Unsteady Aerodynamics of Free-to-Roll Nonslender Delta Wings

A. McClain,* Z. Wang†, E. Vardaki‡ and I. Gursul§ University of Bath, Bath BA2 7AY, United Kingdom

An experimental investigation on free-to-roll delta wings with Λ=50° has been conducted. Roll time histories showed that multiple trim positions are possible. Only nonzero roll angles, or a combination of zero and nonzero roll angles, are possible, depending on the angle of attack. It was found that the free-to-roll dynamics is closely correlated with the static lift characteristics at zero roll angle. In a small range of incidences, self-excited roll oscillations are observed. The effects of leading-edge shape and wing thickness on the self-excited roll oscillations were investigated. The self-excited roll oscillations are also observed for the wing with sharp leading-edge (for which the separation point is fixed), but are much smaller in amplitude. As the amplitude of the motion is amplified for a round leading-edge, characteristics of flow separation at the leading-edge are a contributing factor. It is suggested that the interaction of the reattachment lines play an important role in the self-excited roll oscillations.

Nomenclature c = chord length Re = Reynolds number t = thickness U∞ = free stream velocity α = angle of attack Λ = leading-edge sweep angle φ = roll angle φ0 = initial roll angle

I. Introduction Unsteady aerodynamics of delta wings in roll motion is important for various applications including high speed

civil transport, spacecraft, fighter aircraft, unmanned combat air vehicles and micro air vehicles. Most of the knowledge in this area is on slender wings1-5. Equilibrium positions at nonzero roll angles and wing rock are among the important phenomena concerning the unsteady aerodynamics of slender wings. Previous studies on slender wings revealed the existence of critical states2 and the importance of vortex breakdown location3,4.

Jenkins et al2 showed that a delta wing configuration with 65 degree sweep angle had multiple stable trim points in roll. In the free-to-roll experiments, the model is released from an initial roll angle, and then is free to roll. The phase plane (roll rate versus roll angle) trajectories, corresponding to two free-to-roll time histories for the 65 degree wing at α = 30°, showed very different behaviour. For the initial roll angle φ0 = -58.3°, the trajectory finds the stable equilibrium point at zero roll angle, while for φ0 = 53.1°, the final equilibrium position is around φ = 21°. The existence of equilibrium positions at nonzero roll angles was also confirmed at other angles of attack for this slender delta wing configuration. The measured static rolling moment is around zero at these nonzero trim angles, and it is believed that asymmetric vortex breakdown is behind this behaviour.

For nonslender delta wings, experiments conducted for statically and dynamically rolled wings6 showed the similarities to and differences from the slender wings. Around the stall angle, self-excited roll oscillations7-9 were observed for a sweep angle of Λ = 45°. Somewhat similar oscillations were observed for a sweep angle of Λ = 50° * Postgraduate Student, Department of Mechanical Engineering. † RCUK Academic Fellow, Department of Mechanical Engineering. ‡ Research Officer, Department of Mechanical Engineering, Professional Member AIAA. § Professor, Department of Mechanical Engineering, Associate Fellow AIAA.

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45th AIAA Aerospace Sciences Meeting and Exhibit8 - 11 January 2007, Reno, Nevada

AIAA 2007-1074

Copyright © 2007 by Ismet Gursul. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

in a different facility10,11. These oscillations are unusual because not only are they observed for a nonslender wing, but also because the mean roll angle is nonzero. Wing rock has more typically been observed for slender wings1 with Λ > 75° with corresponding mean roll angle of zero. Self-excited roll oscillations of nonslender wings with Λ ≤ 50° appear to be more complex in their aerodynamic origins than slender wing rock. Similarities to and differences from slender wing rock are speculated in Ref. 12 and 13. However, flow physics of free-to-roll dynamics of nonslender wings is not completely understood yet. The main objective of this paper is to present results of an experimental investigation on a free-to-roll delta wing with Λ = 50°. The effects of leading-edge shape and wing thickness on unsteady aerodynamics are investigated. Nature of the self-excited roll oscillations and corresponding vortex topology are discussed.

II. Experimental setup Wind tunnel experiments were conducted in the high speed working section of the 2.13 m x 1.52 m closed circuit

facility. Models were supported using the high-alpha rig as shown in Fig. 1. The wing and sting were attached to the high-alpha rig with a ball bearing. Experiments were conducted at a constant free stream velocity of U∞ = 30m/s, giving a Reynolds number of Re = 420,000. Maximum blockage for the wind tunnel was approximately 1.5% at α = 35°. The delta wing models had a sweep angle of 50° and a total of six models were tested. The leading-edge shapes are shown in Fig. 2. Table 1 lists the chord length and thickness/chord ratios for all wings. The wing with the sharp leading-edge was made of aluminum whereas all other wings were made of polyethylene.

