Full text of DOI:10.1007/s00348-002-0433-8

Experiments in Fluids 33 (2002) 188–195
DOI 10.1007/s00348-002-0433-8
Development and application of streakline visualization
in hypervelocity flows
P. Lemieux, H.G. Hornung
188
Abstract A method for visualizing streaklines in hyper-
velocity flows has been developed. The method uses the
high temperatures produced in hypervelocity flows to
ablate small amounts of sodium deposited onto a wire
stretched across the flow and to broaden the lines in the
sodium spectrum. By using a dye laser, tuned to a wave-
length close to one of the sodium D-lines, as the light
source in shadowgraph or Schlieren visualization, streak-
lines seeded with sodium become visible through ab-
sorption and/or enhanced refractivity. The technique has
been used to investigate the stability of the shear layer
produced by the curved bow shock on a cylindrically
blunted wedge. The results suggest that the shear layer is
unstable, exhibiting structures with a wavelength that is
comparable to half the nose radius of the body.
implementation of a similar technique in the short-dura-
tion flows of hypervelocity shock tunnels.
2
Streakline visualization in hypervelocity flows
Visualization using smoke is not realizable at the flow
conditions typical of shock tunnels. On the other hand,
Germain (1994) has been successful in applying the atomic
sodium seeding method of Blendstrup et al. (1979) to
visualize boundary layer flows at these conditions and
provided the basis for a new flow visualization technique.
The new technique, called sodium wire streakline vi-
sualization (SWSV), combines the method of Blendstrup
et al. (1979) with the smoke-wire idea. It uses the hot gas
flow of the shock tunnel to produce streaks by ablation of
sodium from a wire. By tuning a narrow bandwidth light
source to a frequency close to an absorption line, streaks
containing sodium may be visualized through a combi-
nation of absorption and enhanced refractivity, depending
on the difference between the line center and light source
frequencies.
The seeding is made relatively safe and simple by the
high temperature of hypervelocity flow, as it enables
sodium to be introduced in the form of sodium chloride,
deposited at discrete source points on a steel wire stret-
ched across the flow. The hot gas ablates and dissociates
the sodium chloride, thus seeding the test gas continuously
with atomic sodium emanating from the wire. Typical
conditions encountered in the stagnation region of the
wire are 7,000 K and 100 kPa, at which, in equilibrium,
sodium chloride is 99% dissociated. Thus, the technique
works because of either or both of the following effects:
1
Introduction
A curved shock produces a shear layer with smoothly
varying vorticity. The vorticity generated at the shock is a
function of the shock angle, curvature, and density ratio
across the shock (Hayes and Probstein 1966). A study was
undertaken to investigate the stability of such shear layers,
as produced by the curved bow shock on a blunt wedge in
hypervelocity flows. One of the goals of this study was to
use flow visualization techniques capable of highlighting
instabilities in the shear layer, if these were found to exist.
The idea was to duplicate the success of the smoke-wire in
similar studies in subsonic flows.
In the traditional smoke-wire setup, the streak lines
consist of smoke generated by oil that vaporizes as it runs
down a heated wire placed upstream of a model in a wind
tunnel. Provided that the wind tunnel flow has sufficiently
low turbulence, this method can be used even at super-
sonic speeds (Goddard et al. 1959). In stability studies in
particular, the smoke-wire has proved to be a valuable
research tool and is widely used in qualitative and quan-
titative studies (e.g., Fric and Roshko 1994). A review of
the literature, however, does not reveal any successful
• The absorption at or near one of the strong atomic
sodium lines (D1 at 589.593 nm and D2 at 588.996 nm).
• The enhanced refractivity of sodium gas near such a
line, which can be several orders of magnitude higher
than that of air.
