The aerodynamic design optimization of an airfoil is carried out at a transitional low Reynolds number in the framework of multi-fidelity surrogate modeling. Two multi-fidelity surrogate-based optimization methodologies are proposed. The first method involves the co-Kriging surrogate model with prediction-based high-fidelity model update strategy. The second method uses the Kriging model of the low-fidelity function, and subsequent co-Kriging modeling with high-fidelity infills done using the gradient-free trust-region approach. The high-fidelity solutions are obtained by solving the Reynolds-averaged Navier-Stokes equations with the flow transition modeled by the γ-Re_θ model. The low-fidelity solutions are obtained by a panel code in conjunction with the e^N method. The proposed optimization methodologies are applied to two different objective functions in the transitional low Reynolds number regime, namely, (i) maximization of lift coefficient, and (ii) maximization of endurance factor. Significant improvements in each of the objective functions are obtained using both these methodologies.

在多保真替代模型的框架内，在过渡低雷诺数下进行了翼型的空气动力学设计优化。提出了两种基于多保真代理的优化方法。第一种方法涉及协同克里格代理模型与基于预测的高保真模型更新策略。第二种方法使用低保真度函数的Kriging模型，然后使用无梯度信任区域方法完成具有高保真填充的后续共同Kriging建模。高保真的解决方案通过求解雷诺平均Navier-Stokes方程与由建模的流动过渡获得γ -再_θ模型。低保真解决方案是通过面板代码结合e^N法。所提出的优化方法应用于过渡低雷诺数体系中的两个不同的目标函数，即（i）升力系数最大化，和（ii）耐力因子最大化。使用这两种方法都可以显着改善每个目标函数。