• Version
• 106 Downloads
• 468.95 KB File Size
• 1 File Count
• January 17, 2017 Create Date
• January 17, 2017 Last Updated

National Advisory Committee for Aeronautics, Technical Notes - On the Form of the Turbulent Skin Friction Law and Its Extension to Compressible Flows

A derivation of the form of the incompressible turbulent skin—
friction law for an insulated flat plate is made in such a way that it
may be extended to compressible flows. The ratio of compressible to
incompressible skin friction is obtained, and the results are shown to
be in agreement with existing experimental results.

The magnitude of the skin-friction drag encountered by a flat plate
immersed in a fluid at Reynolds numbers large enough to insure turbulent
flow has been one of the basic problems of aerodynamics. From the theo—
retical approaches of Prandtl and von Karman (for a resume, see refer-
ence l) and the experimental work of numerous investigators, principally
Nikuradse and Ludwieg and Tillmann (see references 2 and 3), much has
been learned of the forms of the turbulent boundary—layer velocity pro-
file and the skin friction associated with these forms in incompressible
flows, although the exact mechanisms involved are still not completely
understood.

Recently, the magnitude of the turbulent skin friction on a flat
plate at high Mach numbers has become of great interest, and several
papers have been written on this subject presenting both theoretical
treatments of the problem and the results of skin-friction measurements
at Mach numbers between 1.5 and 3.0. (See references h to 8.)

The agreement between these theories and the experimental data that
exist is, in general, satisfactory. The status of the problem, however,
is such that a simple physical approach to the extension of the income
pressible skin-friction laws to the compressible case would seem desir-
able. The purpose of this paper is to present such a simple physical
picture.