Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T03:11:49.085Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of a weak shock wave undergoing reflexion from a wall

Published online by Cambridge University Press:  28 March 2006

M. B. Lesser  and
R. Seebass
M. B. Lesser
Affiliation:
Cornell University, Ithaca, New York
R. Seebass
Affiliation:
Cornell University, Ithaca, New York
Get access Rights & Permissions [Opens in a new window]

Abstract

The Navier–Stokes equations are used to study the unsteady structure of a weak shock wave reflecting from a plane wall. Both an adiabatic and an isothermal wall are considered. Incident and reflected shock structures are found by expanding the dependent variables in asymptotic series in the shock strength; the first-order terms are shown to satisfy an equation analogous to Burgers equation. The structure of the wave during reflexion is obtained from an expansion in which the first-order terms satisfy the acoustic equations. The isothermal wall boundary condition requires the introduction of a thermal layer adjacent to the wall. In this case viscosity and convection play a role secondary to the wall temperature boundary condition in determining the structure of the reflected wave. The presentation is simplified by introducing a generalized Burgers equation that gives the same first-order results as the Navier–Stokes equations. Correct second-order results are obtained from this equation simply by applying a correction to the result for the temperature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 31 , Issue 3 , 26 February 1968 , pp. 501 - 528
Copyright
© 1968 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

Baganoff, D. 1964 Pressure gauge with one-tenth microsecond risetime for shock reflection studies Rev. Sci. Instr. 35, 288–95.Google Scholar
Baganoff, D. 1965 Experiments on the wall-pressure history in shock-reflexion processes J. Fluid Mech. 23, 209–28.Google Scholar
Burgers, J. M. 1948 A mathematical model illustrating the theory of turbulence Adv. Appl. Mech. 1, 171–201. New York: Academic Press.
Clarke, J. F. 1967 The reflexion of a plane shock wave from a heat conducting wall. Proc. R. Soc A 299, 221–37.Google Scholar
Goldsworthy, F. A. 1959 The structure of a contact region, with application to the reflection of a shock from a heat-conducting wall J. Fluid Mech. 5, 164–76.Google Scholar
Hayes, W. D. 1956 Gasdynamics Discontinuities. Section D, General Theory at High Speed Aerodynamics (W. R. Sears, ed.) Princeton University Press. Also Princeton Aeronautical Paperbacks, no. 5, 1960.
Lagerstrom, P. A., Cole, J. D. & Trilling, L. 1949 Problems in the theory of viscous compressible fluids. Calif. Inst. Tech. GALCIT Rept.Google Scholar
Lighthill, M. J. 1956 Viscosity effects in sound waves of finite amplitude. Surveys in Mechanics (eds. Batchelor and Davis). Cambridge University Press.
Moran, J. P. & Shen, S. F. 1966 On the formation of weak plane shock waves by impulsive motion of a piston. J. Fluid Mech. 25, 705–18.Google Scholar
Petty, J. S. 1966 Reflection of a plane shock wave from a normal isothermal wall. Bull. Am. Phys. Soc. (Series II), 4, 618.Google Scholar
Richtmeyer, R. D. 1957 Difference Methods for Initial Value Problems. New York: Interscience Publishers.
Scala, S. M. & Gordon, P. 1966 The reflection of a shock wave at a surface Phys. Fluids, 9, 1158–66.Google Scholar
Spence, D. A. 1961 Unsteady shock propagation in a relaxing gas. Proc. R. Soc. A 264, 221–34.Google Scholar
Sturtevant, B. & Slachmuylders, E. 1964 End-wall heat transfer effects on the trajectory of a reflected shock wave Phys. Fluids, 7, 1201–7.Google Scholar
Taylor, G. I. 1910 The conditions necessary for discontinuous motion in gases. Proc. R. Soc. A 84, 371–7.Google Scholar
Tychonov, A. N. & Samarski, A. A. 1964 Partial Differential Equations of Mathematical Physics. San Francisco: Holden Day.
Van Dyke, M. D. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic Press.
Von Mises, R. 1958 Mathematical Theory of Compressible Fluid Flow. New York: Academic Press.
Zabusky, N. J. 1967 Symposium on Nonlinear Partial Differential Equations. University of Delaware, 27–29 December 1965. To be published.