基于高阶谱差分的扑翼面运动学数值优化

摘要

基于高阶谱差分（SD）格式的高成本效益的优化方法被用以优化扑翼面的运动学，从而达到最大推进效率。具体来说，基于梯度的优化算法与高阶谱差分的纳维-斯托克斯流动求解器被耦合用以研究一系列NACA 对称翼型的最优运动学。在此研究中，翼型做沉标和俯仰运动。数值优化在粗网格上进行。得到最优解后，在密网格上用高阶 SD 求解器捕获处于最优运动学状态下扑翼面的详细涡结构。提出的数值优化框架被用以研究翼型厚度，雷诺数和俯仰中心位置对最佳巡航飞行的影响。通过研究相关流场，气动力以及等效攻角（AOA）的变化，我们解释了与最佳扑翼面运动相关的流动物理特性。%A high-order spectral difference (SD)scheme based cost-effective optimization approach is proposed to optimize the kinematics of flapping airfoils for maximum propulsive efficiency.Specifically,a gradient-based optimization algorithm is coupled with a high-order SD Navier-Stokes solver to search for the optimal kinematics of a series of NACA 4-digit airfoils undergoing combined plunge and pitch motion on a coarse mesh.Then the high-order SD solver is used to capture the detailed vortex structures associated with the optimal kinematics of the flapping flight on a fine mesh.The proposed numerical optimization framework is used to study the effects of airfoil thickness,Reynolds number,and pitching pivot location for optimal cruise flight.The flow physics behind optimal airfoil oscillation is explained by examining the corresponding flow fields,aerodynamic forces and the variation of effective angle of attack.