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Impingement of a von Kàrmàn Vortex Street on a Dynamically Pitching Delta Wing, Part 2 - Small Cylinder Results

Roy Y. Myose*

Department of Aerospace Engineering, Wichita State University, Wichita, KS 67260-0044

and

Ismael Heron†

Bombardier Learjet, Wichita, KS 67209

A series of experiments was conducted at Wichita State University to study the effect on the vortex burst position when a von Kàrmàn vortex street from a small cylinder was impinged upon a 70-degree sweep-back delta wing. Phase comparisons between different experimental runs were accomplished, to a limited degree, by controlling the circular cylinder’s vortex shedding. A small fin was attached on the cylinder’s downstream side, and the cylinder-fin arrangement was rotated at a frequency equal to the cylinder’s natural shedding frequency. The start of the delta wing’s pitch-up was then synchronized with the fin’s rotational position. Dye flow visualization showed that the vortex burst position appeared to jump forward towards the apex and then moved gradually back toward the trailing edge in sync with the passage of the von Kàrmàn vortices. The range of forward to rear-most variation in the burst position was about 10 to 30% of chord at an angle of attack of 35 degrees, and diminished to about 5 to 10% of chord at higher angles of attack.

Nomenclature c delta wing root chord length d circular cylinder diameter f von Kàrmàn vortex shedding frequency Rec delta wing chord length based Reynolds number, U∞c/ν Red circular cylinder diameter based Reynolds number, U∞d/ν St Strouhal number, fd/U∞ U∞ freestream velocity x streamwise direction α angle of attack κ non-dimensional pitch rate, (dα/dt)c/(2U∞) ν kinematic viscosity

Introduction Recent interest in highly maneuverable military aircraft, capable of operating over a large range of angles of attack, has refocused attention on delta-shaped wings. One of the hallmark features of delta-shaped wings and strakes is the presence of a pair of vortices called leading-edge vortices. At non-zero angles of attack, there is a pressure difference between the upper suction surface and the lower pressure surface which causes a flow around the leading-edges. The flow detaches along the leading-edge into a shear layer that curls up into a spiral. The center of the spiral is tight enough that it forms, in essence, a pair of strong counter-rotating vortices. These leading-edge vortices induce velocities on the flow field and additional suction over the delta

* Professor, Associate Fellow AIAA. † Senior Engineer Flight Sciences, Member AIAA.

