DNS-based optimisation of airfoils for Martian helicopters using PyFR

The Martian atmosphere has a lower density and lower speed of sound compared to Earth. These conditions require Martian rotor blades to operate in a low-Reynolds-number (1,000 to 10,000 based on chord) compressible regime, that is atypical for terrestrial helicopters. Non-conventional airfoils with sharp leading 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 such airfoils. However, flow over the airfoils is characterized by unsteady roll-up of coherent vortices, and transition to turbulence. Hence RANS/URANS solvers may have limited predictive capability, especially at higher angles of attack. The current study overcomes this limitation by undertaking optimization using high-order accurate Direct Numerical Simulations (DNS) via the compressible flow solver in PyFR. Specifically, a triangular airfoil is optimized at an angle of attack of $\alpha = 12^{\circ}$ with spanwise-periodic DNS. Multi-objective optimization is performed to maximize lift and minimize drag, yielding a Pareto front of non-dominated airfoils. Q-criterion isosurfaces, lift coefficient spectra, pressure coefficient distributions, velocity line integral convolutions and skin friction distributions are analyzed for airfoils on the Pareto front to elucidate the flow physics that yield optimal performance. The optimized airfoils achieve up to a 48% increase in lift and a 28% reduction in drag compared to a reference triangular airfoil previously tested experimentally in the Mars Wind Tunnel at Tohoku University. The work constitutes the first use of DNS for aerodynamic shape optimization.