响应面方法在跨声速翼型气动优化设计中的应用研究

基于响应面方法进行了跨声速翼型的气动优化设计研究。通过采用分次优化、逐步逼近的方法有效地解决了应用响应面方法进行多变量优化设计时拟合精度较低的问题。首先进行了翼型的反设计来验证该方法的可靠性,然后进行了跨声速翼型减阻优化设计。流场控制方程均采用N-S方程。响应面模型采用完全二阶多项式来构造,试验点的选取满足D优化准则。优化设计算例表明:进行分次优化所构造的模型精度满足设计要求,优化结果误差均小于1%;方法实用有效,减阻设计中阻力系数减少了19.34%。

Improving Aerodynamic Optimization Design of Transonic Airfoils with Response Surface Methodology for Design Variables as Many as about Sixteen

Response Surface Methodology(RSM) has been used to improve successfully model precision for design variables as many as about ten~(1]).But if design variables higher than ten,say about sixteen,are needed,the quadratic polynomials can no longer satisfy precision requirement;higher polynomials are needed for design variables as many as about sixteen but they will bring almost prohibitive computational burden.We aim to solve this dilemma with using quadratic polynomials twice or thrice.In the full paper,we explain how to use quadratic polynomials repeatedly.Here we just give a briefing.First,we can divide the design space into several smaller design spaces.Then each design can be performed in a smaller design space until the results are good enough.In general two smaller design spaces are enough for transonic airfoil design with about sixteen design variables.For sixteen design variables,the design results obtained with using quadratic polynomials twice are:(1) the fitting errors are less than one percent;(2) the drag coefficient is reduced by 19.34 percent in drag-reducing design.