# A data-based approach for fast airfoil analysis and optimization

 Title A data-based approach for fast airfoil analysis and optimization Publication Type Conference Papers Year of Publication 2018 Authors Li, J, Bouhlel, MAmine, Martins, JRRA Conference Name 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference Date Published jan Publisher AIAA Conference Location Kissimmee, FL Keywords adjoint methods, airfoil design optimization, surrogate modeling Abstract Airfoils are of great importance in aerodynamic design, and there is a need for tools that can evaluate and optimize their performance. Existing tools are usually either accurate or efficient, but not both. This paper presents a tool that can analyze airfoils in both subsonic and transonic regimes in about one hundredth of a second, and optimize airfoil shapes in a few seconds. We use camber and thickness mode shapes derived from over one thousand existing airfoils to parameterize the airfoil shape, which reduces the number of design variables. More than one hundred thousand RANS evaluations associated with different airfoils and flow conditions $(M,\alpha)$ are selected in a well-defined way to obtain aerodynamic coefficients ($C_l ,\, C_d$ and $C_m$) and their gradients. The gradients for the RANS evaluations are computed using an adjoint method. This data is used to train a surrogate model that combines gradient-enhanced kriging, partial least squares (GE-KPLS), and mixture of experts. Two global models composed of dozens of GE-KPLS models are constructed in the subsonic and transonic regimes. These surrogate models provide fast aerodynamic analysis and gradient computation, which are coupled with a gradient-based optimizer to perform rapid airfoil shape design optimization. In a validating test of 2741 airfoils and 989 airfoils in the subsonic and transonic regimes, the mean differences of the surrogate models from RANS evaluations in the drag coefficient are 0.09 and 0.8 counts, respectively. We also validate the airfoil optimization for various cases by comparing with drag minimization based on direct RANS analysis. The largest differences in $C_d$ are 0.04 counts for subsonic cases, and 2.5 counts for transonic cases. This approach opens the door for interactive airfoil analysis and design using any modern computer or mobile device. URL https://doi.org/10.2514/6.2018-1383 DOI 10.2514/6.2018-1383 Citation Key Li2018