Light absorption
As has been shown by Blendstrup et al. (1979), enhanced
refractivity and absorption are remarkably strong effects
in sodium and concentrations of one part in 1,000 or even
10,000 are sufficient to produce the effects necessary for
visualization. The effect of the seeding on the flow is
therefore negligible. At the conditions of hypervelocity
flow, the Doppler broadening of the line (resulting from
the thermal motion of the atoms) is very strong, so that the
Received: 5 December 2001 / Accepted: 22 February 2002
Published online: 3 May 2002
Ó Springer-Verlag 2002
P. Lemieux, H.G. Hornung (&)
Graduate Aeronautical Laboratories,
California Institute of Technology,
Pasadena, CA 91125, USA
E-mail: hans@galcit.caltech.edu

tuning accuracy required is much reduced. Other line-
broadening mechanisms are unimportant at our condi-
refractivity peaks occur at approximately half a half-width
on either side of the absorption peak of a spectral line.
tions (pressure, electric or magnetic broadening), so that Tuning the light source to the refractivity peak thus can
the line shape may be taken to be Gaussian, as if produced make techniques that rely on refractive-index gradients
by Doppler effects alone.
(Schlieren, differential interferometry) much more sensi-
tive, so that they will easily pick up streaklines even
though absorption is much reduced at this wavelength.
3
Experimental setup
The shock tunnel facility where SWSV was developed and
used is the T5 Hypervelocity Shock Tunnel at the Graduate
Aeronautical Laboratories of the California Institute of
Technology. T5 is a free-piston shock tunnel, in which the
driver gas is heated adiabatically by piston compression.
The transient heating achieved by this method permits
operation at higher driver gas temperatures. Descriptions
of the operation of piston-driven shock tunnels in general
are available in the literature (Lukasiewicz 1973; detailed
descriptions of the T5 facility specifically may be found in
189
´
Belanger 1993, Germain 1994, and Wen 1994).
Three shock tunnel operating conditions were selected
for the experiments performed with SWSV. These are listed
in Table 1, along with their corresponding test section free-
stream conditions and expected equilibrium normal shock
density ratios, and span a large range of reservoir enthal-
pies and free-stream conditions available in the facility.
Fig. 1. Test of the SWSV concept. Flow is from left to right. Left:
Model before the shot, a 3-inch-diameter sphere with a wire seeded
with sodium chloride at various locations. Right: Effect of the hot gas
flow on the salt, creating a sheet seeded with atomic sodium which
absorbs all the light downstream of the wire. The luminosity of the
flow in the stagnation region of the sphere is just visible. The drag on
the wire causes it to bend in the direction of the flow. The marks in
the field of view upstream of the wire and below the sphere in the left
figure are due to spots on the optical windows and are not part of the
flow
3.1
Experimental test of the absorption technique
In a preliminary series of experiments aimed at substan-
tiating the concept of SWSV, a wire, seeded with sodium
chloride, was stretched in front of a sphere. This setup was
placed in the T5 test section and subjected to flow con-
dition 1 in Table 1. An example of the results of this study,
shown in Fig. 1, illustrates that the method clearly works,
but also that the flow is easily contaminated by excess
sodium on the wire.
Further tests were performed using a 4-in.-diameter
cylinder at the same flow conditions as in Fig. 1. The wire
was seeded at intervals of approximately 25 mm; each site
consisted of a salt crystal of roughly 3 mm in length and a
fraction of a millimeter in thickness around the wire. The
resulting flow is shown in Fig. 2.
While results such as this showed that streaklines can
be traced using this technique and would provide a valu-
able tool in the study of the stability of the shear layer
produced by the shock, further experiments showed that
placing the wire downstream of the shock significantly
improved the repeatability and reliability of the technique
and made the seeding of specific areas of the flow easier.
Fig. 2. Streaklines through the shock produced by a cylinder. The
laser is tuned sufficiently far from the center of the line, so that there
is no excessive light absorption. Note that the higher temperature of
the flow downstream of the shock causes the sodium to absorb more
light in that region than upstream of the shock
3.2
Experimental test of the enhanced refractivity method
Streaklines may also be visualized by using the enhanced
refractivity near a spectral line. Positive and negative
Table 1. Nominal T5 conditions
and approximate density ratios
for SWSV study
hres (MJ/kg) Pres (MPa)
M¥
U¥ (m/s)
q¥ (kg/m3)
T¥ (K)
q2/q1
Condition 1
Condition 2
Condition 3
11
20
4
20
27
14
5.7
5.0
6.2
4,300
5,500
2,700
0.018
0.018
0.036
1450
3020
580
8.5
10.8
6.2

is fairly large and depends on the broadening of the line.
