• Version
• 35 Downloads
• 345.63 KB File Size
• 1 File Count
• December 8, 2016 Create Date
• December 8, 2016 Last Updated

National Advisory Committee for Aeronautics, Technical Notes - On Compressibility Corrections for Subsonic Flow Over Bodies of Revolution

A study of the subsonic flow past an infinitely'long corrugated
circular cylinder is presented to show the relation between two-dimensional
and axisymmetrical flow. In fact, a solution.is obtained which contains
as limiting cases both the Prandtl-Glauert correction for two—dimensional
flow and the Gothert correction for flow past slender bodies of revolution.
Included in the paper are velocity-correction formulas for a cylinder
with a single bump and for a corrugated cylinder in the presence of walls.

The present paper is concerned with the form of the compressibility
corrections for subsonic flow which follow from the linear—perturbation
theory. It is now well known that there are essential differences
between the compressibility corrections for two-dimensional flow and the
corresponding corrections for flow about slender bodies of revolution.
This problem has been the subject of several papers by various authors.
(See, for example, references 1 and 2.)

The analysis presented herein shows that the relation between two—
dimensional and axisymmetrical flow can be clearly demonstrated in the
solution for the flow past an infinitely long corrugated cylinder.l In
fact, a solution is obtained which contains as limiting cases both the
Prandtl-Glauert correction for two—dimensional flow and the Gothert
correction for flow past slender bodies of revolution. Although the
results for these two limiting cases are already known, the result
obtained in the present paper shows the nature of the transition from
one limiting case to the other. The nature of this transition has been
treated from a different point of view in reference h, where the bodies
considered consisted of a family of ellipsoids ranging from the ellipsoid
of revolution/to the infinitely long elliptic cylinder It is of
interest that the present example is a natural extension of the two—

dimensional wavy wall treated by Ackeret in a classical paper (reference 5).
Dr. C. 0. Lin has pointed out to the author that flow past a corrugated
circular cylinder has previousLy been considered by Th. von.Karman
(reference 3) in a different connection as an example of the
calculation of wave drag for supersonic flow past bodies of revolution.

It should be mentioned that the results presented herein were
obtained in June 19%, while the author was associated with the National
Advisory Committee for Aeronautics at Langley Air Force Base, Va.