Vorticity Concentration at the Edge of the Inboard Vortex Sheet

Abstract

Flow visualization and velocity measurements are used to show that the outer edge of the trailing vortex sheet from an untwisted rotor blade rolls up into a discrete vortical structure which is opposite in sense and comparable in strength to the tip vortex. This occurs both in hover and forward flight, and at both upstream and downstream edges of the wake in forward flight. The roll-up process and the trajectories of the tip vortex and the counterrotating vortex are examined using digitized laser sheet video images. Azimuth-resolved velocity data, obtained under an isolated, two-bladed teetering rotor in a wind tunnel at low advance ratio, are used to quantify vortex strengths. INTRODUCTION Figure 1 shows the classical model of the rotor wake in hover, developed from the early experimental work of Gray1 and Landgrebe2. The wake is dominated by the tip vortices, which concentrate vorticity in small core regions, and carry a large amount of kinetic energy with them. Early attempts to model the behavior of the rotor wake used simple models of the velocity field induced by these vortices. To get better accuracy in modeling the wake and the loads on the rotor blades, it was found necessary to include the vorticity trailed 1: Graduate Research Assistant. Member, AHS 2: Associate Professor. Member, AHS 3: Post-Doctoral Fellow. member, AHS behind the blade in a thin shear layer, which can be modeled as an vortex There is also some rollup of vorticity at the hub into a root vortex; however, this contains relatively little kinetic energy. Examination of Figure 1(a) shows that the outer edge of the vortex sheet moves down faster than the corresponding tip vortex. This can be seen by considering the signs of vorticity of the tip vortex and the vortex sheet, as shown in Figure 1(b). Unlike the circulation distribution of a fixed wing, the bound circulation of the rotating blade generally peaks well inboard of the tip, so that the sign of DΓ/Dr changes. Thus, the tip vortex leaves the blade with a sense of rotation opposite to that of the inboard vortex sheet. Mutual induction between the tip vortex and the vortex sheet must thus inhibit the downward motion of the tip vortex, and accelerate that of the edge of the sheet. Figure 1 was developed by detailed observation of patterns formed by clouds of microscopic particles, illuminated by strobed lights or continuous lights. The patterns were captured using cameras with short shutter exposure times. The figure leaves unspecified the continuity between the tip vortex and the vortex sheet. This aspect of the rotor wake is the subject of this paper. Early experimental investigations of the rotor wake were motivated by pursuit of precise rotor performance prediction. Gray1 modeled the rotor wake by a tip vortex filament and an inboard vortex sheet composed of several vortex filaments based on the visualization of a single-bladed rotor in hover. In his experiments, the visible portions of the inboard vortex sheet and the tip vortex were not close enough to permit observation of the phenomena at the junction. Distortion of the inboard vortex sheet was not observed in the visualization. Landgrebe et al.2 extended such models to multi-bladed rotors. The interaction between the vortex sheet and the tip vortex was neglected and consequently the inboard vortex sheet was prescribed as a rigid sheet of distributed vorticity fixed to the spatial locations of blade passage. Later vortex modeling of prescribed wake analysis for the rotor wake in hover3 or in forward flight4 also treated the inboard vortex sheet as an undistorted sheet of vortex filaments. These models contributed to a very large