基于Navier-Stokes方程跨声速翼型和机翼气动优化设计

Aerodynamic optimization design of transonic airfoil and wing based on Navier-Stokes equations

将响应面方法引入到气动优化设计上来,进行了基于N-S方程跨声速翼型、机翼气动优化设计。通过去掉完全二阶多项式响应面模型中的二阶交叉项,大大减少了构造高维响应面模型所需要的计算量。合理地选择优化设计空间,保证了构造的响应面模型具有较高精度。跨声速翼型、机翼减阻优化算例结果表明该方法能有效地适用于气动优化设计问题,设计质量高,方法实用可靠,有较高的工程应用前景。

Aerodynamic Shape Optimization （ASO） technology based on Computational Fluid Dynamics （CFD） becomes a very active object in the CFD field. A Response Surface Methodology （RSM） for ASO using the compressible Reynolds-Averaged Navier-Stokes （RANS） equations is implemented and tested. The flow solver is based on RANS equations which provide more accurate models of the flow field, than Euler equations previously employed, so the reliability of optimization results is greatly enhanced. In the past work the full quadratic polynomials are employed to construct RS modelfor ASO problem. The number of function evaluations （CFD analysis, in our cases） required for a full quadratic polynomials RS model increase with the square of the number of design variables, seriously preventing its use in high-dimensional design optimization especially using RANS. In contrast, the proposed modification to the RS model which cancel the second-order cross items of the full quadratic polynomials can greatly reduce the computation cost, and can approximate the original function, without significantly sacrificing the accuracy of the approximation when the range of design variables are carefully selected. Design cases, including drag minimization for transonic airfoil and wing are performed. The result indicated that the method can be effectively used to construct high accuracy RS models for ASO problem in which the fitting errors are less than two percent, and can be successfully applied to improve aerodynamic performance of transonic airfoil and wing at single design point, subject to specified constrains. This method is utility and valid, and will be very attractive for practical use.