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National Advisory Committee for Aeronautics, Technical Notes - Prandtl Meyer Flow for a Diatomic Gas of Variable Specific Heat

Tables and charts, which give the results of an analysis that
accounts for variation in specific heats of a nonviscous compress-
ible fluid (diatomic gas) during the Prandtl-Meyer flow process
(commonly called the flow around a corner), are presented. Com-
parison is made to the constant—specific-heat solution with the
ratio of specific heats 7 = 1.4 and with this ratio corresponding
to the total fluid temperature. The comparison showed that variation
in specific heats appreciably affected the magnitude of some of the
parameters pertinent to this flow but that a close approximation to
the variable-specific heat solution could be obtained by the use of
a constant value of the ratio of specific heats corresponding to
the total fluid temperature.

In the supersonic flow of a fluid from a high- to a relatively
low-pressure region, the resultant expansion is accomplished through
the medium of expansion waves, which simultaneously turn and diverge
the fluid streamlines. Supersonic flow of a fluid around a sharp
convex corner of a wall represents one such expansion process.
Understanding of this expansion process is of fundamental importance
in some supersonic-flow problems inasmuch as the solution for this
particular process can be used to describe other expansion processes,
such as expansion along the curved boundary of a two—dimensional
supersonic wing or supersonic nozzle, or expansion in a free-jet
stream such as would exist in underexpanding supersonic nozzles or
in the clearance space between.turbine nozzles and turbine blades.

The solution of the corner flow of a nonviscous compressible
fluid given by Prandtl and Meyer is based.pn the assumption that
the ratio of specific heats remains constant during the expansion.
When high fluid temperatures and high expansion pressure ratios are
simultaneously involved, however, the variation of specific heats
during the process may become appreciable.

In a study made at the NACA Lewis laboratory, the Prandtl
Meyer solution has been extended to the case of a diatomic gas having
variable specific heats. The effect of specific-heat lag on the flow
process is assumed.negligible. The results are presented in con:
venient tabular and chart form. The flow variables presented are
streamline angle, ray angle, mach angle, local Mach.number, pressure
ratio, temperature ratio, ratio of local velocity to velocity at a
Mach number of unity, and the ratio of the density-velocity product
to its value at a Mach number of unity.