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V. RAGHAV JOURNAL OF THE AMERICAN HELICOPTER SOCIETY 3) As the flow adjacent to the blade in the separated region moves at low speed relative to the rotating blade, the radial stresses at the surface may be transported to a substantial height above the surface into this flow, in contrast to the case of attached flow (see Fig. 5(b)). Using these results, the following characteristics of the flow can be hypothesized: 1) The occurrence of a large radial flow can in turn have a strong influ- ence on the separation process itself and thus have a role in determining the shape of the separation line (see Fig. 5(a)). 2) The near-surface flow field will form a radial jet both above and below the blade surface due to the radial acceleration on the surface. 3) This jet will itself be highly vortical as the flow at the blade surface obeys the zero-slip condition with respect to the rotating blade, while the flow immediately above that layer is accelerated radially outward (see Fig. 5(b)). 4) The vortical jet is highly susceptible to shear layer instability due to the unsteady nature of the flow leading to break up of this layer. From the above, it can be concluded that not just the magnitude and profile of the radial velocity field in this region are of interest. Equally important are the characteristics and behavior of this radial jet, which might contribute to the poststall evolution of lift and pitching moment. Results and Discussion Radial flow The radial flow over the rotor occurs as a result of centripetal and reactive centrifugal forces due to rotation, irrespective of blade stall. The influence of the centrifugal reactive or pumping force could be signifi- cant in adverse pressure gradients where the flow is retarded (Ref. 14). Although three-dimensional flow separation can itself manifest as fluc- tuations in spanwise flow, there exists no physical mechanism to develop a sustained flow in the radial direction due to three-dimensional separa- tion alone. The radial flow characteristics are discussed in detail in the following sections. Profiles of radial velocity. As hypothesized, the rotation of the blade gives rise to a radial jet flow that develops over the surface. However, the no-slip condition must apply at the blade surface and thus a viscous boundary layer exists. Moreover, the attached flow at the bottom surface of the blade also experiences the same radial acceleration. Therefore, the radial flow velocity field should show radial jet layers adjacent to both the upper and lower blade surfaces. It is also noted that this boundary layer is very thin, and it is not expected that PIV will resolve this in the present experiments. Owing to these reasons, the double-peaked radial velocity profile adjacent to the blade surface appeared as a single peak at the middle of the blade thickness. This was observed at all the radial stations in Fig. 6. It shows that the radial jet is confined to the region close to the blade. The jet appears to exist above and below the blade trailing edge. This is due to the fact that the measurement was taken 2 mm downstream of the trailing edge, as indicated in the discussion regarding the inability to capture the blade boundary layer. For the moment, it can be assumed that the peak of the jet is what is seen but that the radial velocity must drop from the maximum value to zero in the distance between the peak location and the surface of the rotor. This assumption is used to estimate the vorticity in the boundary layer above the blade. For the moment, the phenomena on the bottom surface of the blade are ignored. The steps that went into producing the plots of radial velocity are, first, the velocity vectors were ensemble averaged; second, using image processing, the blade surface is located from images of laser sheet visu- alization; finally, the radial velocity component is transformed so that it Fig. 6. Profile of the variation of average radial velocity at various radial locations, normalized with respect to blade tip speed. is parallel to the blade surface (the blade is flapped up +4◦) to consider the vorticity in the boundary layer. Figure 6 shows the axial variation of the averaged radial velocity profiles normalized by blade tip speed. The salient feature is that the magnitude of the radial velocity peak essentially decreases on moving outboard along the blade, quite the opposite of the expected increase in radial velocity. The uncertainty in the peak value due to spatial resolution is estimated to be less than 0.61% of the peak height of the velocity profile. The error was estimated by extrapolating the data after ignoring the peak to obtain an extrapolated peak and then comparing it to the measured peak. Discrete structures in the cross-flow plane. A literature review on the separated flow over lifting surfaces revealed studies on stalled fixed wings, but very little on dynamic stall in flows over “true” rotating blades. Three-dimensional flow patterns were detected on airfoils based on surface visualizations by Gregory et al. (Ref. 35) and surface oil streaklines by Winkelmann and Barlow (Ref. 36). Weihs and Katz in Ref. 37 reported cells in the poststall flow field over straight wings. Sim- ilarly coherent structures and cells in the separated flow were observed by Yon in Refs. 38 and 39. Yon also reported the fluctuations attributed to these cells in the wake of a stalled rectangular wing. Low-frequency oscillations were observed in the case of two-dimensional leading edge separation by Broeren and Bragg (Ref. 40). Spanwise separation cells were seen to arise from trailing-edge separation, but this was primarily steady. Thus, from the above discussion it appears that spanwise cells have been observed in the stalled flow over fixed wings, even on nom- inally two-dimensional airfoil models. However, they are driven by the shear at the top of the separated flow region, which is the only source of vorticity in that situation once the flow is separated. This is very different from the case of a rotating blade where high shear stress in the form of radial stresses is present at the blade surface. In addition, recent numer- ical studies on a S822 wind turbine airfoil (Ref. 33) showed the effect of cross-flow on a rotating blade. The blade rotation resulted in a radial velocity component toward the blade tip in the separated flow region. The study postulated the existence of stationary and traveling cross-flow vortices over the span of the blade. Figure 7 shows the vorticity contours in the cross-flow plane at two radial locations in the trailing edge plane. Clearly, the jet shear layer has broken into several discrete structures in the windows shown. In addition, the vorticity entrained in the structures increases on moving outboard. Furthermore, the structures also appear to be lifting off the surface (re- ferred to as “peel” or “jump” off) at the more outboard locations, a 022005-6PDF Image | Radial Flow Rotating Blade Retreating Blade Stall
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