VORTICITY CONCENTRATION AT THE EDGE OF THE INBOARD VORTEX SHEET

Submitted to the Journal of the American Helicopter Society VORTICITY CONCENTRATION AT THE EDGE OF THE INBOARD VORTEX SHEET J.M. Kim 1, N.M. Komerath 2, S.G. Liou 3 School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia 30332 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 Gray 1 and Landgrebe 2. 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 "inboard vortex sheet". 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. Gray 1 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 hover 3 or in forward flight 4 also treated the inboard vortex sheet as an undistorted sheet of vortex filaments. These models contributed to a very large 2

improvement in the accuracy with which rotor flows could be calculated. However, a common thread can be found in the helicopter aeromechanics literature over the years: the free-wake geometry that gives the "correct" rotor load distribution and rotor trim is not the geometry that one would calculate from first principles. Improvements in accuracy have been sought by going to increasing levels of sophistication and detail in the computation: this has kept free-wake computation at the edge of computer capabilities. This problem accounts for the prevalence, even in very recent times, of "prescribed-wake" models of the rotor flow field. Free wake analysis 5 of the hovering rotor with a highly resolved vortex filament distribution displayed some distortion of the inboard vortex sheet due to the interaction with the tip vortex. Ref.5 also describes an indirect experiment to simulate the formation of the "mid-vortex" from the vortex sheet distortion. This experiment circumvented the problems of direct visualization or velocity field measurement in the rotor wake. A half-span wing was used to generate a strong tip vortex. Another half-span wing mounted downstream had a positive twist to simulate the increasing circulation from the root to the tip of a rotating blade. The vortex from upstream interacted with the wake from the twisted wing. Vorticity contours constructed from velocity measurements in the wake of the twisted wing showed a counter-rotating mid-vortex. However, distortion of the vortex sheet itself could not be identified from the results. In the remainder of this paper, we use the term "counterrotating vortex" (CRV) to describe concentrations of vorticity of sign opposite to that of the rotor tip vortex. A counter-rotating vortex was observed by two of the present authors in velocity data acquired during the interaction between a rotor wake and an airframe surface 6. At that time, roll-up of the inboard vortex sheet was postulated as one possible mechanism for this secondary vortical structure, but conclusive proof was not available. Another possible 3

source suggested in Ref.6 was the airframe surface effect on the rotor tip vortex. Later velocity measurements by the authors on the interaction of the rotor wake with the separated flow behind a backward facing step 7 also showed clear evidence of a CRV. The initial motivation of the present experiments was to check the origins of that structure, as well as the hypothesis that it was due to airframe surface interaction. EXPERIMENTAL TECHNIQUES The model rotor system consists of a teetering hub and two rectangular blades with 0.46m radius. It was mounted in the 2.1 x 2.7 m (7x9 ft) test section of the John J. Harper Wind Tunnel, as shown in Figure 2. This system has seen extensive prior use in rotor/airframe interaction research 8-10. Each blade has 86mm chord, NACA 0015 section and 10-degree collective pitch without twist. The rotor is driven by an electric motor which is connected to the rotor through a shaft suspended from the tunnel ceiling. This geometry allows study of the isolated rotor wake with an absolute minimum of interference due to the hub, mast, and motor housing, etc. The lack of static or cyclic pitch variation is a disadvantage in studying various operating conditions, but a strong advantage for physical modeling and isolation of the phenomena. A 30-Watt copper vapor laser was used to generate a light sheet, as shown in Figure 3. A mineral oil seeder mounted downstream of the test section of the closed-circuit tunnel was used for the velocity measurements. A heated smoke-wire system was used upstream to provide denser seeding for flow visualization. For some of the flow visualization, both seeders had to be located upstream. A video camera was mounted outside the test section to observe the light sheet. A second videocamera provided a continuous readout of the rotor azimuth by observing a graduated disc mounted on the rotor shaft above the tunnel. This image was merged with the flow visualization videotape. The recorded images were analyzed using a frame grabber and graphics software on a Macintosh 4