47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-96

Copyright © 2009 by Myose and Heron. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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wing which can account for up to 30% of the total lift at moderate angles of attack.1 For example, a 70-degree swept delta wing continues to increase its lift until about 40-degrees angle of attack.2 In comparison, symmetric two dimensional airfoils typically stall out at around 10- to 15-degrees angle of attack. Unfortunately, there are limits to the benefits produced by the leading-edge vortices. As the angle of attack is increased, there is a sudden breakdown in vortex structure followed by degeneration into a non-coherent turbulent-like flow. This phenomena, also known as vortex bursting, can be defined as a sudden expansion in radial size and an abrupt decrease in the axial velocity of the vortex.3 Once this occurs, lift is no longer enhanced aft of the burst point. Thus, the development and subsequent breakdown of leading-edge vortices is crucial to the performance of delta wing aircraft. If the delta wing is pitched to a given angle of attack and then maintained at that angle until the transient flow features die down, it is said to be tested under “static” conditions. As this process is repeated at increasing values of α, the vortex burst will be located at “fixed” positions that are closer to the apex of the delta wing as discussed earlier. In comparison, the dynamic case is the situation where the delta wing is continuously pitched, never allowing the flow features to become steady. When the delta wing is dynamically pitched upwards at a given rate, the location of the vortex burst is farther towards the trailing edge compared to the same angle of attack under static conditions.4-7 This produces a phase lag in the burst location, allowing transient values of lift to exceed those obtained during static testing. Similarly, pitching down the delta wing results in a vortex burst location forward of the static case. This produces a phase lead and a reduction in lift, compared to similar static angles of attack. Such phase lag or lead in the dynamic case means that a time delay or hysteresis effect occurs, where there is a difference in the measured lift coefficient value if the angle of attack is increasing or decreasing.8 The magnitude of the phase lag or lead increases as the pitch rate increases.7 The faster the pitch up rate, the higher the angle of attack before the vortex burst appears over the surface of the delta wing. Modern combat aircraft use either slender delta wings or highly swept leading-edge extensions (i.e., strakes) that harness vorticity. These aircraft take advantage of the phase lag hysteresis effect in an attempt to increase the performance envelope. In many cases, the increase in performance has led to aircraft with “hyper-agility,” or the ability to maneuver at very fast rates. Take, for example, the case of the Su-27 aircraft undergoing a Cobra maneuver. In this case, the aircraft enters the pitch up phase at 190 knots indicated airspeed (kias). During a 2- to 5-second time frame, the aircraft reaches 90-degrees angle of attack or more while the airspeed drops substantially to about 70 kias. The aircraft subsequently points nose down in order to accelerate and exit at a much lower angle of attack.9,10 In order to properly simulate “hyper-agile” maneuvers such as the Cobra, researchers have been focusing lately on experiments and simulations that are closer to the Reynolds number spectrum of full-scale aircraft.11 However, this involves the use of large, expensive, and heavily mechanized models and mounts that are necessary to replicate the high-rate maneuvers in pitch (and/or yaw and roll).12 Even with this, it is seldom possible to replicate the exact full-scale Reynolds numbers. Another problem with this approach is the control of the freestream velocity fluctuation that naturally occurs during many of these “hyper-agile” maneuvers. Many water and wind tunnels are not capable of decelerating their flow velocity rapidly enough, especially those large enough to accommodate the mounts necessary to accomplish the full-scale Reynolds numbers and the motions being simulated. At the opposite edge of the Reynolds number spectrum, renewed interest in MAV’s and UAV’s have promoted research into time-dependent methods of achieving high wing-loadings, high maneuverability, and small physical size. With these issues in mind, a low-cost movable delta wing mount was developed for use in the Wichita State University water tunnel in order to study the effect of simultaneous rapid pitch and freestream velocity changes. The vortex burst position was measured as a function of the pitch rate and acceleration or deceleration of the freestream velocity. Past work has described the development of the towing system13, some preliminary work,14 fast pitch-up under deceleration,15 and deceleration and acceleration at moderate and fast pitch-up and pitch-down rates.16 The present investigation does not consider changes in the overall freestream condition, i.e., the delta wing is towed at a steady fixed speed. However, it does consider a different kind of variation in the incoming flow upon the delta wing. In order to provide payload carrying capability, most aircraft have a fuselage body. At moderate to high angles of attack, the fuselage forebody forms vortices which are somewhat similar to the leading-edge vortices of delta wings. These forebody vortices mix and interact with the leading-edge vortices, and under certain conditions (e.g., at high angles of attack), the forebody vortices can shed asymmetrically (before the leading-

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edge vortices shed in wing rock motion). This leads to a periodic yawing motion called “coning” which occurs in the 3- to 5-Hz range depending upon freestream velocity and angle of incidence.17 The shedding of the forebody vortices is similar to von Kàrmàn vortex shedding which is observed in circular cylinders and other bodies of revolution.18 The forebody vortex shedding is Reynolds number dependent: when the Reynolds number is sufficiently close to transitional, small micro-asymmetries on the surface or in the flow field force transition on one side of the forebody. This causes the separation point to move farther around the circumference towards the lee side of the cylinder and causes a side force to be generated. The ensuing sideways motion of the body creates a “moving wall” effect where the local relative velocity increases or decreases due to the movement of the solid boundary. This then results in the opposite side being forced into turbulent transition which produces a restoring side force. This back-and-forth yawing motion becomes harmonic, and manifest themselves as excursions in the 3- to 5-Hz range.19 Although the angle of attack is very high, the phase lag effect during a pitch-up maneuver means that the forebody vortex shedding may be occurring while the delta wing has a coherent and organized leading-edge vortex structure. At its most basic level, the shedding of forebody vortices and the effect it has on the leading-edge vortices should be somewhat similar to that of a von Kàrmàn vortex street and leading-edge vortices. Both the forebody vortices and von Kàrmàn vortices are harmonic and periodic, and both involve the convection of vorticity with velocity vector fluctuations. By introducing a circular cylinder of appropriate diameter, von Kàrmàn vortices with frequencies in the 3- to 5-Hz range can be made to impinge upon the leading edge vortices of a delta wing. The goal is to study the effect of impinging von Kàrmàn vortices on delta wing vortex burst behavior, and the present paper is part of a series of experiments on this topic. Past papers have considered the fixed angle of attack case20,21, preliminary results for the pitch-up case22, and the full results for the large circular cylinder (3-Hz) case23.

