Sensitivity of hypersonic flows to distributed surface roughness using input-output analysis

This paper presents a new numerical method for investigating the effect of distributed surface roughness on laminar to turbulent boundary layer transition in hypersonic flows. For years, linear stability theory (LST) and the parabolized stability equations (PSE) have been the tools of choice for analysis and prediction of laminar to turbulent transition for plates, sharp cones, and geometries for which the parallel or slowly-varying boundary layer assumptions are valid. Recently, LST and PSE have been unable to accurately predict transition N-factors in more complex flows, including blunt cones and cones with fins. The complex physics occurring in these flows prevent the LST or PSE from giving accurate results because the assumptions under which they were derived are no longer valid. Input-output analysis does make the assumptions of either the LST or PSE approaches, and, when paired with numerical Jacobians extracted out of a non-linear CFD code, it becomes a powerful tool for analyzing these complex flows. In this paper, the method is examined and verified using a 7^o half-angle sharp cone at Mach 6. N-factors from input-output analysis capture second mode growth as well as non-modal, spatial transient growth. The method is then applied to examined the sensitivity of the flow to input location along the cone wall corresponding to distributed surface roughness.