II computer. Velocity measurements, resolved according to rotor azimuth, were made with a laser Doppler velocimeter. The signal was collected in the back-scatter mode. The two components of velocity, along the tunnel freestream direction and the vertical direction, were measured independently and then combined at each measuring location. EXPERIMENTS A longitudinal cross section of the rotor wake was visualized in the vertical plane through the tunnel axis under hovering (advance ratio µ = 0) and low-speed forward flight (µ = 0.1) conditions. For the rotor used, tunnel blockage and ground effect have been shown to be negligible for µ > 0.06 (Ref. 12). For the present objectives of observing rollup of the vortex sheet close to the rotor, ground effect in the hovering condition was considered to be an acceptable error. The rotor speed was held at 1050 rpm or 525rpm, as needed to get good flow visualization images. In hover, it was difficult to get good images, since the smoke from the smoke wires could not be directed properly; however, the tip vortex and vortex sheet were visible briefly at the same time using the combined seeding devices of the mineral oil seeder and the smoke wires. Figure 4 shows a gray-scale image captured from the longitudinal cross section of the rotor wake at µ = 0.1. A tip vortex is seen upstream and a pair of vortices are seen downstream. Flow visualization usually works much better at low flow velocities, for several reasons. To improve the visualization quality, experiments were performed at very low rotor speed (35 rpm). This was enabled by the video imaging technique. The images were recorded as the rotor was slowing down to a stop. The aximuth readout, as well as the visual image of the blade passing through the light sheet, were used to measure the speed, knowing the framing speed of the video camera. Figure 5(a) shows a tip vortex and Blade No. 1 passing the light sheet. At this phase, the rotor has moved 180 degrees since the tip vortex left the tip of Blade No. 2. After another 45 degrees of blade rotation, a new tip 5

vortex from Blade No. 1 and its coupling with a vortex sheet are also visible in Figure 5(b). Figure 5(c) is the image taken approximately 45 degrees later in rotor azimuth than Figure 5(b). Here, the tip vortex from Blade No. 2 and the vortex sheet from Blade No. 1 are in close proximity. The outboard tip of the vortex sheet is distorted to form a counter-rotating vortical structure. The distortion is attributed to tip vortex interaction since the direction of the distortion matches that of the induction due to the tip vortex. It should be noted that the tip vortex from Blade No. 1 is not visible in the Figure 5(c) because the seeding happened to be absent from that region in this image. Figure 6 shows that such counter-rotating vortex pairs also exist in hover (Figure 6a), and at the aft portion of the rotor wake in forward flight (Figure 6b). Azimuth-resolved vortex trajectories were measured at 1050 rpm and µ = 0.1. Vortex locations were measured by comparing the visualization images with a reference grid board image. The blade azimuth was read from the image of the azimuth value inserted in each visualization image using a video mixer, as indicated before. Figure 7(a) shows the trajectories of the tip vortex and CRV in the front portion of the rotor wake. The vortex ages in rotor azimuth value are indicated by numbers near symbols in the trajectory curve. It takes 50 degrees of blade rotation for the CRV to be first seen clearly in the visualization plane. At this phase the pairing tip vortex has the age of 230 degrees, since the previous blade rotated 230 degrees after it had shed the tip vortex section seen in this image. The three vortices in Figure 4 can be closely located on the trajectories in the Figure 7 as two tip vortices with the age of 180 and 360 degrees and the CRV with the age of 180 degrees. Interaction between two vortices with different rotational direction is observed to some extent. The distances between two adjacent symbols increase in the tip vortex trajectory, where the symbols were drawn with a uniform interval of 30-degree blade azimuth, showing the increase in convection speed of the vortices The tip vortex trajectory changes its direction after the CRV's formation. The slope of the dotted line connected 6

