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Instability measurements of an axisymmetric, laminar separation bubble were made over a sharp cone-cylinder-flare with a $12^{\circ }$ flare angle under hypersonic quiet flow. Two distinct instabilities were identified: Mack's second mode (which peaked between 190 and 290 kHz) and the shear-layer instability in the same frequency band as Mack's first mode (observed between 50 and 150 kHz). Both instabilities were measured with surface pressure sensors and were captured with high-speed schlieren. Linear stability analysis results agreed well with these measured instabilities in terms of both peak frequencies and amplification rates. Lower-frequency fluctuations were also noted in the schlieren data. Bicoherence analysis revealed nonlinear phase-locking between the shear-layer and second-mode instabilities. For the first time in axisymmetric, low-disturbance flow, naturally generated intermittent turbulent spots were observed in the reattached boundary layer. These spots appeared to evolve from shear-layer-instability wave packets convecting downstream. This work presents novel experimental evidence of the hypersonic shear-layer instability contributing directly to transition onset for an axisymmetric model. [ABSTRACT FROM AUTHOR]

Hot-wire measurements in a Mach 3.5 quiet tunnel were made in the wake of a roughness patch on a flat plate. These measurements were used to determine mode shapes and frequencies of the dominant instabilities leading to boundary-layer transition. The egg-crate roughness pattern is an analytic function described by a sinusoidal equation, similar to an array of discrete elements that are positioned in a spanwise and streamwise grid, but containing both protuberances and dimples. This is an intermediate configuration towards understanding the underlying physics of a pseudorandom distributed roughness, and ultimately, the underlying physics of roughness-induced boundary-layer transition. The roughness pattern had a wavelength of 6.25 mm, with a nominal amplitude of 272µm (0.49 times the boundary layer thickness at the first row of protuberances). The roughness was positioned near the leading edge of the flat plate and contained 3.5 wavelengths in the streamwise direction and 7.5 wavelengths in the spanwise direction. The dominant instability was centred near 74 kHz at a free stream unit Reynolds number of 12.9 × 106 m-1 and resembled an antisymmetric mode downstream of each of the protuberances in the roughness patch. Computations using linear stability analysis based on the plane-marching parabolized stability equations (PSE) showed limited agreement with measurements when comparing the growth of the wake instability. Better agreement with the measurements was observed when considering the modification of first mode waves by the egg-crate roughness patch and the solution of the three-dimensional harmonic linearized Navier-Stokes equations was used as the in-flow to the PSE. The agreement confirms the significance of disturbance growth both upstream of and above a finite length roughness patch and the effect on the growth of instabilities in the wake. [ABSTRACT FROM AUTHOR]

Experiments are performed to investigate the effect of nose-tip bluntness on the instability mechanisms leading to boundary-layer transition on a 7◦ 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 RN < 2.54 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 RN 2.54 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. [ABSTRACT FROM AUTHOR]

Non-modal linear stability analysis results are presented for hypersonic flow over an elliptic cone with an aspect ratio of two at zero angle of attack, completing earlier modal instability analysis of flow around the same geometry. The theoretical framework to perform transient growth analysis of compressible flows on a generalized two-dimensional frame of reference is developed for the first time and is then applied to solve the initial-value problem governing non-modal linear instability on planes perpendicular to the cone axis, taken at successive streamwise locations along the elliptic cone. Parameter ranges examined here are chosen so as to model flight of the Hypersonic International Flight Research Experimentation 5 (HIFiRE-5) test geometry at altitudes of 21 km and 33 km, corresponding to Mach numbers 7.45 and 8.05 and unit Reynolds numbers Ré = 1.07 × 107 and 1.89 × 106, respectively. Results obtained indicate that the significance of the non-modal growth for laminar–turbulent transition increases with increasing flight altitude (decreasing Reynolds number). At a given set of flow parameters, transient growth is stronger in the vicinity of the tip of the cone and in azimuthal locations away from both of the minor (centreline) and major (attachment line) axes of the cone. Linear optimal disturbances calculated at conditions of maximal transient growth are found to peak in the crossflow region of the elliptic cone. These structures are elongated along the streamwise spatial direction, while being periodic along the spanwise direction with periodicity lengths of the same order of magnitude as the well-known structures identified as crossflow vortices in both experiments and simulations. [ABSTRACT FROM AUTHOR]

