## 4 Validation against Measurements
### Hover Flight Simulations in IGE Flight Conditions
The development of the boundary layer creates a vertical displacement effect (an upwards transpiration velocity related to the displacement thickness of the boundary layer) which affects the shape of the vortex ring. The distortion of the vortex ring in the viscous modeling option begins earlier than in the inviscid one (already at the end of the 3 rd revolution). The reason for that is twofold: (i) the ring in the viscous option travels downwards with a higher velocity due to higher loading and (ii) it interacts with the boundary layer of the ground. At the end of the 4 th period, the thickness of the boundary layer has further increased while a stronger interaction with the vortex ring is observed. The cross section of the vortex ring obtains an elliptical shape. As a result of getting closer to the ground, its interaction with the boundary layer on the ground gets stronger. The outer edge of the ring is closer to the edge of a thicker boundary layer as compared to the inner edge. Transpiration velocities are therefore higher over the outer edge of the ring and the ring appears to rotate around its axis. At the end of 6 th and 10 th revolution, the vortex ring moves upwards and away from the ground as if it rebounds \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Period** & **[Z/R] Inviscid** & **[r/R] Inviscid** & **[Z/R] Viscous** & **[r/R] Viscous** \\  & **Wall** & **Wall** & **Wall** & **Wall** \\ \hline
1 st & 0.98 & 1.02 & 0.985 & 1.02 \\
2 nd & 0.80 & 1.08 & 0.79 & 1.07 \\
3 rd & 0.58 & 1.18 & 0.53 & 1.19 \\
4 th & 0.45 & 1.34 & 0.39 & 1.41 \\
6 th & 0.28 & 1.76 & 0.51 & 1.86 \\
10 th & 0.22 & 2.14 & 0.65 & 2.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of IGE values of vortex ring center location for hover flight at \(Z/R=1\). Figure 12: Comparison of the vertical and in-plane velocities at the level of the rotor (\(Z/R=1\)). Inviscid condition on the ground (**left**) and viscous condition (**right**). (at \(Z/R=0.51\) and \(Z/R=0.65\), respectively, see Table 2), while wake tip vortices start to interact with the boundary layer on the ground. Figure 13 shows the details of the flow field on an axial symmetry plane at the end of the 6 th period. The window focuses on the interaction zone of the vortex ring with the boundary layer on the ground. As Table 2 also indicates, at this instant the vortex core is located halfway between the ground and the rotor plane. The recirculating flow of the vortex extends down to the ground level and interacts with the ground boundary layer. In the close-up plot, the anti-clockwise rotating flow of the vortex ring that entrains the boundary layer, is clear (left side of the focus window). Maximum flow velocities are obtained below the vortex center, at a distance \(Z/R=0.1-0.15\) from the ground level. The increasing thickness of the boundary layer (right side of the plot) pushes the vortex away from the ground, realizing the so called re-bound effect. The above comparison has revealed that as the distance from the ground gets smaller, two features that can only be reproduced by taking into account viscosity become decisive: First, the induced velocities in the wake are higher leading to higher loading and secondly, the vortex ring rebounds from the ground pushed by the displacement generated in the ground boundary layer. With respect to loading, which was the initial motivation of this work, in Figure 14 the results obtained with the potential flow solver [13] are compared to measurements indicating that at \(Z/R>1.5\), the agreement is very good. It also captures the \"knee\" of the \(CT\) variation at \(Z/R=1.7-2.0\). Below \(Z/R=1.5\) there is increasing deviation that becomes maximum at \(Z/R=1\). At this position, predictions with HoPFlow using the viscous option reconfirm the importance of the ground boundary layer by fully recovering the measured value.