9/21/97

Mark A. Klein
USAF Senior Knight


Wright Laboratory - Aeromechanics Division
WL/FIMA - Aerodynamic Components Rersearch Branch

Currently in Ph.D. Program @

School of Aerospace Engineering

Summer 1997 Experimental Results

Results from 45° Delta Wing:

Previous experiments have shown that an F-15 model generates nearly periodic velocity fluctuations near the top of the vertical tails. A flat-plate, delta wing with the same wing planform shape and size as the model F-15 (i.e. sweep angle of 45°) also exhibits similar fluctuations at the same geometrically defined tail position. Figure 1 shows that the peak frequency variation with freestream speed and angle of attack is comparable between the model and representative delta wing. This delta wing model was selected for further testing because of its connection with the F-15 model and because even without the vortex burst phenomenon present, fluctuations were clearly present.

To investigate whether a region exists on this delta wing model where Rayleigh's theorem for an unstable boundary layer due to centrifugal instabilities is violated, a quantitative three-dimensional velocity field is needed. Three components of velocity were taken in a plane at the X = 7.776" downstream location. Due to limited LV capabilities, each component of velocity was taken separately. The steady mean flow conditions made this possible. Each mean velocity component was determined from an average of the 25,000 points of data collected at each planar grid point.

Figure 2 shows the planar vector field obtained in tunnel fixed coordinates. The leading edge in this figure is located at Y=7.776". Visible in the streamwise component of velocity (U-contours) is the leading edge shear layer region. Below the leading edge shear is the primary vortex. The primary vortex is not a well defined, strong "jet-like" vortex as seen on highly swept configurations; it is clearly "wake-like" in nature, showing even mean flow reversal. This mean flow reversal may be spurious due to the measurement plane not being perpendicular to the vortex axis. What is definite is that the mean axial flow in the primary vortex is much less than the freestream. The in-plane velocity vectors in the figure show the vortex swirl as broad and not tightly wrapped.

One of the primary reasons for needing this type of velocity data is to identify regions of high shear and to investigate other quantitative details about a delta wing vortex. To illustrate the rotational nature of the vortex, a vertical line of closely spaced spanwise velocity data is shown in Figure 3. Between 0.5" and 2" from the model surface, the spanwise velocity is nearly linear and switches from positive to negative. This is the same condition seen in rigid body rotation: linear increasing tangential velocity along rays from the axis of rotation. In the region below Z = 0.5", there appears to be fairly unsteady nature to the mean profile followed by a rapidly decelerated surface shear layer. The rather benign velocity profile above Z = 0.5" suggests little to look for in the way of unstable shear profiles. Below Z = 0.5", the velocity profile suggest something interesting is occurring. These features seem consistent with the idea of vortical structures developing out of the vortex/surface shear region due to centrifugal instabilities. Further testing will be devised to investigate this region.

Centrifugal Instability Investigation

Introduction:

It has been shown that counter-rotating structures (Görtler vortices) form in the vortex/surface interaction region over a delta wing at angle of attack. These structures convect around the primary vortex in a helical fashion, causing nearly periodic velocity fluctuations in the flowfield. A centrifugal instability is hypothesized as the driving mechanism for the generation of the structures which form with a preferred frequency as a function of velocity and angle of attack. Figure 4 shows a summary of the results obtained by Hubner (Ref. 1). Through the past research by Hubner and this present research, many questions have been answered regarding the origin of the fluctuations, but there are also many unanswered questions and new questions that need further research to answer. Specifically, what is the mechanism that selects the dominant peak frequency and generates the frequency characteristics seen in experiments? Can experimentally investigating the centrifugal instability mechanism offer insight into this, such that a frequency prediction tool can be developed? Can the results of this investigation be applied to an actual fighter aircraft to reduce tail buffeting? These questions are to be answered by the my research.

Background on Rotating Cones:

To investigate the centrifugal instability mechanism in an approximately conical vortex flow near a surface, an equivalent centrifugal instability experiment is devised using the knowledge that rotating cones produce counter-rotating vortices similar to those seen on the delta wing. Figure 5 shows flow visualization of the boundary layer transition of a 15° total included angle cone rotating in axial flow; Uinf.=1.8 m/s, and N=2000 r.p.m (Ref.2). Seen in this figure is a laminar flow region at the front of the cone; a transition region in the middle of the cone where well organized spiral vortices are present, and a turbulent region at the aft of the cone where the organization has broken down. In Figure 6 a close-up, cross-sectional view of the spiral vortices, each spiral structure is shown to be composed of two counter-rotating vortices (Ref. 3). These vortices are defined as a Görtler vortex pair. Figure 7 shows the transition region of the boundary layer on this 15° cone rotating in still fluid; Uinf.=0 m/s, and N=500 r.p.m (Ref. 3). At the no flow condition, the vortices are toroidal and travel down the cone before becoming turbulent.Figure 8 presents a diagram of the rotating cone experiments and data identifying the flow conditions necessary for the formation of the vortices (Ref. 2). Also identified in this figure are the critical and transitional Reynolds numbers. These identify the furthest upstream position where periodic structures can be measured (Rec) and the downstream position where all periodicity is lost and the flow is fully turbulent (Ret). It is important to note the conditions that result in the forming of Görtler vortices, because not at all rotation speeds for a given cone angle do these structures form. This implies that a similar set of conditions may be necessary for these instabilities to form in a vortex flow over a delta wing.