between the tip vortex and the CRV decreases as the vortex pair ages. These three interactional phenomena agrees with the direction of velocities induced by each vortex. The vortex trajectories in the aft portion of the wake are shown in Figure 7(b). The CRV is located under the tip vortex. The distance between the vortex pair is about twice longer than in the corresponding part of the front portion of the wake. VELOCITY FIELD RESULTS Vertical- and streamwise-component velocity were measured one component at a time using the LDV in the region where the CRV's structure was observed in the visualization tests. The advance ratio and rotor speed in the rotor wake generation were set at 0.1 and 1050 rpm respectively. The measuring volume of the LDV moved successively to the grid points covering an 165x114 mm area with 6.35-mm spacing. The region covered by velocity measurements is indicated by the frame inside Figure 7(a). At each location, 50,000 velocity data were sampled and sorted into 60 bins, each bin representing a 6-degree interval of rotor azimuth. The data in each bin were averaged to yield phase-resolved velocity. Vorticity contours at each blade azimuth were constructed from the twocomponent data. The vorticity contours in Figure 8(a) show the flow features at 300 degrees of blade azimuth. The tip vortex can be seen as a positive vorticity concentration, the CRV as a negative vorticity concentration. A small but distinguishable negative vorticity band is seen suspended from the top of the CRV contour to the border of the measurement window. The position of this band with respect to the tip vortex is identical with the vortex sheet in the visualized image. Figure 8(b) is a flow image at the same test condition. The locations of the vortex cores both in the vorticity contour and the visualization are identical. The rotational direction of the vortices in the visualization agrees with that in the vorticity contour. In Figure 9, results are shown at two other values of rotor azimuth, one before 7

(270 degrees) and one after (330 degrees) the azimuth in Figure 7. The mutual induction effects of the tip vortex and the CRV are clearly seen. The tip vortex is being slowed in its motion in both the downstream and downward directions. This shows why the wake envelope contracts, and explains the shape of the contraction. At 330 degrees of blade azimuth, we see the vortex sheet distorted severely as the CRV is accelerated downward. We see from these measurements that the edge of the inboard vortex sheet rolls up into a strong structure rotating counter to the tip vortex. The roll-up is perhaps initiated by the proximity of the tip vortex of the same age as the vortex sheet, but it is really enhanced when the fast-moving sheet interacts with the older sections of the tip vortex filament. The presence of counter-rotating structures implies a local maximum of flow velocity between them: i.e., a spiral ring of jet-like flow is caused. This is evident when observing the dynamics of the seeded flow in the laser sheet. These observations, and the high value of concentrated vorticity in the CRV, have obvious implications for future free-wake modeling efforts, and can perhaps lead to improved fidelity in free-wake calculations. Circulation around the two vortices was calculated integrating the vorticity over the area where each vortex shows vorticity concentration. The contours of integration were chosen to be far enough away to lie in regions of near-zero vorticity. The circulation value around the CRV approaches 50% of that of the tip vortex. These results are plotted in Figure 10 for three rotor azimuth values. The values are seen to remain largely unchanged with rotor azimuth in this range. CONCLUSIONS Extensive flow visualization and velocity field measurement were performed to investigate the counter-rotating vortical structure in a rotor wake. 1. The inboard vortex sheet is severely distorted when its location is close to the tip vortex, becoming a well-defined counter-rotating vortex(crv). 8

