The method of integral relations was successfully applied to compressible nonadiabatic turbulent boundary layers on a flat plate. The theory is designed to accept any desired eddy-viscosity model. A particular eddy-viscosity model was incorporated into the method, and the equations were programmed for application to a flat plate with no pressure gradient. The variations of the skin-friction coefficient with Reynolds number, Mach number, and temperature ratio were calculated using this program, and the results are in good accord with similar results calculated by the Spalding-Chi method and the Rubesin T' method. An analysis was made to predict to what extent turbulent separation of the free-interaction type can be inhibited by means of surface cooling. It was observed experimentally that free-interaction is applicable to separated turbulent boundary layers up to the separation point or beyond. The free-interaction model used in the analysis is based on adding the boundary-layer displacement thickness to the actual body dimensions in calculating the induced pressures. The critical temperature ratios calculated on this basis are generally greater than adiabatic wall temperature except in the supersonic range up to a Mach number approaching 3, where moderate cooling is required to inhibit separation.

The report describes the results of a wind-tunnel test program on an ogive-cylinder-flare combination to determine the extent of laminar separation as a function of wall temperature for fixed free-stream Reynolds number per unit length at a free-stream Mach number of 8.0. The objective of the tests was to see if separation could be eliminated entirely by cooling the wall to a sufficiently low value. Pressure and temperature distributions spanning the separation region were made on a quick-insertion model, but the location of the separation point could not be obtained during the tests. Accordingly, a combined experimental-theoretical method was developed for determining the separation point location. Correlation of the separation length with model temperature ratio indicated that the separation distance was small and was rapidly approaching zero at the lowest wall temperature ratio achieved experimentally. The apparent critical wall temperature ratio so indicated by the data was lower than the theoretical ratio. It was not possible to achieve sufficiently low temperatures to see if separation could be entirely eliminated. Possible reasons for the difference between experiment and theory are discussed.

This is the last part of a four-part series of reports describing an investigation of the inhibition of boundary-layer separation of the free-interaction type at high speeds through the use of surface cooling. The purpose of this report is to extend the other work of the authors to configurations representative of axisymmetric compression spikes. The analysis is developed and a computer program written for a spike which consists of a conical nose on which separation occurs followed by compression surface. No data were found to compare with the theory. A calculation made with the pressure gradient prescribed by the body shape rather than by free interaction is compared with experiment. The comparisons, which were made for skin friction, heat transfer, and pressure distributions, were good. The significant effect of wall cooling in delaying separation for the prescribed pressure gradient case is shown. It is also shown that a free-interaction solution can be joined to a prescribed pressure gradient solution so that the solution will go smoothly through separation to reattachment.

The purpose of the report is to extend previous analytical work of the authors to colder walls by including a term of higher order in the assumed total temperature profile. The analysis is developed for both flat-plate-wedge and cylinder-flare configurations. The effect of this higher order term on the theoretical critical temperature ratio, found in the earlier work for separation of the free-interaction type, is discussed. At the beginning of interaction the boundary layer is assumed to be of the Blasius type and the flow at the edge of the boundary layer throughout the interaction is assumed to be isentropic. Comparisons between the theoretical calculations and experiments are presented for both two-dimensional and axisymmetric configurations. The ratio of wall temperature to free-stream stagnation temperature varies from 1.0 to 0.2. The agreement between the theoretical and experimental pressure distributions is considered good. A comparison between theoretical and experimental heat-transfer distributions indicates only fair agreement.