Experimental Method An existing water tunnel facility was used to create a towing facility where dynamic pitching and dynamic freesteam could be obtained. The upper illustration of Figure 1 shows a schematic diagram of the water tunnel located in Wichita State University’s National Institute for Aviation Research.24 This facility is a closed-loop tunnel containing 3500 gallons of water, and consists of a 2- by 3- by 6-feet test section. The facility has excellent optical access providing two side views, a bottom view, and an end view. The water tunnel is capable of producing flow velocities up to 1 ft/s using an impeller pump driven by a 5-hp variable-speed motor. For the purposes of the present investigation, however, the tunnel was used as a simple water tank with the pump turned off. The photograph in the lower half of Figure 1 shows the towing system with an inverted delta wing mounted on a carriage (which is not visible). The carriage itself rides on top of a track which is built into an aluminum frame. A lightweight “false ceiling” is built into the frame to suppress bow waves which may be created by towing the model support strut if there were a free surface. Towing speeds of 0.4 ft/s + 5% is obtained by pulling the carriage with a spring-tensioned nylon wire and a DC motor. The delta wing model (70-degree sweepback, 12-inch root chord, 1/8-inch thick, sharp leading edge beveled at a 30 degree angle) is mounted upside down, such that “pitch-up” involves rotating the delta wing apex down towards the floor of the water tunnel. This arrangement reduces the likelihood of carriage derailment since the delta wing provides additional down force for the carriage wheels. The towing speed is kept constant at 0.4 ft/s in the present investigation so that the Reynolds number based on the delta wing’s 12-inch root chord length corresponds to 33,000. Visible in the photograph of Figure 1 is the tandem strut mounting mechanism for the delta wing. The larger diameter strut is attached to a hinge on the delta wing’s pressure side. The smaller diameter strut located on the downstream side is attached to a cam mechanism on the carriage which is driven by a small DC motor. This allows the delta wing to be pivoted about the 50% root chord location at non-dimensional pitch rates up to κ=0.2. For the delta wing vortex burst location measurements, dye flow visualization was used. The resulting flow visualization image was video-taped and information such as the towing carriage velocity and delta wing angle of attack were also recorded. The flow visualization images and the relevant information were subsequently analyzed using a computer-assisted image analysis software tool. Additional details about the towing system, measurement technique, and results of the delta wing vortex burst validation tests are presented

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in reference 13. A brass ¼ inch diameter cylinder was used to create the von Kàrmàn vortex street upstream of the delta wing, as illustrated in Figure 2. This cylinder was located ¼ chord (i.e., 3 inches) upstream of the apex when the delta wing is at zero degrees angle of attack. Based on a freestream (towing) speed of 0.4 ft/s, the Reynolds number of the circular cylinder is 625. Using 0.21 for the circular cylinder Strouhal number,25 the corresponding natural shedding frequency is about 5 Hz. In order to reduce phase differences between different experimental runs, a ½ inch long 0.02 inch thick fin (spanning almost the entire cylinder span) was attached to the downstream side of the circular cylinder. The cylinder/fin arrangement was then rotationally driven +45 degrees at a frequency equal to the natural shedding frequency of the cylinder. This forced rotation provided a means of controlling the time (i.e., phase) at which von Kàrmàn vortices were shed off of the cylinder. There does not appear to be any results in the literature for forced rotation of a circular cylinder with a fin. However, Cimbala and Leon26 and Cimbala and Garg27 conducted experiments on a circular cylinder with a fin that was free to rotate. They found that a cylinder with a fin which is free to rotate about its length will move to a fixed stable angle with respect to the freestream velocity vector. The angle where the fin rested became greater as the “chord” length of the fin increased. In Cimbala’s experiments, the fin was free to move, and did so to a steady fixed angle as a consequence of the presence of the vortex wake system. The present forced rotation system was conceived as a “reversal” of this cause-effect relationship. Flow visualization experiments performed in a two-dimensional water table indicated that the von Kàrmàn vortices were shed when the fin moved to its furthest angle. This phase locking could be achieved for frequencies close to the natural shedding frequency of the cylinder. Although dye injection hardware was located on both the port and starboard sides of the delta wing, dye was only injected out of the port side, i.e., the side closest to the camera (see Figure 1 and the left-hand illustration of Figure 2). A different color dye (than the dye from the delta wing) was injected into the von Kàrmàn vortices of the circular cylinder to mark the location of the vortex filaments which then convected downstream to impinge upon the delta wing. Although both counter-clockwise and clockwise rotation von Kàrmàn vortices are illustrated in Figure 2, only the port side vortices were visualized because the dye injection port was located at the base of the fin. This meant that the fin prevented any dye from forming a visible vortex on the starboard side. There are a few limitations with this experimental set-up that need to be acknowledged: 1. The location of the vortex burst is accomplished by identifying where the core flares out (bubble burst),

