Stability derivatives of sharp cones in viscous hypersonic flow

Abstract

Using approximate forms of the existing pressure relations for an inclined flat plate, a theory has been developed for the determinat ion of static and dynamic stability derivatives of steady and oscillating sharp wedges in viscous laminar hype rsonic flow. The pressure field over the wedge has been assumed to consist of directly intersecting and suitably matched regions of weak and strong viscous pressure interactions. The concepts of static and dynamic viscous pressure interactions have been introduced, which are related to the effective change of the deflection angle and the normal velocity, respectively, of the wedge surface due to the presence of boundary layer. Closed expressions have been derived for the stability derivatives using a generalized form of the piston theory in which the regions of simple-shock or weak-shock approximations were graphically matched to the region of st rong-shock approximation. Static derivatives, which are affected only by the static viscous interaction, are given partly in the fonn of viscous derivatives, obtained by use of the piston theory, and partly in the form of viscous correction factors, which can be applied to inviscid derivatives obtained by arbitrary means. Viscous effects are shown to act in a stabilizing manner for moments taken about axes forward of the one-third chord position and a destabilizing manner for more rearward axis positions. Dynamic de rivatives are affected by both the static and dynamic viscous interactions. The effect of the static interaction on the damping-in-pitch derivative is shown to be always positive.