发表机构
École Polytechnique Fédérale de Lausanne; Politecnico di Milano（洛桑联邦理工学院; 米兰理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过三维计算和弱非线性分析，研究俯仰与偏航对Ahmed体层流尾迹分岔的影响，揭示不完美分岔导致的主次分支稳定性变化及丰富分岔图。
AI 中文摘要
我们研究了俯仰和偏航对Ahmed体（宽高比$W/H=1.2$，长高比$L/H=3$的钝体）层流绕流分岔的影响。当与来流完全对齐时，其尾迹首先经历叉形分岔，导致静态垂直或水平偏转，并在更大的雷诺数$Re$下通过二次Hopf分岔变为振荡。正如不完美叉形分岔中常见的那样，任何微小的不对齐都会在低$Re$下预选一个稳态，称为“主”分支。在更大的$Re$下，通过鞍结分岔产生一个不连通的“次”分支。这里，我们使用三维计算研究不对齐的影响。我们首先使用线性稳定性分析关注纯俯仰和纯偏航两种情况。在两种情况下，次分支在入射角超过一个较小值后立即变得不稳定。在纯偏航情况下，主分支通过水平Hopf分岔变得不稳定，该分岔由偏航失稳。在纯俯仰情况下，主分支经历垂直Hopf分岔和水平叉形分岔的交叉，分别由俯仰失稳和稳定。这促使我们使用DNS研究这种非线性竞争，该竞争已在接近地面的对齐Ahmed体中被观察到。然后，我们使用弱非线性分析研究同时偏航和俯仰的影响。两个定常模态之间的竞争产生了丰富的分岔图，使我们能够预测稳定解的数量以及不同状态之间的相空间轨迹。
英文摘要
We study the effect of pitch and yaw on the bifurcations of the laminar flow past an Ahmed body, a bluff body of width-to-height ratio $W/H=1.2$ and length-to-height ratio $L/H=3$. When perfectly aligned with incoming flow, its wake first undergoes pitchfork bifurcations leading to a static vertical or horizontal deflection, and becomes oscillatory via a secondary Hopf bifurcation at larger Reynolds number $Re$. As commonly observed for imperfect pitchfork bifurcations, any small misalignment preselects one of the steady states, referred to as the "primary" branch, at low $Re$. At larger $Re$, a disconnected "secondary" branch is born via a saddle-node bifurcation. Here, we investigate the effect of misalignment using three-dimensional computations. We first focus on pure pitch and pure yaw with linear stability analysis. In both cases, the secondary branch becomes unstable as soon as the incidence exceeds a small value. In the pure yaw case, the primary branch becomes unstable via a horizontal Hopf bifurcation, destabilised by yaw. In the pure pitch case, the primary branch sees the crossover of vertical Hopf and horizontal pitchfork bifurcations, destabilised and stabilised by pitch, respectively. This motivates use of DNS to study this nonlinear competition, already observed for aligned Ahmed bodies in ground proximity. We then study the effect of simultaneous yaw and pitch with a weakly nonlinear analysis. The competition between the two stationary modes gives rise to rich bifurcation diagrams, allowing us to predict the number of stable solutions and phase space trajectories between different states
