基于面元法的三维机翼数值设计

利用一种数值迭代方法设计出具有给定目标压力分布形式和环量及厚度分布的三维机翼.取一初始机翼,应用考虑尾涡衰减及卷曲的面元法计算三维机翼的流体动力性能,对机翼几何形状进行小的扰动并计算由此引起的压力变化,形成雅可比行列式,求解出几何修正因子以改变机翼几何形状,多次迭代后得到具有目标压力分布形式的机翼.再由给定的环量及厚度分布修改目标压力,重新设计机翼,最后得到符合设计要求的三维机翼.重点讨论了数值设计中尾涡模型、目标压力分布形式、几何控制点对设计结果的影响,及如何加快计算收敛.算例分析表明,设计方法收敛快速、有效可行,计及尾涡衰减及卷曲能够得到更准确的设计结果,目标压力分布形式和几何控制点的选取决定了设计机翼的光顺性.

Numerical design of three-dimensional wing based on surface panel method

A numerical method was presented to design the three-dimensional wing with a target pressure distribution form and a specified circulation and thickness distribution. The surface panel method with roll-up and attenuation wake model was used to calculate the hydrodynamic characteristics of the wing. The geometry of an original wing was changed in a small range and due to this change, the pressure increment was calculated. From the obtained Jacobian matrix, the geometrical correctors were derived. The original wing was modified to form a new one. By iterative calculation the wing with the initial target pressure distribution was designed. By correcting the initial target pressure distribution with a specified circulation and thickness distribution and repeating the design procedure, the three-dimensional wing was obtained which met all conditions. The impact of wake model, pressure distribution form and geometric control points on the design results were discussed, as well as the way to accelerate convergence. Sample designs were performed to demonstrate the fast convergence, effectiveness and robustness of the procedure. The analysis of design results shows that using roll-up and attenuation wake model can increase the designing accuracy and that the pressure distribution form and geometric control points are important to the smoothness of the designed wing.