# Assessment of a Mid-Fidelity Numerical Approach for the Investigation of Tiltrotor Aerodynamics
## 3 Numerical Models  
### Proprotor Numerical Model  
The numerical activity started with the modelling of the single proprotor of the XV-15 tiltrotor, because, owing to the availability of the experimental results concerning this configuration in hover, this test case was used to validate DUST simulation parameters that are therefore used for the analysis of the full aircraft. With this aim, the results from the experimental activity conducted on the full-scale XV-15 single proprotor equipped with metal blades in hover were considered for validation. The experimental campaign took place at the Outdoor Aerodynamic Research Facility (OARF), as described in the work by [PERSON] et al. [39]. The experimental data are collected in the work by [PERSON] et al. [40], reporting an error in the measurements of the collective pitch of \(4^{\circ}\). Therefore, the data that are presented in the following have been corrected accordingly. [PERSON] [41] reported the whole set of experimental data measured in hover in 2017 in a more modern and legible document. The blade of the XV-15 proprotor was modelled according to the geometry described in [39; 42]. Table 1 reports the main characteristics of the proprotor that are used in the experiments, while Table 2 reports the airfoils distribution used for the blade geometry. A numerical model of the full-scale XV-15 right-hand proprotor was built for DUST simulations while considering the airfoil geometry, chord, twist, sweep, and dihedral distributions reported in [39]. Each of the three blades was modelled using lifting line elements that included the viscosity contributions to aerodynamic loads through tabulated sectional aerodynamic data. The tabulated data of the blade airfoils were computed by XFOIL simulations [43], before the stall angle of attack. The two-dimensional aerodynamic load curves were corrected to be extended to the \(\pm 180^{\circ}\) range of angles of attack using the methods that are described in [44; 45]. Time and spatial dependence studies were performed for the single proprotor test case in hover, with the blade collective pitch angle set to \(\theta=11^{\circ}\). This value was selected because it is similar to the blade collective pitch angle of the full-vehicle in hover condition, as reported in [46]. Thus, numerical simulations were performed with DUST, fixing the spatial discretisation to 20 lifting line elements for each blade and changing the time discretisation of the simulation between 20 and 80 time steps throughout a length of ten rotor revolutions (\(N_{rev}\)). This time dependence analysis shows that the average thrust and torque coefficients that were obtained over the last two revolutions change negligibly with a time discretisation finer than \(9^{\circ}\) for the blade azimuthal angle for each rotor revolution (40 time steps). Therefore, a spatial dependence analysis was performed, fixing the time discretisation of the simulations to 40 time steps for the rotor revolution and changing the number of lifting line elements between 20 and 70 to model each of the three blades. The simulation results show negligible variations in the thrust and torque coefficients, increasing the spatial discretisation over 35 lifting line elements. Consequently, the time and spatial discretisations that were outlined by the dependence analysis were used for the validation of the numerical model by comparison with the experiments. The complete description of the dependence studies is reported in [47]. Thus, simulations with DUST were performed for the XV-15 full-scale proprotor, reproducing the hover condition and the sweep of blade collective pitch angles reported in [39]. The numerical simulations were advanced in time with a discretisation of \(9^{\circ}\) of the blade azimuthal angle for each rotor revolution, while each blade was modelled using 35 lifting line elements.