Bayesian Forward Design Methodology for Laminar Transonic Airfoils with Cross Flow Attenuation at Large Sweep Angles

Drag reduction forms a key area of focus in aerodynamics with a significant emphasis on delaying the laminar to turbulent transition of boundary layers over the wing of aircraft. There is enough evidence to suggest that achieving such transition delays is particularly challenging for backward swept wings with large leading edge sweep angles, which give rise to crossflow and attachment line instabilities, in addition to the Tollmien-Schlichting waves. The sustenance of extended laminar flow regions at high sweep angles has been demonstrated in recent studies, by designing airfoils with specially curated leading edge profiles, which generate pressure distributions that can suppress crossflow. Such airfoils are called Crossflow Attenuating Natural Laminar Flow (CATNLF) airfoils. However, the design of such airfoils is presently restricted to inverse methodologies due to the inability of the conventional geometry parameterization techniques in representing the specialized leading edge profiles of CATNLF airfoils. The aim of this study is to illustrate that a parametric representation of CATNLF airfoils can be realized using Bezier curves, thereby enabling their forward multi-point design using gradient-free Bayesian optimization. The developed design framework in terms of geometry parameterization and optimization formulation is able to deliver airfoils that can sustain natural laminar flow up to around 50% chord length on the upper surface, with a leading edge sweep angle greater than 27 degrees at a Mach number of 0.78 and a Reynolds number of 20 million within a range of lift coefficients Cl = 0.5 ± 0.1, making them a suitable design choice for a medium-range transport aircraft.