Experimental Investigations of the Interaction of
Supersonic Wing-Tip Vortices with a Normal Shock
by
F. Leopold, H. Richard ª, M. Raffel ª, F. Christnacher
French-German Research Institute of Saint-Louis (ISL), Saint-Louis, France
ª Institute of Aerodynamics and Flow Technology, DLR, Göttingen, Germany
E-mail: leopold@isl.tm.fr
ABSTRACT
The interaction of a concentrated vortex with a shock wave may occur in many instances in the operational
environment of supersonic aircraft and missiles. The interaction may be the result of vortices created by the
forward components of a supersonic vehicle convecting downstream and interacting, for example, with shock
waves present in front of air intakes or other wings. The objective of the present work was to conduct an
experimental study simulating the interaction of streamwise wing-tip vortices with normal shock waves in a
Mach 3 flow.
Therefore, an experimental study was conducted to simulate the interaction of streamwise wing-tip vortices and
normal shock waves (fig.1). In this paper two recently developed visualization techniques are shown. The results
of the Background Oriented Scattering (BOS), invented at DLR, are compared to the flow-field visualizations,
obtained by using the ISL holographic filters. To elucidate the complex flow containing shock waves, backflow
and large-scale fluctuations, measurements using a laser Doppler velocimeter (LDV) were carried out (fig.2).
20
15
650
600
550
500
450
400
350
300
250
200
150
100
50
0
-50
-100
10
Y
5
0
-5
-10
-15
-20
20
Figure 1:. Index gradients visualized by use of holographic
filters
30
40
50
X
60
70
80
Figure 2: Velocity vectors after the vortex breakdown in
front of the tail wing
1. INTRODUCTION
In three-dimensional flows, boundary layer separation leads to the formation of vortical structures (herein called
vortices) caused by the rolling-up of the viscous flow sheet, previously confined in a thin layer attached to the
wall. The vortices leave this region and perturb the outer non-dissipative flow. Such vortices appear in a large
number of circumstances and often play a dominant role in the overall flow properties (Delery, 1994). Especially
in supersonic flow, the interaction of the vortices with shock waves could lead to a performance deterioration. In
practice, such encounters involve the interaction of three-dimensional curved line vortices with shock fronts.
Several experiments indicate that the flow field generated by the shock wave/vortex interaction can result in the
destruction of the vortices with a large-scale turbulent structure similar to those observed during low-speed
vortex breakdown (Cattafesta & Settles, 1992, Kalkhoran et al., 1996, Kalkhoran et al., 1998). The objective of
the present work is to conduct experimental studies simulating the interaction of streamwise wing-tip vortices
with normal shock waves at Mach number 3.
2. TEST MODEL AND WIND TUNNEL FACILITY
The test model used for this investigation consists of a conical nose, a cylindrical center section (diameter D =
40 mm), a canard wing and a tail wing. The form of the canard wing corresponds to a parallelogram, where each
side measures 0.25 D. The height of this wing is 0.5 D and the angle of attack is 20 degrees (fig. 3). The
experiments were carried out in the 0.3 m × 0.3 m continuous supersonic wind tunnel at ISL. The model-related
Reynolds number ReD is 2.1 × 106; the tunnel free-stream static pressure p is equal to 131 hPa. The test model is
mounted on a sting assembly along the wind tunnel center line, as shown in figure 4.
Figure 3: Sketch of the test model
Figure 4: Test model with naval nozzle for Mach
number 3
3. FLOW VISUALIZATION TECHNIQUES
3.1 Background Oriented Scattering (BOS)
In contrast to laser speckle velocimetry, where speckle patterns are generated by a double exposure of densely
seeded flows in a light sheet in order to determine flow velocity (Raffel et al., 1998), in density speckle
photography (Köpf, 1972, Debrus et al., 1972), the generation of laser speckle patterns makes it possible to
obtain density gradient information (fig. 4). The density speckle photography relies on an expanded parallel
laser beam, crossing an object containing refractive index changes (Wernekink & Merzkirch, 1987). Compared
to density speckle photography, the BOS method (Meier, 1999) further simplifies the recording. The speckle
pattern, usually generated by an expanded laser beam and ground glass, is replaced by a pattern on a surface in
the background of the test volume (fig. 5). This pattern has to have a high spatial frequency that can be imaged
with a high contrast. It usually consists of tiny, randomly distributed dots (fig. 6). The recording has to be
performed as follows: first a reference image is generated by recording the background pattern observed without
any flow before the experiment. Secondly an additional exposure through the flow under investigation (i.e.
