AN INVESTIGATION OF VORTEX FLOWS

OVER LOW SWEEP DELTA WINGS

G. S. Taylor*, T. Schnorbus†, and I. Gursul‡

Department of Mechanical Engineering, University of Bath,

Bath BA2 7AY, United Kingdom.

This paper presents the results of a recent investigation into the vortex structure over a non-

slender delta wing with leading edge sweep, Λ = 50°. A flow visualisation study in water tunnel experiments has shown profound sensitivity of the vortex structure to Reynolds number. As Reynolds number was reduced, the trajectory of the vortex core moved inboard toward the wing centre-line, and the onset of breakdown was noticeably delayed. The results provide the first experimental evidence of the dual vortex structure that has been observed in previous computational studies. The formation of these dual vortices was also sensitive to Reynolds number, and its formation was not observed at the very low end of values considered. Digital Particle Image Velocimetry (DPIV) measurements of the cross-flow have yielded axial vorticity data at a number of streamwise stations and incidences. At low incidences only a very weak vortex structure was observed with a strong shear layer forming very close to the wing surface. As incidence was increased the shear layer lifted from the surface but reattachment was still observed. Increasing incidence also resulted in a movement of the reattachment line towards the model centre-line, until ultimately reattachment failed.

Introduction Despite these similarities, there are a number of ways in which the flows over high- and low-sweep delta wings differ, as was first identified in an experimental study by Ernshaw and Lawford9. The vortices over low sweep wings are formed much closer to the surface of the wing10, 11, so close in fact that the secondary separation of the boundary layer interacts with the separated shear layer, effectively splitting the primary vortex into two separate concentrations of vorticity6. It has also been shown that the flow over low sweep wings is sensitive to Reynolds number10, which is contrary to the accepted insensitivity of similar flows over slender delta wings12, and is a direct result of the interaction between the leading edge vortices and the surface boundary layer. While the high axial velocities associated with the vortex core formed over a slender wing have been noted in some studies6, 7, at low Reynolds numbers these jet-like velocities have not been observed5.

The subject of leading edge vortices generated over slender (Λ > 60°) delta wings is one that has attracted much attention in literature. Particularly in the case of thin wings with sharp leading edges, the flow topology is now reasonably well understood. However, the same cannot be said of the flow over plan-forms with lower leading edge sweep, and renewed interest in understanding these flows has arisen recently. Much of this renewed interest may be attributed to future Unmanned Air Vehicle (UAV) and Micro Air Vehicle (MAV) designs that utilise such plan-forms, and the resulting need to understand such flows in order to implement these designs successfully.

There are many similarities between the global flow structures observed over high- and low-sweep wings. Separation of the boundary layer on the windward surface at the leading edge results in a leading edge vortex, the core of which is located roughly one core diameter above the lifting surface in slender wings1. The presence of the vortex imparts an outboard flow to surface boundary layer beneath it, which then undergoes secondary separation as it approaches the leading edge. These features are well documented over slender delta wings2, 3, 4, and to a lesser extent non-slender wings5, 6, 7. There are further similarities. The existence of time-averaged vortical sub-structures in the free shear layer is a feature common to both forms of flow7, 8.

Although there has been much recent activity in the field of non-slender wing flows, there is much that remains unclear regarding instantaneous and time-averaged structure of the vortices formed in such flows. The purpose of this paper is to present the results of an experimental investigation into the behaviour of the leading edge vortices of a wing with 50° leading edge sweep over a range of conditions. Particular emphasis is given to the sensitivity of the flow to Reynolds number, and comparisons are made with a recent

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33rd AIAA Fluid Dynamics Conference and Exhibit23-26 June 2003, Orlando, Florida

AIAA 2003-4021

Copyright © 2003 by Ismet Gursul. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

computational study6. Flow visualization and Particle Image Velocimetry (PIV) measurements for a 50° sweep delta wing were conducted in a water tunnel study. The effects of Reynolds number, incidence, and roll angle on the formation of leading-edge vortices and the effect vortex breakdown are considered.

