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Nearly equilibrium dissociating boundary-layer flows by the method of matched asymptotic expansions

Published online by Cambridge University Press:  28 March 2006

George R. Inger
George R. Inger
Affiliation:
Aerospace Corporation, El Segundo, California
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Abstract

The approach to equilibrium in a non-equilibrium-dissociating boundary-layer flow along a catalytic or non-catalytic surface is treated from the standpoint of a singular perturbation problem, using the method of matched asymptotic expansions. Based on a linearized reaction rate model for a diatomic gas which facilitates closed-form analysis, a uniformly valid solution for the near equilibrium behaviour is obtained as the composite of appropriate outer and inner solutions. It is shown that, under near equilibrium conditions, the primary non-equilibrium effects are buried in a thin sublayer near the body surface that is described by the inner solution. Applications of the theory are made to the calculation of heat transfer and atom concentrations for blunt body stagnation point and high-speed flat-plate flows; the results are in qualitative agreement with the near equilibrium behaviour predicted by numerical solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 26 , Issue 4 , December 1966 , pp. 793 - 806
Copyright
© 1966 Cambridge University Press

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References

Broadwell, J. E. 1958 A simple model of the nonequilibrium dissociation of a gas in Couette and boundary layer flows. J. Fluid Mech. 4, 113.Google Scholar
Cheng, H. K. 1957 Interim report on investigations related to hypersonic flow and boundary layer phenomena. Cornell Aero. Lab. Rept. no. AF-1180-A-1.Google Scholar
Chung, P. M. 1960 A simplified study of the nonequilibrium Couette and boundary layer flows with air injection. NASA TN no. D-306.Google Scholar
Chung, P. M. & Anderson, A. D. 1960 Dissociation relaxation of oxygen over an adiabatic flat plate at hypersonic Mach numbers. NASA TN no. D-190.Google Scholar
Fay, J. A. & Riddell, F. R. 1958 Theory of stagnation point heat transfer in dissociated air. J. Aero. Sci. 25, 73–85, 121.Google Scholar
Fox, H. & Libby, P. A. 1963 Some perturbation solutions in laminar boundary layer theory. Part II. The energy equation. Polytech. Inst. of Brooklyn PIBAL Rept. no. 752.Google Scholar
Hirschfelder, J. O. 1957 Heat transfer in chemically reacting gas mixtures. J. Chem. Phys. 26, 2.Google Scholar
Inger, G. R. 1963 Nonequilibrium stagnation point boundary layers with arbitrary surface catalycity. AIAA J. 1, 1776.Google Scholar
Inger, G. R. 1964 Highly nonequilibrium boundary layer flows of a dissociated multicomponent gas mixture. Int. J. Heat & Mass Transfer 7, 1151.Google Scholar
Lees, L. 1956 Laminar heat transfer over blunt-nosed bodies at hypersonic flight speeds. Jet Prop. 26, no. 4, 259.Google Scholar
Lenard, M. 1962 A reaction rate parameter for gasdynamics of a chemically reacting gas mixture. J. Aero. Sci. 29, 995.Google Scholar
Lenard, M. 1963 Gas dynamics of chemically reacting gas mixtures near equilibrium. Dynamics of Manned Lifting Planetary Entry (eds. S. Scala, A. Harrison and M. Rogers). New York: J. Wiley and Sons.
Rae, W. J. 1963 A solution for the nonequilibrium flat plate boundary layer. AIAA J. 1, 10, 2279–88.Google Scholar
Rosenhead, L. 1963 (ed.) Laminar Boundary Layers: Fluid Motion Memoirs. Oxford.
Van Dyke, M. D. 1964 Perturbation Methods in Fluid Mechanics, Applied Math. and Mech. volume viii. London: Academic Press