Report of Progress on Measurements of Friction Coefficients, Recovery Factors, and Heat-Transfer Coefficients for Supersonic Flow of Air in a Pipe

Abstract

Measured values are presented for friction coefficients, recovery factors, and heat-transfer coefficients for a stream of air flowing through a pipe at Mach numbers ranging from 2.5 to 1.2. The friction coefficients are in good agreement with those of Keenan and Neumann. At a diameter Reynolds number at inlet of about 1 × 10⁵, which is intermediate between values observed by Keenan and Neumann, frictional effects of a very low order were observed. Maximum frictional effects occurred at a diameter Reynolds number at inlet of about 1.5 × 10⁵. Friction coefficients are, in general, considerably lower than those for fully developed turbulent flow of incompressible fluids at the same values of the Reynolds number. For laminar boundary layer, it appears that the recovery factor is in close agreement with the results of the Pohlhausen analysis, namely (Pr)^1/2 or 0.865. For turbulent boundary layer the recovery factor appears to vary from about 0.79 where the Mach number is 1.3 to about 0.865 where the Mach number is 2.2. It cannot be determined from the present tests whether this variation is primarily an effect of variation in Mach number, although it probably is. The measured values of heat-transfer coefficient in the region of laminar boundary layer seem to be roughly in accord with the Pohlhausen analytical values for incompressible flow over a flat plate. In the region of greatest turbulence in the boundary layer, agreement with the McAdams correlation of data for turbulent flow in pipes is good. The major portion of the data obtained appears to be in the region of transition in the boundary layer from laminar to turbulent flow. Most of the observed values of heat-transfer coefficient are smaller by far than the corresponding ones for fully developed turbulent flow—the ratio of one to the other being as small as 1 to 10.