Roll angle was measured with a potentiometer with an estimated uncertainty of 1°. Force balance measurements were undertaken using a six-component, strain-gauged internal balance. Signals from the force balance were recorded using a desktop PC with a 12-bit A/D data acquisition card. Signals were recorded at a sampling frequency of 1000 Hz. The estimated uncertainty of lift coefficient is 4%. Surface flow visualisations were achieved using lengths of thin fluorescent thread taped to the wing. Surface flow visualisations were captured using a digital video camera with a resolution of just under 2 million pixels.

A limited number of experiments (mainly flow visualisation) were conducted in a water tunnel. The tunnel is an Eidetics Model 1520 free-surface tunnel with a 0.381 m x 0.508 m working section, and can achieve speeds up to 0.45 m/s through a closed circuit continuous flow system. A delta wing model with sharp leading-edges (t/c = 2.25%) was tested. The Reynolds number based on the chord length was Re = 26,600. As the separation point is fixed, the effect of Reynolds number is expected to be small. In these experiments, the objective was to understand the vortex topology. The model was set at fixed roll angles according to the wind tunnel experiments and flow visualisation was carried out. In these experiments, fluorescent dye was released from slots near the leading-edges, hence it “marked” the vorticity shed with separation. Planes normal to the free stream velocity were illuminated with an Argon-Ion laser.

III. Results Roll time histories showed that multiple trim positions are possible. Only nonzero roll angles, or a combination

of zero and nonzero roll angles, are possible, depending on the angle of attack. Hence it is useful to consider the force characteristics as a function of incidence, before presenting the roll time histories. Figure 3 shows the variation of lift coefficient for all wings. It is seen that the wings with sharp leading-edges have sharp stall characteristics whereas the wings with rounded leading-edges exhibit much milder stall. First, the roll characteristics of the thick wing (t/c = 10%) will be discussed in the pre-stall, stall, and post-stall regions.

At angles of attack for which vortex breakdown was over the wing, several equilibrium positions at nonzero roll angles were found, depending on the initial roll angle. Figure 4 shows the time history of roll angle for the free-to-roll wing for α = 15° for the initial roll angle φ0 = 0° (top) and φ0 = 45° (bottom). It is seen that, after the wing is released, new equilibrium roll angles are established (φ ≈ 25° and φ ≈ 35°), depending on the initial roll angle. A systematic study was conducted by varying the initial roll angle with increments of 5 degrees of roll angles over a large range of negative and positive roll angles. Negative equilibrium roll angles (mirror images) are also possible depending on the initial roll angle. It is interesting that zero roll angle is not an equilibrium position for this angle of attack. The existence of multiple roll “attractors” is somewhat similar to the observations for a slender wing2 (Λ = 65°) however, the main difference is that the zero roll angle is not an attractor for the nonslender wing for pre-stall incidences. Figure 5 shows the flow visualisation pictures for α = 20° and α = 25°, which indicate the reattachment lines for both sides at the equilibrium roll angles (around φ ≈ 40°). For increasing angles of attack, the results are similar in the pre-stall region. The asymmetric location of the reattachment lines is observed as expected.

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The flow physics behind this observation that zero roll angle is not a stable position is not clear, but is believed to be associated with reattachment, rather than vortex breakdown.

Around the stall angle, self-excited roll oscillations are observed as shown in Fig. 6. These large amplitude roll oscillations for the thick wing with rounded leading-edge are very different than the slender wing rock. The frequency and amplitude of these oscillations appeared to be independent from the initial roll angle. Self-excited roll oscillations around a nonzero attractor are not understood well. Figure 7 shows the tuft flow visualisation at three instants, corresponding to the minimum, average, and maximum roll angles, during the self-excited roll motion. The two reattachment lines are most visible for the maximum and average roll angles.

For angles of attack larger than the stall angle for this wing, the existence of zero and nonzero trim angles was observed by varying the initial roll angle, as shown by the two examples in Fig. 8. For small initial roll angles, the model reaches equilibrium around zero roll angle. For larger initial roll angles, a nonzero trim angle is observed. Finally, when the angle of attack is increased sufficiently away from the stall angle, there is only one trim position at zero roll angle, regardless of the initial roll angle, as shown in Fig. 9 for α=35°. Figure 10 shows the corresponding flow visualisation. It is interesting that, when there is no flow reattachment, the only trim position is zero roll angle. Another observation is that vortex or shear layer interactions such as vortex shedding do not induce self-excited roll oscillations, at least in this case.

