Shock-wave and boundary-layer phenomena near a flat surface

Abstract

Shock-wave and turbulent boundary-layer phenomena near the smooth flat metal floor of a specially designed supersonic tunnel are studied from traverses made with pitot, static pressure and surface tubes and from direct shadow and Töpler striation photographs. Near-normal and oblique shock-wave systems, with or without a bifurcated foot, are considered. A near-normal shock wave and the Mach shock wave of an oblique incident and reflected wave system bifurcate when the strength, x , of the wave above the point of bifurcation attains a definite value. The height of the bifurcated foot and the angle between the two limbs at first increase rapidly with an increase in x above this value and afterwards much more slowly. The surface pressure rises steeply immediately behind the front limb of a bifurcated foot, whilst the back limb eases the distortion of flow behind. The boundary layer thickens rapidly and the surface friction falls steeply to zero in the space between the two limbs. The loss of stagnation pressure, and so the drag, is smaller than that associated with the flow through the main wave. The rise in surface pressure and the thickening of the boundary layer are less severe, and the surface friction does not fall to zero, behind the foot of a wave which is not bifurcated. A comparison of the properties of a bifurcated shock wave in an infinite inviscid stream with those measured in the tunnel shows that the boundary layer increases the angles ξ 1 , ξ 2 (see figure 3) which the front and back limbs make with the undisturbed stream direction and also the angle of refraction ϵ i at the front limb. The increases in and are associated with the thickening of the boundary layer behind the front limb; whilst the angle ( ξ 2 - ξ 1 ) between the limbs, which is also increased, is dependent on the manner in which the surface layer thickens.