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National Advisory Committee for Aeronautics, Technical Notes - Experimental Investigation of the Turbulent Boundary Layer Temperature Recovery Factor on Bodies of Revolution at Mach Numbers from 2.0 to 3.8

The local temperature-recovery factor of a turbulent boundary layer
produced by natural transition on a thin-walled, metal, 10° cone was
measured at Mach numbers of 1.97 and 3.77 and at length Reynolds numbers,
based on the surface kinematic viscosity, from k X 105 to k X 108. The
recovery factor in the fully developed turbulent zone was found to have

a value of 0.882 i 0.008 which was essentially independent of both mach
number and Reynolds number. The recovery factor was somewhat greater
toward the end of the region of boundary-layer transition but did not
exceed 0.892.

The recovery factor was also measured on a #00 cone-cylinder com»
bination at mach numbers of 3.10 and 3.77 and at length Reynolds numbers
from.3 x 105 to l x 106. An increase in local turbulent recovery factor
above that on the 10° cone of less than 2 percent was observed; the
maximum value was 0.896. A recovery factor in the turbulent boundary
layer of 0.885 t 0.011 is considered to be adequately representative of
the values Obtained with both bodies in the present investigation.

Similar results have been found by previous investigators at lower Mach
numbers.

The temperature which occurs at the insulated surface of a vehicle
in supersonic flight may be thought to result from two superimposed
effects. The first effect, which determines the static temperature
Just outside the boundary layer, is due to the shape of the body; the
second is brought about by the frictional dissipation of kinetic energy
in the boundary layer. In most cases the static temperature can be
calculated with good accuracy, and for Mach numbers up to 225 the tem-
perature rise through turbulent boundary layers can be determined by
recourse to information such as that given in references 1 through 3.

For Reynolds numbers of about one million and for Mach numbers
less than 2.5 the information contained in references 1 through 3 indi-
cates that when the boundary layer is turbiflent, about 89 percent of the
available kinetic energy can be expected to appear as heat at the
surface of a body. However, for Mach numbers greater than about 2.5
the available theory and experiments (references 11- and 5) are not in
agreement. The data of reference 5 indicate that very large values of
the tln'bulent—boundary—l'ayer recovery factor (0.92 to 0.97) are to be
expected at Mach numbers of 2.87 and #25, while the theory of refer-
ence 1! indicates that the recovery factor for a l/7-power turbulent—
boundary—layer velocity profile should decrease to 0.863 at a local
Mach number of 1+.25.