An Analysis of Supersonic Flow in the Region of the Leading Edge of Curved Airfoils, Including Charts for Determining Surface-pressure Gradient and Shock-wave Curvature

Inviscid flow in the region of the leading edge of curved airfoils with attached shock waves is investigated. Tables and charts are presented for determining the surface-pressure gradient and the shock-wave curvature in supersonic flow of an ideal diatomic gas. The results cover a range of Mach numbers from 1.5 to infinity and deflection angles from zero up to those approaching shock detachment. Calculations of surface-pressure gradient and shock-wave curvature are also made for curved airfoils in supersonic flow of a calorically imperfect, diatomic gas. These calculations are quantitatively applicable in cases where the air temperatures, downstream of the shock wave, do not exceed about 5000 deg Rankine. When flow conditions approach those at which shock waves detach from airfoils, the surface-pressure gradient and shock-wave curvature vary widely from the values predicted by a generalized shock-expansion method. Otherwise, the use of the shock-expansion method introduces only small errors, particularly in the case of ideal gas flows. The effect of caloric imperfections in air is to increase these errors. An approximate procedure for determining the flow field a short distance downstream of the leading edge is also presented.