during the blow down) leads to a displaced image of the background pattern (fig. 7). As shown in figure 8 the
resulting images of both exposures can then be evaluated by correlation methods (Raffel et al., 1999, Richard et
al., 2000). Without any further effort existing evaluation algorithms, which have been developed and optimized
e.g. for particle image velocimetry (or other forms of speckle photography) can then be used to determine
speckle displacements (Ronneberger et al., 1998). By means of the BOS technique, the directions and the
magnitudes of density gradients can be extracted in the flow region between the canard and the tail wings.
Figure 5: Principle of the background-oriented schlieren technique (BOS)
background paper
with dots
patterns
light source
flow
wind tunnel with
model
camera
Figure 6: Optical set-up of the BOS method for wind tunnel tests
shock
vortex
Figure 7a: Recording of the displaced image of the
background pattern due to the Mach 3 flow
Figure 7b: Reference picture with the pattern in the
background
Figure 8: Displacement data obtained by the BOS technique. Vectors are proportional to dρ/dx and dρ/dy.
Color contours display the magnitude of the displacement
Figure 9: Optical set-up of the visualization using a holographic filter
3.2 Visualization using a holographic filter
This filter, which was initially developed for edge enhancement in optical image processing, allows the
visualization of the index gradients in all directions which are perpendicular to the optical axis (Christnacher,
1992). The principle of the optical system is described in figure 9. In a four-focal system, the g(x, y) function in
the output plane is equal to the convolution between the f(x, y) function in the input plane and the impulse
response of the filter h(x, y). To visualize the gradients in f(x, y), the impulse response of the filter has to satisfy
the following equation for every point in the output plane:
g(x,y) = f(x,y)*h(x,y) = ||grad f(x,y)||.
Consequently, in order to obtain this function, the filter must have the following impulse response:
h( x, y) =
∂
∂
+i
.
∂x
∂y
For the optical implementation of this function, several holographic gratings are superposed on the same
photosensitive plate. The final image is the vectorial addition of each diffracted image by the different gratings.
If each image is correctly shifted and has the corresponding phase, the vectorial addition of all the images will
represent the gradients of the input image. A cw laser with 400 mW at 532 nm is used as the light source. The
beam is expanded to the desired field size (15 cm in diameter). After passing through the test section, the light is
focused by a lens on the holographic filter. Further, the diffracted image is digitized by a single-shot camera.
Due to the cw laser illumination, the time of exposure can be chosen with the high-speed camera (Leopold &
Christnacher, 1997, Leopold et al., 1998).
Two types of camera are used. The FlashCam camera from PCO achieves times of exposure ranging from 1 µs
to 40 ms at video rate. The DiCam camera, also from PCO, is an intensified version which allows us to obtain
smaller times of exposure from 5 ns to 1 ms at 8 Hz. These delays correspond to a normal laser pulse. Figure 10
shows the untreated image of the flow between the two wings. The time of exposure is 20 ns, when even the
turbulent structures of the flow are frozen. The pseudo-color image in figure 11 (the time of exposure is 100 ms)
helps to make the distinction between the different density gradients.
Figure 10: Visualization of the flow field between the canard and the tail wings with a time of exposure of 20 ns
Figure 11: Visualization of the whole flow field (diameter: 20 cm) with a time of exposure of 100 ms
Figure 12: Comparison between the BOS method (left) and the visualization using a holographic filter (right).
