Linearized potential theory of propeller induction in a compressible flow Page: 3 of 48
This report is part of the collection entitled: National Advisory Committee for Aeronautics Collection and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
2 NACA TN 2983
potential, which is also a solution of the compressible equation of
motion. This far-wake potential extends only downstream of the pro-
peller and provides the jump in potential at the trailing vortex sur-
faces and the downstream feature that the far wake must be the same as
for incompressible flow except for random wave motion or noise. There-
fore, the problem reduces to superposing the elliptic and hyperbolic
fields in such a manner that certain physical conditions are met at
the propeller plane where the far-wake potential is cut off, an obvious
condition being continuity of the velocity vector. The cut-off of the
far-wake potential at the propeller plane creates the lifting lines
there, since this termination of the surfaces of a potential discon-
tinuity is equivalent to a lifting line.
In the differentiation of the potential at the lifting line, a
difficulty is to be anticipated in that a lifting line has infinite
wave drag in supersonic flow, and this condition is part of the theory
inasmuch as no restrictions are placed on tip Mach number. Some of
the hyperbolic induction attributed to the lifting line must therefore
be separated. This unwelcome induction is found in the hyperbolic
field but is absent in the elliptic field, as would be expected.
For the most part, only the case of propeller operation in a closed
circular wind tunnel is considered, although the way the potential may
be obtained in free air is indicated. The only reason for emphasizing
the tunnel is that, where series occur in the tunnel theory, integrals
occur for free air. The series seem more amenable to investigation
than the integrals, and it is believed that free air is the limiting
case in which the tunnel diameter approaches infinity.
SYMBOLS
B number of blades
M advance Mach number, V/a
V advance velocity
R.P. real part
a velocity of sound
t timeaxial disturbance velocity, positive downstream
ua
Upcoming Pages
Here’s what’s next.
Search Inside
This report can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Report.
Davidson, Robert E. Linearized potential theory of propeller induction in a compressible flow, report, September 1953; (https://digital.library.unt.edu/ark:/67531/metadc56771/m1/3/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.