Pressure fields over hypersonic wing-bodies at moderate incidence

Abstract

Delta wings with conically subsonic cones-bodies mounted on their compressive side are analysed in the hypersonic small disturbance regime. The weakly three-dimensional conditions associated with slender parabolic Mach cones are used to validate a linearized rotational approximation of the flow field. A combined integral–series representation is obtained for the pressure distribution between the wing-body and shock wave for arbitrary body cross-sections, and is specialized to give analytical formulae for arbitrary-order polynomial transversal contours. Numerical results are presented for wedge, parabolic and higher order cross-sections illustrating the dominant character of the cross-flow stagnation singularity associated with sharp wing-body intersections having a finite slope discontinuity. It is shown that the pressure has a logarithmic infinity at this secondary leading edge, as in corresponding Prandtl–Glauert irrotational flows. The relation of this finding to Lighthill's theorem on cross-stream vorticity is discussed. Other features of the pressure field are considered with particular emphasis on their relationship to a recently derived area rule for such configurations, and possibilities for favourable interference.