旋涡作用下多物体受力规律研究

By using a special momentum approach and with the help of interchange between singularity velocity and induced flow velocity, we derive in a physical way explicit force formulas for two-dimensional inviscid flow involving multiple bound and free vortices, multiple airfoils and vortex production. These force formulas hold individually for each airfoil thus allowing for force decomposition and the contributions to forces from singularities (such as bound and image vortices, sources and doublets) and bodies out of an airfoil are related to their induced velocities at the location of singularities inside this airfoil. The force contribution due to vortex production is related to the vortex production rate and the distance between each pair of vortices in production, thus frame-independent. The formulas are validated against a number of standard problems. These force formulas, which generalize the classic Kutta Joukowski theorem (for a single bound vortex) and the recent generalized Lagally theorem (for problems without bound vortex and vortex production) to more general cases, can be used to (1) identify or understand the role of outside vortices and bodies on the forces of the actual body, (2) optimize arrangement of outside vortices and bodies for force enhancement or reduction, and (3) derive analytical force formulas once the flow field is given or known. A number of applications will be considered, including the leading edge vortex problem, impulsively started flow, multiple wings and falling of an elliptic plate. For instance, we will study aerodynamic forces and kinematics for a falling elliptic plate, for which there is interaction due to multiple vortex loops.

针对多点涡、涡生成和多物体流动问题，分析点涡之间、点涡与物体之间的相互干扰，导出各物体受力显式表达式，并最终表示为物体内部点涡与外部流场对物体内部诱导速度的关系。将每个物体所受的升力和涡诱导阻力表示为各该问题内部镜像涡与固定涡以及物体外部自由涡与外部其它物体对该物体内部各点诱导速度的显式函数。将每个物体的受力表示为该物体内部点涡强度与生成速率、涡脱落以及外部物体与外部点涡诱导作用的显式关系。对力的物理组成进行分解，包括固定涡升力机制（即经典的儒科夫斯基升力定理给出的机制）、诱导升阻力机制、涡脱落与涡生成机制等。参照升力线理论构造固定机翼、昆虫等扑翼和下落物体之类问题的三维效应修正。针对昆虫前缘涡问题、突然启动问题、多翼型问题和纸片下落等典型多点涡甚至多物体干扰问题给出解析受力表达式。研究椭圆形物体下落的一些规律，研究展弦比等特性对下漂角、下落速度和可能的动力学规律。

获得了多物体多点涡运动引起的气动力变化的一般表达式并通过若干经典流体力学问题进行了验证； 获得了小迎角和大迎角突然启动问题旋涡生成描述方法以及非定常气动力解析表达式并得到了数值计算的验证；提出了旋涡作用力地图，可以用于识别单个或者集中旋涡的位置、强度和方向对气动力的影响，找到了增强气动力的临界区域；将大迎角运动的气动力演化分解为可重复的力的释放、力的增强、失速和力的恢复四个阶段。这些研究结果不仅给出了深入分析旋涡运动对气动力演化影响的方法，而且揭示了若干重要规律，具有相应的学术与实际意义。