Natural Laminar-Flow Airfoil Optimization Design Using a Discrete Adjoint Approach

Natural laminar-flow wings are one of the most promising technologies for reducing fuel burn and emissions for commercial aviation. However, there is a lack of tools for performing shape optimization of wings based on computational fluid dynamics considering laminar-to-turbulent transition. To address this need, we develop a discrete adjoint-based optimization framework where transition is modeled. The core of this framework is a Reynolds-averaged Navier-Stokes solver that is coupled with a simplified e(N) method to predict Tollmien-Schlichting and laminar separation-induced transition that consists of a laminar boundary-layer code and a database method for flow stability analysis. The transition prediction is integrated with a Spalart-Allmaras turbulence model through a smoothed intermittency function, which makes it suitable for gradient-based optimization. A coupled-adjoint approach that uses transpose Jacobian-vector products derived via automatic differentiation computes the transition prediction derivatives. Lift-constrained drag minimizations of airfoils for a single-point design and a multipoint design problem are performed. The results show that the optimizer successfully reduces the drag coefficient by increasing the extent of laminar flow. The multipoint optimization formulation produces an airfoil with a significant amount of laminar flow that is maintained at several flight conditions. The proposed methods make it possible to perform aerodynamic shape optimization considering laminar-to-turbulent transition in airfoil optimization.