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National Advisory Committee for Aeronautics, Technical Notes - A Determination of the Laminar, Transitional, and Turbulent Boundary Layer Temperature Recovery Factors on a Flat Plate in Supersonic Flow

Knowledge of the temperature recovery at the surfaces of insulated
bodies in high—speed compressible flow is prerequisite to investigations
of convective heat transfer under similar conditions. Existing informa—
tion concerning the temperature recovery in compressible boundary layers
at supersonic speeds is relatively meager. A summary of the results of
Several analytic investigations of the temperature recovery for the case
of a laminar boundary layer on a flat plate is given in reference 1. The
summary indicates that the temperature-recovery factor r defined by the
equation

< 7—1 2
Taw=Ti <l+r-—-2 M1) (1}

is independent of the Mich and Reynolds numbers and depends solely upon
the Brandt]. mmber. The consensus of these analytical results is that
NACA TN 2077 ‘ 3

r = Prl/2 (2)

when 0.72 < Pr < 1.2 , 0 < M < 10, and the temperature exponent for visco—
sity and thermal conductivity varies from.0.5 to 1.25. The question as
to whether the Prandtl number is to be evaluated at the free—stream.tem—
perature, the adiabatic surface temperature, or some intermediate temper;
ature is left unanswered by all the solutions since each imposed the con—
dition that the Prandtl number was invariant within the boundary layer.
Although there is some uncertainty as to the values of Prandtl number for
air over the range of temperatures encountered in wind tunnels, there are
indications that it varies from 0.705 to 0.750 over the range of tempera—
tures from 100° F to —200° F. (See references 2 through 5.)

The preceding analytical results were substantiated somewhat by Eber
(reference 6) who performed tests on insulated cones. It is possible to
compare recoveryhfactor data of cones with that of flat plates by elimina-
ting the effect of the cone angle through the use of the free—stream.ve10—
city and temperature behind the attached conical shock wane. Eber found
r = 0.85i:0.025 for a Mach nunmer range from 1.2 to 3.1.