In Fig. 6, the self-excited roll oscillations are demonstrated for the thick wing with rounded leading-edges. The self-excited roll oscillations are also observed for the thin wing with sharp leading-edge, but are much smaller in amplitude as shown in Fig. 11. This is the first experimental observation of such oscillations for nonslender delta wings with sharp leading-edges. Hence, even when the separation point is fixed for the sharp leading-edge, these oscillations occur. As the amplitude of the motion is amplified for a round leading-edge, characteristics of flow separation at the leading-edge are a contributing factor. In both cases, these oscillations are observed around the stall angle, where the reattachment of asymmetric flows is the most important factor.

It is also interesting that these self-induced oscillations are observed over a small range of incidence. The mean roll angle and the amplitude of roll oscillations are shown as a function of incidence in Fig. 12 for the thick wing with rounded leading-edge and the thin wing with sharp leading-edge. In this experiment, the wing is set free to roll at the smallest or largest angles of attack, and then the angle of attack is increased or decreased, without any setting of the initial roll angle. Prior to stall, the mean roll angle is nonzero and there are virtually no roll oscillations. In a critical and small range of incidence, the roll oscillations become large. With further increase in incidence, the mean roll angle becomes zero and the roll oscillations diminish. Comparison with the lift curves shown in Fig. 3 indicates that these self-excited roll oscillations occur around the stall angle. Note that stall occurs earlier for the sharp-edged wing.

For the thin wing with sharp leading-edges, it is expected that the effect of Reynolds number is negligible. Therefore, limited water tunnel flow visualisation was carried out. Figure 13 shows the laser fluorescence flow visualisation at equilibrium roll angles (taken from the wind tunnel experiments) for incidences α = 10°, 15°, and 20°. The visualised plane is located at x/c = 0.8. As the angle of attack is increased, several observations can be made. Firstly, the reattachment line on the left side moves to the right very quickly as the left vortex expands in the spanwise direction. Meanwhile, the vortex on the right side becomes smaller and more coherent. It is seen that the distance between the two reattachment lines becomes smaller with increasing angle of attack. Figure 14 shows laser fluorescence flow visualisation at minimum, average, and maximum roll angles for α = 22.5° for which self-excited roll oscillations were observed in the wind tunnel experiments. It is suggested that the interaction of the reattachment lines play an important role in the self-excited roll oscillations.

Figure 15 shows the effect of wing thickness on the aerodynamics of the free-to-roll wings in the wind tunnel. The mean roll angle and the amplitude of roll oscillations are shown as a function of incidence for wings with various leading-edge profiles. Trends are similar to those in Fig. 12, while the amplitude of the roll oscillations is smaller than that of the thick (10%) wing. Comparison with the lift curves shown in Fig. 3 indicates that the free-to-roll dynamics is closely correlated with the lift characteristics.

Ongoing work includes PIV measurements at static and dynamic roll angles to understand the flow structure and physics of the self-excited roll oscillations. Also, active flow control methods such as shear layer excitation and passive flow control methods such as boundary layer tripping are being investigated to explore the potential to attenuate these undesired roll oscillations.

IV. Conclusions An experimental investigation on free-to-roll delta wings with Λ = 50° has been conducted. Roll time histories

showed that multiple trim positions are possible. Only nonzero roll angles, or a combination of zero and nonzero

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roll angles, are possible, depending on the angle of attack. It was found that the free-to-roll dynamics is closely correlated with the static lift characteristics at zero roll angle.

In a small range of incidences, self-excited roll oscillations are observed. The effects of leading-edge shape and wing thickness on the self-excited roll oscillations were investigated. The self-excited roll oscillations are also observed for the wing with sharp leading-edge (for which the separation point is fixed), but are much smaller in amplitude. As the amplitude of the motion is amplified for a round leading-edge, characteristics of flow separation at the leading-edge are a contributing factor. Flow visualisation in wind tunnel and water tunnel suggests that the reattachment lines become closer to each other for the conditions of self-excited roll oscillations. It is suggested that the interaction of the reattachment lines play an important role in the self-excited roll oscillations.

These roll oscillations are observed in a small range of incidence and the amplitude of the oscillations decreases with decreasing wing thickness-to-chord ratio. This suggests that proper choice of leading-edge shape and wing thickness can attenuate the self-excited roll oscillations. This kind of passive control technique can be augmented with active flow control method such as shear layer excitation.

V. Acknowledgements This work is sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF,

under grant number FA8655-06-1-3058, and also by the EPSRC Academic Fellowship in Unmanned Air Vehicles.