Experimental Setup

All experiments were conducted using the water tunnel facility at the University of Bath. The tunnel is an Eidetics Model 1520 free-surface tunnel with a 0.381 x 0.508 m working section, and can achieve speeds up to 0.45 m/s through a closed circuit continuous flow system, as shown in Figure 1. The tunnel has four viewing windows; three surrounding the test section, and one downstream allowing axial viewing. The height of the test section above the floor allows flow visualisation from below as well as from the sides.

Experiments were performed using delta wing models of 50° leading edge sweep. As shown in Figure 2, each edge of the model had a 45° bevel on the pressure surface, including the trailing edge. Bevelling of the models to create a sharp leading edge was required to ensure proper formation of the leading edge vortices13. Models were mounted in the tunnel using a sting projecting from the rear of the model, as shown in Figure 3. The sting was attached to the model using screws countersunk into the models suction surface. The models had a chord length, c = 89mm, and a thickness, t = 2mm, giving a thickness to chord ratio, t/c = 2.2%. The free stream velocity was varied in the range U∞ = 0.05 – 0.4m/s, giving Reynolds numbers in the range Rec = 4,300 – 34,700. The maximum blockage ratio was of the order of 2% at α = 30°.

Visualisation of the vortex trajectories was achieved using food colouring diluted 1:4 with water. The dye was injected into the flow near the apex of the models via a pressurised delivery system incorporating simple gate valves to control the exit velocity of the fluid. To ensure that the dye itself did not affect the formation of the vortices over the leading-edges, the exit velocity was carefully controlled. Thin metal tubes were used to transport the dye to the apex of the models.

A digital video camera with a capture rate of 25 frames per second, and a resolution of 570,000 pixels was used to capture images. The camera was interfaced to a desktop computer via a commercially available digital video capture board, which allowed real time viewing and capture of camera images. Post-processing of the data was performed using MATLAB software. The measurement uncertainty of the breakdown location from a single image was estimated to be approximately 0.01c.

Digital Particle Image Velocimetry (DPIV) measurements were undertaken to facilitate a fuller understanding of the flow. Illumination of the planes of interest was achieved using a pair of pulsed mini Nd:YAG lasers with a maximum energy of 120mJ per

pulse located underneath the working section of the water tunnel. A combination of cylindrical and spherical lenses was used to generate a light sheet of sufficient divergence and focus. Images were captured using an 8-bit digital stills camera with a resolution of 4.2 million pixels. A Hart cross-correlation algorithm14 was used to analyse the images and to produce velocity vectors suitable for further postprocessing. Each field was averaged over 100 instantaneous frames with an interval between frames of 0.267s to yield a time average spanning around 90c/U∞, and velocity vectors were calculated at over 5,000 points in each field. The flow was seeded with hollow glass particles of mean diameter of 4µm. All PIV data was taken at a free-stream velocity of U∞ = 0.3m/s, corresponding to Rec = 26,700.

Results

Effect of Reynolds Number Initial experiments used dye flow visualisation to

study the behaviour of the leading edge vortices for a range of incidences and Reynolds numbers. In general, large scale unsteadiness was found in flow field, particularly at low Reynolds numbers. The images presented in Figure 4 show the extremes of breakdown location at an incidence of α = 7.5° over the range of Reynolds numbers considered.

It is immediately obvious from Figure 4 that viscosity played an important role in the formation of the leading edge vortices in this range of Reynolds numbers. At Rec = 4300, only a very loose vortex structure was apparent, with the individual turns of the shear layer discernable. The failure to completely roll up into a concentrated vortex core was presumably the reason that no form of breakdown was observed in this condition. Increasing the Reynolds number appeared to result in a more compact vortex core, and at Rec = 8700, classical breakdown of the vortices was observed. Also apparent under these conditions was the formation of an additional vortex outboard of the primary vortex close to the leading edge, which indicated the existence of the dual vortex structure that has been observed in a previous computational study6. Further discussion of the features of the dual vortex structure is given in the following section.

