基于NURBS方法的机翼气动外形优化

Aerodynamic Shape Optimization for Wing Based on Non-uniform Rational B-spline

飞行器气动外形优化就是将设计对象的空气动力学性能分析与最优化方法相结合,通过不断改变设计对象的外形,使其气动性能在满足一定约束条件下达到最优。气动外形优化是一个涉及几何参数化、动网格、流场计算和寻优算法的综合应用平台。随着计算流体力学(CFD)的发展以及高性能计算机的使用,气动外形优化在现代飞行器设计中的作用愈加重要。为此建立了基于非均匀有理B样条(NURBS)参数化方法的机翼气动外形优化平台。优化过程中采用弹性网格变形法,由雷诺平均Navier-Stokes方程组和Baldwin-Lomax代数湍流模型求解流场,并用离散伴随方法进行目标函数梯度求解,最后结合序列二次规划(SQP)方法进行优化迭代。通过对ONERA M6机翼在跨声速条件下进行优化分析,结果表明在保持升力系数和机翼容积不变,马赫数Ma=0.84、迎角α=3.06°时,优化后机翼表面压力系数有明显变化,上翼面λ激波明显减弱,相对于原始外形优化后机翼阻力系数减小0.002 5,降幅达13.1%;优化实例验证了该方法有效可行。

Aerodynamic design optimization is to find the optimum of aircraft aerodynamic performance under certain constraints by changing the shape of the designed object. It facilitates the design process by automating both the performance analysis and the optimization method. Aerodynamic design optimization is an integrated application of geometry parameterization, grid update, flow field solver and optimization method, and it has contributed to the design of aircraft with the maturity of computational fluid dynamics （OFD） and the progress of computer performance. This paper presents an aerodynamic wing shape optimization method based on non-uniform rational B-spline （NURBS）, in which the mesh deformation is used with a spring-based smoothing method. The Reynolds-averaged Navier-Stokes equations with an algebraic turbulence model of Baldwin-Lomax are used to solve the flow field, and a discrete-adjoint method inexpensively computes the sensitivities of the function with respect to design variables, to build the gradient of the objective function. Finally, an sequential quadratic pro- gramming （SQP） method is employed to find the optimum. An aerodynamic shape optimization is performed to minimize the drag of wing ONERA M6 at transonic Ma = 0.84 and α = 3.06°. As a result of the optimization, the pressure coefficient on the up-wing surface is changed obviously, and the λ shock wave is much reduced. The drag coefficient loses 25 drag counts, which means a 13.1% drag improvement with the constraints of the lift and volume. This application to an aerodynamic design optimization validates the system of optimization and design based on NURBS.