Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T12:15:01.718Z Has data issue: false hasContentIssue false

The boundary layer in a shock tube

Published online by Cambridge University Press:  29 March 2006

J. D. A. Walker And
Affiliation:
Department of Mathematics, University College London
S. C. R. Dennis
Affiliation:
Department of Applied Mathematics, University of Western Ontario

Abstract

The boundary layer that forms on the walls of a shock tube, after the diaphragm which initially separates two gases at different pressures is burst, is investigated. Both the driver and driven gases are assumed to have the same thermal properties and the shock tube wall is maintained at constant temperature. Crocco variables are used and a method is presented for solving the compressible boundary-layer equations within the tube in similarity variables. Three cases, corresponding to different initial pressure ratios of the driver and driven gases, are calculated which are representative of weak and medium-strength shock and expansion waves.

Type
Research Article
Copyright
© 1972 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

Ban, S. D. & Kuerti, G. 1969 J. Fluid Mech. 38, 109.
Becker, E. 1962 Z. Flugwiss. 10, 4/5, 138.
Blasius, H. 1908 Z. Math. Phys. 56, 1.
Chapman, D. R. & Rubesin, M. W. 1949 J. Aero. Sci. 16, 547.
Charatis, G. & Wilkerson, T. D. 1959 Phys. Fluids, 2, 578.
Cohen, N. B. 1957 N.A.C.A. Tech. Note, no. 3943.
Dennis, S. C. R. 1972 J. Inst. Math. Applics. 10, 105.
Dennis, S. C. R. & Walker, J. D. A. 1972 Phys. Fluids, 15, 517.
Fox, L. 1957 The Numerical Solution of Two-Point Boundary Value Problems. Oxford University Press.
Gaydon, A. O. & Hurle, I. R. 1963 The Shock Tube in High Temperature Chemical Physics. New York: Reinhold.
Goldstein, S. 1930 Proc. Camb. Phil. Soc. 26, 1.
Greenspan, D. 1968 In Lectures on the Numerical Solution of Linear, Singular and Non linear Differential Equations, chap. 10. Prentice Hall.
Hall, M. G. 1969 Proc. Roy. Soc. A 310, 401.
Lam, S. H. & Crocco, L. 1958 Princeton Rep. no. 428. (See also Aposr Tech. Note, no. 58-581.)
Mirels, H. 1955 N.A.G.A. Tech. Note, no. 3401.
Mirels, H. 1956 N.A.CA. Tech. Note, no. 3712.
Mirels, H. 1971 In Shock Tube Research, Proc. 8th International Shock Tube Symp. Imperial College, London, p. 6. Chapman & Hall.
Rayleigh, Lord 1911 Phil. Mag. 21, 697.
Rosser, J. B. 1967 Mathematics Research Centre, University of Wisconsin, Tech. Summ. Rep. no. 797.
Seapiro, A. H. 1960 The Dynamics and Thermodynamics of Compressible Fluid Flow. New York: Ronald Press.
Spalding, D. B. 1967 Numerical Methods for Viscous Plows, Acard Conf. Proc. no. 60.
Stewarson, K. 1951 Quart. J. Mech. Appl. Math. 4, 182.
Stewartson, K. 1960 Adv. Appl. Mech. 6, 1.
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Fluids. Oxford University Press.
Stewartson, K. 1972 Quart. J. Mech. Appl. Math. to appear.
Varga, R. S. 1962 Matrix Iterative Analysis. Prentioe-Hall.
Walker, J. D. A. 1971 Ph.D. thesis (appendix V), University of Western Ontario, London. Canada.