Optimization of Triangular Airfoils for Martian Helicopters Using Direct Numerical Simulations

Mars has a lower atmospheric density than Earth, and the speed of sound is lower due to its atmospheric composition and lower surface temperature. Consequently, Martian rotor blades operate in a low-Reynolds-number compressible regime that is atypical for terrestrial helicopters. Nonconventional airfoils with sharp edges and flat surfaces have shown improved performance under such conditions, and second-order-accurate Reynolds-averaged Navier-Stokes (RANS) and unsteady RANS (URANS) solvers have been combined with genetic algorithms to optimize them. However, flow over such airfoils is characterized by unsteady roll-up of coherent vortices that subsequently break down/transition. Accordingly, RANS/URANS solvers have limited predictive capability, especially at higher angles of attack where the aforementioned physics are more acute. To overcome this limitation, we undertake optimization using high-order direct numerical simulations (DNSs). Specifically, a triangular airfoil is optimized using DNSs. Multi-objective optimization is performed to maximize lift and minimize drag, yielding a Pareto front. Various quantities, including lift spectra and pressure distributions, are analyzed for airfoils on the Pareto front to elucidate flow physics that yield optimal performance. The optimized airfoils that form the Pareto front achieve up to a 48% increase in lift or a 28% reduction in drag compared to a reference triangular airfoil studied in the Mars Wind Tunnel at Tohoku University. The work constitutes the first use of DNSs for aerodynamic shape optimization.