TY - JOUR
T1 - Prediction of Transition Locations in Regions of the Minor Axis of Hypersonic Elliptic Cones Using the BiGlobal-$e^N$ Method
AU - Zhao , Lei
AU - Zhou , Wenqiang
AU - Li , Xinliang
AU - Zhang , Shaolong
AU - Zhang , Yongming
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 805
EP - 832
PY - 2024
DA - 2024/05
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0183
UR - https://global-sci.org/intro/article_detail/aamm/23112.html
KW - BiGlobal stability, transition, boundary layer, hypersonic elliptic cone, minor axis.
AB - <p style="text-align: justify;">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 $N_{\max\_{all}}$ factor is proposed, which represents the maximum amplification factor that all BiGlobal unstable modes can reach. Using a comparison of the $N_{\max\_{all}}$ 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.</p>