Linear Stability Analysis of Nose Bluntness Effects on Hypersonic Boundary Layer Transition

摘要

For hypersonic flow over spherical cones of small nose radii, it has been experimentally observed and theoretically explained that the nose bluntness effect leads to a delay of boundary-layer transition. In contrast, this trend reverses when the nose radii are larger than some critical values in the large nose bluntness range. This transition reversal phenomenon was mainly reported in Stetson and Rushton's transition experiments of a Mach 5.5 flow [1] and Softley's Mach 10-12 experiments [2] in 1967. Several linear stability analyses have been performed since the 1990s to study the nose bluntness effects on transition; none were able to show the reversal of instability onset due to nose blunting. All of the previous stability analyses, however, suffered from the fact that they were conducted only on test cases in which the actual transition reversal was not experimentally observed. The objective of the current study is to conduct a linear stability analysis on Stetson and Rushton's Mach 5.5 experiments in which the reversal is observed. Three cones with nose radii of 0.156,0.5, and 1.5 in., covering both the small and large bluntness regions, are used to study the effect of nose bluntness on stability and transition. It is found that, if only the second-mode instabilities are considered, the onset of instability is always delayed as the nose bluntness increases. The linear stability theory calculations show no reversal on the growth of the second-mode instability.