A further increase in Reynolds number resulted in the upstream progression of the breakdown of the vortices, which is a curious result considering the accepted insensitivity of vortices and vortex breakdown over more slender wings12. At low Reynolds numbers the breakdown, where present, appeared to be more axisymmetric in nature, and the transition from coherent to broken vortex was rapid. However, at the higher Reynolds numbers, the form of the breakdown became less clear, and the transition seemed to be less abrupt. Care must be taken in interpreting these results, however, since diffusion of the dye at the higher Reynolds numbers may have given the impression of a less distinct breakdown region.

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Further effects of viscosity have also been identified in this research. Figure 5 shows a series of images clearly showing that the trajectory of the vortex shifted inboard towards the model centre-line as the Reynolds number was reduced. Similar variation of vortex location has been observed over more slender wings15. This variation in the location of the vortex core is plotted for all incidences in Figure 6, and compared with data presented in literature5, 6, 13. Ol and Gharib5

state that the qualitative features of the flow, such as the location of the primary vortex, do not change significantly with Reynolds number, even as low as Rec = 6200. In the present experiments, however, a clear shift of vortex location was observed as the Reynolds number was varied. A strong dependence of the vortex trajectory on incidence was also noted at low Reynolds numbers, and a degree of scatter exists in the data indicating that the flow may be sensitive to small changes in experimental set-up and measurement technique. As Reynolds number was increased, this sensitivity of the vortex trajectory to incidence reduced, which is consistent with the inviscid theory of Moore and Pullin11. The computational results of Gordnier and Visbal6 compare well with the experimental results of this investigation, although they exhibit slightly larger variation with incidence at the Reynolds number considered.

The images presented in Figure 4 indicate that the outboard vortex of the pair undergoes breakdown further upstream than does the primary vortex in all the cases considered herein, confirming the suggestion that this feature may provide a precursor which may be used to predict the onset of breakdown of the primary vortex5.

Vortex Breakdown Figure 8 shows a series of images demonstrating the

variation of the vortex breakdown location with incidence for a fixed Reynolds number, Rec = 13,000. Under these conditions, the breakdown of the leading edge vortices progressed forward as the incidence of the wing was increased. Once more, in all these cases the secondary vortex breaks down upstream of the primary vortex. An interesting feature was the occurrence of breakdown over the wing at α = 2.5°. At such a low incidence one would not normally expect to observe breakdown, especially so far forward on the wing. As indicated by Figure 6, the spanwise location of the vortex did not appear to be affected significantly by incidence at this Reynolds number.

Large fluctuations in the breakdown location of the primary vortex were observed in Figure 4 and Figure 8. Similar unsteady behaviour of the breakdown location is known to exist over slender delta wing configurations, where fluctuations of the order to 10% of the chord length have been observed16. Variations of the extremes of breakdown location over the range of incidences and Reynolds numbers considered are plotted in Figure 9. From this figure fluctuation magnitudes of the order of 50% of the chord are observed in some cases, implying that the flow over non-slender wings is significantly more unsteady than over more slender planforms. The root-mean-square (rms) breakdown location was calculated for both primary leading edge vortices at Rec = 26,700 from the time-history of breakdown locations, and was found to be independent of incidence, being roughly equal to (xBD/c)rms ≈ 0.06. This is significantly greater than (xBD/c)rms ≈ 0.03 observed over more slender planforms17.

