A Velocity Potential-Based Finite State Model for Ground Effect Analysis

A velocity potential-based finite state model (VPBFSM) has been developed to analyze an isolated rotor in ground effect. The model uses mass source distributions to represent the ground and enforces the non-penetration of flow boundary condition. In previous VPBFSM approaches to impose this boundary condition, the r = j terms were excluded to avoid singularities. This exclusion required adjustments to the source strengths and ground rotor size in order to impose the boundary condition properly, which reduced the model's robustness. In the present study, the r = j terms are incorporated using a solution for the gradient of the velocity potential from the literature, which avoids singularities. This inclusion allows for effectively enforcing the boundary condition without requiring adjustments. The model is applied to an isolated rotor in full, inclined, and partial ground effect cases, including analysis of the R-50 rotor using geometric and aerodynamic data from the literature. Results for full ground effect show excellent correlation with the Hayden model. The normalized induced torque also exhibits good agreement with experimental data for full, inclined, and partial ground effect cases.