Numerical study of flow instabilities at hypersonic speeds
Date
2022
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Publisher
University of Delaware
Abstract
The accurate prediction of flow transition from laminar to turbulence is imperative for sustainable and controlled hypersonic flight. At hypersonic speeds(4$<$Mach$<$10) the modal growth scenario revolves around four main flow disturbances i.e. second mode, first mode, crossflow mode and G\"{o}rtler mode. Understanding the mechanism behind the modal growth/suppression and modal interaction is a prime pathway to understanding transition. In this thesis, these flow physics are studied in the context of nose-bluntness effects, multi-mode interactions and modal decomposition. First, a physical mechanism by which nose bluntness suppresses second-mode instability is proposed. Considered are 7 degree half-angle straight cones with nose bluntness radii of 0.15 mm, 3.556 mm, 5 mm, 9.525 mm, 12.7 mm and 25.4 mm at tunnel conditions relevant to the AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. It is shown that second-mode suppression is achieved via entropy layer modulation of the basic state density gradient. A weakening of the density gradient disrupts the acoustic resonance necessary to sustain second-mode growth. These results are consistent with the thermoacoustic interpretation which posits that second-mode instability can be modelled as thermoacoustic resonance of acoustic energy trapped within an acoustic impedance well. Second, the effect of nose bluntness on crossflow instability for a Mach 6 yawed cone is considered at two different Angle of Attack (AoA). Linear parabolized stability equations investigation is performed on crossflow vortices along vortex lines calculated by the inflection point method. It is found that small changes in nose bluntness significantly alters the trajectory of crossflow vortices, the strength of the crossflow instability and the most unstable wavenumber of the crossflow vortices. Strength of the crossflow instability is decreased by decreasing the gradient of crossflow velocity component at inflection point. Further, the most unstable wavenumber is decreased by increasing the height from the wall of the crossflow velocity component inflection point. These results may be of particular importance to experimentalists studying the effect of ablation on crossflow instability. Third, motivated by recent interest in receptivity analysis and the importance of accurate numerical-experimental amplitude based comparison, the answer to the question: How receptive are downstream disturbances to upstream disturbances? is sought. A new mechanism is identified (``energy-frequency-shifting'') in which finite-bandwidth disturbances transfer energy to their frequency space neighbors. The effect of this energy transfer mechanism is quantified by comparing the wave packet formulations of the Nonlinear Parabolized Stability Equations to the traditional discrete formulation at both quiet wind tunnel conditions as well as typical flight conditions. The mechanism is found to be most significant in the 0.1-1\% disturbance amplitude range (based on normalized pressure) and is found to be responsible for a 15-30\% increase in disturbance amplitude. Finally, a common interpretation is presented for four powerful modal decomposition techniques: “proper orthogonal decomposition,” “smooth orthogonal decomposition,” “state-variable decomposition,” and “dynamic mode decomposition.” It is shown that, in certain cases, each technique can be interpreted as an optimization problem and similarities between methods are highlighted. By interpreting each technique as an optimization problem, significant insight is gained toward the physical properties of the identified modes. This insight is strengthened by being consistent with cross-multiple decomposition techniques. To illustrate this, an inter-method comparison of synthetic hypersonic boundary layer stability data is presented.
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Keywords
Compressible flow, Computational fluid dynamics, Flow instablities, Hypersonic flow, Modal analysis, Transition to turbulence