3.3 Comparison between the two visualization methods
Both visualization methods allow the visualization of the norm of the index gradients which are perpendicular to
the optical axis (fig. 12). The two techniques show the different characteristics of a flow around a canard-wing
configuration, such as shock wave formation, wing tip vortex, boundary layer separation, vortex breakdown and
shock/vortex interaction. The big advantage of the BOS method lies in the simple set-up. No lenses are required
for the visualization based on this method. Therefore the observed flow field can be very huge (Richard et al,
2000). For the treatment of the pictures obtained, algorithms generally used in the particle image velocimetry
(PIV) domain are applied. Therefore, the direction of the density gradients can be extracted, but the spatial
resolution is limited by the PIV software. This can be clearly observed in unsteady, small zones with very high
turbulent intensities. This is probably the reason why the BOS method underestimates the density gradients in
these flow regions. By contrast, holographic filters allow the visualization of density gradient norm without any
treatment at every pixel of the CCD camera. Especially at very short times of exposure (10 ns) and due to the
high spatial resolution the unsteady behavior of the shock/vortex interaction can be clearly shown by the
visualization using holographic filters. Moreover, to show these fluctuations, a dynamic sequence can be easily
recorded on video tape.
4. LASER DOPPLER VELOCIMETRY
4.1 Set-up of the laser Doppler velocimeter (LDV)
1.82
1.57
1.35
1.14
0.97
0.81
0.68
0.56
0.47
number density
The velocity field between the canard and the tail wings has been measured using a two-component fringe mode
laser Doppler velocimeter (LDV). The emission part of the LDV system is essentially composed of a 4-watt
argon ion laser, a multicolor beam splitter (“Colorburst” of TSI) with a 40 MHz frequency shift capability. The
reception part consists of an F/4 80-200 mm zoom
lens, a multimode fiber link and a photo multiplier a
DES aerosol
with a color separator. For reasons of improved
0.06
signal-to-noise ratio, an off-axis forward-scatter
0.05
LDV arrangement has been chosen. The LDV
0.04
signals are processed by a TSI IFA 750 Digital
0.03
Burst Correlator and analyzed with respect to the
0.02
mean velocity and its variance. For the seeding of
0.01
the flow an aerosol of di-(2-ethyl-hexyl) sebacate
(DES) is introduced into the settling chamber of the
0.00
wind tunnel. A typical DES size distribution,
droplet size / micron
measured at the exit of the Laskin nebulizer (Drew
et al. 1978), is shown in figure 13. The mean
diameter of this distribution is equal to 0.72 m.
Figure 13: Typical aerosol size distribution (Schäfer et al., 2001)
20
15
650
600
550
500
450
400
350
300
250
200
150
100
50
0
-50
-100
10
Y
5
0
-5
-10
-15
-20
20
30
40
50
X
60
70
80
Figure 14a: Velocity vectors for the plane z = -7.5 mm
Figure 14b: Velocity vectors for the plane z = -1 mm
20
20
650
600
550
500
450
400
350
300
250
200
150
100
50
0
-50
-100
10
Y
5
0
-5
-10
15
5
-10
-15
30
40
50
X
60
70
-20
20
80
Figure 14c: Velocity vectors for the plane z = 0 mm
40
50
X
60
70
80
20
650
600
550
500
450
400
350
300
250
200
150
100
50
0
-50
-100
10
5
0
-5
-10
-15
15
650
600
550
500
450
400
350
300
250
200
150
100
50
0
-50
-100
10
5
Y
15
Y
30
Figure 14d: Velocity vectors for the plane z = 1 mm
20
-20
20
0
-5
-15
-20
20
650
600
550
500
450
400
350
300
250
200
150
100
50
0
-50
-100
10
Y
15
0
-5
-10
-15
30
40
50
X
60
70
80
Figure 14e: Velocity vectors for the plane z = 2.5 mm
-20
20
30
40
50
X
60
70
80
Figure 14f: Velocity vectors for the plane z = 7.5 mm
20
20
650
600
550
500
450
400
350
300
250
200
150
100
50
0
-50
-100
10
Y
5
0
-5
-10
10
5
0
-5
-10
-15
-20
20
10000
9500
9000
8500
8000
7500
7000
6500
6000
5500
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
15
Y
15
-15
30
40
50
X
60
70
-20
20
80
30
40
50
X
60
70
80
Figure 15a: Mean velocity contours for the plane z = 2.5 Figure 15b: Contour plot for the Reynolds stress term
mm
for the plane z = 2.5 mm
20
20
120
115
110
105
100
95
90
85
80
75
70
65
60
55
50
10
Y
5
0
-5
15
5
0
-5
-10
-10
-15
-15
-20
20
30
40
50
X
60
70
80
Figure 15c: Contour plot for the standard deviation of
the velocity u’ for the plane z = 2.5 mm
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
10
Y
15
-20
20
30
40
50
X
60
70
80
Figure 15d: Contour plot for the standard deviation of
the velocity v’ for the plane z = 2.5 mm
4.2 Experimental results
The LDV velocity measurements were restricted in the longitudinal direction to the zone between the canard and
the tail wings and in the normal direction from the wall to the top of the tail wing. The origin of the coordinates
x and y is at the top end of the canard wing (fig. 3). The coordinate z is measured from the symmetry plane of
the tail wing. Figure 14 shows the results of the LDV measurements presented as velocity vectors for planes at
different z positions. These vector plots clearly display the two recirculation bubbles behind the shock/vortex
interaction, especially for the plane z = 2.5, where the vortices leave the canard wing. In particular, they provide
evidence of the large velocity gradients which are found around the vortex breakdown, as well as at the
boundary layer separation in front of the second wing.
