RBF 整体网格变形技术与多体轨迹仿真

摘要

在多体分离的 CFD 动态轨迹仿真中，计算网格需要准确刻画固壁边界之间幅度很大的相对运动。理想的状况是采用整体网格，在不增删网格节点和不改变原网格拓扑结构的条件下，通过网格变形来刻画多体边界间的相对运动。为此，以先前发展的径向基函数（RBF）网格变形技术为基础，通过引入一种改进的拉普拉斯光顺算法，大幅改善了单独 RBF 网格变形技术在处理大幅度边界位移时的网格质量下降和网格拓扑破坏问题，成功实现了多体分离中的超大幅度网格变形。在改进的拉普拉斯算法中，针对四面体、三棱柱、六面体、金字塔四种网格单元类型提出了一套统一的网格质量评估标准，并将其用于非结构混合网格下的拉普拉斯光顺。通过耦合求解非定常Navier—Stokes 方程和刚体六自由度运动方程，利用典型跨声速下机翼与外挂物分离问题对以上网格变形和光顺技术进行验证，将计算获得的外挂物投放过程的空间位置、姿态角和气动力与风洞实验结果进行了对比分析，结果显示：在不采用网格嵌套和局部重生的前提下，与改进的拉普拉斯光顺相结合的 RBF 网格变形技术可以有效地解决多体分离过程中的网格大幅度变形问题，且网格质量能够满足精确刻画外挂物投放飞行轨迹的要求。%Multi—body separation is a kind of common mechanical problem which exists widely in the field of Aeronautics and Astronautics.Because of its complexity,studying this kind of problems is very difficult either using flight or wind tunnel test.Therefore,the establishment of an unified,efficient and accurate numerical method for simulating multi—body separation has great application value.In multi—body trajectory simulation,computational grids need to accurately depict the large magnitude of relative motion among all solid boundaries.The ideal approach is using a single set of mesh,without adding or deleting the grid nodes or changing the original grid topolo—gy,just through mesh deformation to depict the relative movement.On the basis of radial basis function (RBF)mesh deformation technology,the intelligent Laplacian smoothing algorithm is introduced,which greatly improve the ability of pure RBF mesh deformation technology to avoid quality decreasing and topology damaging,and successfully simulate the process of multi—body separation.The flow solver includes four types of grid cell,which respectively are tetrahedron, triangular prism,hexahedron and pyramid.A new unified mesh quality assessment standard is presented as the execute criterion of intelligent Laplacian smoothing.This mesh deformation and smoothing technology is fully integrated into Navier—Stokes equations and 6—DOF moving equations to validate its feasibility by a typical store separation problem.The computational results are com—pared with experimental data,which demonstrate the accuracy and ability of presented method in dealing with the large magnitude of relative motion among multiple moving boundaries.