Characterization of instability mechanisms on sharp and blunt slender cones at Mach 6

Abstract

Experiments are performed to investigate the effect of nose-tip bluntness on the instability mechanisms leading to boundary-layer transition on a $7^{\circ }$ half-angle cone in a Mach-6 free stream. The development of disturbances is characterized using a combination of high-speed calibrated schlieren images and pressure measurements, and the data are compared with results computed using the parabolized stability equations. The approximately 414 mm long cone model is equipped with an interchangeable nose tip ranging from sharp to 5.08 mm in radius. For nose tips with a radius $R_{N}<2.54\ {\rm mm}$ , second-mode instability waves are the dominant mechanism leading to transition. Time-averaged frequency spectra computed from the calibrated schlieren visualizations and pressure measurements are used to compute the second-mode most-amplified frequencies and integrated amplification rates ( $N$ factors). Good agreement is observed between the measurements and computations in the linear-growth regime for the sharp-nose configuration at each free-stream condition. Additionally, a bispectral analysis identifies quadratic phase locking of frequency content responsible for the growth of higher harmonics. For nose tips of $R_{N}\geqslant 2.54\ {\rm mm}$ , the schlieren visualization region is upstream of the entropy-layer swallowing length, and second-mode waves are no longer visible within the boundary layer; instead, elongated, steeply inclined features believed to be associated with non-modal instability mechanisms develop between the entropy-layer and boundary-layer edges. Simultaneously acquired surface pressure measurements reveal high-frequency pressure oscillations similar to second-mode instability waves associated with the trailing edge of these non-modal features.

Assimilation of wall-pressure measurements in high-speed flow over a cone

“…The experimental spectra and signal intensity, used in the data assimilation, are shown with symbols in figure 2. At position s 1 , the spectrum is dominated by a peak between f = 225-275 kHz, which is expected due to the presence of unstable second modes on straight cones (Kennedy et al 2022). As the boundary layer thickens downstream, the frequency for the peak energy decreases.…”

“…The total test time was approximately 0.2 seconds, which was separated into two approximately timestationary periods, lasting 100 milliseconds. Data from the second period is analyzed for this work (for detailed characteristics of AFRL Ludwieg Tube, see Kimmel et al 2017;Kennedy et al 2022).…”

“…Once the fast-acting valve was opened, the gas accelerated through the nozzle to calculated free-stream conditions of U ∞ = 904 m s −1 , T ∞ = 54 K and ρ ∞ = 0.0274 kg m −3 , yielding a unit free-stream Reynolds number Re ∞ /L = 7.11 × 10 6 m −1 . The total test time was approximately 0.2 s, which was separated into two approximately time-stationary periods, lasting 100 ms. Data from the second period are analysed for this work (for detailed characteristics of the AFRL Ludwieg Tube, see Kimmel et al 2017;Kennedy et al 2022).…”

“…The herein adopted methodology systematically uses experimental measurements to rigorously determine the disturbance environment. Our particular focus will be the experiments by Kennedy et al (2022), where wall-pressure measurements were recorded on a 7 • straight cone with a sharp nose in the Mach-6 Ludwieg tube facility at the Air Force Research Laboratory (AFRL). The instrumentation layout is typical for this type of research, with pressure probes arranged in a streamwise ray to provide time-resolved information on streamwise amplification of instabilities; in addition, three azimuthal probes are placed to assess axi-symmetry of the pressure fluctuations.…”

“…The wall-pressure data indicate that the second mode feature prominently without full breakdown to turbulence. Recent computations using the axisymmetric nonlinear parabolized stability equations (NPSE) qualitatively capture the trend of the N-factor, without quantitative agreement (Kennedy et al 2022) or guidance on how to objectively select the upstream disturbance spectra. Furthermore, the role of three-dimensional waves and their relative amplitudes remains unknown since the simulations were axisymmetric.…”