In addition to the time average flow quantities, information about the velocity fluctuations, in particular about
the turbulence intensities and, as an indicator of turbulent energy, the Reynolds stress term, can be extracted
from the LDV measurements. The standard deviations for the surface parallel u’ component (x direction) and the
surface normal v’ component (y direction) of the velocity are calculated as follows:
u' =
1 n
( ui − u ) 2
∑
n − 1 i =1
v' =
1 n
( vi − v ) 2
∑
n − 1 i =1
10
10
Y
5
0
10000
9500
9000
8500
8000
7500
7000
6500
6000
5500
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
5
Y
650
600
550
500
450
400
350
300
250
200
150
100
50
0
-50
-100
0
-5
-5
-1
0
Z
1
-1
2
Figure 16a: Mean velocity contours for the plane x =
50 mm
0
Z
1
2
Figure 16b: Contour plot for the Reynolds stress term
for the plane x = 50 mm
10
10
Y
5
0
120
115
110
105
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
5
Y
150
145
140
135
130
125
120
115
110
105
100
95
90
85
80
75
70
65
60
55
50
0
-5
-5
-1
0
Z
1
2
Figure 16c: Contour plot for the standard deviation of
the velocity u’ for the plane x = 50 mm
-1
0
Z
1
2
Figure 16d: Contour plot for the standard deviation of
the velocity v’ for the plane x = 50 mm
The Reynolds stress term for the two components u and v is given by the following expression:
1 n
R = ∑ (ui vi ) 2 − uv
n i =1
The contour plots of figure 15 for the velocity, Reynolds stress term and standard deviations clearly show the
high velocity fluctuations in the vicinity of the different shock waves, provoked by the shock/vortex interaction.
These high fluctuations suggest, in agreement with the unsteady character shown in the flow visualizations, that
the velocities in these regions are measured alternately before and behind the shocks. The intersections (fig. 16),
which are perpendicular to those shown before, show the evolution of the velocity and fluctuation distributions
after the breakdown of the vortex but in front of the tail wing. It confirms that the velocities in front of the tail
wing are negative, which leads to an enormous deterioration in the performance of this wing. The contour plots
for the different fluctuations suggest that the flow keeps a nearly axisymmetric structure around the recirculation
zone of the collapsed vortices.
5. CONCLUSIONS
The experimental study involving the interaction of concentrated streamwise wing-tip vortices and a normal
shock front was carried out at Mach 3. Two different visualization techniques (BOS, holographic filter) and
LDV measurements indicate a significant change in the structure of the streamwise vortices upon encountering a
normal shock wave. The observations reveal that the interaction leads to the formation of an unsteady conical
shock wave far upstream from the tail wing as well as a highly turbulent flow downstream. The LDV
measurements near the region of the vortex breakdown clearly indicate two cells in the recirculation bubble with
high recirculation velocities and large fluctuations. Nevertheless, it could be shown that the time-averaged (in
the sense of Reynolds averaging) vortex flow keeps a nearly axisymmetric structure organized around the
recirculation zone. This picture of the flow may be a sufficient approximation for most applications where only a
prediction of the mean field is required.
