基于目标环量分布的机翼减阻反向设计

Drag-reduction inverse design of wings based on lifting-line theory

为了优化直升机升阻比,研究了飞机设计过程中减小诱导阻力的措施,提出了一种机翼几何扭转角的反向设计方法。该方法通过确定目标升力分布形式,对沿翼展方向选取的设计点进行几何扭转角设计,实现目标分布。基于升力线理论,建立用傅里叶正弦级数表示的升力线理论积分微分方程的矩阵表示形式,编制了低速平直机翼的气动力、气动载荷分布的计算程序和几何扭转角的反向设计程序。最后,基于目标环量分布获得了几何扭转机翼,并通过程序预测和数值模拟方法对优化结果进行了仿真。计算结果表明:设计后的几何扭转机翼展向环量分布达到目标椭圆分布形式,几何扭转机翼诱导阻力减小了17.07%,总阻力减小了15.43%,计算状态升阻比提高了6.5%。该方法对选取控制剖面进行设计,可实现性较强,具有一定工程应用价值。

The way how to reduce the induced drag in an aircraft design was researched and an inverse design method of geometric twist for the aircraft design was proposed to optimize its ratio of lift to drag. By defining the target circulation distribution, the method designed the geometric twists for controlled sections along the wing spanwise to implement the target distribution. A matrix expression for the integro-differentiat equations of Prandtl＇s lifting-line theory described by Fourier sine series was established. Then, the aerodynamic calculation, aerodynamic spanwise distribution calculation and geometric twist angle inverse design were programmed and a geometric twist wing was designed to achieve elliptical spanwise distribution. Finally, the optimized results were simulated by the forecast of program and Computational Fluid Dynamic （CFD）. The simulation results indicate that the lift spanwise distribution of twisted wing is elliptic, the induced drag and total drag are decreased by 17.07% and 15.43%, respectively, and the ratio of lift to drag is improved by 6.5%. This method aims at controlled sections, shows better realizability, and gives out a reference for engineering applications.