Issw22
Establishment of the near-wake flow of a cone and wedge
in a transient hypersonic freestream
S. O’Byrne, A.F.P. Houwing, P.M. Danehy
Department of Physics, Faculty of Science, Australian National University, Canberra, ACT 0200, Australia
Abstract: Experiments have been performed which
Forebody
Expansion Fan
investigate the development of separated flow in the
Shock
near-wake of a cone and a wedge in a hypersonic
Boundary
Separation
freestream. Planar laser-induced fluorescence has
Layer
Shear Layer
been successfully used to visualise the flows around the
Re-circulating
bases of a cone and wedge in a Mach 7.6 freestream
Re-attachment
Region
Shock
at various times after flow onset. The images show
Cone
or
Wedge
the time-evolution of the main features of the separated flow. They also indicate that the test time of
Re-attachment
Sting
Point
the free-piston shock tunnel used in these experiments
CL
is sufficiently long to establish a steady flow in both
the forebody and near-wake regions. Further exper- Figure 1. Schematic representation of the flowfield in the
iments are required to determine whether the wedge near wake of a wedge or cone in a supersonic flow.
flow is two-dimensional.
Key words: PLIF, flow visualisation, hypersonic
flow, wake flow, separated flow
1. Introduction
Separated base flows such as those in the near wake
of hypersonic vehicles are of interest to the aerospace
research community because they have a significant effect on the drag and manoeuvrability of such vehicles.
There is a commonly-accepted need for experimental
data for hypersonic base flows, to assist with the formulation of accurate numerical models.
Figure 1 shows the main features found in the hypersonic near-wake flow around a wedge or cone. Viscous flow in the boundary layer separates from the
model near the corner and forms a shear layer, which
is deflected by the expansion of the flow towards the
model’s centre-line. At some point downstream of the
base, the shear layer re-attaches to the sting, generating a positive pressure gradient in the process. The
slower portion of the shear layer which does not have
sufficient momentum to overcome this pressure gradient, is deflected back towards the base of the model,
forming a re-circulating region of flow. The faster
fluid is deflected horizontally by the presence of the
sting. The deflection of the supersonic flow causes a
re-compression shock wave to form. The position of
the re-attachment depends strongly upon the viscous
interactions in the separating shear layer, the nature
of which is not well understood.
Paper 3880
As described in Tanner (1984), supersonic base
flows are essentially non-oscillatory, in that the scale of
turbulent structures generated by separation are small
compared to the size of the base region. Thus, it is
expected that the separation will take the form of a
standing eddy rather than the vortex streets which often occur in subsonic flows. This makes such flows
suitable for study in free-piston shock tunnels, provided the steady flow time is long enough to ensure
that the interaction described above has reached equilibrium.
Free-piston shock tunnels can be used to generate a
wide range of hypersonic flow conditions, yet a major
difficulty associated with using these facilities is their
extremely short flow duration. This problem becomes
particularly serious when examining separated flows,
because the time required for flow to establish in the
separated region usually depends on viscous interactions which take place much more slowly than those
for inviscid flows.
This paper describes a series of flow visualisations obtained using planar laser-induced fluorescence
(PLIF). These experiments examine whether the separated flow around two model geometries reaches a
steady state during the 350–400 µs test time available
to the T2 free-piston shock tunnel.
22nd International Symposium on Shock Waves, Imperial College, London, UK, July 18-23, 1999
2
Establishment of hypersonic near-wake flow
1.1. Criterion for Separated Flow Establish- the shock speed and nozzle-reservoir pressure to be
measured. These values, along with the tunnel filling
ment
pressures, were used to calculate the freestream flow
Previous
investigations
(Holden (1971)
and properties, summarised in Table 1. These flow condiHolden (1994)) used skin friction, surface pres- tions were chosen because they had been characterised
sure and heat transfer measurements to determine by Palma (1998) and the core flow was known to have
the flow establishment time. These experiments were a diameter of approximately 65 mm. The test gas used
performed in facilities for which the steady test time in the experiments was a mixture of 99% nitrogen and
was much longer than the establishment time. The 1% oxygen. Because the test gas is held for several
results suggested that the flow establishment distance hundred microseconds at the stagnation temperature
is of the order of 50 base diameters for a separated in the nozzle reservoir, the molecular oxygen and some
near-wake flow.
of the molecular nitrogen dissociate and form nitric oxide (NO) which is used as the absorbing species for the
2. Experiment
PLIF visualisations. The 1% mole fraction was chosen as a compromise between maximising PLIF signal
2.1. Models
strength and minimising laser beam attenuation.
