## 4 Validation against Measurements  
### Hover Flight Simulations Outside the Ground Effect (OGE)  
The wind tunnel test case in which the rotor hovers at \(Z/R=4\) is considered as the OGE case. The measured as well as the predicted thrust values of the OGE case are shown in Table 1. Despite their many differences, both numerical methods (HoPFlow and GenUVP) predict well the thrust. The two prediction methods are based on the same airfoil polars in order to calculate the loading, which explains their agreement [30]. Figure 7 shows a snapshot of the OGE flow field of the hovering rotor as computed by HoPFlow after 10 rotor revolutions. Vectors and velocity contours are illustrated over a vertical plane that passes through the center of the rotor. The black box in the plot indicates the extent of the CFD grid that covers the blades. Noticeable is the continuity of the predicted flow field, in particular in the vicinity of the CFD grid boundary, which indicates that the coupling of the Eulerian method (solved within the CFD grid) with the Lagrangian method (solved over the whole computational domain) is performed in a consistent manner. Even though the actuator line model accounts for the blades as body forces that alter the momentum balance of the free flow, the model consistently reproduces the rotor wake flow in contrast to actuator disk method. This is mainly due to the fact the body forces are applied in the rotating frame of the blade and not on fixed annular elements that neglect the blades rotation as in actuator disk method. Figure 8 illustrates wake vorticity iso-surfaces at the early stages of the wake development. The figure suggests that the actuator line model captures the trailed vorticity released by the tips and roots of the blades. In Figure 9 the wake vorticity after 10 revolutions is shown. Trailed vorticity can still be recognized near the blade tips. However, in this hover case, due to the low convection velocity, wake \begin{table}
\begin{tabular}{c c c} \hline \hline
**Measured Thrust Coefficient** & **Predictions GenUVP** & **Predictions HoPFlow** \\ \hline
0.007270 & 0.007290 & 0.007285 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: OGE thrust coefficient comparison of measured data against predictions (convergent values after 10 rotor revolutions). Figure 5: CFD mesh cut at a specific radial station of the blade. Figure 6: CFD mesh around the actuator line and the ground. spirals remain closely packed and strongly interact with each other producing thus the contracting shear layer of the far wake and the torus shape starting vortex ring. A similar wake pattern is obtained in the Genuvp free wake simulation (not shown in the plots). In Figure 7, wake velocities over an axi-symmetry plain are shown. The wake vortex ring travels downstream with an average velocity of 3-4 m/s (after 10 rotor revolutions the ring has traveled 1D downwards). This ring starts to form at the very beginning of the simulation as a result of the interaction of the starting shed vortices emitted by the  
Figure 8: Trailing tip and root vortices at an early stage of the simulation. Figure 7: Velocity magnitude and vectors of the OGE case over an axi-symmetry plane (snapshot at the end of the 10 th period). Figure 9: Trailing tip and root vortices after 10 rotor revolutions. different blades. Moreover, the contracting jet flow that develops under the rotor disk is also visible in the flow field plot. As expected, the rotor inflow velocity varies along the blade span and obtains its maximum value within the range 70-95% of the rotor radius. In this radial range, local blade thrust also obtains its maximum value. The absence of the fuselage, hub and rotor mast, justify the hole in the flow field appearing close to the rotor center. The absence of aerodynamic loading leads to a flow field that appears to be almost stagnant in this region.