or the location of the first sharp kink (spiral burst). As such, the identified location may or may not coincide with the actual core stagnation point. The assumption that the two are close, if not coincident, has been done in the past.

2. Some of the features observed cannot be explored further using this system, thus a certain amount of interpretation must be exercised. Nevertheless, the uncertainty should be within ± 0.05c.

3. Dye can migrate between the von Kàrmàn vortex and the delta wing leading edge vortex. However, highly contrasting colors (red and blue) were used as dye markers for the two different vortex systems. Furthermore, color filtering was used whenever necessary during image processing to minimize this potential problem issue.

4. There was more fore-aft “play” in the cylinder end roller “skate” (see Figure 2) with the small cylinder, compared to the large cylinder case23. Different roller “skate” lengths and water-resistant lubricants were tried, but the oscillation frequency for the small cylinder had more variation (i.e., slightly off from 5 Hz) compared to the large cylinder case.

5. Literature (cf. Koochesfahani28,29 and Triantafyllou et al.30) on airfoils undergoing oscillatory pitch motion indicate that a slight amount of thrust is generated. This means that the cylinder wake may exhibit a slight jet-like velocity profile rather than a typical wake velocity profile. However, the ¼ chord upstream location of the cylinder corresponds to a distance of 12 cylinder diameters. It would be expected that the thrusting jet-like velocity profile will dissipate with downstream distance. However, no attempt was made to quantify this dissipation.

6. Since the delta wing’s angle of attack changes, the von Kàrmàn vortices do not remain perpendicular to the delta wing’s leading edge vortices. This means that the orientation of the two-vortex system’s rotational axes changes as the delta wing is pitched up.