Two model geometries (a wedge and a cone) were choFlow properties at the cone surface (outside the
sen for this study. They are presented in Fig. 2. Each
◦
boundary
layer) were obtained from the tabular
model had a 30 half-angle and 6-mm base height.
data
of
Sims
(1964) for supersonic perfect gas flows
This height suggests, according to the criterion menaround
cones
at zero incidence. These data were
tioned above, a flow establishment time of 250 µs for
used
to
calculate
Reynolds number at the shoulder
the wedge and 200 µs for the cone. As shown in
of
the
cone
and
are
summarised in Table 1. The
the diagram, the wedge model was instrumented with
Reynolds
number
for
the
cone flow was calculated us12 thermocouples for measuring heat transfer. Those
ing
the
reference
temperature
method described in
measurements will not be discussed in this paper.
Germain and Hornung (1997), which determined the
transition Reynolds number for cone flows in the T5
6 mm
free-piston shock tunnel to be 5 × 105 . Work on
flat plate transition in the T4 free-piston shock tuno
Flow
nel found that transition for such flows occurs at a
30
Reynolds number of 1 × 106 . The Reynolds numbers
51 mm
in these tests are much lower, so it is realistic to expect that the shear layer would be laminar both before
separation and after re-attachment.
Thermocouples
6 mm
9 mm
50 mm
Flow
16 mm
9 mm
35 mm
Figure 2. Schematic diagram of cone and wedge models.
2.2. Facility and Flow Conditions
The experiments were performed using the T2 freepiston shock tunnel facility at the Australian National
University. Stalker (1967) contains a detailed description of this facility. For the experiments described
herein, the primary diaphragm had a burst pressure
of 46.9 MPa. A 7.5◦ half-angle conical nozzle with
a throat diameter of 6.35 mm and a nozzle-exit diameter of 73.6 mm was used to generate a Mach 7.6
freestream. Pressure transducers located at the nozzle
reservoir and another point in the shock tube allowed
Paper 3880
The test time used for previous experiments at this
flow condition was 350 µs after shock reflection. After
the initial pressure increase associated with the shock
reflection, the nozzle-reservoir pressure stays roughly
constant for approximately 300 µs. Then the reservoir pressure decreases at a rate of about 2 MPa per
100 µs. A typical nozzle reservoir pressure trace showing this behaviour is included as Fig. 3. The test time
was determined by adding the nozzle transit time to
the time just prior to the decline in nozzle reservoir
pressure, as shown in the figure.
These experiments examine the flow properties at a
variety of times after shock reflection, from the nozzle
starting flow 60 µs after shock reflection to 800 µs after
shock reflection, when there is a significant amount of
driver gas contamination in the flow and the nozzle
reservoir pressure has decreased to about 80% of its
value at the test time.
22nd International Symposium on Shock Waves, Imperial College, London, UK, July 18-23, 1999
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Establishment of hypersonic near-wake flow
Nozzle Reservoir Conditions
Pressure (MPa)
Temperature (K)
Enthalpy (MJ/kg)
29.7 ± 0.7
4535 ± 50
5.2 ± 0.1
Nozzle Exit Conditions
Pressure (kPa)
Temperature (K)
Density (kgm−3 )
Mach Number
4.5 ± 0.2
438 ± 10
0.035 ± 0.001
7.6 ± 0.1
Reservoir Pressure at
350 - tn t µs
30
25
Freestream
Test Time
20
15
10
0
Cone Surface Conditions
Pressure (kPa)
Temperature (K)
Reynolds Number
Mach Number
35
Nozzle reservoir pressure (MPa)
Table 1. Summary of flow properties in the shock tunnel nozzle reservoir, freestream and at the model surface. Nozzle reservoir and freestream conditions taken
from Palma (1998).