Dual Vortex Structure The dual vortex structure was elucidated by taking

PIV measurements of the cross-flow plane. Figure 7 shows contours of constant axial vorticity in the cross flow plane at x/c = 0.4 for α = 7.5° and Rec = 8,700. The primary vortex is clearly shown as the large concentration of vorticity centred at about y/s = 0.5. The secondary separation is identified as a region of vorticity, of opposite sign, just outboard of the primary vortex. However, the figure also demonstrates clearly the dual vortex structure, with a third concentration of vorticity, with a sign consistent with the primary vortex but significantly weaker, just outboard of the secondary vortex. Outboard of this lies a region of distributed vorticity associated with the separated shear layer. Hence, the first experimental evidence of the dual vortex structure with the same sign of vorticity upstream of breakdown is presented in this study. These results are consistent with the computational simulations of Gordnier and Visbal6 performed at a higher Reynolds number, Rec = 20,000, who also noted the sensitivity of this dual vortex structure to Reynolds number, with only a single concentration of vorticity being observed at low Reynolds number. This observation is confirmed by the lack of dual vortices in Figure 4 at Rec = 4300. Considering the significant interaction between the boundary layer and primary vortex demonstrated in this and previous research, the fact that its behaviour was Reynolds number sensitive is perhaps unsurprising.

The time averaged breakdown location was studied at Rec = 26,700 for a wing with varying roll angle for a range of incidences, as shown in Figure 10. The effect of roll angle was small at low incidences, but as the angle of attack increases the locations of the primary vortex breakdowns on either side of the wing diverge. The vortex generated by the leeward leading edge reduced in strength so delaying the breakdown; conversely, the vortex generated by the windward leading edge experiences an increase in strength and breakdown is promoted. Interestingly, at α = 15°, although the breakdown of the leeward vortex is significantly delayed by the roll angle, the opposite vortex did not appear to move forward significantly. This feature was observed at all the incidences considered.

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Cross-flow Structure The nature of the flow was studied using DPIV

measurements in the cross-flow plane at x/c = 0.2, 0.4, 0.6 and 0.8 over a range of incidences and Rec = 26,700. The results of these measurements are shown in Figures 11 – 16, which show velocity vectors plotted on contours of time-averaged axial vorticity in these planes over a range of angles of attack. Note that the contour levels change between plots; the axes are normalised by local semi-span, and vorticity by local semi-span and free-stream velocity; and that some vectors have been omitted from these plots to aid clarity.

Figure 11 shows the cross-flow structure at α = 5°. At this low incidence, no region of concentrated vorticity was observed other than the distributed vorticity associated with the shear layer. The structure of the flow was similar to the computational results of Gordnier and Visbal6 for a similar Reynolds number. There was a limited region of flow reversal very close to the surface of the wing at this incidence, and all activity was constrained to a region extending no further than 0.15s above the wing surface. At α = 10° (Figure 12) a more coherent vortex structure was observed, particularly at x/c = 0.8, where inboard of the shear layer lay a region of concentrated vorticity associated with the primary vortex. The dual vortex structure was not captured in these images due to the breakdown of the vortex upstream of the measurement planes for this Reynolds number and incidence. As incidence was increased to 15°, a stronger shear layer was formed as shown in Figure 13. It is curious that toward the apex, flow beneath the shear layer did not exhibit significant amounts of swirl due to the presence of breakdown upstream, while the swirling nature of the flow was re-established further down the wing. This behaviour was also noted in Figure 14, which shows the cross-flow vorticity fields for α = 20°. The figures presented thus far also indicate the movement of the primary reattachment line inboard towards the wing centre-line. By α = 20°, the reattachment line approached the centreline. At α = 25° and 30° (Figure 15 and Figure 16), the shear layer lifted significantly away from the suction surface, and reattachment of the shear layer failed. At α = 25° and x/c = 0.4, discrete concentrations of vorticity are observed in the shear layer, possibly indicating the existence of time averaged vortical sub-structures similar to those observed in previous investigations7, 8, 18.

Conclusions

It has been shown that the formation of the vortices over a low sweep delta wing is strongly Reynolds number dependent. As Reynolds number was reduced, the trajectory of the primary vortex shifted towards the centre-line of the wing, and at very low Reynolds numbers only a very weak vortex structure was observed, with incomplete roll-up of the vortex sheet

failing to generate a concentrated vortex core. Further, the breakdown of the leading edge vortices was delayed significantly. Comparisons with data presented in literature have shown that at low Reynolds numbers, the vortex trajectory is highly dependent on incidence, and that a degree of scatter exists in the data. As Reynolds number is increased the flow approaches an asymptotic state, with further increases in the Reynolds number resulting in only small variations in the trajectory of the leading edge vortices. At these high Reynolds numbers, little variation of the trajectory with incidence was observed, which agrees well with the inviscid theory11.

