Secondary Instability of Second Mode Disturbances in Hypersonic Boundary Layers

Second mode disturbances dominate the primary instability stage of transition in a number of hypersonic flow configurations. The highest amplification rates of second mode disturbances are usually associated with 2D (or axisymmetric) perturbations and, therefore, a likely scenario for the onset of the three-dimensionality required for laminar-turbulent transition corresponds to the parametric amplification of 3D secondary instabilities in the presence of 2D, finite amplitude second mode disturbances. The secondary instability of second mode disturbances is studied for selected canonical flow configurations. The basic state for the secondary instability analysis is obtained by tracking the linear and nonlinear evolution of 2D, second mode disturbances using nonlinear parabolized stability equations. Unlike in previous studies, the selection of primary disturbances used for the secondary instability analysis was based on their potential relevance to transition in a low disturbance environment and the effects of nonlinearity on the evolution of primary disturbances was accounted for. Strongly nonlinear effects related to the self-interaction of second mode disturbances lead to an upstream shift in the upper branch neutral location. Secondary instability computations confirm the previously known dominance of subharmonic modes at relatively small primary amplitudes. However, for the Purdue Mach 6 compression cone configuration, it was shown that a strong fundamental secondary instability can exist for a range of initial amplitudes of the most amplified second mode disturbance, indicating that the exclusive focus on subharmonic modes in the previous applications of secondary instability theory to second mode primary instability may not have been fully justified. 1. BACKGROUND AND OBJECTIVE By virtue of its influence on surface heat transfer, skin friction, and separation characteristics, boundary layer transition from a laminar to a turbulent state tends to dominate the design and performance of hypersonic flight vehicles. At hypersonic Mach numbers, the first mode instability becomes less important or, in many cases, is not a factor in the transition process. For an axisymmetric body at zero angle of attack in a hypersonic flow (as well as in cases where the boundary layer is essentially two-dimensional), the crossflow instability is absent as well. In these cases, the predominant instability mechanism involves the second mode disturbances. The most unstable second mode instability is axisymmetric (e.g. on a cone at zero angle of attack) or two-dimensional (e.g. on a flat plate) in nature. Thus, the oblique breakdown mechanism, which is believed to dominate first mode transition in supersonic flows, becomes less relevant at hypersonic Mach numbers. Therefore, a good and thorough understanding of the breakdown of two-dimensional or axisymmetric second mode waves is essential for understanding this important scenario for transition. Similar to its counterpart in incompressible flows (the Tollmien-Schlichting wave) [1], the second mode wave is susceptible to three-dimensional secondary instability when its amplitude becomes sufficiently large [2,3]. Because the second mode instability and the associated secondary instability in hypersonic flows usually attain frequencies in the range of hundreds of kilo-Hertz to a few mega-Hertz, which is beyond the currently available high-frequency sensors, the computational approach is the only way to study them in detail. The objective of this research is to study the breakdown mechanism via secondary instability of the finite https://ntrs.nasa. gov/search.jsp? R=20120010339 2020-02-20T18:48:42+00:00Z