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

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 model for 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.