Nonmodal Growth of Traveling Waves on Blunt Cones at Hypersonic Speeds

摘要

The existing database of transition measurements in hypersonic ground facilities has established that, as the nose-tip bluntness is increased, the onset of boundary-layer transition over a circular cone at zero angle of attack shifts downstream. However, this downstream movement in transition slows down and eventually reverses at sufficiently large values of the nose Reynolds number. Because modal amplification is too weak to initiate the measured frustum transition at moderate to large bluntness values, nonmodal growth is investigated as the potential basis for a physics-based model. The present analysis investigates the nonmodal growth of traveling disturbances initiated within the nose-tip vicinity. Results show that both planar and oblique traveling disturbances that peak within the entropy layer experience appreciable energy amplification for successively higher disturbance frequencies as the nose bluntness is increased. For relatively small bluntness values, the initial nonmodal growth is followed by a partial decay that is overcome by an eventual, modal growth as Mack-mode waves. For larger bluntness values, the Mack-mode waves are not amplified anywhere upstream of the experimentally measured transition location, but the traveling waves still undergo a significant amount of nonmodal growth. These findings do not provide a definitive link between optimal growth and the onset of frustum transition on moderately blunt cones, but they are qualitatively consistent with the experimental observations of an initial peak near the nose tip followed by a decay and growth in disturbance energy, as well as the appearance of inclined structures above the boundary-layer edge.