# Assessment of a Mid-Fidelity Numerical Approach for the Investigation of Tiltrotor Aerodynamics
## 3 Numerical Models
### Wing-Prorotor Numerical Model  
In order to better evaluate the capabilities of DUST in capturing the main aerodynamic features related to rotor/wing interaction for tiltrotor configurations, simulations were performed over a simplified numerical model made by the XV-15 proprotor described in Section 3.1 and a simplified rectangular wing, as suggested by the numerical work by [PERSON] [18]. The numerical model of the wing was built using a symmetric NACA 0023 airfoil at incidence \(\alpha=5^{\circ}\) instead of the cambered NACA 64A223 airfoil used for the XV-15 tiltrotor, as in the work by [PERSON] [18]. No sweep or dihedral was introduced to the wing model, while the full span of 9.8 m (386 inches) and the chord of 1.6 m (63 inches) were considered. The wing was modelled with surface panels, while the same numerical model built by lifting line elements for proprotor blades was kept for this configuration. The wake of both wing and proprotor was modelled by vortex particles. The goal of this activity was to provide a direct comparison between the DUST simulations and the CFD results that were obtained by [PERSON] [18]. Thus, the cruise condition at 220 kts with the proprotor operating at 517 RPM was considered in this preliminary study. A spatial dependence study on the wing mesh was performed with DUST by running simulations of the single-wing model in cruise with different surface panel densities. In particular, simulations were performed fixing the spanwise discretisation to 102 surface panels and changing the chordwise discretisation between 100 and 300 surface panels. This dependence study, as reported in detail in [47], shows that the use of 300 surface panels for chordwise discretisation leads to an error of the computed lift of the wing below 2% of the value obtained by CFD [18]. Thus, the latter spatial discretisation was considered for the wing model as a fair compromise between accuracy and limited computational effort. Figure 3 shows a picture of the numerical model built for the wing-prorotor system, including the reference systems that are used to discuss the numerical results. The origin of the wing reference system (\(X-Y-Z\)) is positioned at the midspan, while the origin of the radial coordinate (\(r\)) of the blades is positioned at the center of the rotor disk with the azimuthal angle of the blade \(\psi\) defined in Figure 3.  
A preliminary set of numerical simulations was performed with DUST for the single proprotor operating at 517 RPM for adjusting the collective pitch angle of the blades to trim the proprotor thrust to the value reported by CFD simulation in [18] for the same test case. Subsequently, the wing was added into the DUST simulations. This procedure allowed us to more clearly evaluate the aerodynamic interaction effects that were provided by the  
Figure 3: Layout of the numerical model of the wing/prorotor system; details of the surface mesh are shown in the zoomed inboard wing region.  
wing. All of the DUST simulations were advanced in time using the time discretisation selected for the single proprotor test case--i.e., 40 time steps for rotor revolution for a total simulation length of ten rotor revolutions. The developed wake for the wing-proprotor simulation in cruise consisted of around 18 thousands vortex particles.