Natural laminar flow wing optimization using a discrete adjoint approach

Natural laminar flow is one of the most promising ways to reduce the drag of future aircraft configurations. However, there is a lack of efficient tools for performing shape optimization considering laminar-to-turbulent transition. This is in part because including crossflow instabilities in the optimization is challenging. This paper addresses this need by developing a discrete, adjoint-based optimization framework where transition is modeled considering both Tollmien and Schlichting waves and crossflow instabilities. The framework is based on a Reynolds-averaged Navier–Stokes computational fluid dynamics solver coupled with a transition simulation module externally by incorporating into the Spalart–Allmaras turbulence model through a smooth intermittency function. The transition simulation module consists of a laminar boundary-layer equations solver and a simplified stability analysis method based on the Drela–Giles method and the C1 criterion. A Jacobian-free coupled-adjoint method is used to compute the gradients of the transition prediction. Lift-constrained drag minimization of a transonic infinite span wing with 25∘ of sweep is performed. The optimizer successfully reduces the drag coefficient by 43.34%, owing to an extended laminar region on the wing surface, and finds a pressure distribution that strikes a balance between the Tollmien–Schlichting wave and crossflow instability transition mechanisms.