非定常流动的快速拉格朗日涡方法数值模拟

采用快速拉格朗日涡方法数值模拟有复杂旋涡运动的非定常流动. 利用离散涡元模拟旋涡的产生、聚集和输送过程. 拉格朗日描述法用来计算离散涡元的移动，而移动速度则利用广义毕奥-萨伐尔公式结合快速多极子展开法计算，修正的涡半径扩散模型用来模拟离散涡元的黏性扩散. 突然起动圆柱和大攻角下突然起动翼型的非定常有涡流动的数值模拟，及其与试验结果的对比验证了方法的有效性. 另外，大攻角下突然起动翼型的计算结果给出了翼型起动后吸力面旋涡的产生、发展，周期性非定常流动的形成，以及尾流旋涡结构等一些重要的流动特征.关键词] 非定常流有涡流动快速涡方法 

NUMERICAL SIMULATION OF UNSTEADY VORTICAL FLOWS BY A FAST LAGRANGIAN VORTEX METHOD

In this paper, a fast Lagrangian vor tex method is used to numerically simulate unsteady vortical flows. Discrete vortices are used to model the vorticity generation, accumulation and transport mechanisms for the unsteady separated flow fields. The velocity field is computed using a generalized Biot-Savart formula combined with a fast summation algorithm. The discrete vortices are transported by the local velocity field and the viscosity diffusion is considered with a corrected vortex core spreading model. The effectiveness of the present method is examined through comparing the numerical simulation of the unsteady separated flows past a cylinder and a NACA0012 airfoil with available experimental results. Specific results are provided for an impulsively started NACA0012 airfoil at a high angle of attack. Detailed unsteady behavior at discrete time steps for the early stages of the flow development as well as the fully developed flow pattern is presented and discussed.