Direct numerical simulations were carried out for a straight and a flared cone at Mach 6 and zero angle of attack to investigate the effects of geometry on the linear and nonlinear stages of the laminar–turbulent transition process. The cone geometries and the flow conditions of the simulations are chosen to closely match those of the experiments conducted at the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. In the linear (primary) instability regime the flared cone resulted in larger integrated growth rates ($N$ factors) and a higher dominant second mode frequency. Investigations of the secondary instability regime revealed that the flared cone also leads to a stronger fundamental resonance, characterized by larger integrated growth rates of the secondary instability waves after resonance onset. For both cases, the so-called controlled fundamental breakdown simulations were carried out, which showed the development of similar patterns of streamwise hot streaks on the surface of the cones. Streamwise streaks were also observed in the Purdue experiments (for the flared cone only) using temperature-sensitive paint. A detailed comparison of the results obtained for both geometries indicated that the streak development is caused by the same nonlinear mechanisms.

在6马赫数和零迎角下对直圆锥形和喇叭形圆锥进行了直接数值模拟，以研究几何形状对层流-湍流过渡过程的线性和非线性阶段的影响。选择模拟的圆锥几何形状和流动条件，使其与在普渡大学的波音/ AFOSR 6马赫安静隧道（BAM6QT）进行的实验紧密匹配。在线性（主要）不稳定性状态下，喇叭形圆锥体导致较大的整体增长率（$ñ$系数）和较高的主导第二模式频率。对次要不稳定状态的研究表明，扩口圆锥体还导致了更强的基本共振，其特征是共振开始后次要不稳定波的综合增长率更高。对于这两种情况，都进行了所谓的受控基本击穿模拟，该模拟显示了锥体表面上类似的沿流方向热条纹的发展。在普渡（Purdue）实验中（使用扩口锥）还使用热敏涂料观察到了流向条纹。对两种几何结构的结果进行的详细比较表明，条纹的发展是由相同的非线性机制引起的。