MODEL FOR ROTOR TIP VORTEX-AIRFRAME INTERACTION .1. THEORY

The flowfield generated by a helicopter in flight is extremely complex, and it has been recognized that interactions among components can significantly affect helicopter performance. In the present work a simplified model for the interaction of a rotor tip vortex with the helicopter fuselage is developed. The tip vortex is idealized as a single three-dimensional vortex tube, and the fuselage is modeled as an infinite circular cylinder. The Biot-Savart law is employed to describe the flow induced by the vortex, and the flow is assumed to be inviscid and irrotational outside the core of the vortex. The numerical calculations indicate that a large adverse pressure gradient develops under the vortex on the fuselage causing a rapid drop in the pressure there; large variations in the curvature of the vortex are not observed. Numerical solutions for the vortex position and for the pressure on the airframe are calculated for the case where the vortex is embedded in a three-dimensional steady mean flow; the effect of vortex core size is also investigated. The nature of the initial stages of the breakdown of local axisymmetry of the core of the vortex filament is suggested based on both the numerical and experimental results.