Analysis of a Velocity Potential-Based Finite State Model for Ground Effect

In this study, Velocity Potential-Based Finite State Model (VPBFSM) formulations are used to analyze a rotor in ground effect by representing the ground as mass source distributions and enforcing the non-penetration of flowboundary condition. Previous studies enforced this condition by iteratively adjusting source strengths and ground rotor size, but the results showed sensitivity in satisfying the boundary condition. This paper presents a VPBFSM formulation that directly imposes the boundary condition by utilizing a complete set of Legendre function expansions to determine the source strengths in terms of the rotor loading, thereby eliminating the need to adjust source strengths or ground rotor size. The method is applied to an R-50 unmanned helicopter rotor using geometric and aerodynamic data from the literature to analyze full and inclined ground effect cases. Results for full ground effect show average inflow predictions closely aligned with the Hayden model. Inflow distributions for both full and inclined cases exhibit expected physical trends, notably the reduction in inflow on the sections of the rotor nearer to the ground. Additionally, normalized induced torque values show good agreement with experimental measurements, demonstrating the accuracy and reliability of the proposed approach.