摘要
理论方面,本文提出速度场物质导数的Lie导数与Lie导数补的分解,并将其用于辨识二维流场的剪切与旋转区域,可作为辨识漩涡/旋转区域的一种新方法;应用基于曲面主方向的正交系的非完整基理论发展可变形壁面上的涡量动力学,获得了壁面上涡量与涡量流的新表达式,这种表达式充分揭示了力学与几何之间的关系。数值方面,基于显含时间的曲线坐标系的涡量-流函数方法,研究二维封闭腔体做匀角速度旋转时腔内不可压缩流场的时空演化,腔体形态包括规则扇环形、波纹壁扇环形、可变形壁面扇环形。基于流场分析,归纳了腔体内部大尺度漩涡的生成机理与流场随时间的演化特征。
In terms of theory,this paper proposes the decomposition of the Lie derivative and the complement of the Lie derivative of the material derivative of the velocity field,and the decomposition is used to identify the shear and rotation regions of the two-dimensional flow field,which can be taken as a new method to identify the vortex/rotation region.The theory of nonholonomic basis of orthogonal coordinate system based on principal directions of surface is applied to develop the vortex dynamics on the deformable wall,and new expressions of vorticity and vorticity flux on the wall are obtained,which fully reveal the relationship between mechanics and geometry.In terms of numerical study,based on the vorticity-stream function method based on the curvilinear coordinates system including time explicitly,the spatio-temporal evolutions of the incompressible flow fields in several cavities when the two-dimensional closed cavities rotate at an uniform angular velocity have been studied,and the cavity configurations includes regular fan-ring sector,corrugated wall fan-ring sector,and deformable wall fan-ring sector.Based on the flow field analysis,the formation mechanism of large-scale vortexes in the cavity and the evolution characteristics of the flow field with time have been summarized.
作者
史无双
傅渊
张大鹏
谢锡麟
SHI Wushuang;FU Yuan;ZHANG Dapeng;XIE Xilin(Department of Aeronautics and Astronautics,Fudan University,Shanghai 200433,China)
出处
《复旦学报（自然科学版）》
CAS
CSCD
北大核心
2023年第2期148-164,共17页
Journal of Fudan University：Natural Science
基金
国家自然科学基金面上项目(11972120,11472082)
国家自然科学基金重点项目(12032016)。
关键词
旋转扇环形
Lie导数与Lie导数补
可变形边界
边界涡量与涡量流
剪切带与剪切环
漩涡结构
fan-ring sector
Lie derivative and the complement of the Lie derivative
deformable wall
wall vorticity and vorticity flux
shear band and shear ring
vortex structure