AKNOWLEDGEMENTS
The authors wish to express their thanks to Edgar Augenstein and Emmanuel Bacher for their contributions to
the flow visualisations and to Christophe Demeautis, Pascale Duffner and Karim Djoudi for their assistance in
the LDV measurements.
REFERENCES
Cattafesta, L.N. and Settles, G.S. (1992). “Experiments on Shock/Vortex Interaction”, AIAA-92-0315.
Christnacher, F. (1992). “Etude de l’adaptation d’un système optique de reconnaissance de formes à un
environnement sévère”, Thèse Université de Haute-Alsace, Mulhouse, France, ISL-R 107/93.
Debrus, S., Francon, M., Grover, C.P., May, M. and Robin, M.L. (1972). “Ground glass differential
interferometer”, Appl. Optics, 11, pp. 853.
Delery, J.M. (1994). “Aspects of vortex breakdown”, Prog. Aerospace Sci., 30, pp. 1-59.
Drew, R.T., Bernstein, D.M. and Laskin, S. (1978). “The Laskin Aerosol Generator”, J. Toxicology and
Environmental Health, 4, pp. 661-670.
Kalkhoran, I.M., Smart, M.K. and Betti, A. (1996). “Interaction of Supersonic Wing-Tip Vortices with a Normal
Shock“, AIAA Journal, 34, pp. 1855-1861.
Kalkhoran, I.M., Smart, M.K. and Wang, F.Y. (1998). “Supersonic vortex breakdown during vortex/cylinder
interaction”, J. Fluid Mech, 369, pp. 351-380.
Köpf, U. (1972). “Application of speckling for measuring the deflection of laser light by phase objects”, Opt.
Commun., 5, pp. 347-350.
Leopold, F., Augenstein, E., Damp, S., Christnache, F. and Bacher, E. (1998). „LDA Measurement and
Visualization of the Supersonic Flow around a Longitudinal Cylinder with Different Surface Roughness”,
Proc. 9th International Symposium on Appl. of Laser Techniques to Fluid Mechanics, Lisbon, Portugal.
Leopold, F. and Christnacher, F. (1997). “Flow Visualization with Holographic Filters of Coherent Structures in
a Supersonic Wake”, ISL/PU 327/97.
Meier, G.E.A.. (1999). „Hintergrundschlierenverfahren, Deutsche Patentanmeldung“, DE 199 42 856 A1.
Raffel, M., Richard H. and Meier, G.E.A.. (1999). “On the applicability of background oriented optical
tomography”, Experiments in Fluids, 28, pp. 477-481, 2000.
Raffel, M., Willert, C. and Kompenhans J., (1998).: “Particle Image Velocimetry”,
Book series: 'Experimental Fluid Mechanics', Eds. R.J. Adrian, M. Gharib, W. Merzkirch, D. Rockwell, J.H.
Whitelaw, ISBN 3-540-63683-8, Springer-Verlag, 255 pages.
Richard, H., Raffel, M. and Meier, G.E.A.. (2000). “Background oriented stereoscopic schlieren applied to a
helicopter in flight”, forum of the American Helicopter Society, Virginia, USA..
Richard, H., Rein, M., Meier, G.E.A., Kompenhans, J., and Raffel, M. (2000). „On the applicability of a
background oriented schlieren (BOS) method”, Proc. 10th Int. Symp. on Appl. of Laser Techniques to Fluid
Mechanics, Lisbon, Portugal.
Ronneberger, O., Raffel, M. and Kompenhans, J. (1998). „Advanced evaluation algorithms for standard and
dual plane particle image velocimetry”, Proc. 9th Int. Symp. on Appl. of Laser Techniques to Fluid Mechanics,
Lisbon, Portugal.
Schäfer, H.J., Augenstein, E., Esch, H. and Emunds, H. (2001). “Experimental investigations of transverse jet
interaction on a missile body using laser velocimetry and flow visualization”, Proc. 19th International Congress
on Instrumentation in Aerospace Simulation Facilities (ICIASF), Cleveland/OH, USA.
Wernekink, U. and Merzkirch, W. (1987). “Speckle photography of spatially extended refractive-index fields”,
Appl. Optics, 26, pp. 31-32.