Linear Global Nonmodal Instability Analysis of High-Speed Flows

Identification of all physical mechanisms responsible for the flow breakdown from laminar to turbulent remains elusive in many high-speed boundary layer flows. Predicting the onset of transition and understanding the linear mechanisms responsible for transition in supersonic and hypersonic is critical to controlling instability mechanisms and preventing a multifold increase in the thermal protection system required. In the traditional modal theory, low amplitude external disturbances are generated by receptivity mechanisms and grow exponentially, leading the flow to transition. On the other hand, for flows subjected to high external disturbance levels, a bypass of the modal amplification path can happen and a nonmodal stability analysis becomes an additional route to transition that needs to be studied. The present thesis aims to address both modal and nonmodal stability analysis of highspeed spatially-inhomogeneous boundary-layer flows. In this effort, a massively parallel code, Linear Global instability for Hypersonic Transition (LiGHT) has been developed to solve multi-dimensional complex non-symmetric eigenvalue problems (EVP) and Singular Value Decomposition (SVD) problems arising in the solutions of global linear fluid flow instability. The code has been applied to four canonical flow configurations. The first flow studied has been the main motivator of the present thesis: it concerns hypersonic flow over the HiFIRE-5 elliptic cone model, which is investigated at two different flight altitudes. A new physical mechanism, unveiled by transient growth analysis, revealed that optimal conditions are associated with streamwise velocity streaks in the crossflow region. These streaks are in good qualitatively agreement with experimental results. Moreover, a quartic dependence of the maximum energy gain on the local Reynolds number was found in the highest altitude analysed, contrasting with the quadratic dependence found at the lower altitude and known from the incompressible regime. The most significant finding of the analysis on the elliptic cone concerns the role of the flight altitude: nonmodal instability becomes progressively more important as the flight altitude increases, corresponding to density and unit Reynolds number decreases. At the highest altitude examined, transient growth can be the only linear stability physical mechanism that can give rise to laminar-turbulent transition. The second and third examples are related to understanding the importance of the shock layer in the global instability modes. In the second flow studied, instability in the region ahead of the windward face of a circular cylinder is investigated, including the bow shock in the stability analysis domain. In the third example, flow over a compression ramp is interrogated, including the separation and reattachment shocks. Results obtained in both of these cases suggest that the shocks appear to be an integral part of the modes and cannot be neglected from the analysis. The fourth and last flow investigated is the hypersonic flow over a flat plate with a base flow generated from kinetic theory. Results obtained reveal that linear stability can indeed be predicted with sufficient quality, opening a new scenario to investigate high-speed flows