Numerical and experimental studies have demonstrated laminar–turbulent transition in hypersonic boundary layers over sharp cones via the modal growth of planar Mack-mode instabilities. However, due to the strong reduction in Mack-mode growth at higher nose bluntness values, the mechanisms underlying the observed onset of transition over the cone frustum are currently unknown. Linear non-modal growth analysis has shown that both planar and oblique travelling disturbances that peak within the entropy layer experience appreciable energy amplification for moderate to large nose bluntness. However, due to their weak signature within the boundary-layer region, the route to transition onset via non-modal growth of travelling disturbances remains unclear. Nonlinear parabolized stability equations (NPSE) and direct numerical simulations (DNS) are used to identify a potential mechanism for transition over a 7-degree blunt cone that was tested in the AFRL Mach-6 high-Reynolds-number facility. Specifically, computations are conducted to study the nonlinear development of a pair of oblique, unsteady non-modal disturbances in the regime of moderately blunt nose tips. Excellent agreement was demonstrated between the NPSE and DNS predictions. Results reveal that, even though the linear non-modal disturbances are primarily concentrated outside the boundary layer, their nonlinear interaction can generate stationary streaks that penetrate and amplify within the boundary layer, eventually inducing the onset of transition via the breakdown of these streaks. The results indicate that a pair of oblique, controlled non-modal disturbances can produce transition at the location measured in the experiment when their initial amplitude is chosen to be approximately 0.15 % of the free-stream velocity. [ABSTRACT FROM AUTHOR]

Steady laminar flow over a rounded-tip 2 : 1 elliptic cone of 0.86 m length at zero angle of attack and yaw has been computed at Mach number 7:45 and unit Reynolds number Re′ =1:015×107 m-1. The flow conditions are selected to match the planned flight of the Hypersonic Flight Research Experimentation HIFiRE-5 test geometry at an altitude of 21.8 km. Spatial linear BiGlobal modal instability analysis of this flow has been performed at selected streamwise locations on planes normal to the cone symmetry axis, resolving the entire flow domain in a coupled manner while exploiting flow symmetries. Four amplified classes of linear eigenmodes have been unravelled. The shear layer formed near the cone minor-axis centreline gives rise to amplified symmetric and antisymmetric centreline instability modes, classified as shear-layer instabilities. At the attachment line formed along the major axis of the cone, both symmetric and antisymmetric instabilities are also discovered and identified as boundary-layer second Mack modes. In both cases of centreline and attachment-line modes, symmetric instabilities are found to be more unstable than their antisymmetric counterparts. Furthermore, spatial BiGlobal analysis is used for the first time to resolve oblique second modes and cross-flow instabilities in the boundary layer between the major- and minor-axis meridians. Contrary to predictions for the incompressible regime for swept infinite wing flow, the cross-flow instabilities are not found to be linked to the attachment-line instabilities. In fact, cross-flow modes peak along most of the surface of the cone, but vanish towards the attachment line. On the other hand, the leading oblique second modes peak near the leading edge and their associated frequencies are in the range of the attachment-line instability frequencies. Consequently, the attachment-line instabilities are observed to be related to oblique second modes at the major-axis meridian. The linear amplification of centreline and attachment-line instability modes is found to be strong enough to lead to laminar-turbulent flow transition within the length of the test object. The predictions of global linear theory are compared with those of local instability analysis, also performed here under the assumption of locally parallel flow, where use of this assumption is permissible. Fair agreement is obtained for symmetric centreline and symmetric attachment-line modes, while for all other classes of linear disturbances use of the proposed global analysis methodology is warranted for accurate linear instability predictions. [ABSTRACT FROM AUTHOR]