GLOBAL ANALYSIS OF TRANSITIONAL HYPERSONIC FLOW OVER CONE AND CONE-FLARE GEOMETRIES

Abstract

Accurately predicting the laminar-to-turbulent boundary-layer transition on hypersonic vehiclesremains one of the principal challenges in characterizing the expected heat loads and skin friction the vehicle will experience in flight. Ground facilities, while incapable of replicating the complete set of flow conditions found at hypersonic flight, play a critical role in providing physical measurements of the transition process. The experimental characterization of hypersonic boundary-layer disturbances, however, has traditionally faced limitations in its ability to provide spatiotemporally dense data sets comparable to those of computational fluid dynamics (CFD) investigations. The present work aims to provide global off-body measurements of hypersonic boundary-layer disturbances at frequencies much greater than that of the fundamental instability, enabling the exploration of nonlinear phenomena and more extensive comparisons between experimental and computational studies. The current methodology utilizes the fact that hypersonic-boundary layer disturbances havebeen observed to propagate at measurable and statistically predictable velocities. Particularly for the second-mode instability, the density gradient fields acquired by a calibrated schlieren system provide an avenue for resolving dense high-frequency spatiotemporal data. Disturbance propagation velocities extracted from the schlieren images are used to conduct a time-interpolation of the disturbances, which transforms spatially-available descriptions of the travelling waveforms into up-sampled temporal signals at specific pixel locations. When performed across the entire schlieren field of view, the resulting time-resolved signals have a new sampling frequency much greater than the original camera frame rate and a spatial density equal to the camera resolution. This enables the spectral analysis of high-frequency disturbances, including superharmonics of the fundamental instability, which are not originally resolvable from raw time series of the video data. The methodology is employed here in three different experimental data sets, comprising a7° half-angle sharp cone at zero incidence in Mach 6 flow, a 7° half-angle sharp cone at variable incidence in Mach 14 flow, and a cone-flare geometry composed of a 5° frustum with compression angles of +5°, +10°, and +15° at zero incidence in Mach 14 flow. A comprehensive global analysis is conducted on the linear and nonlinear development of the second-mode instability waves in each case. Pointwise measures of the autobicoherence are used to identify specific triadic interactions and the locations of their highest levels of quadratic phase coupling. Significant resonance interactions between the second-mode fundamental and harmonic instabilities are found along with interactions between these and the mean flow. Bispectral mode decomposition is employed to educe the flow structures associated with these interactions. A similar analysis is performed for the power spectrum, with power spectral densities computed for each pixel’s timeseries and spectral proper orthogonal decomposition employed to derive the modal structure and energy of the flow at specific frequencies. The instability measurements taken on the cone-flare geometry are the first of their kind atMach 14. The analysis reveals that incoming second-mode waves undergo extended interactions with the shock waves present at the corner, consistently leading to amplification of the waves and accelerating their nonlinear activity. The disturbance energy is also found to strongly radiate along the shock waves, a behavior that appears to be intensified at high Mach numbers. In the case of separated flow at the corner, additional low-frequency disturbances arise along the shear layer. Self-resonance of these disturbances leads to the radiation of elongated structures upstream of reattachment, which extend outward from the shear layer and terminate at the separation shock. This shear-layer disturbance is determined to be dominantly unstable between separation and reattachment but is significantly damped after reattachment.