圆锥低超声速有攻角绕流非对称涡流的数值模拟与非线性分岔的研究

Numerical Simulation and Bifurcation Investigations on the Symmetry/Asymmetry Vortex Flows over a Cone at Angles of Attack for Low Mach Numbers

本文用数值方法研究了圆锥低超声速有攻角绕流的对称和非对称定常解、扰动响应以及在更大攻角（α＝３０°）时出现的准周期解问题。研究指出：小攻角下对称流态是结构稳定的，当攻角增大并超过某一临界攻角时，对称流态变得结构不稳定，从而演变为结构稳定的非对称定常解。如攻角再进一步增大并超过另一临界值时，出现第二次结构不稳定，定态解又演变为准周期振荡解。这表明，以攻角作为参数，随攻角的增大，先出现定态解到另一定态解的分岔，进一步出现具有时间周期解的Ｈｏｐｆ分岔。结构不稳定性是产生上述分岔的物理原因。

An efficient finite difference Navier Stokes solver is used to study the natural occurrence of symmetry/asymmetry steady separated flows,the response of the disturbances and the temporarily periodic solutions at high incidences in this paper.The study documents that the steady symmetric solution is structure stable at low incidence.When the angle of attack is increase up to one critical value,the symmetric state would lose its stability,and change into the asymmetric state which is structure stable.With further increasing,the steady asymmetric flow becomes unstable,the secondary bifurcation occurs,which led to temporal periodic state emanates from stationary state.This is kown as Hopf bifurcation.Structure stability is the main mechanism of the above transition.