Fast Low-fidelity Wing Aerodynamics Model for Surrogate-based Shape Optimization

Variable-fidelity optimization (VFO) can be efficient in terms of the computational cost when compared with traditional approaches, such as gradient-based methods with adjoint sensitivity information. In variable-fidelity methods, the direct optimization of the expensive high-fidelity model is replaced by iterative re-optimization of a physics-based surrogate model, which is constructed from a corrected low-fidelity model. The success of VFO is dependent on the reliability and accuracy of the low-fidelity model. In this paper, we present a way to develop a fast and reliable low-fidelity model suitable for aerodynamic shape of transonic wings. The low-fidelity model is component based and accounts for the zero-lift drag, induced drag, and wave drag. The induced drag can be calculated by a proper method, such lifting line theory or a panel method. The zero-lift drag and the wave drag can be calculated by two-dimensional flow model and strip theory. Sweep effects are accounted for by simple sweep theory. The approach is illustrated by a numerical example where the induced drag is calculated by a vortex lattice method, and the zero-lift drag and wave drag are calculated by MSES (a viscous-inviscid method). The low-fidelity model is roughly 320 times faster than a high-fidelity computational fluid dynamics models which solves the Reynolds-averaged Navier-Stokes equations and the Spalart-Allmaras turbulence model. The responses of the high-and low-fidelity models compare favorably and, most importantly, show the same trends with respect to changes in the operational conditions (Mach number, angle of attack) and the geometry (the airfoil shapes).