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Results Broadly speaking, three different test conditions were considered with the small cylinder: (1) delta wing pitched up over a large α range (15 to 55 degrees) at a fast pitch-up rate of κ=0.2, (2) pitched up over a small α range (35 to 55 degrees) at κ=0.2, and (3) pitched up over a small α range (35 to 55 degrees) at slow pitch-up rate of κ=0.1. In each case, the delta wing was towed from a standstill and reached steady state (static) conditions at the specified angle of attack (15 or 35 degrees) before pitch-up was commenced at the specified pitch rate. The command to commence pitch-up was given when the circular cylinder’s fin was located at one of four different positions: (1) port, (2) center moving toward starboard, (3) starboard, and (4) center moving toward port. Typically three experimental runs were made (to provide repeats) for each of these four different fin positions as the start of the pitch-up maneuver. Each run typically involved analyzing 60-100 different flow visualization images, for a net total of 6301 video frames from the 76 different runs associated with two different cylinder sizes (for Parts 1 and 2). For the sake of brevity, one representative experimental run is shown for each test condition (α range, pitch rate κ, and fin position). The first group of Figures (Figures 3 to 6) deal with a large α range (15 to 55 degrees) at the fast pitch up rate of κ= 0.2. The discontinuities in the vortex burst position appear to be related to the position of the cylinder: the passing of the port vortex filament appears to synchronize with the aft movement of the burst location of the port leading edge vortex very well (in most cases). In most cases, the time period between oscillations changed from one peak to the next. At the same time, by tracing the von Kàrmàn vortex filaments’ position histories (solid slanted lines), it can be seen that the discontinuities in the leading edge vortex burst position coincide with the passage of the filaments, even when the frequency (or the period between successive port excursions of the cylinder) is irregular. In this set of Figures, the average vortex burst propagation average appeared to jump forward at a very fast rate at first (between 15 < α < 30 degrees), followed by a slow forward progression in the neighborhood of 0.1 x/c per second, stabilizing at 0.1 x/c. The character of the jump in the burst position was such that the magnitude of the change in burst location with the passage of the von Kàrmàn filaments varied slightly with angle of attack α. At low values of α, the magnitude was largest (around 0.2 x/c), reducing in magnitude as the angle α increased. This is may be a consequence of a change in the strength of the vortex burst. At low angles of attack, there is a small enough swirl velocity so that the mixing from the von Kàrmàn filaments promotes a large change in position. As the swirl velocity increases with the pitch-up, it becomes more difficult for the passing filaments to “dislodge,” or move the burst axially. This behavior had also been observed, to some extent, with the fixed cylinder and the large oscillating cylinder.21-23 Continuing with the small α-range (35 to 55 degrees) in Figures 7 through 10, the same trend, generally speaking, was replicated in this case. In fact, the forward movement in the burst location occurs during the first 5 or 10 degrees of α movement, followed by an almost static burst behavior, indicating that the equilibrium position had been reached. This initial movement was in some cases more like a discrete jump, rather than a smooth movement. The last group of Figures (Figures 11 to 13) shows the effect of the slower pitch rate (κ= 0.1) with the small α-range. This group of images involved somewhat reduced (physical) sizes compared to other cases. The combination of pitch rate, small range of angles of attack, and small cylinder, resulted in very small features. In the interest of maintaining the highest level of accuracy a number of runs were thrown out based on the following criteria: 1. Because of the sometimes large mixing that occurs during the collision between vortices, a clear and

defined burst location is necessary in order for the frame to count. If the burst location is not apparent, then that frame was skipped.

2. If more than 2/3 of the frames were skipped throughout the run, or if enough frames were skipped consecutively such that the plotted data became disjointed, the run was eliminated from consideration. This reduced the number of runs available for analysis.

In general, these experiments (with slower pitch rate and reduced α-range) exhibited a smaller disturbance in the vortex burst location due to the von Kàrmàn filament passage than in previous experiments. The forward propagation of the burst was also at a slower pace, less than 0.1x/c per second. At a fast pitch rate (Figure 14), the burst propagation movements occurred both forward and aft of the no-cylinder burst locations (bold line). At low values of α the envelope was observed to encompass a maximum

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of 0.3x/c fore and aft of the bold line (at α= 35 degrees), with complete runs falling either forward (such as the center-starboard and starboard phase cases) or aft (such as the port phase cases). As the angle of attack increases, the envelope converges somewhat, but not symmetrically. The runs whose burst positions started aft of the bold line (at a lower α) remained a considerable distance aft at the highest values of α, while the runs forward of the bold line migrated aft. This gives the impression, at very high values of α, that the burst propagation movements were constrained to locations aft of the bold line. This behavior also gives the impression of two distinct groups of data, with one group shifted vertically with respect to the other. It should be noted, however, that the starboard side burst should be experiencing a mirror image response. That is, the starboard side leading edge vortex would burst forward of the bold line while the port side burst would be aft. Conversely, the starboard side burst would be aft of the bold line while the port side burst would be foreward. It should be noted that the limited number of runs for the small cylinder case makes the observations somewhat preliminary. If these observations are correct though, one possible explanation is that the small cylinder had more energy (due to the faster angular movement of the small cylinder), and was thus able to excite perturbations within the leading edge vortex core at levels high enough to trigger bursting farther upstream (or downstream). One additional note is that the small cylinder was able to produce enough thrust to deflect the cylinder. A second possible explanation is that the shorter wavelength between von Kàrmàn filaments was able to excite certain instabilities. For example, a spring-mass system will tend to resonate when excited at or near its natural frequency, thus exhibiting a filtering effect. This higher frequency of excitation may have triggered components of internal instabilities in the vortex core, leading to a faster growth than otherwise in a normal non-disturbed flow. Figure 15 (small angle of attack range from 35 < α < 55 degrees) indicate that the burst location is almost symmetrically distributed fore and aft of the no-cylinder bold solid line. This same behavior, perhaps with a slightly smaller range of movement, was also observed in Figure 16 (small α-range slow pitch-up rate). Since the experiment was repeated with a small α-range at both high and low pitch rates, at face value one must conclude that starting the pitch-up at α= 15 degrees changes the extent of the expected vortex burst location shift to an envelope mostly aft of the bold solid line.

