Uncertainty-Based Design Optimization of NLF Airfoil Based on Polynomial Chaos Expansion

The high probability of the occurrence of separation bubbles or shocks and early transition to turbulence on surfaces of airfoil makes it very difficult to design high lift and high-speed Natural-Laminar-Flow (NLF) airfoil for high altitude long endurance unmanned air vehicles. To resolve this issue, a framework of uncertainty-based design optimization (UBDO) is developed based on the polynomial chaos expansion method. The \( \gamma { - }\overline{\text{Re}}_{\theta t} \) transition model combined with the shear stress transport \( k - \omega \) turbulence model is used to predict the laminar-turbulent transition. The particle swarm optimization algorithm and surrogate model are integrated to search for the optimal NLF airfoil. Using proposed UBDO framework, the aforementioned problem has been regularized to achieve the optimal airfoil with a tradeoff of aerodynamic performances under fully-turbulent and free transition conditions. The tradeoff is to make sure its good performance when early transition to turbulence on surfaces of NLF airfoil happens. The results indicate UBDO of NLF airfoil considering Mach number and lift coefficient uncertainty under free transition condition shows a significant deterioration when complicated flight conditions lead to early transition to turbulence. Meanwhile, UBDO of NLF airfoil with a tradeoff of performances under fully-turbulent and free transition conditions holds robust and reliable aerodynamic performance under complicated flight conditions.