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National Advisory Committee for Aeronautcs, Research Memorandum - An Empirically Derived Method for Calculating Pressure Distributions Over Airfoils at Supercritical Mach Numbers and Moderate Angles of Attack

Air, when flowing past moderately thick airfoil sections
at seven- or eight—tenths the velocity of.sound, attains local
velocities in_excess of sonic. Analysis of such mixed subsonic
and supersonic types of flow presents difficulties which are
greater than those of either purely subsonic or supersonic
flow.

A general compressibility correction for pressure coef—
ficients_has been derived by Karman and Tsien (reference 1)
which, when applied to potential theory pressure distributions,
gives the distribution_over an airfoil in any desired wholly
subsonic flow. In the regime of purely supersonic flow,
Prandtl and Meyer (reference 2) deriyed a theory of the-
pressure distribution over.a curved surface by considering
the effects on an initially semi—infinite uniform flow at
sonic velocity When it‘is deflected around a corner. It
was round that the local supersonic Mach numbers attained by"
the-stream are a function only of.the total angle through
which the-stream is turned. This th60ry can be used to
obtain the pressure distributibns over'airfoils at supersonic
Mach numbers. The supersonic flow region in the Vicinity of
airfoils at high subsonic free—stream Mach numbers is limited
in extent so that the Prandtl—Meyer theory cannot be applied
directly.

Pressure distributions over a number of airfoils at high
Mach numbers have recently been obtained in the Ames
l— by 5~l/2—foot high-speed wind_tunnel. _The airfoils are of
the conventional sections NACA 0015, 23015, hhl5 and hhlZ,
and the low-drag sections NACA 652—215 (a = 0.5) and 66,2—215
(a= 0.6). These pressure distributions were obtained at
Reynolds numbers of approximately 2,000,000 and are considered
to be accurate representations of freevair results up to Mach
numbers of 0.810 for moderate angles of attack. The effects
of Reynolds number variation on highrspeed pressure distri-
butions are not known. Therefore, it is not possible to
estimate what restrictions are imposed on the generality of
an analysis based on these pressure measurements as a result
of the moderate test Reynolds number.

Experimental section drag coefficients were obtained by
wake surveys simultaneously with the pressure distributions.
At moderate angles of attack, the drag coefficients show no
appreciable variation with Mach number until the local
velocity of sound is exceeded at some point on the airfoil
surface. The free—stream-Mach number at which local sonic
velocity first occurs is the critical Mach number. Above
the critical Mach number, there is a more or less marked
increase in the-airfoil drag coefficient.