Airfoil optimization for rotors operating in the ultra-low Reynolds number regime

Ultra-low Reynolds number aerodynamics has gained significant attention in recent times, primarily due to the proliferation of micro-aerial vehicles and their utilization in low-density environments such as the Martian atmosphere and high altitudes in Earth's atmosphere. The Martian atmosphere presents a unique combination of low Reynolds numbers and high subsonic Mach numbers, necessitating the use of unconventional airfoil designs in this regime. This study focuses on optimizing airfoils for rotors operating in the compressible ultra-low Reynolds number regime. We demonstrate the capability of XFOIL, a panel method code incorporating an integral boundary layer formulation, to accurately predict airfoil loads when the flow remains attached. We determine the optimal camber and maximum camber positions by analyzing the four digits, two percent thickness, National Advisory Committee for Aeronautics XX02 airfoil family using XFOIL. Subsequently, we employ a multi-objective optimization approach, utilizing a Class Shape Transformation airfoil parameterization to maximize lift and minimize drag. We select several points from the resulting Pareto front and evaluate their performance through unsteady compressible Navier-Stokes simulations. Our findings reveal that incorporating sharp leading-edge variations in these airfoil designs enhances the peak efficiency by over 10%, primarily attributable to the development of laminar separation bubbles on the suction side of the airfoils. Importantly, these modified airfoils maintain favorable performance at low angles of attack.