The first experimental evidence of the dual vortex structure observed in previous computational studies has also been provided. This dual vortex structure is also sensitive to changes in Reynolds number, with the outboard vortex of the pair not being observed at the very low end of the values considered.

Large fluctuations of breakdown location were observed, reaching up to 50% of the chord length at low Reynolds numbers and at small incidences, indicating significant unsteadiness in the flow. Root-mean-square breakdown locations are also greater than those observed over slender wings.

Digital Particle Image Velocimetry (DPIV) measurements in the cross-flow plane have yielded images of the time-average vorticity field at a number of streamwise stations. At low incidences only a very weak vortex structure was observed despite the formation of a strong shear layer close to the wing surface. Regions of vorticity of the opposite sign to that of the shear layer were observed in a limited region close to the surface of the wing. As incidence was increased, the shear layer became elongated and lifted from the wing. Reattachment of the shear layer failed above α = 25°, indicating the onset of stall.

Acknowledgements

This material is based upon work supported by the European Office of Aerospace Research and Development, Air Force Office of Scientific Research, Air Force Research Laboratory, under Contract No. F61775-02-C4024.

References

1. Leibovich, S., “Vortex Stability and Breakdown: Survey and Extension”, AIAA Journal, Vol. 22, No. 9, pp. 1192-1206, 1984. 2. Rockwell, D., “Three-Dimensional Flow Structure on Delta Wings at High Angle-of-Attack: Experimental Concepts and Issues”, AIAA 93-0050, 31st AIAA Aerospace Sciences Meeting & Exhibit, 11-14 January 1993, Reno, NV. 3. Visbal, M. R., “Computational and Physical Aspects of Vortex Breakdown on Delta Wings”, AIAA 95-0585, 33rd AIAA Aerospace Sciences Meeting & Exhibit, 9-12 January 1995, Reno, NV.

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4. Delery, J. M., “Aspects of Vortex Breakdown”, Progress in Aerospace Sciences, Vol. 30, pp. 1-59, 1994.

11. Moore, D. W. and Pullin, D. I., “Inviscid Separated Flow over a Non-Slender Delta Wing”, Journal of Fluid Mechanics, Vol. 305, pp. 307-345, 1995. 5. Ol, M. V. and Gharib, M., “Leading-Edge Vortex

Structure of Nonslender Delta Wings at Low Reynolds Number”, AIAA Journal, Vol. 41, No. 1, pp. 16-26, 2003.

12. Erickson, G. E., “Water-tunnel Studies of Leading-Edge Vortices”, Journal of Aircraft, Vol. 19, No. 6, pp. 442-448, 1982.

6. Gordnier, R. E. and Visbal, M. R., “Higher-Order Compact Difference Scheme Applied to the Simulation of a Low Sweep Delta Wing Flow”, AIAA 2003-0620, 41st AIAA Aerospace Sciences Meeting & Exhibit, 6-9 January 2003, Reno, NV.

13. Miau, J. J., Kuo, K. T., Liu, W. H., Hsieh, S. J., Chou, J. H. and Lin, C. K., “Flow Developments Above 50-Deg Sweep Delta Wings with Different Leading-Edge Profiles”, Journal of Aircraft, Vol. 32, No. 4, pp. 787-794, 1995.

7. Honkan, A. and Andreopoulos, J., “Instantaneous Three-Dimensional Vorticity Measurements in Vortical Flow over a Delta Wing”, AIAA Journal, Vol. 35, No. 10, pp. 1612-1620, 1997.

