基于空间分布弹性模量的快速动网格方法

A Fast Dynamic Mesh Method Based on Spatially Distributed Elasticity Modulus

为解决基于单一弹性模量的快速动网格方法的网格扭曲问题,提出了一种基于空间分布弹性模量的快速动网格方法。根据流场网格的大小在空间的分布设定虚拟弹性体的弹性模量的空间分布。组集每一个网格的单元刚度矩阵得到虚拟弹性体的整体刚度矩阵,进而得到虚拟弹性体变形的静力平衡方程,并与结构振动方程和耦合面位移插值方程联立推导出结构-虚拟弹性体整体的动力学方程,通过振型截断方法计算结构和流场网格变形。对于标准弹性梁流固耦合和Agard Wing 445.6颤振问题中出现非法网格(网格最小角为0°)的工况,该方法得到的弹性梁流场网格变形后的最小角均维持在67°以上,而机翼流场网格变形后的最小角均维持在36°以上。

A fast dynamic mesh method based on spatially distributed elasticity modulus is developed to settle the mesh distortion of the fast dynamic mesh method based on one single elasticity modulus.The space distribution of elasticity modulus is set according to the size distribution of meshes in space of meshes.The stiffness matrix of the whole pseudo elastic solid is derived by combining element stiffness matrixes of all meshes.Then the dynamic equation for the structure-pseudo elastic solid system is derived using the static equilibrium equation of the pseudo elastic solid,the vibration equation of the structure and the displacement interpolation equation of the fluid structure interface.Deformation is calculated for the structure and the pseudo elastic solid using the modal superposition of the structure-pseudo elastic solid system.A flow mesh with the minimum face angle equal to 0 deg is called an illegal mesh.The present method is tested on an illegal mesh with the standard beam and Agard Wing 445.6.The minimum face angle after deformation given by the present method is above 67 deg for the flow mesh of the beam and the minimum face angle after deformation is above 36 deg for the flow mesh of the wing.