Aerodynamic shape optimization at low Reynolds number using multi-level hierarchical Kriging models

The aerodynamic performance characteristics of an unmanned aerial vehicle airfoil and wing are optimized in the low Reynolds number regime using a variable-fidelity Multi-Level Hierarchical Kriging (MHK) surrogate modeling framework. This methodology employs aerodynamic data obtained from computational grids of varying grid resolution. This approach results in an efficient framework for optimizing expensive aerodynamic functions with the aid of lower fidelity data. The MHK-based optimization framework is first applied to enhance the aerodynamic properties of an Eppler E214 airfoil. The endurance factor of the airfoil is improved by 28%. Next, the aerodynamic characteristics of a small unmanned aerial vehicle wing is optimized. The endurance factor of the optimal wing is improved by 12.5%, with a substantial 45 drag count reduction. The optimal wing is of a swept wing design with a leading edge sweep of 13.6°. The evolution of a swept wing as the optimal wing design is an interesting outcome of the present study. Though the effect of wing sweep is well studied in high-subsonic and supersonic flows, its effect in the incompressible low Reynolds number regime is quantified in the present study. The wing sweep increases the suction on the outboard portion of the wing leading to a higher lift coefficient of the optimal wing. Further, the drag coefficient of the optimal wing is also reduced compared to the baseline wing. Much of this drag reduction comes from the reduction in the pressure drag component. Thus the wing sweep not only increases the lift coefficient, but also decreases the drag coefficient. This leads to a significant increase in the lift-to-drag ratio and the endurance factor of the optimal wing design. The present results demonstrate the optimization efficiency of the MHK modeling approach in the sensitive low Reynolds number regime.