VI. References 1Arena, A.S., and Nelson, R.C., “Experimental Investigations on Limit Cycle Wing Rock of Slender Wings”, Journal of

Aircraft, vol. 31, no. 5, Sept-Oct. 1994, pp. 1148-1155. 2Jenkins, J. E., Myatt, J. H., and Hanff, E. S., “Body-Axis Rolling Motion Critical States of a 65-Degree Delta Wing,”

Journal of Aircraft, Vol. 33, No. 2, 1996, pp. 268-278. 3Hanff, E. S., and Huang, X. Z., “Roll-Induced Cross-Loads on a Delta Wing at High Incidence,” AIAA Paper 91-3223, 9th

AIAA Applied Aerodynamics Conference, 23-25 September 1991, Baltimore, MD. 4Huang, X. Z., and Hanff, E. S., “Prediction of Normal Force on a Delta Wing Rolling at High Incidence,” AIAA Paper 93-

3686, AIAA Atmospheric Flight Mechanics Conference, 9-11 August 1993, Monterey, CA. 5Gordnier, R.E., “Computation of Vortex Breakdown on a Rolling Delta Wing”, Journal of Aircraft, vol. 32, no. 3, 1995, pp.

686-688. 6Vardaki, E., and Gursul, I., “Vortex Flows on a Rolling Nonslender Delta Wing”, AIAA-2004-4729, 22nd AIAA Applied

Aerodynamics Conference, 16-19 August 2004, Providence, Rhode Island. 7Ueno, M., Matsuno, T., and Nakamura, Y., “Unsteady Aerodynamics of Rolling Thick Delta Wing with High Aspect Ratio”,

AIAA-98-2520, 16th Applied Aerodynamics Conference, June 15-18, 1998, Albuquerque, NM. 8Matsuno, T., Yokouchi, S., and Nakamura, Y., “The Effect of Leading-Edge Profile on Self-Induced Oscillations of 45-

Degree Delta Wings”, AIAA-2000-4004. 9Matsuno, T., and Nakamura, T., “Self-induced Roll Oscillation of 45-Degree Delta Wings”, AIAA-2000-0655, 38th AIAA

Aerospace Sciences Meeting and Exhibit, 10-13 January 2000, Reno, NV. 10Hüschler, S., “Wing Rock of Nonslender Delta Wings”, Research Project Report, University of Bath, June 2003. 11McClain, A., “Aerodynamics of Nonslender Delta Wings”, MPhil Thesis, University of Bath, Department of Mechanical

Engineering, March 2004. 12Ericksson, L.E., “Wing Rock of Nonslender Delta Wings”, Journal of Aircraft, vol. 38, no. 1, January-February 2001, pp.

36-41. 13Ericksson, L.E., and Beyers, M.E., “An Analysis of Self-Induced Roll Oscillations of a 45-Degree Delta Wing”, AIAA-

2003-0737.

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Figure 1. Schematic of the experimental setup. Figure 2. Schematic of leading-edge shapes.

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LE Profile Chord (mm)

Thickness to Chord (t/c)

Reynolds number

Sharp-Edged Single Bevel 200 4% 420,000 Semi-circular 200 4% 420,000

2:1 Ellipse 200 4% 420,000 4:1 Ellipse 200 4% 420,000

Sharp-Edged Double Bevel 200 1.52% 420,000 Semi-circular 200 10% 420,000

Table 1. Main dimensions and Reynolds number for models.

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Figure 3. Variation of lift coefficient with incidence for the

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Figure 4. Time histories of roll angle for two values of initial roll angle, α = 15°.

Figure 5. Tuft visualisation for α = 20° (left) and α = 25° (right).

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Figure 6. Time history of roll angle for α = 27.5°, φ0 = 10° for rounded leading-edge.

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Figure 7. Tuminimum, av

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Figure 8. Time histories of roll angle for two values of initial roll angle, α = 32.5°.

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Figure 10. Tuft visualisation for α = 35° in the post-stall region.

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Figure 12. Variation of mean (top) and standard deviation(bottom) of roll angle as a function of angle of attack for sharp androunded leading-edges.

Figure 11. Time history of roll angle for α = 22.5°, φ0 = 25° for sharp leading-edge.

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α=10°

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Figure 13. Laser fluorescence flow visualisation at equilibrium roll angles for incidences α = 10°, 15°, 20°.

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Figure 14. Laser fluorescence flow visualisation at minimum, average, and maximum roll angles forα = 22.5°.

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Figure 15. Variation of mean (top) and standard deviation (bottom) of rollangle as a function of angle of attack for 4% thick wings.

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