Internal shock waves in supersonic ideal gas flows past wedge-plate and cone-cylinder configurations

Abstract

The problem of internal shock waves (IS) and the reasons for their appearance in inviscid and non-heat-conducting gas flows past wedge-plate (WP) and cone-cylinder (CC) configurations without an angle of attack are studied for the case of an attached bow shock wave and a supersonic flow behind it. For the CC case the axis of the cylinder coincides with the direction of incoming flow. It is shown that, within the limits of validity of the isentropic approximation used in describing flows with weak shocks, the WP is streamlined without IS forming. On the other hand, the sufficient condition for the appearance of IS in the flow modes under discussion is that the flow overexpands directly past the corner representing the point where the generatrices of the wedge (cone) and plate(cylinder) meet. The appearance or non-appearance of such an overexpansion can be established for any intensity of the attached shock wave (AS) in a supersonic flow behind it, without any additional simplifications whatsoever. Computations carried out have shown that the flow past CC contains an IS over the whole range of Mach numbers M ∞ of the incoming flow under investigation. In contrast to this, in the case of WP, flows are possible with overexpansion (the pressure behind the corner is less than the pressure in the incoming flow), as well as with underexpansion, and both situations can be observed, in particular, in the case of a weak AS and low supersonic velocities of the incoming flow, while in the case of the so-called transonic approximation (TA) overexpansion always occurs behind the corner (see /1/〉). The lack of overexpansion behind the corner by no means implies that there is no IS for the WP. The fact is that in such cases the change in pressure along the plate can also be non-monotonic. This may happen e.g. if the rarefaction waves emerging from the corner are reflected from the WP, or from its segment, like the compression waves. Recognition of the latter circumstance leads to additional narrowing of the region in which fully supersonic flows past the WP can be realized without IS.