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National Advisory Committee for Aeronautics, Technical Notes - Method of Determining Initial Tangents of Contours of Flow Variables Behind a Curved, Axially Symmetric Shock Wave

A general method for calculating the initial tangents of contours
of constant density, pressure, and Mach number behind a curved, axially
symmetric shock wave has been derived. Initial tangents of density con—
tours are obtained that fair well into contours determined from inter-
ferograms for the flow about a sphere at Mach number 1.62. Streamlines
and contours of constant mach number throughout this flow field have
also been deduced from contours of constant density obtained by inter-
ferometry. The flow field obtained from the shock wave by the method
of characteristics is compared with that obtained by interferometry.

Various phases of the problem of flows behind curved shock waves
have been treated theoretically by many investigators. Crocco, in a
pioneer paper (reference 1), investigated two-dimensional flow behind
a curved attached shock wave. Significant contributions were made later
by Maccoll, Drougge, and Guderley. Maccoll (reference 2) calculated
the flow around various bodies with detached shock waves at near—sonic
velocities. Drougge (reference 3) calculated the pressure distribution
on conical tips with detached shock waves. Guderley (reference A)
investigated the transition between flow with a detached shock wave and
flow with an attached shock wave. Thomas, in a series of papers of
which reference 5 is representative, considered the curvature of attached
shock waves and the pressure distribution on bodies behind attached sh0ck
waves.

Lin and Rubinov (reference 6) obtained general relations for flow
behind curved shock waves and developed a method for calculating the sub—
sonic flow between the shock wave and the body. This method was applied
by Dugundji (reference 7) to calculate the pressure distribution along
the axis between a sphere and a shock wave. Busemann (reference 8)
reviewed analytical methods for the treatment of two—dimensional flows
with detached shock waves and discussed the main features of mixed
subsonic and supersonic flows. Ferri (reference 9) presented a method
for Obtaining the pressure drag in two-dimensional or axially symmetric
flow behind a detached shock wave when the location and shape of the
shock wave are known. Mbeckel (reference 10) gave an approximate method
for predicting the form and the location of detached shock waves.