Rotating Cone Analogy Experiment:

To check the conditions that produce fluctuations on a delta wing, the velocity field is needed in a planner region. This is given in the LV results from the 45 deg. delta wing. According to Rayleigh's Theorem (Ref.4), the flow becomes unstable if the azimuthal velocity decreases outward at a rate greater than 1/r. As shown in Figure 3, The region below the vortex near the surface experiences a deceleration, which violates Rayleigh's Theorem for a stable velocity profile. A rotating cone has similar cross-flow behavior; pure cross-flow at the surface which decelerates radially to pure axial flow due to a freestream, if one is present. If we define the radius of the rigid body "cone" rotation as the radius of rigid body rotation of the 45 deg. delta wing vortex, an approximate 1.0 in. radius cone can be defined at this downstream location. Defining a "cone" based on this, produces a 15° total included angle cone. Because of the model surface is such close proximity to the vortex, the outer portions of the vortex are more oval than circular. To calculate the rotation speed of the "cone" surface, spanwise velocity at the perimeter of the 1.0 in. radius "cone" is used. The range of rotational speeds is between 525 and 740 rpm, and depends on the position around the perimeter of the "cone". This falls directly in the range of rotations that Kobayashi, et. al. found generated Görtler vortices for solid cones. In their tests, the 15 degree cone was rotated up to 3400 rpm with freestream speeds varying from 0 to 14 m/s.

Because the delta wing vortex has similar flow conditions as those external to a rotating cone, this shows promise for devising an experiment that could simulate the instability mechanism found in vortical flows. The effects of other instabilities present in the flowfield cause contentious problems that could be eliminated by such an experiment. Specifically, the fluctuations in vortex breakdown location and fluctuations due to spiral breakdown would be eliminated. The shear layer instability mechanism may not be eliminated because the rotation of a cone in close proximity to the delta wing surface will induce a flow that may cause flow separation and a shear layer at the leading edge. Figure 9 shows a simple schematic of the proposed experiment. First, the delta wing is mounted in the wind tunnel at zero degrees angle of attack. This is done such that no vortex forms in the place where the cone will be positioned. Because the two vortices that form over a delta wing are counter-rotating, a line of symmetry forms at the centerline of the model. To match this boundary condition with a rotating cone system, two cones are placed symmetrically about the centerline of the model and rotated in opposite directions, but at the same speed. Each cone is placed with it's apex at the apex of the delta wing and oriented at the angles determined from the delta wing vortex flow visualization data. The cones are rotated by shafts each attached to variable speed AC/DC motors. A stiff structure supports the cantilevered rotating cones and allows angle changes in the vertical and lateral positions of the cones. The support structure is completely independent of the model support and will be designed to minimize vibrations.

Results from Single Rotating Cone:

In order to test the interaction between a rotating cone and a delta wing surface in the rotating cone analogy experiment, a baseline test needed to be performed with only a rotating cone to attempt to match the results of Kobayashi, et. al. Because this is a transition process, it is probable that tunnel specific effects will be seen in the data results. A verification set of experiments was run for two reasons: first, to test whether the instability phenomenon was present in our fairly low budget experiment, and second, to test our ability to get appropriate data results with our diagnostic techniques. The following sections summarize the results obtained from experiments performed at Georgia Tech from 5/97 to 9/97.

Flow Visualization:

The transition process on the rotating cones generates very interesting and complex flow features as shown in the flow images by Kobayashi, et. al. The visualization of these structures provides the necessary view point such that all other more quantitative data can be interpreted. Our first goals were to verify the presence of vortical structures in our experimental set-up and to test whether less sophisticated smoke seeding techniques would allow their visualization.

The visualizations by Kobayashi were obtained by coating the model surface with titanium tetrachloride, a chemical which the EPA and AE building occupants would dislike. This flow seeding method was not available. Two methods of seeding were used for visualizations in this experiment: incense smoke and theatrical fog. Flow illumination was achieved with a 3 cm thick strobed white light sheet and with a 2 mm argon-ion laser sheet. Images were captured with a standard 1/2" video recorder. As with all flow visualization experiments, only at very low flow velocities can any clear results be seen. This is also the case with the Kobayashi experiments.

The flow visualization results from this experiment were quite exceptional. Figure 10 shows toroidal structures developing near the front part of the cone, growing in size as they convect back and finally, disperse as large structures. This image shows the front 8" of a 12" cone rotating at 2100 r.p.m. in stagnate flow. A natural convection is setup solely by the rotation of the cone. The structures in this figure are very similar to those seen in Figure 3.