Summary A series of experiments was conducted at Wichita State University to study the effect on the vortex burst position when a von Kàrmàn vortex street from a small cylinder was impinged upon a 70-degree sweep-back delta wing. Phase comparisons between different experimental runs were accomplished, to a limited degree, by controlling the circular cylinder’s vortex shedding. A small fin was attached to the cylinder’s downstream side, and the cylinder-fin arrangement was rotated at a frequency equal to the cylinder’s natural shedding frequency. The cylinder was rotated +45 degrees at a frequency of 5 Hz. The start of the delta wing’s pitch-up was then synchronized with the fin’s rotational position, either fully port, center moving toward starboard, starboard, or center moving toward port. Dye was used to visualize the delta wing’s leading edge vortex burst as well as the von Kàrmàn vortices using a different colored dye. Results showed that the visualized vortex burst position on the delta wing appeared to jump forward towards the apex and then moved gradually back toward the trailing edge in sync with the passage of the von Kàrmàn vortices. The range of forward to rear-most variation in the burst position was about 10 to 30% of chord at an angle of attack of 35 degrees, and diminished to about 5 to 10% of chord at higher angles of attack.

References

1. Polhamus, E. “A Concept of the Vortex Lift of Sharp-Edge Delta Wings Based on a Leading-Edge Suction Analogy,” NASA TN D-3767, Dec. 1966.

2. Earnshaw, P.B. and Lawford, J.A., “Low-Speed Wind Tunnel Experiments on a Series of Sharp-Edged Delta Wings,” Aeronautical Research Council, R M No. 3424, 1964.

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4. LeMay, W.P., Batill, S.M., and Nelson, R.C., “Vortex Dynamics on a Pitching Delta Wing,” AIAA

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Journal of Aircraft, Vol. 27, No. 2, 1990, pp. 131-138. 5. Miller, L.S., and Gile, B.E., “Effects of Blowing on Delta Wing Vortices During Dynamic Pitching,”

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AIAA Journal, Vol. 32, No. 4, 1994, pp. 716-725. 7. Myose, R.Y., Hayashibara, S., Yeong, P.C., and Miller, L.S., “Effect of Canards on Delta Wing Vortex

Breakdown during Dynamic Pitching,” AIAA Journal of Aircraft, Vol. 32, No. 2, 1997, pp. 168-173. 8. Al-Garni, A.Z., Ahmed, S.A., Sahin, A.Z., and Al-Garni, A.M., “An Experimental Study of a 65-Degree

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10. Kolano, E., “Flying the Flanker,” Flight Journal, http://flightjournal.com/articles/su27/Su27_5.asp 11. Ericsson, L. E., “Effect of Fuselage Geometry on Delta-Wing Vortex Breakdown,” AIAA Journal of

Aircraft, Vol. 35, No. 6, Nov. 1998. 12. Schaeffler, N. W., and Telionis, D. P., “Apex Flap Control of Dynamic Delta Wing Maneuvers,” AIAA

Paper 96-0662, 1996. 13. Heron, I. and Myose, R. Y., “Development of a Dynamic Pitch and Unsteady Freestream Delta Wing

Mount For A Water Tunnel,” AIAA Paper 2003-3527, June 2003. 14. Heron, I. and Myose, R. Y., “Vortex Burst Behavior Under Dynamic Freestream,” AIAA Paper 2005-

0063, January 2005. 15. Heron, I. and Myose, R. Y., “Delta Wing Vortex Burst Behavior Under Dynamic Freestream, Part 1 -

Fast Pitch-up During Deceleration,” AIAA paper 2007-6725, August 2007. 16. Myose, R.Y. and Heron, I., “Delta Wing Vortex Burst Behavior Under Dynamic Freestream, Part 2 -

Deceleration and Acceleration at Moderate and Fast Rates,” AIAA paper 2007-6726, August 2007. 17. Ericsson, L.E., “Cobra Maneuver Unsteady Aerodynamic Considerations,” AIAA Journal of Aircraft, Vol.

