旋转坐标系N-S 方程无网格/网格混合算法

为了模拟涡桨发动机等绕固定轴旋转的桨叶流场,发展了一种求解旋转体非定常黏性绕流的无网格/网格混合算法。算法基于求解旋转坐标系纳维尔-斯托克斯方程展开,避免了旋转角速度特征物理量的插值运算;计算域采用整体网格和物面附近局部无网格离散,通过引入无网格和网格对偶点,实现了混合算法绕流信息的跨区交换,并给出了一种对偶点调整选取的方法;基于无网格点云空间导数逼近方法离散控制方程,并结合隐式LU-SGS算法,给出了混合算法求解非定常问题的双时间步隐式推进格式。结果表明:所提算法通过2维振荡翼型非定常绕流、旋转圆柱黏性绕流和模拟发动机桨叶旋转运动的3维悬停旋翼绕流进行了考核,所得升力系数等重要气动数据的变化趋势与文献试验或计算值一致,典型截面处所示的激波强度和位置亦与文献值吻合,展现出算法在模拟旋转部件绕流问题方面具有广阔的工程应用前景。

Hybrid Gridless/Grid Algorithm for Solving Navier-Stokes Equations in Rotating Coordinate System

In order to simulate the flow field of the propellers rotating over a fixed axis in a turboprop engine,a hybrid gridless/grid algorithm was developed for solving unsteady viscous flows over rotating abodies.The algorithm was based on solving the Navier-Stokes equation in the rotating coordinate system,which avoided the interpolation of the characteristic physical quantities of the rotating angular velocity.The computational domain was discretized by overall grid and local gridless near the object surface.By introducing gridless and grid dual points,the cross region exchange of flow information around the hybrid algorithm was realized,and a method for adjusting and selecting dual points was given.Based on the gridless point cloud spatial derivative approximation method to discretize the control equations,and combined with the implicit LU-SGS algorithm,an implicit dual time-stepping marching scheme for solving unsteady problems was proposed by hybrid algorithm.The results show that the proposed algorithm is tested by two-dimensional pitching airfoil unsteady flow,rotating cylinder viscous flow and three-dimensional rotating blades in hover which imitate the propellers.The trend of important aerodynamic data such as lift coefficient obtained is consistent with the test or calculated values in the literature,and the shock intensity and position shown at the typical section are also consistent with the values in the literature.It shows the broad engineering application prospect of the algorithm in simulating the flow over rotating bodies.