NFFD控制点分布对气动外形优化的影响

Effects of NFFD control points distribution on aerodynamic shape optimization

基于非均匀有理B样条的自由型面变形(NFFD)技术具有对变形对象普适性和控制点影响区域局部性的特点,广泛应用于气动外形优化。本文通过扩展控制体和合理布置外侧控制点,实现了NFFD技术在参数化曲面并改变曲面形状时,同步变形控制体内的表面网格和空间网格,并从理论上保证了控制体边界内外的网格协调。基于离散伴随方法求取梯度,分别采用拟牛顿(QN)法和序列二次规划(SQP)优化方法,通过从初始翼型NACA0012到标准翼型EH1590的反设计,研究了NFFD控制点数量和分布对设计结果的影响。在某飞翼标模单点全机升阻比优化应用中,改进控制点分布后获得了更高的升阻比,收敛速度显著提高。

The NURBS based free-form deformation （NFFD） , which is universal for representation of ob- ject geometry, and whose control point influence zone is local for geometry deformation, is used widely for aer- odynamic shape optimization. By extending the control volume and locating the outer control points appropri- ately, NFFD is used to parameterize the surface, deform the surface grid and volume grid in one single process. The grid cells both inside and outside control volume are preserved consistent theoretically after shape deformation. With the gradient of object function calculated by discrete adjoint method, both the quasi-Newton （QN） and sequential quadratic programming （SQP） optimization techniques are applied to inverse airfoil de- sign from the initial airfoil, NACA0012, to the standard flying-wing airfoil, EH1590. The effects of the num- ber and distribution of control points on optimization result are discussed. In the case of the lift-to-drag ratio optimization for a whole aircraft with flying-wing in a single design state, the convergence speed is improved obviously and higher lift-to-drag ratio is obtained by improving the distribution of control points.