Journal Article

Natural Laminar Flow Wing Optimization Using a Discrete Adjoint Approach


Y. Shi, C. A. Mader, and J. R. R. A. Martins


Structural and Multidisciplinary Optimization, 64541–562, 2021



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.