Three-dimensional effects in shock detachment from a wedge

Abstract

Introduction C first the plane inviscid supersonic flow of a perfect gas over a symmetrical wedge whose plane of symmetry is aligned with the freestream. If the wedge angle is sufficiently small, the shock wave caused by the flow deflection is not strong enough to decelerate the flow to subsonic speed. No information can then travel upstream of the leading edge of the wedge, to which the shock must therefore be attached. Furthermore, no information about the finite extent of the wedge can reach the leading edge. Thus, the flow near the leading edge does not know anything about the only length scale in the problem, with the necessary result that the shock is straight there. This situation is drastically modified as soon as the wedge angle is increased to a value where the shock is just strong enough to cause the flow to become subsonic. At that point, the shock wave becomes curved and, with further increase in the wedge angle, it becomes detached from the leading edge. The remarkable simplicity of the entirely supersonic flow is thus destroyed—when subsonic regions exist—by the availability of information about a length scale. A sketch of the two configurations is given in Fig. 1. The effect of interest here is the gradual nature of the process of shock detachment as the wedge angle is increased. This continuous behavior is not self-evident, although it is undisputed in transonic flow. Certainly, the straight-shock solution breaks down by a discontinuous process at a particular wedge angle: information about the length of the wedge becomes available suddenly. It may be that the range of deflection angles over which the detachment distance grows is related to the fact that the deflection angle just causing the flow to become sonic (ds) is smaller than the maximum deflection angle possible with an attached shock ( d m ) . Thus, there exists a small range of d in which the shock is attached, but the postshock flow is subsonic. This range decreases rapidly with increasing Mach number, which may be taken as a suggestion that the rate at which the detachment distance increases as the wedge angle is increased may become greater at high Mach numbers. Indeed, a set of experiments in argon at M= 16 confirm this expectation. Hornung and Smith used the rate of growth of the detachment distance as an indication of the relaxation effects in dissociating gas flows. A comparison of measurements in relaxing and perfect gas flows gave good confirmation of this phenomenon. However, it was pointed out in Ref. 1 that other mechanisms could also tend to reduce the rate of growth. In the present Note, we concentrate on the effect of finite aspect ratio on the rate of growth of the detachment distance with increasing wedge angle in a high Mach number perfectgas flow. The aim is to obtain quantitative information about this effect from an experimental investigation.