## 3 Materials and Methods
### Computational Methodology
#### 3.3.1 CREATE-AV Helios  
The simulation framework used for the CFD portion of this study is the Department of Defense (DoD) High Performance Computing Modernization Program (HPCMP) code, CREATE-AV Helios version 11.0 [36; 37; 38]. Helios is an overset code developed by the U.S. Army Technology Development Directorate specifically for rotorcraft. Although it was originally used for helicopters, it was recently validated for small rotorcraft on the scale of drones and UAVs [12; 23; 39; 40]. For this work, the Reynolds-averaged Navier-Stokes (RANS) equations are solved in the inertial frame, using the off-body solver SAMCART coupled to the near-body solver mStrand. A rendering of the overset mesh system near the blade tip is shown in Figure 2. A detached eddy simulation (DES) approach was used for the simulations in this study; therefore, the turbulent scales are resolved using LES when the grid is sufficient, and URANS is used otherwise [9].  
SAMCART is a Cartesian grid solver that implements a 5 th order central difference scheme with 4 th order viscous terms for its spatial discretization and 2 nd order backward differentiation in time. mStrand is a multi-strand finite volume solver that automatically  
Figure 1: Experimental set-up of the acoustics measurements. Top view of the azimuthal array, which characterizes the azimuthal directivity (**left**). The linear array was set up to characterize the polar directivity (**right**).  
Figure 2: Close-up view of a slice of the Helios overset mesh system. The near-body volume mesh, whose solution is computed by mStrand, is colored blue and body-fitted around the grey APC rotor. The off-body volume mesh, colored in red, is structured in nature and solved by SAMCart. The solution in the overlap region is automatically interpolated.  
generates the volume mesh during runtime, based on the surface discretization. mStrand uses a vertex centered approach with 2 nd order spatial terms, and similarly uses 2 nd order backward differentiation in time [41; 42]. Other researchers have used NASA's OVERFLOW for the near body, which is capable of using a 5 th order spatial scheme with 2 nd order discretization for the viscous terms [10; 11; 32; 33; 35; 43; 44; 45; 46; 47; 48; 49]. However, the mesh generation procedure for OVERFLOW is more complicated than that of mStrand, which automatically generates the volume mesh [50]. Therefore, there is a trade-off, and we have selected mStrand for this study. The domain connectivity is handled by PUNDIT, described in further detail by [PERSON] et al. [51]. The Spalart-Allmaras (SA) turbulence model was chosen for this study, due to its robustness and accuracy, and is implemented in both the near body and off body [52]. Although laminar-turbulent transition models have been shown to improve torque predictions for low Reynolds number rotors, they are not used because they were also shown to lead to poor thrust predictions and increased computational cost [12].  
The simulations were set up to match the isolated rotor, co-rotating dual rotor, and counter-rotating dual rotor configurations of the experiments. For all of the simulations, a time step of 0.25\({}^{\circ}\) azimuth was selected, corresponding to 1440 time steps per rotor revolution, based on prior rotorcraft CFD research [12; 39; 42; 53]. Adaptive mesh refinement (AMR) was turned on in the off-body solver after two rotor revolutions. A total of 10 rotor revolutions were simulated, with the first 5 being used to allow the starting vortex to propagate away and properly develop the inflow. The acoustic calculations were then based on the last five. The results of simulations conducted in the present work will be referred to as the Helios results.