32, No. 1, 1995, pp. 214-216. 18. Beyers, M. E., and Ericsson, L. E., “Unsteady Aerodynamics of Combat Aircraft Maneuvers,” AIAA

Paper 97-3647, 1997. 19. Sibilski, K., “Problems Of Maneuvering At Post-Critical Angles Of Attack-Continuation and Bifurcation

Methods Approach,” AIAA Paper 2003-0395, 2003. 20. Heron, I. and Myose, R. Y., “Impingement of a von Kàrmàn Vortex Street on a Delta Wing,” AIAA paper

2004-4731, August 2004. 21. Heron, I. and Myose, R. Y., “Impingement of a von Kàrmàn Vortex Street on a Delta Wing,” AIAA

Journal of Aircraft, Vol. 42, No. 4, 2005, pp. 1084-1087. 22. Heron, I. and Myose, R. Y., “Impingement of a von Kàrmàn Vortex Street on a Dynamically Pitching

Delta Wing,” AIAA paper 2006-0057, January 2006. 23. Heron, I. and Myose, R. Y., “Impingement of a von Kàrmàn Vortex Street on a Dynamically Pitching

Delta Wing, Part 1 - Large Cylinder Results,” submitted for presentation at the 2009 AIAA Aerospace Sciences Meeting.

24. Johnson, B.L., “Facility Description of the Walter H. Beech Memorial 7 x 10 foot Low-Speed Wind Tunnel,” AR93-1, National Institute for Aviation Research, Wichita State University, June 1993.

25. Roshko, A., “On the Development of Turbulent Wakes from Vortex Streets,” NACA Report 1191, 1951. 26. Cimbala, J.M. and Leon, J., “Drag of Freely Rotatable Cylinder/Splitter-Plate Body at Subcritical

Reynolds Number,” AIAA Journal, Vol. 34, No. 11, November 1996, pp. 2446-2448. 27. Cimbala, J.M. and Garg, S., “Flow in the Wake of a Freely Rotatable Cylinder with Splitter Plate,” AIAA

Journal, Vol. 29, No. 6, June 1991, pp. 1001-1003.

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28. Koochesfahani, M.M., “Vortical Patterns in the Wake of an Oscillating Airfoil,” AIAA Journal, Vol. 27, No. 9, September 1989, pp. 1200-1205.

29. Koochesfahani, M.M., “Vortical Patterns in the Wake of an Oscillating Airfoil,” AIAA Paper 87-0111, January 1987.

30. Triantafyllou, M.S., Techet, A.H., and Hover, F.S., “Review of Experimental Work in Biomimetic Foils,” IEEE Journal of Oceanic Engineering, Vol. 29, No. 3, July 2004, pp. 585-593.

Figure 1: Schematic diagram of Wichita State 2- by 3-feet water tunnel (top)24 and photograph of test section showing the towing system with an inverted delta wing and oscillating cylinder in front of the delta wing (bottom).

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Figure 2: Schematic diagram of the towed delta wing – circular cylinder system (left) and envisioned leading edge vortex – von Kàrmàn vortex street interaction (right). Note that the illustrations on the right-hand side have been inverted from the actual physical mechanism illustrated on the left, which pitches downward.

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at A

pex)

Angle of Attack (deg)

PortStarboard

Figure 5: Large α range (15 to 55 degrees), fast pitch-up rate (κ = 0.2), start of pitch-up (at time t=0) synchronized with fin located at starboard position.

11

53.35045403530

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Elapsed Time (s)

Bur

st L

ocat

ion

(x/c

, x=0

at A

pex)

Angle of Attack (deg)

PortStarboard

Figure 6: Large α range (15 to 55 degrees), fast pitch-up rate (κ = 0.2), start of pitch-up (at time t=0) synchronized with fin located at center position moving toward port.

51.550454035

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Elapsed Time (s)

Bur

st L

ocat

ion

(x/c

, x=0

at A

pex)

PortStarboard

Angle of Attack (deg)

Figure 7: Small α range (35 to 55 degrees), fast pitch-up rate (κ = 0.2), start of pitch-up (at time t=0) synchronized with fin located at port position.

