• Version
• 44 Downloads
• 1.70 MB File Size
• 1 File Count
• December 12, 2016 Create Date
• December 12, 2016 Last Updated

National Advisory Committee for Aeronautics, Technical Notes - Theoretical Investigation and Application of Transonic Similarity Law for Two Dimensional Flow

The transonic similarity law for two-dimensional flow derived
by von Karma’n has been investigated by an iteration procedure
similar to that of the Rayleigh-Janzen and Ackeret—Prandtl—Glauert
methods. The results, which show that the potential can be expressed
as ‘a power series in a single parameter that depends on Mach number,
thickness ratio, and ratio of specific heats, are in agreement with
those. of von Ka’rmén. The iteration procedure has been applied to
obtain the second approximation for the flow past a Kaplan section
in similarity form. The snot solution by Kaplan for the second
approximation has been examined and found expressible in the same
similarity form. The exact numerical results to three approximations
obtained by Kaplan for the Kaplan section and the circular archave
been reduced to transonic similarity form.

The difficulty of calculating and measuring explicitly fluid
flow patterns past given bodies has led to attempts at extracting
information non the equations of motion without actually solving
them, that is, in the form of similarity laws. A similarity law
gives the solution for a whole class of related bodies at related
conditions if the solution for only one of these bodies at one set
of conditions is known. A well—known example of a similarity law
is the Prandtl-Glauert rule, which relates potential flows‘past thin
airfoils at low subsonic speeds.

Similarity rules for two-dimensional steady-state potential
flow in the transonic speed range have been derived by von Karman
in reference 1. The treatment has been extended by Lin, Reissner,
and Tsien in reference 2 to include unsteady two-dimensional
transonic potential flows. These derivations utilized small-
perturbation methods in the physical plane in which two basic
simplifying assumptions were made: namely, (1) that the effect of
stagnation points, if these exist in the flow field was negligible
in the region of interest in the flow field; and (2 that the
boundary condition of zero velocity component normal to the body
contour could be satisfied near the body rather than on the body
itself. The first assumption is also made herein. The validity of
the second assumption was investigated at the NAGA Lewis laboratory
and is reported herein.