200
400
600
800
1000
Time after shock reflection (µs)
93
1597
95 400
3.36
Figure 3. Typical pressure trace recorded at the nozzle
reservoir, showing the delay between the reservoir conditions and the freestream conditions during the test time.
a 30-mm focal length cylindrical lens and a 1000mm focal length spherical lens was used to form the
Pressure (kPa)
108
frequency-doubled light into a sheet. The sheet was
Temperature (K)
1680
approximately 60-mm wide and approximately 0.8Reynolds Number
420 000
mm thick. The energy of the doubled dye laser outMach Number
3.0
put was approximately 4 mJ, with a Gaussian spectral
width of 0.18 cm−1 and a pulse duration of 25 ns. A
small portion of the beam was diverted before reaching
the sheet-forming optics and passed through a hydro2.3. PLIF Visualisation System
gen/oxygen flame, to calibrate the tuning of the laser
Planar laser-induced fluorescence (PLIF) is a tech- before each tunnel run.
nique which has proved useful for both visualisation
Doubling
and quantitative flowfield measurements in a variety
0.5 m
Crystal
308 nm
Spectrometer
450 nm
of supersonic and hypersonic flows (see, for example,
XeCl Excimer
Dye Laser
Prism
Laser
Palmer and Hanson (1994) and Palma et al. (1998)).
PLIF involves the use of a sheet of laser light tuned to
225 nm
Computer
excite an electronic transition in an atomic or molecSheet
Flame
forming
ular species. The molecule fluoresces and the fluoBeam Dump
optics
Timing transducers
rescence is then captured, typically using an intensified CCD camera. The intensity of the fluorescence
depends upon the temperature of the flow and the
T2 Shock Tunnel
number density of molecules in the state excited by
Camera mounted
the laser. Flow features which cause changes in these
below test section
quantities, such as shock waves, expansion waves and
Figure 4. Schematic diagram of the PLIF visualisation
mixing regions, can be visualised using the differing system.
signal intensities in these regions.
Wedge Surface Conditions
The experimental arrangement of the PLIF visualisation system is shown in Fig. 4. Laser radiation
at a wavelength of 308 nm, provided by a XeCl excimer laser (Lambda Physik EMG150ETS), was used
to pump a tunable dye laser (Lambda Physik Scanmate II) operating at wavelengths near 450 nm. The
output of the dye laser was then frequency-doubled
using a BBO-I doubling crystal. A combination of
Paper 3880
After a pre-set delay, the PLIF system was triggered by the arrival of the shock at the nozzle-reservoir
pressure transducer. After a second pre-set delay,
which accounted for the time between the laser trigger
pulse and the firing of the laser, a Princeton Instruments intensified CCD camera (576 by 384 pixels, 16bit dynamic range) was triggered and the fluorescence
recorded. The gate time of the intensifier was 800 ns.
22nd International Symposium on Shock Waves, Imperial College, London, UK, July 18-23, 1999
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Establishment of hypersonic near-wake flow
when the flow is establishing. This was especially true
for the wedge flow. Dark, cloud-like regions of the flow
were also noted in several images. It was presumed
that these were due to the presence of driver-gas in
Images were corrected for the spatial energy profile
the nozzle flow, as the driver gas contained no nitric
of the laser sheet by normalising to PLIF images oboxide and therefore should not fluoresce. The occurtained in a quiescent mixture of 1% NO in N2 prior to
rence of these pockets of gas became more prevalent at
the experiments.
later delays, but they were still present in some images
before and during the nominal test time.
2.4. Transition Selection
A Schott glass UG-5 filter was placed in front of the
camera to filter out laser scatter whilst allowing the
non-resonant fluorescence to pass into the camera.
PLIF signal is dependent on a number of flow properties, including the number density of nitric oxide
and the velocity, temperature and pressure of the flow.
