THEORETICAL AND EXPERIMENTAL INVESTIGATION OF AERODYNAMIC-HEATING AND ISOTHERMAL HEAT-TRANSFER PARAMETERS ON A HEMISPHERICAL NOSE WITH LAMINAR BOUNDARY LAYER AT SUPERSONIC MACH NUMBERS

摘要

The effect of a strong, negative pressure gradient upon the local rate of heat transfer through a laminar boundary layer on the isothermal surface of an electrically heated, cylindrical body of revolution with a hemispherical nose was determined from wind-tunnel tests at a Mach number of 1.97. The investigation indicated that the local heat-transfer para¬meter, Nu/Re, based on flow conditions just outside the boundary layer, decreased from a value of 0.65 ±0.10 at the stagnation point of the hemi-sphere to a value of O.43 ±0.05 at the Junction with the cylindrical afterbody. Because measurements of the static pressure distribution over the hemisphere indicated that the local flow pattern tended to become stationary as the free-stream Mach number was increased to 3.8, this dis-tribution of heat-transfer parameter is believed representative of all Mach numbers greater than 1.97 and of temperatures less than that of dis-sociation. The local heat-transfer parameter was independent of Reynolds number based on body diameter in the range from 0.6x106 to 2.3x106.nThe measured distribution of heat-transfer parameter agreed within ±18 percent with an approximate theoretical distribution calculated with foreknowledge only of the pressure distribution about the body. This method, applicable to any body of revolution with an isothermal surface, combines the Mangier transformation, Stewartson transformation, and thermal solutions to the Falkner-Skan wedge-flow problem, and thus evaluates the heat-transfer rate in axisymmetric compressible flow in terms of the known heat-transfer rate in an approximately equivalent two-dimensional incompres¬sible flow.nMeasurements of recovery-temperature distributions at Mach numbers of 1.97 and 3.04 yielded local recovery factors having an average value of 0.823±0.012 on the hemisphere which increased abruptly at the shoulder to an average value of 0.840±0.012 on the cylindrical afterbody. This result suggests that the usual representation of the laminar recovery factor as the square root of the Prandtl number is conservative in the presence of a strong, accelerating pressure gradient.