12

5450454035

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Elapsed Time (s)

Bur

st L

ocat

ion

(x/c

, x=0

at A

pex)

PortStarboard

Angle of Attack (deg)

Figure 8: Small α range (35 to 55 degrees), fast pitch-up rate (κ = 0.2), start of pitch-up (at time t=0) synchronized with fin located at center position moving toward starboard.

5350454034.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Elapsed Time (s)

Bur

st L

ocat

ion

(x/c

, x=0

at A

pex)

PortStarboard

Angle of Attack (deg)

Figure 9: Small α range (35 to 55 degrees), fast pitch-up rate (κ = 0.2), start of pitch-up (at time t=0) synchronized with fin located at starboard position.

13

535045403533.7

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Elapsed Time (s)

Bur

st L

ocat

ion

(x/c

, x=0

at A

pex)

Angle of Attack (deg)

PortStarboard

Figure 10: Small α range (35 to 55 degrees), fast pitch-up rate (κ = 0.2), start of pitch-up (at time t=0) synchronized with fin located at center position moving toward port.

50454035

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Elapsed Time (s)

Bur

st L

ocat

ion

(x/c

, x=0

at A

pex)

PortStarboard

Angle of Attack (deg)

Figure 11: Small α range (35 to 55 degrees), slow pitch-up rate (κ = 0.1), start of pitch-up (at time t=0) synchronized with fin located at port position.

14

50454033

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Elapsed Time (s)

Bur

st L

ocat

ion

(x/c

, x=0

at A

pex)

Angle ofAttack (deg)

PortStarboard

Figure 12: Small α range (35 to 55 degrees), slow pitch-up rate (κ = 0.1), start of pitch-up (at time t=0) synchronized with fin located at starboard position.

34 40 45 51

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Elapsed Time (s)

Bur

st L

ocat

ion

(x/c

, x=0

at A

pex)

PortStarboard

Angle of Attack (deg)

Figure 13: Small α range (35 to 55 degrees), slow pitch-up rate (κ = 0.1), start of pitch-up (at time t=0) synchronized with fin located at center position moving toward port.

15

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

20 25 30 35 40 45 50 55

Angle of Attack α (deg)

Bur

st Lo

catio

n (x

/c, x

=0 a

t Ape

x)No Cylinder

Port k=0.2, 15 to 55, Exp 1 (205)

Port k=0.2, 15 to 55, Exp 3 (208)

Stbrd k=0.2, 15 to 55, Exp 2 (218)

Stbrd k=0.2, 15 to 55, Exp 3 (223)

Ctr Stbrd k=0.2, 15 to 55, Exp 3 (241)

Ctr Prt k=0.2, 15 to 55, Exp 1 (244)

Burst Location Envelope

Figure 14: Burst envelope for large α range (15 to 55 degrees) at fast pitch-up rate (κ = 0.2).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

20 25 30 35 40 45 50 55 60

Angle of Attack α (deg)

Bur

st L

ocat

ion

(x/c

, x=0

at A

pex)

No Cylinder

Port k=0.2, 35 to 55, Exp 1 (210)

Port k=0.2, 35 to 55, Exp 1 (213)

Stbrd k=0.2, 35 to 55,Exp 1 (230)

Ctr Stbrd k=0.2, 35 to 55, Exp 2 (232)

Ctr Port k=0.2, 35 to 55, Exp 2 (249)

Burst Location Envelope

Figure 15: Burst envelope for small α range (35 to 55 degrees) at fast pitch-up rate (κ = 0.2).

Fig. 3

other run

Fig. 5

other run

Fig. 4

Fig. 6

Fig. 7

other run

Fig. 9

Fig. 8

Fig. 10

16

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

20 25 30 35 40 45 50 55

Angle of Attack α (deg)

Bur

st L

ocat

ion

(x/c

, x=0

at A

pex)

No Cylinder

Port k=0.1, 35 to 55, Exp 1 (258)

Stbrd k=0.1, 35 to 55,Exp 1 (262)

Ctr Port k=0.1, 35 to 50, Exp 2 (253)

Stbrd k=0.2, 35 to 55, Exp 3 (265)

Burst Location Envelope

Figure 16: Burst envelope for small α range (35 to 55 degrees) at slow pitch-up rate (κ = 0.1).

Fig. 11

Fig. 12

Fig. 13

other run