Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-19T11:42:46.717Z Has data issue: false hasContentIssue false
  • English
  • Français

On the flow near a weak shock wave downstream of a nozzle throat

Published online by Cambridge University Press:  29 March 2006

A. F. Messiter  and
T. C. Adamson
A. F. Messiter
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor
T. C. Adamson
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor
Get access Rights & Permissions [Opens in a new window]

Abstract

In a transonic nozzle flow in which the velocity is slightly supersonic in some neighbourhood of the nozzle throat, a shock wave may be present either very close to the throat or else somewhat further downstream. In the latter case, relatively simple series solutions in general provide an asymptotic description of the fluid motion except very close to the shock wave. These outer solutions are reviewed for symmetric two-dimensional flow, and it is shown that the shock-wave jump conditions are not satisfied. A correction is then derived in the form of an inner solution for a small region immediately behind the shock. The resulting solution exhibits the singularities in the pressure gradient, streamline curvature and shock-wave curvature which are expected to occur at the intersection of a normal shock wave and a curved wall. An extension to axisymmetric flow is also given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 69 , Issue 1 , 13 May 1975 , pp. 97 - 108
Copyright
© 1975 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

Adamson, T. C., Messiter, A. F. & Richey, G. K. 1974 Arch. Mech. Stos. 6, 617–628.
Adamson, T. C. & Richey, G. K. 1973 J. Fluid Mech. 60, 363–382.
Ferrari, C. & Tricomi, F. G. 1968 Transonic Aerodynamics. Academic.
Gadd, G. E. 1960 Z. angew. Math. Phys. 11, 51–58.
Oswatitsch, K. & Zierep, J. 1960 Z. angew Math. Mech. 40, 143–144.
Szaniawski, A. 1965 Arch. Mech. Stos. 17, 79–85.
Tomotika, J. & Tamada, K. 1950 Quart. Appl. Math. 7, 381–397.