ranking in comparison with the conventional second-order effects. Numerical computations illustrate the problem and give quantitative results in a few selected cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 3 , 18 September 1969 , pp. 513 - 535
Copyright
© 1969 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

Burggraf, O. R. 1966 Asymptotic solution for the viscous radiating shock layer A.I.A.A. J. 4, 1725.Google Scholar
Conti, R. & van Dyke, M. 1969 Inviscid reacting flow near a stagnation point J. Fluid Mech. 35, 799.Google Scholar
Hersh, A. S. 1968 Ph.D. thesis, University of California at Los Angeles.
Lee, R. S. & Cheng, H. K. 1969 On the outer-edge problem of a hypersonic boundary layer J. Fluid Mech. 38, 161.Google Scholar
Lighthill, M. J. 1957 Dynamics of a dissociating gas. Part 1 J. Fluid Mech. 2, 1.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic Press.