Adjacent flow regions will show significant differences
in all of these properties. Therefore, in order to use
PLIF effectively as a visualisation tool, an appropriate
choice must be made for the transition excited by the
laser.
3.2. Time Evolution of Flow
Figure 5 contains a series of images obtained at various
delay times for both the wedge (parts (a) through (e))
and cone (parts (f) through (j)) flows. Each of the flow
regions shown in Fig. 1 is apparent in these images and
there is good contrast between neighbouring regions.
The relatively low rotational quantum number chosen causes high signals in the lower-temperature parts
Temperature and pressure were calculated in each of the flow such as the freestream and the corner exof the main flow regions shown in Fig. 1. Then the pansion and lower signal strengths in the post-shock
PLIF signal in each region was calculated using a num- region, for a given velocity and density.
ber of different isolated transitions, to determine the
Figure 5 (c) and (h) were obtained during the nommost appropriate choice of transition for visualisation
inal test time, 350 µs after shock reflection. Images
of the flow. Particular attention was paid to the efobtained using delays between 300 and 400 µs were
fect of the choice of transitions having different rotanearly identical, indicating constant flow conditions
00
tional quantum numbers (J ). The rotational quanbetween these times. The dark spot in the expantum number governs the temperature range over which
sion region of image (b) is a diaphragm fragment. Imthe PLIF signal shows significant variations. It was
ages (e) and (j) were obtained at a delay of 800 µs
00
noted that transitions having J values between 12.5
after shock reflection for the wedge and cone models
and 17.5 were most sensitive to the range of temperarespectively. The dark regions mentioned above are
tures in the modelled flowfield. The s R21 (J 00 = 13.5)
particularly apparent in these images. It is also no2 +
2
transition in the A Σ ← X Π(0, 0) absorption band
table that for Fig. 5 (e) the wake neck becomes very
−1
of nitric oxide at 44349.2 cm was found to provide
wide, although this is not the case for the cone. This
the best contrast between neighbouring regions of the
may be due to the flow not being two-dimensional.
flowfield for both cone and wedge geometries. It also
provided a relatively large signal in the re-circulating
It is clear from this sequence of images that the
region, making that region clearly visible, despite its re-attachment point moves downstream as the flow
relatively low density. This transition was used for all establishes and as it dies away. This is because the
of the results presented in this paper.
re-circulation region fills during establishment and, in
the latter stages of the flow, moves downstream due
3. Results and Discussion
to the decrease in freestream pressure. If the flow
reaches equilibrium, a series of images should show
3.1. Repeatability of Visualisation Results
an identical position of both the forebody shock and
re-attachment point. Figure 6 (a) is a plot of shock
The images presented in Fig. 5 were obtained by runangle for the wedge and cone models as a function of
ning the tunnel several times and firing the laser at a
time. This graph shows that the conical flow produces
different time after shock reflection for each run. This
a shock with an angle close to that predicted by theory
method assumes that the flow is reasonably repeatable
after about 100 µs and the shock remains at this angle
on a shot-to-shot basis. With this in mind, several imthroughout the test. The shock angle for the wedge
ages were obtained at the same delay time for different
flow, on the other hand, appears to oscillate during
tunnel runs. It was found that for both model geomethe flow time. This may have been because the 50tries, the positions of the main flow features, including
mm width of the wedge is close enough to the nozzle
the re-attachment point, changed very little for sevcore flow diameter to cause the shock to be affected
eral images obtained at the test time, although there
by the nozzle boundary layer.
was some variation between tunnel runs for images
obtained during the first 250 µs after shock reflection,
Figure 6 (b) is a plot of the re-attachment position,
Paper 3880
22nd International Symposium on Shock Waves, Imperial College, London, UK, July 18-23, 1999
5
Establishment of hypersonic near-wake flow
80 µs
(a)
(f)
150 µs
(b)
(g)
350 µs
(c)
(h)
500 µs
(d)
(i)
800 µs
(e)
(j)
Figure 5. PLIF images showing the time-evolution of separated base flow. Images (a) - (e) were obtained for the
wedge model, while images (f) - (j) were obtained at the same delays for flow around the cone model.
