Hybrid inverse/optimization design approach for transonic natural-laminar-flow airfoils

Inverse design and direct optimization are representative methods for aerodynamic design of natural-laminar-flow (NLF) airfoils. The inverse method usually pursues the shape whose pressure distribution best matches prescribed “target pressure distribution”, while the optimization method often directly explores minimum drag subject to aerodynamic and geometric constraints. This paper develops a hybrid inverse/optimization design approach to take the advantages of both methods. It is formulated as a normalized minimization of two objectives for inverse design and direct optimization, respectively. The first objective is defined as a squared error between designed pressure distribution and target distribution, which is prescribed over part of airfoil surface; the second objective is total drag or any other integrated quantities. A surrogate-based optimizer is employed to solve the constrained optimization problem, whose objective and constraint functions are evaluated by a Reynolds-averaged Navier-Stokes flow solver featuring automatic transition prediction. First, the developed method is validated by design of a NLF airfoil at a single design point Ma=0.72, Re=. Then, it is extended to multi-point design in order to improve the offdesign aerodynamic performance Ma=0.75. It is shown that the developed method can handle multiple constraints at multiple design conditions, while the useful experience of a designer can be introduced by partially prescribing target pressure distribution over the airfoil.