14. Hart, D. P., “The Elimination of Correlation Errors in PIV Processing”, 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 1998. 15. Traub, L. W., Moeller, B, and Rediniotis, O., “Low-Reynolds-Number Effects on Delta-Wing Aerodynamics”, Journal of Aircraft, Vol. 35, No. 4, pp. 653-656.

8. Mitchell, A. M. and Molton, P., “Vortical Substructures in the Shear Layers Forming Leading-Edge Vortices”, AIAA Journal, Vol. 40, No. 8, pp. 1689-1692, 2002.

16. Lowson, M. V., “Some Experiments with Vortex Breakdown”, Journal of the Royal Aeronautical Society, Vol. 68, pp. 343-346, 1964.

9. Ernshaw, P. B. and Lawford, J. A., “Low-Speed Wind-Tunnel Experiments on a Series of Sharp-Edged Delta Wings”, ARC Reports and Memoranda, No. 3424, March 1964. 17. Gursul, I., and Yang, H., “On Fluctuations of

Vortex Breakdown Location”, Physics of Fluids, Vol. 7, No. 1, pp. 229-231, 1995.

10. Gursul, I., Taylor, G., and Wooding, C., “Vortex Flows over Fixed-Wing Micro Air Vehicles”, AIAA 2002-0698, 40th AIAA Aerospace Sciences Meeting & Exhibit, 14-17 January 2002, Reno, NV.

18. Gordnier, R. E. and Visbal, M. R., “Unsteady Vortex Structure over a Delta Wing”, Journal of Aircraft, Vol. 31, No. 1, pp. 243-248, 1994.

Figure 1: Schematic of water tunnel facility at the University of Bath.

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Figure 2: Model design and principle dimensions.

Figure 3: Model set-up in water tunnel.

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Rec = 4,300

Rec = 8,700

Rec = 13,000

Rec = 17,300

Rec = 34,700

Figure 4: Extremes of vortex breakdown location over Λ = 50° wing at α = 7.5° for selected Reynolds numbers.

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Current Investigation

Gordnier and Visbal6 (CFD)

Ol and Gharib5 (Flow Vis)

Ol and Gharib5 (PIV)

2.5° 5° 7.5° 10° 12.5° 15° 20°

Miau et al13 (PIV)

Figure 5: Flow visualisation of leading edge vortices at α = 15° for (from top) Rec = 8,700, 13,000, and 17,300.

Rec

y/s

0 10000 20000 30000 400000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 6: Variation of vortex position with Reynolds number.

Figure 7: Cross-flow vorticity field at x/c = 0.4, α = 7.5°, Rec = 8,700, clearly showing double vortex structure.

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α = 2.5°

α = 5°

α = 7.5°

α = 10°

α = 15°

Figure 8: Extremes of vortex breakdown location over Λ = 50° wing at Rec = 13,000 for a range of Reynolds numbers.

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x B

D/c

0

0.5

1

1.5

α=2.5°

α=5°

α=7.5°

α=10°

Rec

0 10000 20000 30000 40000

α=15°

(xBD/c) mean

0

0.2

0.4

0.6

0.8

1

α = 2.5°

α = 5°

α = 10°

φ0 10 20 30 40

Leeward VortexWindward Vortex

α = 15°

Figure 10: Variation breakdown locations of leeward and windward vortices with roll angle and incidence at Rec = 26,700.

Figure 9: Variation of extremes of breakdown location of primary leading edge vortices with Reynolds number.

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Figure 11: Axial vorticity field in cross flow planes for α = 5°, Rec = 26,700.

Figure 12: Axial vorticity field in cross flow planes for α = 10°, Rec = 26,700.

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Figure 13: Axial vorticity field in cross flow planes for α = 15°, Rec = 26,700.

Figure 14: Axial vorticity field in cross flow planes for α = 20°, Rec = 26,700.

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Figure 16: Axial vorticity field in cross flow

planes for α = 30°, Rec = 26,700. Figure 15: Axial vorticity field in cross flow planes for α = 25°, Rec = 26,700.