measured in base heights, as a function of time after
shock reflection. The trends for each model geometry
are equivalent, with the wedge’s separated region being further from the base than the cone’s. It can be
seen from this graph that there is a time window be-
Paper 3880
tween 300 and 400 µs after shock reflection for which
the distance of the re-attachment point from the base
does not appear to vary. This indicates that the separated region has reached a steady state during that
time. Previous results (O’Byrne et al. (1998)) for a
22nd International Symposium on Shock Waves, Imperial College, London, UK, July 18-23, 1999
6
Establishment of hypersonic near-wake flow
determined data. It is envisaged that the thermocouple measurements, combined with PLIF visualisation
of flow away from the wedge centreline, will also provide an indication of the two-dimensionality of the
wedge flow. At present it is not known how closely
the flow around the wedge approximates an ideal twodimensional flow.
Forebody shock angle ( )
39
38
37
Theory
36
35
34
(a) 33
Wedge (6 mm step)
Cone (6 mm step)
0
100
200
300 400 500
Delay (µs)
600
700
800
Acknowledgement. The authors would like to thank
Paul Walsh and Paul Tant for the construction of the models used in these experiments and Dr. Neil Mudford for
advice about the positioning of the thermocouples. This
work was funded by a grant from the Australian Research
Council.
References
3
2.5
2
{
Distance from step (base heights)
3.5
1.5
Steady flow
1
(b) 0.5
Wedge (6 mm)
Cone (6 mm)
0
100
200
300 400 500
Delay (µs)
600
700
800
Figure 6. Plots showing the time-development of (a) the
shock angle and (b) the distance of the wake minimum
from the base for both wedge and core flows.
12.5-mm step in the same freestream indicated that
the re-attachment point did not reach a steady value
during the test time but kept increasing. As the criterion determined by Holden (1971) indicates an establishment time of more than 400 µs for the 12.5-mm
step, these results are consistent with Holden’s predictions.
4. Conclusions
These experiments have shown that PLIF can be used
as a sensitive flow visualisation tool for separated flowfields containing significant variations in flow properties. The usefulness of this technique is especially apparent in the imaging of the flow around a cone, where
more traditional line-of-sight techniques can become
insensitive. The results of the visualisations indicate
that there is sufficient steady test time to investigate
flow past a 6 mm step at these flow conditions, which
is consistent with empirically-determined predictions
of previous investigations.
Germain PD and Hornung HG (1997) Transition on a
slender cone in hypervelocity flow. Exp. in Phys.
22:183–190.
He Y and Morgan RG (1994) Transition of compressible high enthalpy boundary layer flow over a flat
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Holden MS (1994) Development and code evaluation
studies in hypervelocity flows in the LENS facility.
AIAA paper 95–0291.
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SL and Houwing AFP (1998) PLIF imaging of the
separated region behind a cone in a hypersonic
flow. In the Proceedings of the 21st Congress of
the International Council of the Aeronautical Sciences.
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in free-piston shock tunnels. Ph.D. Thesis, Australian National University.
Palma PC, Mc Intyre TJ and Houwing AFP (1998)
PLIF thermometry in shock tunnel flows using a
Raman-shifted tunable excimer laser. Shock Waves
8:275–284.
Palmer JL and Hanson RK (1994) Shock tunnel flow
visualisation using planar laser-induced fluorescence imaging of NO and OH. Shock Waves 4:313–
323.
Sims JL (1964) Tables for supersonic flow around right
circular cones at zero angle of attack. NASA SP3004.
Stalker RJ (1967) A study of the free-piston shock
tunnel. AIAA J. 5:2160–2165.
Tanner M (1984) Steady base flows. Prog. in Aerosp.
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Thermocouple measurements are planned for the
wedge model to allow for comparison with previouslyPaper 3880
22nd International Symposium on Shock Waves, Imperial College, London, UK, July 18-23, 1999