Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T04:49:47.845Z Has data issue: false hasContentIssue false
  • English
  • Français

On the instability theory of the melted surface of an ablating body when entering the atmosphere

Published online by Cambridge University Press:  28 March 2006

Saul Feldman
Saul Feldman
Affiliation:
AVCO Research Laboratory, Everett, Massachusetts
Get access Rights & Permissions [Opens in a new window]

Abstract

Some ablating bodies entering the atmosphere will melt or soften. Under deceleration, the soft or melted surface will tend to develop instabilities of the Lamb-Taylor type. Two situations involving viscous incompressible fluids are investigated here: one where the liquid layer has constant viscosity and finite thickness, and the other, where the viscosity increases exponentially with distance away from the interface, and the layer is semi-infinite in extent.

It can be demonstrated, that if one neglects gradients in the flow direction, the rate of growth of interface disturbances in a plane normal to the axis of an axially symmetric blunt body is independent of the flow velocity. The fact that the deceleration and liquid thickness vary with time along a trajectory is also included in the analysis. Results of calculations for the amplification factor and the most amplified wavelength are given.

A mechanism due to the deceleration is postulated, which would cause the formation of longitudinal grooves on the surface of an axially symmetric blunt body while entering the atmosphere.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 6 , Issue 1 , July 1959 , pp. 131 - 155
Copyright
© 1959 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

Allred, J. C., Blount, G. H. & Miller, J. H. 1954 Los Alamos Scientific Lab., Univ. of California Rep. no. LA-1600.
Bellman, R. & Pennington, R. H. 1954 Quart. Appl. Math. 12, 151.
Benjamin, T. Brooke 1957 J. Fluid Mech. 2, 568.
Bethe, H. A. & Adams, M. C. 1959 J. Aero/Space Sci. 26 (To be published in June issue).
Chang, C. T. 1956 Harvard University Division of Engineering and Applied Physics, Combustion Aerodynamics Project interim Tech. Rep. no. 14.
Chang, C. T. 1958 Private communication.
Feldman, S. 1957 J. Fluid Mech. 2, 343.
Lamb, H. 1932 Hydrodynamics, 6th ed. pp. 371, 461. New York: Dover Publications.
Lewis, D. J. 1950 Proc. Roy. Soc. A, 202, 81.
Maringer, R. E., Simcoe, C. R., Manning, G. K. & Jackson, L. R. 1958 Batelle Memorial Institute, Aerodynamic Heating of Iron Meteorites during entry into the Atmosphere. Contract AF 33(616)-5080.
Masson, D. J. & Gazley, C. 1956 Aero. Engng Rev. 15, no. 11, 45.
Sutton, G. W. 1958 J. Aero. Sci. 25, 1.
Taylor, G. I. 1950 Proc. Roy. Soc. A, 201, 192.
Watson, B. C. 1957 Harvard University Division of Engineering and Applied Physics, Combustion Aerodynamics Project interim Tech. Rep. no. 16.