Effective robust design of high lift NLF airfoil under multi-parameter uncertainty

The high probability of developing shock waves and occurring separation bubbles on one or both surfaces makes it very difficult to design the high-performance transonic high lift natural-laminar-flow (NLF) airfoil at low Reynolds number. To solve this problem, a framework of effective robust design optimization (RDO) is developed based on an adjusted polynomial chaos expansion (PCE) method. The adjusted PCE method can provide accurate uncertainty quantification and have less computational cost compared with Monte Carlo simulation. The γ-Re‾θt transition model is combined with the shear stress transport turbulence model to predict the transition region for a laminar-turbulent boundary layer. The Kriging model and global optimization algorithm are integrated to optimize NLF airfoil. The result of deterministic design is proved to be ill-posed and suffering from the drastic increase of drag coefficient at off-design points. The NLF airfoil of RDO only considering Mach number uncertainty shows a lift plateau resulting from separation bubbles on the upper surface when angle of attack exceeds the design point. The NLF airfoil of RDO under both Mach number and lift coefficient uncertainty shows robust performance over a range of flight conditions. These results demonstrate that the proposed framework of RDO considering multi-parameter uncertainty can effectively solve the abovementioned design difficulty.