Two-Dimensional Irrotational Transonic Flows of a Compressible Fluid Page: 3 of 93
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NATIONAL AVISOPx COMMIT.E FOR AERONAUTICS
TECNICAL NOTE NO. 1445
TWO-DIMENSIONAL IRROTATIONAL TRANSONIC FLOWS
OF A COMPHE&'IBIE FLUID
By Yung-Huai Kuo
The method developed in NACA TN No. 995 has been slightly modified
and extended to include flows with circulation. The essential feature of
the modified method is that in analytic continuation of the solution the
alteration of the singularities of the incompressible solution due to the
presence of the hypergeometric functions has been taken into account.
It was found that for finite Mach number the only case in which the
nature of the singularity of the incompressible solution can remain
unchanged is for a ratio of specific heats equal to -1.
Two particular flows, one having a finite circulation and the other
having zero circulation, have been studied. Both flows were derived from
the incompressible flow about an elliptic cylinder of thickness ratio 0.60.
The free-stream Mach number for both cases was taken to be 0.60 in
order to avoid the appearance of limiting lines. The pressure distribution
for the flow without circulation has been compared with that of
incompressible flow over approximately the same body. The discrepancies
between the exact results and those predicted by the approximate Von Krmn--
Tsien and Glauert-Prandtl formulas are so wide as to show definitely that
in this case the effect of geometry cannot be ignored, as is done in both
approximate formulas. In general, it seems that the effect of geometry
cannot be neglected and the conventional "pressure-correction" formulas
are not valid, even in the subsonic region if the body is thick, especially
if there is a supersonic region in the flow.
This report is a continuation of the work reported in NACA TN
No. 995. The method developed in that report has been slightly modified
and extended in the present report to include flows with circulation.
The general concept and method is outlined. without the mathematic al
details in part I. The essential feature of the modified method is
that in analytic continuation of the solution the alteration of the
singularities of the incompressible solution due to the presence of the
hypergeometric functions has been taken into account, as fully discussed
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Kuo, Yung-Huai. Two-Dimensional Irrotational Transonic Flows of a Compressible Fluid, report, June 1948; Washington D.C.. (https://digital.library.unt.edu/ark:/67531/metadc172480/m1/3/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.