Numerical Investigation on the Aerodynamic Design of Quadrotor Blades Operating in the Martian Atmosphere
Creators: name:  M. CARRENO RUIZ 
name:   D. D'AMBROSIO 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: FLIGHT PHYSICS
COMPUTATIONAL AERODYNAMICS
EXPERIMENTAL AERODYNAMICS

description: We present a numerical approach to the aerodynamic optimization of propeller blades for rotors working in flow regimes with Reynolds number smaller than 15,000. Considering gas density and viscosity, rotation speed, and rotor diameter, most of the rotary-wing falls in the so-called ultra-low Reynolds number regime (10$^3$Re10$^4$), while the tip region is in the lower range of the very-low Reynolds number regime (10$^4$Re10$^5$), where separation-induced laminar-turbulent transition may occur. Such conditions characterize rotor blades of Unmanned Aerial Systems (UAS) operating in the Mars\' atmosphere or at very high altitudes (30 km) in the Earth\'s atmosphere. The blade design procedure consists of a two-steps optimization process that includes an initial two-dimensional airfoil design analysis followed by three-dimensional simulations to achieve the chord and twist radial distributions necessary to define the blade geometry. The largest values of the Reynolds number range are likely to include separation-triggered laminar to turbulent transition. For this reason, we performed two-dimensional compressible Navier-Stokes simulations using both laminar and Reynolds-Averaged Navier-Stokes (RANS) models. We also included compressibility effects because low-temperature conditions and (for Mars) the small gas constant give a smaller-than-usual speed of sound, which, added to the high rotation speed needed to produce thrust in a low-density environment, results in a high subsonic Mach number. For these simulations, we used the commercial Computational Fluid Dynamics (CFD) code STAR-CCM+, and we employed its embedded Adjoint Navier-Stokes method to obtain optimal geometries for appropriate values of Mach and Reynolds numbers. We finally compared our optimized airfoils with other efficient geometries proposed in the literature [1,2] for similar operating conditions. To design the three-dimensional blade geometry, we used three tools with different fidelity levels, starting from the simplest Blade Element Momentum Method (BEM), going through the intermediate fidelity Free Vortex Wake Method (FVW), and ending with a complete Navier-Stokes simulation of the blades. To select the best performing geometries, we adopted an Evolutionary Algorithm (EA) that can be fully parallelized and avoids local optimums, which may occur in a rotor performance optimization process due to the high level of coupling between design and operation variables. Using low-fidelity simulation tools is necessary as the computational cost of performing an optimization strategy with full Navier-Stokes CFD simulations is computationally very expensive. As a final check, we compared Reduced Order Models (ROM) and full Navier-Stokes simulations to identify flaws and benefits of different numerical strategies. Since the optimal twist distribution provided by reduced order models might be considerably different[1,2] from the results of a full Navier-Stokes optimization, we used a three-dimensional Adjoint Navier-Stokes method to produce a further performance improvement taking into account three-dimensional effects that only complete CFD simulations can capture. The small aspect ratios required to obtain sufficient thrust in such low-density conditions and the three-dimensional flow that this would imply makes it unclear whether low fidelity tools based on lifting line theory can capture optimal solidity or not. For this reason, we repeated the Navier-Stokes-based optimization process for several chord distributions to verify the influence of rotor solidity on optimal blade performance. References [1] Herve Bezard, Thibault Desert, Jean-Marc Moschetta, and Thierry Jardin. Aerodynamic design of a Martian micro air vehicle. In EUCASS 2019, MADRID, Spain, July 2019. [2] Peter J Kunz. Aerodynamics and design for ultra-low Reynolds number flight. PhD thesis, Standford University, 2003.