基于NS方程的跨声速翼型多目标多约束优化设计

Multiobjective Optimization Design of Transonic Airfoils with Constraints Based on Navier-Stokes Equations

本文将粘性流场分析和数值优化方法耦合起来 ,发展了一种跨声速翼型设计方法 ,用以提高翼型在一个或多个设计点、在多种约束条件下的气动性能。由粘性流场分析程序计算得到的升力、阻力等气动参数构成目标函数 ,数值优化程序对其进行最小化。粘性流场分析采用了雷数平均N S方程 ,这比过去翼型设计中使用的全速势方程或Euler方程更能模拟流动的本质 ,因而设计结果的可靠性大大提高了。优化算法采用传统的拟牛顿法 (Quasi NewtonMethod)和序列无约束极小化方法 (SUMT)。算例研究表明 ,本文发展的跨声速翼型设计方法设计质量高 ,所需机时不多 ,有较大的工程应用价值。

A design method of transonic airfoils is developed which couples viscous flow analysis and numerical optimization to search for a airfoil geometry with improved aerodynamic performance at single or multiple design point, subject to specified constraints. Aerodynamic quantities such as lift,drag are computed by the flow solver for a certain configuration and are used in defining an objective function to be minimized by the optimizer. The flow solver is based on Reynolds averaged Navier Stokes equations which provide more accurate models of the flow field than previously employed full potential equation or Euler equations,so the reliability of optimization results is greatly enhanced.Classical Quasi Newton Method and Sequential Unconstrained Minimization Technique(SUMT) are adopted as optimization algorithms. Two examples are presented which demonstrate the method in this paper is very attractive for practical use because of its high design quality and reasonable computational cost.