面向混合单元动网格计算的雅可比弹簧法  

Jacobian-based Spring Method for Hybrid Element Dynamic Mesh Computations

作　　者：杨帆 杨梦瑶 江中正 陈丽华[1] 李旭东[2] 陈伟芳[1,3] YANG Fan;YANG Mengyao;JIANG Zhongzheng;CHEN Lihua;LI Xudong;CHEN Weifang(School of Aeronautics and Astronautics,Zhejiang University,Hangzhou 310027,China;Beijing Institute of Space Long March Vehicle,Beijing 100076,China;Advanced Aircraft Research Center,Huanjiang Laboratory,Zhuji 311800,China)

机构地区：[1]浙江大学航空航天学院,杭州310027 [2]北京航天长征飞行器研究所,北京100076 [3]浣江实验室先进飞行器研究中心,诸暨311800

出　　处：《宇航学报》2025年第3期519-531,共13页Journal of Astronautics

基　　金：国家自然科学基金(92271204,92471109,92271114,12002306)。

摘　　要：作为最常用的动网格变形方法之一,弹簧法被广泛应用于变体飞行器的变形、气动弹性、多体分离等非定常工程问题的计算。常用的弹簧法刚度系数由线弹簧刚度和扭转弹簧刚度线性叠加组成,但当网格几何尺寸较小时,扭转弹簧刚度远小于线弹簧刚度,导致计算时会忽略扭转弹簧刚度对网格变形能力的影响。此外,扭转弹簧刚度公式包含网格面三角形顶角参数,只适用于三角形网格面,无法适用于包含四边形网格面的混合网格变形计算。为了兼顾动网格变形能力的鲁棒性和多种混合网格单元的适配性,引入雅可比参数替代原来扭转弹簧刚度系数中的三角形网格面顶角正弦值,并采用均值不等式改进雅可比参数计算公式,增大狭长网格单元的刚度,从而增强网格变形量分布的合理性以及减少网格边长度不均匀性对网格变形的影响。进一步改进线弹簧和扭转弹簧的组合刚度系数计算公式,以避免在网格几何尺寸较小的条件下忽略扭转弹簧刚度对动网格变形能力的影响。通过改进传统弹簧法提出雅可比弹簧法,并对矩形平动、翼形转动、DLR-F4机翼变形和半球头部变形进行了计算。计算结果表明:相比传统弹簧法,改进后的动网格弹簧方法能够用于混合网格变形计算,并有效提高了变形能力和变形后的网格质量。The spring method,a prominent technique among dynamic deformation mesh approaches,is widely adopted in unsteady engineering problems,such as calculating morphing flight vehicle deformation,aeroelasticity,multibody separation,and others.The stiffness coefficient typically used in the spring method includes both linear and torsional spring stiffness components.However,as mesh geometric sizes decrease,torsional spring stiffness becomes considerably smaller than linear spring stiffness,resulting in its influence on mesh deformation capability being overlooked.Furthermore,the torsional spring stiffness formula only considers parameters related to triangular mesh face angles,restricting its application to triangular mesh surfaces and rendering it inapplicable to quadrilateral mesh faces in hybrid meshes.To achieve a balance between the robustness of dynamic mesh deformation capability and adaptability to various hybrid mesh elements,Jacobian parameters are introduced to replace the sine values of triangular mesh face angles in the original torsional spring stiffness coefficient.Additionally,an enhanced formula for calculating Jacobian parameters,employing the inequality of arithmetic-geometric means,is adopted to increase the rigidity of slender grid elements.This enhancement ensures a more reasonable distribution of grid deformation and reduces the impact of uneven grid edge lengths on deformation capability.Further adjustments are made to the combined stiffness coefficient calculation formulas for linear and torsional springs,preventing the omission of torsional spring stiffness’s influence on dynamic mesh deformation capability when mesh geometric dimensions are small.By refining the conventional spring method,a Jacobian-based spring method is proposed and applied to calculate translations of rectangles,rotations of airfoils,and deformations of DLR-F6’s airfoil and head variants on hemispheres.The results demonstrate that,compared to traditional spring methods,this improved dynamic mesh spring method is well-sui

关 键 词：动网格 网格变形 混合网格 弹簧法 雅可比法 

分 类 号：V211.1[航空宇航科学与技术—航空宇航推进理论与工程]