Scaling of hypersonic shock/turbulent boundary layer interactions

A separation length scaling method for shock/turbulent boundary layer interactions (STBLIs) is considered. A modification of the scaling method of Souverein et al. [J. Fluid Mech. 714, 505 (2013)] is introduced to account for heat transfer effects. As a further generalization of the model, a control volume analysis applied to a cylinder-with-flare geometry demonstrates that this axisymmetric geometry scales with the same parameters as the two-dimensional interactions. The current modified scaling is evaluated for a large range of STBLI conditions. A database of STBLI flows at Mach 2–3 has been collected from the available literature and includes both reflected shock and compression ramp data with various wall heat transfer conditions. A new Large Eddy Simulation database of Mach 7 and Mach 10 cold wall compression ramp flows with parametrically varying ramp angle is also utilized. In addition, the Mach 10 compression ramp experiments of Elfstrom [J. Fluid Mech. 53, 113 (1972)] as well as the Mach 10 cylinder-with-flare experiments of Coleman (Ph.D. thesis, University of London, 1973) and Brooks et al. (AIAA Paper No. 2017-3325, 2017) are included in the evaluation. It is shown that this new generalized scaling method results in a linear collapse of all incipiently separated STBLI data. No collapse is observed for fully separated interactions. Arguments for the physical mechanisms affecting the separation length scaling for the two STBLI regimes, incipient and fully separated, that are consistent with the data trends are presented. Namely, for incipient cases, the distribution of momentum in the incoming boundary layer is key to separation length scaling. In contrast, for fully separated cases, we postulate that the presence and strength of inviscid vortical structures significantly affects the separation length. Furthermore, we postulate how the distinct flow dynamics of the boundary layer and of the inviscid vortical structures mechanisms found in STBLI interplay and become dominant over the other.

Figure 1

Control volume for the cylinder-flare configuration. The notation of Souverein et al. is adopted here (see Figure 5 in [1]).

Figure 2

Diagram of the cylinder-flare shock position showing the difference between $\ell$ defined for the control volume and the actual flow separation length $L$.

Figure 3

Compilation of Mach 2–3 STBLI data with various heat transfer conditions scaled by $S{e}_{\mathrm{JDD}}^{*}$ (a) and again by the $S{e}_{\mathrm{mod}}^{*}$ (b). Symbol color indicates the wall temperature condition. Black data points are adiabatic walls, red are heated walls, and blue are cold walls.

Figure 4

Skin friction (a) and wall pressure (b) distributions for M7 LES data. Dashed lines indicate attached and incipient separated ramp angles. Solid lines are fully separated ramp angles.

Figure 5

Skin friction (a) and wall pressure (b) distributions for M10 LES data. Dashed lines indicate attached and incipient separated ramp angles. Solid lines are fully separated ramp angles.

Figure 6

Separation scaling data of the hypersonic STBLI database of Table 1. The dashed line is the linear trend reproduced from Fig. 3.

Figure 7

Supersonic and hypersonic scaled STBLI data plotted together with $L^{*}$ versus $S{e}_{\mathrm{mod}}^{*}$ (a) compared to $L^{*}$ versus $\mathrm{\Delta }P/\mathrm{\Delta }{P}_{\text{sep}}$ (b). Symbols are as in Fig. 3 for supersonic data and Fig. 6 for hypersonic data. Filled symbols are incipiently separated and open symbols are fully separated.

Figure 8

2D contours of time-averaged streamwise skin friction for various angles of the M7 LES.

Figure 9

2D contours of time-averaged streamwise skin friction for various angles of the M10 LES.