2. Unsteadiness
As noted earlier, in this context, the term unsteadiness refers to frequencies of relatively high amplitudes in bands which are an order of magnitude or more lower than those associated with fine-scale turbulence in the incoming boundary layer. The problem of unsteadiness, in both nominally 2-D and 3-D circumstances, has been the focus of experimental studies at speeds ranging from transonic to hypersonic over the course of several decades – see e.g., Refs. [1] and [33] for early descriptions – and key results from those and subsequent efforts are summarized in the reviews of Refs. [7] and [10].
Since the publication of Ref. [10], sustained synergistic computational and experimental efforts have been conducted on the study of nominally 2-D situations, including both the ramp and impinging shock flows. Fig. 3(a) shows a schematic of the overall expected mean flow features of a separated impinging shock configuration. Inside the boundary layer, the shock typically bends as it encounters lower Mach numbers and ultimately breaks up into a compression fan [34] and a reflected shock develops as shown. For a given boundary layer, if the shock is strong enough, separation occurs. The compression corner flow shown in Fig. 3(b) has a single major shock associated with the ramp. However, the dynamics in terms of unsteadiness and separation is generally similar to the impinging shock (see Ref. [4] for a discussion on the differences between the two types of interactions). The length of the separation region, Lsep, and the incoming boundary layer thickness are the two larger length scales in the flow. Fig. 3(c) and (d) shows SBLI in canonical axisymmetric situations. The former is taken from Ref. [35] on the HIFiRE-1 configuration discussed in more detail below. The flow represents the counterpart of the 2-D compression ramp, with similar topological features, except for the addition of a shoulder, which is necessary in practical situations. Frame (d), taken from Ref. [36] is the laminar Mach 9 flow past the double-cone 25–55° configuration measured by Holden et al. [37] and [38]. The flow structure for this particular case has been couched in Ref. [36] in terms of a Type V interaction of Edney [39]. Briefly, the two cones yield individual shocks linked at two triple points with a connector shock. A shear layer emanates from the aft triple point, effectively separating the subsonic flow from the near-wall supersonic jet. The viscous interaction associated with the reattachment shock is similar to that described for transonic interactions [40]. Comments on turbulence in such flows are deferred to Section 3.