## 4 Validation against Measurements
### Hover Flight Simulations in IGE Flight Conditions  
In helicopter hover flight in proximity to the ground, the presence of the ground has a significant (an important) effect on wake development. The starting ring vortex and the jet flow developing underneath the rotor disk, after a certain time, impinge on the ground and move outwards forming an outwash flow. The developed flow field deviates significantly from the one of the unconstrained OGE case. In simulations, ground effect can modeled either by solely imposing no-penetration (inviscid option) over the ground or by also adding zero slip (viscous option). Both options end up constraining the motion of the starting vortex, however in a different way. Figure 11 details in terms of vorticiy contours, the evolution of the wake that the two modeling options provide when \(Z/R=1\). The inviscid option is on the left while the viscous option on the right. From top to bottom, snapshots at the end of the 1 st, 2 nd, 3 rd, 4 th, 6 th, and 10 th rotor revolution are shown. Figure 10: Thrust coefficient convergence in OGE conditions. Predictions of HoPFlow. In the inviscid predictions, at the end of the 1 st period the starting vortex ring has formed below the edges of the rotor disk. At the end of the 2 nd period, the ring moves downwards as a result of its self-induced velocity. At the end of the 3 rd period, strong blade tip vortices are shaped and travel downstream. At this moment, the core of the vortex ring is at \(Z/R=0.58\) above the ground level and at \(r/R=1.18\) away from the rotor center while the ring begins to roll up. At the end of the 4 th period, delimited by the strong vortices emitted by the tips of the blades, the contracting rotor wake is now well shaped. The vortex ring moves further down and outwards and also starts to deform (the original circular cross section shape is now distorted) as it interacts with the ground. At the end of the 6 th period, the vortex hits the ground at a radial distance of \(r/R=1.76\). The cross section of the ring is further distorted into an elliptical shape. Finally, at the end of the 10 th period, the vortex travels outwards keeping the distance of its core from the ground constant at \(Z/R=0.22\). In the viscous option, the shape obtained after the end of the first period (Figure 11b vs. Figure 11a) is very similar to that of the inviscid option. The predicted position of the vortex ring is almost identical in the two sets (see also Table 2). However, the magnitude of the vorticity at the tip in the viscous option is higher and so will be the loading. Higher circulation of the vortex ring implies that also higher down-wash will develop in the wake at the early stages of its generation. In Figure 12, the down-wash and the in-plane velocity components over the rotor disk as obtained with the two modeling options are compared. Figure 11: Vorticity contour plots for the IGE case at \(Z/R=1\) (snapshots taken at the end of the 1 st, 2 nd, 3 rd, 4 th, 6 th, and 10 th rotor revolution). Inviscid ground condition (**left**), viscous ground condition (**right**). Although the differences are small, the down-wash velocities (negative sign) over the rotor disk plane are higher in the viscous case (the extent of the blue pattern is greater in the viscous option results). Furthermore, the up-wash induced velocities are higher by the wake outside the rotor disk area as well as the in-plane velocities within the rotor disk area. This explains why in the viscous option, at the end of the 2 nd period, both the vortex ring and the tip vortices of the blades have traveled longer downwards distance as compared to the inviscid case. The same happens at the end of the 3 rd revolution (longer downwards distance traveled by the wake) while in addition to the above the ground boundary layer starts to develop. The shear in this boundary layer is caused by the wake jet flow that at the end of the 3 rd revolution impinges on the ground.