Abstract
An interesting oscillatory flow field over a concave shape, which has not been observed experimentally, has been calculated by numerically solving the unsteady Navier-Stokes equations.The unique characteristic of this flow is that it is not separated and yet is oscillatory in nature.All previously observed oscillatory flow fields contain separated regions. The general characteristics of the flow pattern have been described, together with the hypothesized flow mechanism which produces the oscillation. The flow field appears to be hydrodynamically unstable which results in an oscillatory variation of the flow field downstream of the forebody pressure minimum. Various changes in the afterbody shape do not alter the period of the oscillation and results in minor changes in the magnitude of the pressure oscillation. A number of numerical experiments have been performed and described, the results of which indicate that the oscillation is of physical origin. Further work is continuing to understand these flow fields and the underlying governing flow mechanisms. Experimental verification of this flow phenomenon is presently being pursued by Holden [1974] and a more detailed description of the flow will be forthcoming pending the results of this experimental study.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Bogdonoff, S. M. and Vas, I. E., “Preliminary Investigations of Spiked Bodies at Hypersonic Speeds,” Journal of Aerospace Sciences, Vol. 26, No. 2, pp. 65–74, February 1959.
Bogdonoff, S. M. and Vas, I. E., “Some Experiments on Hypersonic Separated Flows,” ARS Journal, pp. 1564–1572, October 1962.
Centolanzi, F. J., “Heat Transfer to Blunt Conical Bodies Having Cavities to Promote Separation,” NASA Technical Note D-1975, NASA Ames Research Center, Moffett Field, California, July 1963.
Crawford, D. H., “Investigation of the Flow Over a Spiked-Nose Hemisphere-Cylinder at a Mach Number of 6. 8,” NASA TN D-118, NASA Langley Research Center, Langley Field, Virginia, December 1959.
Crocco, L., “A Suggestion for the Numerical Solution of the Steady Navier-Stokes Equations,” AIAA Journal, Vol. 3, No. 10, pp. 1824–1832, 1965.
Goldman, R. L. and Obremski, H. J., “Experimental Investigation of Hypersonic Buzz on a High Cross-Range Shuttle Configuration,” AIAA Paper No. 73–157, AIAA 11th Aerospace Sciences Meeting, Washington, D. C., January 1973.
Holden, M. S., “Experimental Studies of Separated Flows at Hypersonic Speeds, Part I: Separated Flows Over Axisymmetric Spiked Bodies,” AIAA Journal, Vol. 4, No. 4, pp. 591–599, April 1966.
Holden, M. S., Private Communication, 1974.
Kentzer, C. P., “Group Velocity and Propagation of Numerical Errors,” AIAA Paper No. 72–153, Presented at the AIAA 10th Aerospace Sciences Meeting, San Diego, California, January 1972.
Kubota, T., Private Communication, 1973.
Mack, L. M., “Boundary-Layer Stability Theory,” Notes Prepared for the AIAA Professional Study Series, High-Speed Boundary-Layer Stability and Transition, San Francisco, California, June 14–15, 1969.
Mair, W. A., “Experiments on Separation of Boundary Layers on Probes in Front of Blunt-Nosed Spiked Bodies in a Supersonic Air Stream,” Philos. Mag., Vol. 43, No. 342, pp. 695–716, July 1952.
Maull, D. J., “Hypersonic Flow Over Axially Symmetric Spiked Bodies,” Journal of Fluid Mechanics, Vol. 8, Part 4, pp. 584–592, 1960.
Reddall, W. F., III, Private Communication, 1973.
Victoria, K. J. and Widhopf, G. F., “Numerical Solution of the Unsteady Navier-Stokes Equations in Curvilinear Coordinates: The Hypersonic Blunt Body Merged Layer Problem,” Lecture Notes in Physics, 19, Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, Vol. II, Problems in Fluid Mechanics, July 1973, Springer-Verlag.
Wood, C. J., “Hypersonic Flow Over Spiked Cones,” Journal of Fluid Mechanics, Vol. 12, Part 4, pp. 614–624, 1961.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1975 Springer-Verlag
About this paper
Cite this paper
Widhopf, G.F., Victoria, K.J. (1975). Numerical solution of the unsteady navier-stokes equations for the oscillatory flow over a concave body. In: Richtmyer, R.D. (eds) Proceedings of the Fourth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019784
Download citation
DOI: https://doi.org/10.1007/BFb0019784
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07139-6
Online ISBN: 978-3-540-37416-9
eBook Packages: Springer Book Archive