2. The CRV exists both in the leading and trailing edges of the rotor wake in forward flight. It is also found in the wake in hovering. 3. Interaction between the tip vortex and the CRV is observed as position change and acceleration of the vortices. 4. Interaction with the counter-rotating vortex is a significant factor in determining the rate of contraction of the wake envelope. 5. The quantified circulation of the CRV is found to be 50% that of the tip vortex with a sense of rotation opposite to the tip vortex rotation. ACKNOWLEDGEMENTS This work is supported by the Army Research Office under Aerodynamics Task 2 of the Center of Excellence in Rotary Wing Aircraft Technology, Contract No. DAAL88-03-C- 0001. Dr. Tom Doligalski is the Technical Monitor. REFERENCES 1. Gray, R.B., "On the Motion of the Helical Vortex Shed from a Single-Bladed Model Helicopter Rotor and Its Application to the Calculation of the Spanwise Aerodynamic Loading", Princeton University A.E. Dept. Report No. 313, September 1955. 2. Landgrebe, A.J., "The Wake Geometry of a Hovering Helicopter Rotor and Its Influence on Rotor Performance," Journal of the American Helicopter Society, Vol. 17,(4), October 1972. 3. Kokurek, J.D., Tangler, J.L., "A Prescribed Wake Lifting Surface Hover Performance Analysis", Journal of American Helicopter Society, Vol.22,(1), January 1977. 4. Egolf, T.A., Landgrebe, A.J., "Helicopter Rotor Wake Geometry and Its Influence in Forward Flight", NASA CR 3726, October 1983. 5. Müller, R.H.G., "Special Vortices at a Helicopter Rotor Blade", Journal of the American Helicopter Society", Vol.35,(4), October 1990. 6. Liou, S.G., Komerath, N.M., and McMahon, H.M., "Measurement of the Interaction 9

Between a Rotor Tip Vortex and a Cylinder". AIAA Journal, Vol, No. 6, June 1990, p. 975-981. 7. Komerath, N.M., Kim, J.M., Liou, S.G., "Interaction Between a Vortex Dominated Wake and a Separated Flow Field", AIAA Paper 91-1819, AIAA 22nd Fluid Dynamics, Plasma Dynamics & Lasers Conference, Honolulu, Hawaii, June 1991. 8. Brand, A.G., Komerath, N.M. and McMahon, H.M., "A Laser Sheet Visualization Technique for Incompressible Vortex Wakes". Journal of Aircraft, Vol. 25, No. 7, July 1988, pp. 667-668. 9. Mavris, D.M., Komerath, N.M., and McMahon, H.M., "Prediction of Rotor/Airframe Aerodynamic Interactions". Journal of the American Helicopter Society, Vol.34, No.4, October 1989, p. 37-46. 10. Brand, A.G., McMahon, H.M., and Komerath, N.M. "Correlations of Rotor/Wake - Airframe Interactions with Flow Visualization Data". AHS Journal. Vol. 35, No. 4, October 1990, p. 4-15. 11. Komerath, N. M., McMahon, H. M., and Hubbartt, J. E., "Aerodynamic Interactions Between a Rotor and Airframe in Forward Flight," AIAA Paper 85-1606, AIAA 18th Fluid Dynamics and Plasmadynamics and Lasers Conference, Cincinnati, OH, July 1985. 10

LIST OF FIGURES Figure 1: (a) The wake of a single-bladed rotor in hover, showing the tip vortex and vortex sheet( from Ref. 1.) (b) Typical spanwise load distribution on an untwisted rotor blade, showing opposite sense of rotation of tip vortex sheet. Figure 2: Schematic of the rotor system in low speed wind tunnel. Figure 3: Schematic of the laser-sheet flow visualization system. Figure 4: Visualization of the rotor wake in forward flight.(advance ratio=0.1, rotor speed=525 rpm) Figure 5: A series of visualized images of the rotor wake at different blade azimuths. (rotor speed =35 rpm, advance ratio=0.05) (a)at blade azimuth=180 degrees, (b)at blade azimuth=225 degrees, (c)at blade azimuth=270 degrees Figure 6: Visualization of the CRV (a)in the rotor wake in hovering, (b)at the aft portion of the wake in forward flight. Figure 7: Trajectories of the tip vortex and the CRV in forward flight.(advance ratio=0.1, rotor speed=1050 rpm) (a)at front portion of the wake, (b)at aft portion of the wake. Figure 8: Correlation of vorticity contour with flow visualization at blade azimuth=300 degrees. (a)vorticity contour on vector plot, (b)corresponding visualization image. Figure 9: Vorticity contours and velocity vector plots at blade azimuth = 270 and 330, showing vorticity concentrations of the tip vortex and CRV with opposite sense of rotation. Figure: 10 Circulation around the tip vortex and the CRV. 11