Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-13T01:26:26.213Z Has data issue: false hasContentIssue false
  • English
  • Français

The compressible vortex pair

Published online by Cambridge University Press:  26 April 2006

S. D. Heister ,
J. M. Mcdonough ,
A. R. Karagozian  and
D. W. Jenkins
S. D. Heister
Affiliation:
Mechanical, Aerospace and Nuclear Engineering Department, University of California, Los Angeles, CA 90024, USA Present address: School of Aeronautics and Astronautics, Purdue University, IN 47907, USA.
J. M. Mcdonough
Affiliation:
Mechanical, Aerospace and Nuclear Engineering Department, University of California, Los Angeles, CA 90024, USA Present address: Department of Mechanical Engineering, University of Kentucky, KY 40506, USA.
A. R. Karagozian
Affiliation:
Mechanical, Aerospace and Nuclear Engineering Department, University of California, Los Angeles, CA 90024, USA
D. W. Jenkins
Affiliation:
Mechanical, Aerospace and Nuclear Engineering Department, University of California, Los Angeles, CA 90024, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical solution for the flow field associated with a compressible pair of counter-rotating vortices is developed. The compressible, two-dimensional potential equation is solved utilizing the numerical method of Osher et al. (1985) for flow regions in which a non-zero density exists. Close to the vortex centres, vacuum ‘cores’ develop owing to the existence of a maximum achievable flow speed in a compressible flow field. A special treatment is required to represent these vacuum cores. Typical streamline patterns and core boundaries are obtained for upstream Mach numbers as high as 0.3, and the formation of weak shocks, predicted by Moore & Pullin (1987), is observed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 220 , November 1990 , pp. 339 - 354
Copyright
© 1990 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

Anderson, J. A.: 1982 Modern Compressible Flow with Historical Perspective. McGraw-Hall.
Brown, S. N.: 1965 The compressible, inviscid leading-edge vortex. J. Fluid Mech. 22, 17–32.Google Scholar
Garabedian, P.: 1964 Partial Differential Equations. John Wiley.
Hackbusch, W.: 1985 Multi-Grid Methods and Applications. Springer.
Heister, S. D.: 1988 Transverse jets in compressible crossflows. Ph.D. thesis, University of California, Los Angeles.
Kucheman, D.: 1978 The Aerodynamic Design of Aircraft. Pergamon.
Mack, L. M.: 1959 The compressible viscous, heat-conducting vortex. Progress Rep. 20–382. Jet Propulsion Laboratory, Pasadena, CA.
Maxwell, A. R.: 1971 The Hodograph Equations: An Introduction to The Theory of Plane Transonic Flow. Hafner.
Moore, D. W.: 1985 The effect of compressibility on the speed of propagation of a vortex ring. Proc. R. Soc. Lond. A 397, 87–97.Google Scholar
Moore, D. W. & Pullin, D. I., 1987 The compressible vortex pair. J. Fluid Mech. 185, 171–204.Google Scholar
Osher, S., Hafez, M. & Whitlow, W., 1985 Entropy condition satisfying approximations for the full potential equations of transonic fluid flow. Maths Comput. 44, 1–29.Google Scholar
Ringleb, F.: 1940 Exakte Losungen der Defferentialgleichungen einer adiabatischen Gasstromung. Z. Angew. Math. Mech. 20, 185–198.Google Scholar
Shankar, V., Ide, H., Gorski, J. & Osher, S., 1987 A fast, time-accurate, unsteady full potential scheme. AIAA J. 25, 230–238.Google Scholar
Shapiro, A. H.: 1953 The Dynamics and Thermodynamics of Compressible Fluid Flow, vol. 2. Ronald.
Thompson, J. F., Wardi, Z. U. A. & Mastin, C. W. 1985 Numerical Grid Generation, Foundations and Applications. Elsevier/North-Holland.