VortexLatticeMethods()要点.ppt

Aerodynamics of 3D Lifting Surfaces through Vortex Lattice Methods 旋涡运动简介 旋涡运动简介 涡线 ——涡线是充满运动流体的旋涡场中所作的线，它具有这样的性质：在某瞬时该曲线上微团的旋转角速度向量都和曲线相切。 旋涡运动简介 旋涡运动简介 旋涡的诱导速度公式 ——毕奥-萨瓦公式 旋涡运动简介 涡与翼型的升力 大展弦比直机翼的低速气动特性 大展弦比直机翼的气动模型 升力线理论 Vortex Theorems Along a vortex line (tube) the circulation, ?, is constant. A vortex filament (or line) cannot begin or end abruptly in a fluid. The vortex line must be closed extend to infinity or end at a solid boundary. The circulation, ?, about any section is the vortex strength. An initially irrotational, inviscid flow will remain irrotational. Vortex Theorems A lifting surface a sheet of vortices A sheet of vortices can support a jump in tangential velocity (i.e. a force), while the normal velocity is continuous. This means you can use a vortex sheet to represent a lifting surface. Biot-Savart Law The Biot-Savart law states that the increment in velocity dV at a point p due to a segment of a vortex filament dl at q is: Case 1: The infinitely long straight vortex Case 2: The semi-infinite vortex Case 3: The finite vortex The Horseshoe Vortex The Horseshoe Vortex Boundary conditions on the mean surface The vortex lattice method uses an approximate boundary condition treatment. The boundary condition is used on a mean reference surface, rather than the actual surface. Selection of Control Point/Vortex Location Motivation To represent a lifting surface using the horseshoe vortex Questions where do you locate the vortex ? where do you locate a control point to satisfy the surface boundary condition ? Selection of Control Point/Vortex Location The vortex is located at the 1/4 chord point The control point is located at the 3/4 Selection of Control Point/Vortex Location Comments This is known as the “1/4 - 3/4 rule.” It’s not a theoretical law, simply a placement that works well and has become a rule of thumb. The 1/4 - 3/4 rule is widely used, and has proven to be sufficiently accurate in practice. The Classical Vortex Lattice Metho