# Assessment of a Mid-Fidelity Numerical Approach for the Investigation of Tiltrotor Aerodynamics
## 5 Conclusions  
A thorough assessment of the capabilities of a mid-fidelity numerical approach to evaluate the aerodynamic performance and flow physics of a tiltrotor was performed in the present work. Indeed, the results of the numerical simulations performed using the novel mid-fidelity aerodynamic solver DUST based on the vortex particle method were thoroughly compared with the URANS simulation data available in the recent literature for steady flight configurations of the XV-15 tiltrotor aircraft with increasing complexity.  
The outcomes of the present work clearly indicate the limits and capabilities of mid-fidelity aerodynamic numerical solvers with respect to the URANS solvers for the evaluation of the aerodynamic performance and interactional flow features of complex VTOL aircraft configurations. In particular, the quite good agreement with the CFD results that were obtained over the different analysed flight conditions indicates that mid-fidelity solvers based on physics-based vortex particle methods are suitable for investigating the main interactional flow features that characterise tiltrotor aerodynamics. The thorough assessment provided in this work opens a novel scenario for aerospace scientific and industrial communities. Indeed, the greatly lower computational effort that is required to run the simulations with respect to CFD indicates that mid-fidelity solvers, such as DUST, represent a valuable tool that can be used in the preliminary design of novel VTOL aircraft architectures, such as tiltrotors, which require a large number of configurations to be investigated to cover the different stages of their flight mission.  
Conceptualisation, A.Z., V.M.; methodology, A.S., M.P., A.Z.; software, A.S., M.T.; validation, A.S., M.P., M.T.; formal analysis, M.P.; investigation, A.S., M.P.; resources, A.S., M.P.; data curation, A.S., M.P., A.Z.; writing--original draft preparation, A.Z.; writing--review and editing, A.Z.; visualisation, A.Z.; supervision, A.Z., V.M.; project administration, A.Z., V.M.; funding acquisition, V.M. All authors have read and agreed to the published version of the manuscript.  
This research received funding from the Clean Sky 2-H2020 Framework Programme, under the grant agreement N.885971, FORMOSA project.  
Not applicable.  
The data can be obtained upon request from the corresponding author.  
The authors declare no conflict of interest.  
The following nomenclature and abbreviations are used in this manuscript:  
\(a\)  speed of sound [m/s]  
\(c\)  local blade chord  
\(C\)  blade chord-wise force  
CFD  Computational Fluid Dynamics  
\(C_{p}\)  pressure coefficient \(=\Delta P/(0.5\,\rho R^{2}\Omega^{2})\)  
\(C_{P}\)  power coefficient \(=P/(\rho\pi R^{5}\Omega^{3})\)  
\(C_{Q}\)  torque coefficient \(=Q/(\rho\pi R^{5}\Omega^{2})\)  
\(C_{T}\)  thrust coefficient \(=T/(\rho\pi R^{4}\Omega^{2})\)  
\(H\)  rotor H-force [Ibf]  
\(M\)  blade pitching moment  
\(M\)  freestream Mach number \(=V_{\infty}/a\)  
\(M^{2}C_{c}\)  blade sectional chord-wise force coefficient \(=C/0.5\,\rho a^{2}c\)  
\(M^{2}C_{m}\)  blade sectional pitching moment coefficient \(=M/0.5\,\rho a^{2}c^{2}\)  
\(M^{2}C_{n}\)  blade sectional normal force coefficient \(=N/0.5\,\rho a^{2}c\)  
\(N\)  blade normal force  
\(N_{rev}\)  number of rotor revolutions  
\(p\)  rotor power [hp]  
\(Q\)  rotor torque [ft-bf]  
\(r\)  radial coordinate along the blade  
\(R\)  rotor radius [m]  
\(T\)  rotor thrust [Ibf]  
\(u\)  freestream velocity component [m/s]  
URANS  Unsteady Reynolds Averaged Navier-Stokes  
\(v\)  spanwise velocity component [m/s]  
\(V_{\infty}\)  freestream velocity [m/s]