## 5 Conclusions and Discussion  
This paper addresses the near-ground hover flight and attempts to revise earlier potential flow predictions by introducing the effect of flow viscosity in the simulation, in particular the viscous boundary layer that develops on the ground as a result of the rotor down-wash. The simulation environment adopted in this analysis is a hybrid Eulerian  
Figure 14: Normalized thrust coefficient in IGE conditions. Comparison of predictions with GenUVP and HoPFlow against measurements. Figure 15: Rotor thrust variation in IGE condition at \(Z/R=1\). Comparison of HoPFlow predictions for the inviscid wall case against the viscous wall. \begin{table}
\begin{tabular}{c c c c} \hline
**Experiment** & **Inviscid Wall** & **Viscous Wall** & **GenUVP** \\ \hline
1.1441 & 1.1235 & 1.149 & 1.121 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of IGE values of \(CT/CT_{OGE}\) at \(Z/R=1\). Lagrangian CFD solver which can conveniently accommodate solid bodies that move independently the one from the other. The Eulerian and Lagrangian flow solutions are consistently coupled through properly defined boundary conditions for the Eulerian problem and an iterative scheme, in the course of which the Lagrangian solution (material description of flow quantities over the entire flow domain) is adequately corrected. The work aimed to (i) identify the physical mechanisms of the rotor/ground interaction in the presence of a viscous boundary layer on the ground, and (ii) prove that a hybrid solver based on particles is capable of consistently predicting OGE and IGE rotor loads. In this connection, simulations of the hybrid Eulerian-Lagrangian solver HoPFlow have been performed for OGE and IGE (close proximity to the ground of one rotor radius) hover flight conditions considering the ground both as an inviscid and a viscous wall. Comparison of HoPFlow rotor thrust predictions for the OGE case and the IGE case with the ground being modeled as an inviscid wall against predictions by the potential free wake GenUVP code indicated an excellent agreement of the two models, which however underestimated the measured increase in thrust by \(\approx\)2.5%. The above comparison is a verification of HoPFlow predictions but also suggests that the modeling of the ground is of critical importance for the correct account of the rotor ground interactional phenomena and thereby for the accurate prediction of rotor loads in IGE conditions. Besides, the above conclusion was experimentally confirmed by [PERSON] and [PERSON] [5]. HoPFlow predicted the thrust for the IGE hover case with the ground being modeled as a viscous wall perfectly well compared to measurements. Cross-comparison of the flow fields of the two HoPFlow IGE simulations (viscous and inviscid options) suggests that in the presence of the ground a displacement effect is caused, driven by the boundary layer transpiration velocities that pushes the rotor wake and the starting vortex to move upwards. In the inviscid simulation option the starting vortex, after hitting the ground moves parallel to it reaching after 10 rotor revolutions a minimum height of \(Z/R=0.22\). In the viscous simulation option, the starting vortex moves faster downwards due to higher wake induced velocities and as a result of its interaction with the ground boundary layer reaches a minimum distance of \(Z/R=0.51\). Then bounces back to a higher height of \(Z/R=0.65\). Conceptualization, T.A. and V.R. ; methodology, T.A. and G.P. ; validation, T.A. ; formal analysis, T.A., V.R. and S.V. ; writing--original draft preparation, T.A. ; writing--review and editing, T.A., G.P., V.R. and S.V. ; visualization, T.A. ; supervision, V.R. and S.V. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Not applicable. Not applicable. Not applicable. Data Availability Statement: The experimental data presented in Figure 14 and in Tables 1 and 3 are available in [11].