Hybrid inverse/optimization design method for rigid coaxial rotor airfoils considering reverse flow

Double-ended airfoils with round leading and trailing edges outperform conventional round-nose and sharp trailing-edge airfoils when used for the inboard part of a rigid coaxial rotor operating in forward flight, as reverse flow can occupy 80% surface of the retreating blade. However, aerodynamic design optimization for this kind of airfoils is challenging, since it is required to achieve drag reduction over a wider lift range in both forward and reverse flows but there is no method available currently. To address this problem, this article proposes an efficient hybrid inverse/optimization design method that combines inverse design and direct optimization within a surrogate-based optimization (SBO) framework. The weighted objective function consists of two components: prescribed pressure distributions and total drag. The resulting constrained optimization problem is solved by using kriging surrogate model and dedicated infill-sampling method. The proposed method is demonstrated by aerodynamic shape optimizations of a DBLN-526 airfoil and an elliptical airfoil and compared with direct optimization method. For DBLN-526 airfoil case, 7%–30% drag reduction is achieved in the range from zero lift to maximum lift and the optimum airfoil features better stall characteristics. For the case of elliptical airfoil of 40% thickness, significant drag reduction is achieved in both forward and reverse flows and the optimum airfoil features more robust aerodynamic performance at off-design Mach numbers. The results confirm that the proposed method outperforms the conventional direct optimization method and more practical for aerodynamic shape optimization of double-ended airfoils.