Transitional hypersonic flow over slender cone/flare geometries

Abstract

Experiments are performed in a Mach-6 shock tunnel to examine the laminar-to-turbulent transition process associated with a sudden increase in surface angle on a slender body. A cone/flare geometry with a 5 $^\circ$ frustum and compression angles ranging from 5 $^\circ$ to 15 $^\circ$ allow a range of mean flow configurations, spanning an attached shock-wave/boundary-layer interaction to a fully separated one; the unit Reynolds number of the flow is also varied to modify the state of incoming second-mode boundary-layer disturbances. Ultra-high-speed schlieren visualizations provide a global picture of the flow development, supplemented by high-frequency surface pressure measurements. For the 5 $^\circ$ compression, the unsteady flow field is dominated by the second-mode waves, whose breakdown to turbulence is generally accelerated (compared with the straight-cone configuration) by encountering the angle change. As the compression angle is increased to induce separation, lower-frequency disturbances appear along the separated shear layer that exhibit much larger amplification rates than the incoming second-mode waves; the latter effectively freeze in amplitude downstream of the separation point before rapidly breaking down upon reattachment. The shear-layer disturbances become dominant at the largest compression angle tested. Radiation of disturbance energy to the external flow is consistently observed: this generally occurs along mean flow features (flare, separation or reattachment shocks) for the second-mode disturbances and spontaneously for the shear-layer waves. The combined application of spectral proper orthogonal decomposition and a global bispectral analysis allows the identification of important unsteady flow structures and the association of these with prominent nonlinear interactions in the various configurations.

Instability and transition onset downstream of a laminar separation bubble at Mach 6

“…At most stations, the shear-layer instability has a greater amplitude than the second mode, which differs from the 10 flare results (see figure 8, replotted from Benitez et al. 2020) but is similar to what Butler & Laurence (2022) observed on a cone-flare model for larger flare angles. Additionally, downstream of reattachment, the spectra start to broaden at higher Reynolds numbers, with increasing energy in higher frequencies.…”

“…Butler found that energy was being radiated away from the second-mode instability in the shear layer over the separation bubble for the flare. The next year, they published the results sweeping compression angles and Reynolds numbers, highlighting the increase in dominance of the shear-layer instability with increasing flare angle (Butler & Laurence 2022). Their bubble can be classified as transitional, as the reattachment point moved upstream with increasing unit Reynolds number (Becker & Korycinski 1956).…”

“…Their bubble can be classified as transitional, as the reattachment point moved upstream with increasing unit Reynolds number (Becker & Korycinski 1956). Butler & Laurence (2022) have stated the need to study the shear-layer instability in a facility with longer run times and higher-quality flow; this work helps to fill that gap.…”

Global analysis of nonlinear second-mode development in a Mach-6 boundary layer from high-speed schlieren data

“…Advancements in ultrahigh-speed cameras have made capturing schlieren images at frame rates at and above the expected second-mode frequencies possible. Calibration of pixel intensity values to density gradients then enables quantitative measurements of disturbance amplitudes from pixelwise temporal signals [14,[4][5][6]. If analysis is directly applied to the schlieren videos, however, then the bandwidth is Nyquist-limited to frequencies below one half the frame rate, which will generally preclude resolving harmonic development.…”