## 2 Background
### The Significance of Rotor Interactions  
Precise quantification of the impact of rotor interactions is necessary to inform conceptual design choices. Aircraft designers must limit the overall size of their vehicles but also ensure that their rotors are operating with high efficiency. [PERSON] et al. performed experiments of small hovering rotors and used stereoscopic particle image velocimetry (PIV) to capture the induced interaction flow [27]. They found increased tonal and broadband noise with increasing rotor proximity, characterized by enhanced turbulent kinetic energy in the gap region. They found that, although the mean thrust was the same, the thrust fluctuations increased with proximity as well. [PERSON] et al. similarly conducted PIV measurements of side-by-side rotors and also found that increased rotor proximity leads to increased wake interactions, although acoustic measurements were not performed and the performance results were inconclusive [28].  
Some medium fidelity CFD simulations have captured reasonable interactional acoustics trends. For example, [PERSON] et al. used the nonlinear vortex lattice method in combination with the vortex particle method (VPM) to predict the noise of a quadrotor and showed a decrease in noise with rotor separation distance [29]. [PERSON] et al. used a boundary element method (BEM) to characterize the aeroacoustic signature of propeller arrays [30]. They found that the interactional noise caused by twin rotors greatly affected the directivity of the overall noise, with noise increases up to 50 dB, much greater than a simple pressure doubling. Broadband noise was not considered, and the findings were not backed up by experimental results.  
[PERSON] et al. compared URANS and the vortex particle method (VPM) approaches to rotor-on-rotor aerodynamics [24]. However, they used rather coarse time steps for their URANS simulations and used a compact source approximation for the acoustics. Theywere able to capture the first blade passage frequency (BPF) tone of the isolated rotor simulations well, but were unable to predict the increase in the higher harmonic tonal noise from the experiments in their URANS simulations. They did not include their high-fidelity broadband spectrum in their paper. On the other hand, [PERSON] et al. conducted hybrid URANS/LES simulations of inline counter-rotating propellers in hover and discovered a large increase in the broadband noise, compared to the single rotor and negligible change in the higher harmonics [31]. Again, experimental measurements were not available for comparison. There has also been extensive computational work studying the NASA eVTOL common reference models, but the experimental characterization of these models was not conducted [32; 33; 34; 35].  
In this research, a DES, a type of hybrid URANS/LES method, is used to further investigate aerodynamic interactions and their impact on noise. Accompanying experimental data are used for comparison. Isolated rotor measurements and simulations are conducted to capture the aerodynamics and aeroacoustics of a single rotor at various rotor speeds. Then, a single RPM is chosen and used to investigate dual rotors in both co-rotating and counter-rotating configurations. Their tip-to-tip spacing is gradually increased to explore the impact of their interactions on both performance and noise.