【作者】 陈瑜； 谢锡麟； 麻伟巍；

【Author】 CHEN Yu,XIE Xi-lin,MA Wei-wei (Department of Mechanics of Engineering Science.Fudan University,Shanghai,200433. (College of Science,Donghua University,Shanghai,201620)

【机构】 复旦大学 力学与工程科学系； 东华大学 理学院；

【摘要】 本研究将"当前物理构形对应之曲线坐标系显含时间的有限变形理论"应用于二维不可压缩涡-流函数解法,以数值模拟边界可作有限变形运动的二维类圆柱绕流。基本思想及方法表现为:按映照观点,通过构造适当的显含时间的曲线坐标系将物理空间中几何形态不规则且可随时间变化的流动区域微分同胚至参数空间中的几何形态规则且不随时间变化的规则区域,且基于一般曲线坐标系下的场论分析获得按一般曲线坐标系的局部基而展开的二维不可压缩涡-流函数控制方程;差分格式构造上主要基于不等距Lagrange插值公式等。针对壁面可作有限变形运动的二维类圆柱绕流,本文发展了对应二维涡-流函数解法的壁面涡量及壁面流函数边界条件的提法。空间动力学行为分析,主要包括:壁面可作有限变形运动情形下,壁面涡量、壁面切应力、壁面涡量法向通量等沿壁面分布及其同壁面几何特征之间的关系;升阻力系数的时间历程等。基于数值方法,对比研究低Reynolds数工况,胀压圆柱、胀压椭圆柱、表面驻波状圆柱等二维类圆柱尾迹的空间动力学行为。现有的数值研究,证实了所提方法的可靠性及有效性。数值研究表明,边界的有限变形运动可显著地改变流场的空间动力学行为,表现出极其丰富的动力学行为。更多还原

【Abstract】 In this paper the theory of "current physical configurations including time explicitly" is applied to the numerical study of the influences of boundary’s finite deformation to the special dynamics of 2D cylinder wake.To study the influences of the finite deformations of the boundaries to the flows,the point of view of mapping were adopted in the present study that map the real configurations of continuous medium in the physical space to the regular and fixed geometric domains in the parametric space in the diffeomorphism manner.Consequently,the finite deformation theory corresponding to the curvilinear coordinates with respect to the current physical configurations including time explicitly was developed in the point of view of the general continuum mechanics.Based on the present theory,the numerical study to several two dimensional incompressible flows were carried out.And the special dynamics behavior such as boundary vorticity distribution,boundary vorticity flux and drag and lift signal were studied correspondly.The related results reveal that the characters of the flows could be changed drastically due to the finite deformations of the boundaries.On the other hand,the privileges of the present theory to some related studies were supported.更多还原