Interaction of Tip-Vortices in the Wake of a Two-Bladed Rotor in Axial Flight

Abstract

Roliil Jain'A. T. Conlisk Grad~tote Srrtrle,rr Prqfesuor Del~ort,nent of Mecl8onical E,~gbzeerblg, Tlte Ollio State Urrivemir)~In recent experiments, it was observed that the tip vortices shed from a two-bladed rotor can interact significantly. The interaction consists of a turn of the tip-vortex from one hlade rolling aronnd a turn of the tip-vortex from the other blade. Visualized in aplanarlightsheet, thetwo vorticesspiral aronnd each other prior to merging into asinglevortex. One complete cycle of the roll-up process takes about one and one-half rotor cycles. This behavior is analogous to the interaction which takes place between two ring vortices and the numerical calcolations shown here demonstrate this similarity. I t is observed that the pair of rings, placed initially parallel and of the same strength roll aronnd each other, by alternate contraction and expansion of the ring radius. Numerical calculations show that the ring interaction is complicated when the rings are initially inclined with respect to one another. The experimental configuration of a two-bladed rotor in axial flight is considered next. A lifting-line theory is used to niodel each rotor blade and a fully unsteady computation of the motion of the tip-vortices is carried out using a fourth-order accurate Adams-Moulton method to advance the vortices. The modified Biot-Savart law is used to descrihe the vortex structure. I t is shown that the tip-vortex interaction is periodic and deterministic and rcwlts for the tip-vortex paths are seen to be in good agreement with experimental results. Nomenclature r, g, z Cartesian coordinate system x,, y,,, z,, coordinates of a point on a vortex filament normalized by R a" 157

Parallel simulation of unsteady hovering rotor wakes

“…Landgrebe [1] and Tangler et al [2] both observed localized roll-up or 'pairing' of wake vortices, as did Martin et al [3] and Caradonna et al [4,5]. This has been confirmed by theoretical stability analyses [6][7][8], which imply a hovering rotor wake is fundamentally unstable with several unstable modes. Low diffusion numerical simulation methods, for example free-vortex or free-wake [8,9] or vorticity transport methods [10,11], have also shown evidence of unsteady wakes for rotors in hover, seemingly confirming both theoretical and experimental data.…”

Parallel solution of lifting rotors in hover and forward flight

“…Experimental data for rotors in hover, for example, References [2][3][4][5], have suggested the wakes are actually unsteady. This has been confirmed by theoretical stability analyses [6][7][8], which imply a hovering rotor wake is fundamentally unstable with several unstable modes. Other simulation methods, for example, free-vortex or free-wake [8,9] or vorticity transport methods [10,11], with low inherent dissipation, have also shown evidence of unsteady hover wakes, confirming the theoretical and experimental data.…”

Mutual inductance instability of the tip vortices behind a wind turbine

“…Recent experiments by Felli et al (2011) and Leweke et al (2013) as well as numerical studies by Widnall (1972) and Ivanell et al (2010) have confirmed that the mutual inductance instability leads to vortex pairing in the rotor wake, and they indicate that the vortex pairing is the primary cause of wake destabilization. The vortex pairing is a result of the vortex-induced velocities in a form that it is analogous to the leapfrogging motion of two inviscid vortex rings (Jain et al 1998). This phenomenon occurs in a row of equidistant identical vortices, whereby amplifications of small perturbations cause the vortices to oscillate in such a way that neighbouring vortices approach each other and start to group in pairs.…”