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National Advisory Committee for Aeronautics, Report - Transonic Flow Past Cone Cylinders

Experimental results are presented for transonic flow past
cone-cylinder, aaially symmetric bodies. The drag coefiicient
and surface Mach number are studied as the free-stream Mach
number is varied and, wherever possible, the experimental re-
sults are compared with theoretical predictions. Interfero-
metric results for several typical flow configurations are shown
and an example of shock-free supersonic to subsonic compres-
sion is experimentally demonstrated.

The theoretical problem of transonic flow past finite cones
is discussed briefly and an approximate solution of the arially
symmetric transonic equations, valid for a semi-infinite cone,
is presented.

Transonic flow past certain two-dimensional bodies has
been the subject of several recent papers and the phenomena.
are well understood. The theoretical results of Cole (ref. 1),
Guderley and Yoshihara (ref. 2), Vincenti and Wagoner
(ref. 3), and others apply to two-dimensional symmetrical
double-wedge airfoils. The experimental results of Bryson
(ref. 4) and Griffith (ref. 5) substantiate the theoretical work
in a very satisfactory manner. More recently, Vmcenti
and Wagoner (ref. 6) and Guderley and Yoshihara (ref. 7)
have analyzed the transonic flow past two-dimensional un—
symmetrical sections, that is, lifting double-wedge airfoils.
Current experiments on lifting double-wedge airfoils (ref. 8)
at the Guggenheim Aeronautical Laboratory of the California
Institute of Technology indicate that agreement between
theoretical and experimental results will again be obtained.

Two-dimensional and axially symmetric transonic flows
are of considerhble theoretical and practical interest.since
these two specialized problems are limiting cases of the more
complex problem of the flow about an arbitrary three-
dimensional body.

The study of axially symmetric transonic flow is not so
complete as that of two-dimensional flow. In recent years
several papers, notably those of Von Kai-man (ref. 9) and
Oswatitsch and Berndt (ref. 10), have studied the similarity
rules of axially symmetric transonic flow. Also, Yoshihara
(ref. 11) has calculated the flow about a finite cone at a free-
stream Mach number of 1 by a relaxation technique and has
obtained some experimental verification of the theoretical
result.