With the addition of a freestream, the vortical structures are seen to convect around the cone at a slight angle. For Uinf.= 0.38 m/s and N = 600 r.p.m, Figure 11 shows the flow illuminated by a strobe light sheet on the lower side of the cone and a laser sheet on the upper side of the cone. Thus, vortical structures are visible entraining all the smoke seeding at the lower surface, and a cross-sectional view of the structures is visible at the upper surface. Both views show laminar smoke flow at front of the cone, followed by the development of structures: from very small bumps, to periodically organized structures, then finally, to dispersing interactions. The cross-sectional view shows that each structure consists of a pair of counter-rotating vortices drawing a sharp eruption of smoke up from the surface. 

With the camera zoomed in on the upper surface, Figure 12 shows the counter-rotating nature of the vortical structures. In the figure, the "mushrooming" structure appears ribbon-like. This is caused by too long of a camera shutter speed picking up the downstream convection of the continuous vortex pair.

The initial growth and convection of the structures are fairly consistent. The counter-rotating vortices induce an upward velocity on each other and a suction on the fluid at the surface. As the structures rise, other pairs of vortices begin to interact with one another causing them to "tip" one direction or the other. In Figure 12 this begins to occur at the edge of the video image.Figure 13 shows this vortex pair/vortex pair interaction. The image is of the same region on the cone, but with the freestream reduced to 0.29 m/s. A reduction of the freestream velocity will move the transition region on the cone further upstream, thus the image is of more developed structures. At the further downstream location, the vortex near the surface will be quickly drawn under the higher vortex. Thus, as the transition moves downstream, the structures grow in size as well as pair and interact with adjacent structures.

Hot-Film Anemometry:

Flow visualization of the counter-rotating vortices on a rotating works well at very low freestream velocities, but does not work well with any substantial freestream velocity. Another flow diagnostic tool must be used to identify the structures when and where they are present. With hot-film anemometry, the velocity fluctuations caused by the passing of a vortex pair can be measured. For Uinf.=9.0 m/s and N=2100 r.p.m., Figure 14 shows a hot-film voltage trace as a function of time. The one-per-revolution trigger pulse is also shown in the figure. The hot-film is 0.1" off the surface and 6.0" down the cone, which is 1" downstream from the location of first measurable fluctuations. Seen are large spikes corresponding to the passage of vortex cores; approximately 10 spikes per period. This corresponds to a frequency of structure passage of approximately 350 Hz.

Figure 15 shows the voltage trace at a hot-film probe location 10.0" down the cone and 0.1" off the surface. At this downstream location a much lower fluctuation frequency is seen. Only about 3 to 4 fluctuation spikes can be clearly distinguished. As with the flow visualization, the hot-film data also shows structures grow in size downstream and exhibit some sort of pairing and interacting with adjacent structures. Spectral data is not being presented here because the data was taken with too low of a sampling rate to adequately represent spectra of the fluctuations in the higher frequency cases. These tests have very recently been performed again with a higher sampling rate, but the data has not yet been analyzed.

Rotating Cone Analogy Pretest:

As shown in Figure 9, the rotating cone analogy consists of a delta wing at zero angle of attack, two 15° rotating cones and a freestream. Again, its purpose is for investigating the centrifugal instabilities in the conical vortices generated over a delta wing at angle of attack. The details of how to make the flow conditions analogous are to be determined from the compilation of this Summers research results. The previous section discussed a number of results that have been obtained. While this data was still unavailable and my flow visualization set-up was not being used, a quick flow visualization test was run on the full rotating cone analogy set-up. An "educated" guess was used for the cone height off the surface and outboard angle based on vortex positions calculated from previous tests on a generic wing/body model. Figure 16 shows a color enhanced flow visualization image of this experiment. Clearly seen in the figure are vortical structures spiraling around the cones even in close proximity with a solid surface. Also, the rotation of the cones is entraining the flow and causing the flow to shear off the wing leading edge. This preliminary test and figure serve only to spark the imagination over what may be a very interesting research development. And, as D'Alembert once said, "Go on, and faith will come to you!"

References:

1. Hubner, J.P., "An Investigation of Quasi-periodic Structures in the Vortical Flow Over Delta Wing Configurations," Ph.D. Thesis, School of Aerospace Engineering, Georgia Institute of Technology, Aug. 1995.

2. Kobayashi, R. and Kohama, Y, "Spiral Vortices in Boundary Layer Transition on a Rotating Cone," Laminar-Turbulent Transition Conference, Novosibirsk, USSR, July 1984, Springer-Verlag, Berlin, W. Germany and New York, New York, USA, 1985, pp. 573-580.

3. Kobayashi, R. and Izumi, H., "Boundary-Layer Transition on a Rotating Cone in Still Fluid," Journal of Fluid Mechanics, Vol. 127, 1983, pp. 353-364.

4. Schlichting, H., Boundary Layer Theory, 7th ed., McGraw-Hill, New York, 1979, pp. 525-535.