(untitled)
Two-dimensional global (BiGlobal) stability in the region of the minor axis is investigated in the case of hypersonic elliptic cones with major-minor axis ratios of 2:1 and 3:1 at Mach number 6.0, and the BiGlobal-e^N method is proposed to predict the transition location of the boundary layer. Matrix-free BiGlobal stability analysis is used to find unstable modes, including the Y-mode and the Z-mode. The growth rates in the streamwise-frequency plane for these modes are obtained. The N__all factor is proposed, which represents the maximum amplification factor that all BiGlobal unstable modes can reach. Using a comparison of the N__all factor with the transition location measured in a wind tunnel experiment for the 2:1 elliptic cone, the transition prediction criterion is determined, i.e., N_tr = 8.6. In the transition position, the amplification factors of several modes reach a level close to 8.6, which implies that none of them has the absolute superiority sufficient to cause the transition itself. Finally, the BiGlobal-e^N method is employed to predict the transition location in the region of the minor axis of the 3:1 elliptical cone. It is found that a larger major-minor axis ratio leads to stronger instability and an earlier transition. , number=4, journal=Advances in Applied Mathematics and Mechanics, year=2024, month=May, pages=805–832