Unified super/hypersonic similitude for steady and oscillating cones and ogives

Abstract

A unified similitude for super/hypersonic flow has been given for non-slender cones and quasicones with attached shock. The similitude space has been shown to be orthogonal to the bow shock and an accurate scaling law for cone flows of different Mach numbers has been provided. A constant density solution has been obtained which gives simple formulas for shock angle and pressure on a cone. This leads to an axisymmetric shock expansion theory which incorporates the effect of profile curvature of an ogive in inviscid flow or a cone in viscous flow whose boundary layer displacement thickness is known a priori. The hypersonic formulas for pitching moment derivatives of oscillating cones and ogives have been adjusted to extend them to supersonic Mach numbers.

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“…Ghosh [13] has obtained a similitude and two similarity parameters for shock attached oscillating delta wings at large incidence. Crasta and Khan have extended the Ghosh similitude to Hypersonic/supersonic flows past a planar wedge [14] and [18] and Non planar wedge [20], [21], and [22].…”