Boundary-layer drag of bi-convex wing sections with heat transfer at supersonic speeds

Abstract

Previously published methods for the calculation of the skin friction and growth of compressible laminar and turbulent boundary layers in the presence of heat transfer are applied to bi-convex wings of 5~o thickness at Mach numbers of 1.5, 2.5 and 5.0, and Reynolds numbers of 10power6, 10power7 and 10power8 for a range of transition points and a range of heat-transfer conditions. Similar calculations are also made for a flat plate at zero incidence for the same ranges of Reynolds number and Mach number. It is shown that the effect of rearward movement of transition is reduced by increase in Mach number, by reduction in Reynolds number and by increase in the wall to recovery temperature ratio. These results are explained in terms of the relative, sensitivities of the laminar and turbulent boundary layers to these parameters. Some discussion is offered of the effects on skin friction of the interaction between the boundary layer and the external flow and also the effects of small changes in the Prandtl number and viscosity-temperature index are considered. It is shown that in general cooling of the surface causes an increase in drag for all transition points except those very close to the trailing edge. It is concluded that if wing surfaces are cooled to avoid the otherwise serious effects of aerodynamic heating at high speeds then with increase in Mach number it becomes increasingly desirable for the boundary layer to be kept laminar to very near the trailing edge.