Fine wavelength adjustments of the dye laser thus become
necessary to obtain a given level of absorption and to
avoid excessive absorption such as that shown in Fig. 1.
Figure 4 illustrates the method used to tune the laser.
The laser light illuminates a screen after passing through a
propane flame seeded with sodium. The level of absorption
taking place is evident by observing the shadow of the
flame on the back wall: with the laser frequency adjusted
outside of the absorption line, the light passes through the
flame with little or no absorption, and no shadow (except
for the apparatus) appears on the wall; as the frequency of
the laser is adjusted to within the line, however, the width
and contrast of the flame shadow may be used to infer
qualitatively the absorptivity of sodium at this frequency
and temperature. The sensitivity of the dye laser to manual
wavelength adjustments is such that approximately three
revolutions of a microdial linked to a diffraction grating
controlling the dye laser frequency are required to span
the absorption spectrum of one of the D-lines. This reso-
lution was found to be satisfactory for the purposes of the
method and experiments presented here.
190
3.4
Fig. 3. Three streaks, visualized by enhanced refractivity of sodium
Alternative sources of sodium seed
Despite several disadvantages, sodium was used in the
form of salt crystals grown on wires for most of this
with differential interferometry
An example is shown in the visualization of three free- experimental study. Different ways to attach sodium
stream streaklines at test condition 1 (Fig. 3). The streaks chloride to the wire were tested, in the hope of developing
are made visible by Wollaston prism differential interfer- a method that would minimize the possibility of sodium
ometry, without noticeable absorption. The streaks in
Fig. 3 would not have appeared in absorption shadowg-
raphy at the wavelength of the light source used. The
contamination of the flow outside the streaklines and
create a source of atomic sodium that is not so brittle as to
break off in the flow (a problem found in many of the runs
enhanced refractivity method is less sensitive to the light with NaCl).
source wavelength than absorption shadowgraphy.
Late in this development process, pure sodium instead
of sodium chloride was placed at discrete positions on the
wire. Despite the safety issues associated with sodium in
its pure form (it reacts violently with water), there were
advantages which made its use appealing for the purposes
3.3
Apparatus, optical setup, and the development
of the flow-tagging technique
The light source for this experiment consists of a 300-mJ/ of flow tagging:
pulse, frequency-doubled Nd:YAG laser, which is used to
1. The paste-like nature of sodium allows small quantities
pump a dye laser made by Cummings (1995), with the
wavelength adjustable in the 587–594-nm range. These
lasers were used as light sources for both shadowgraphy
and differential interferometry.
to be directly attached to the wire, minimizing handling
and reducing the risk of contamination.
2. Pure sodium eliminates the dissociation step previously
required with NaCl. Hence, higher concentrations of
sodium may be expected to tag the flow. Also, this may
extend the range of applicability of this technique by
reducing the lower limit of temperature where the
method works.
The light source frequency was tuned to the edge of one
of the sodium absorption lines, as it appeared in a propane
flame seeded with sodium, at a temperature of approxi-
mately 1,600 K and atmospheric pressure. Using a for-
mulation by Thorne (1988), the Doppler half-width of the
sodium D-line may be calculated. At this condition, it was
found to have a half-width of approximately 3.5 pm,
whereas, at an assumed flow temperature of 7,000 K
immediately downstream of the normal shock on the
wire, the half-width is more than doubled to 7.4 pm.
Pure sodium was used with success in the experiment,
as shown in Fig. 5. This figure shows two streaks generated
at a reservoir condition of 10 MJ/kg. The streak closest to
the body, barely visible in this picture, was made using the
original NaCl crystal method. Above that streak, another
Thus, though minimal absorption appears to be taking streak was generated using sodium metal. This streak was
place through the propane flame, the absorption level
would be perceptible, but not excessive, in typical flow
placed in the region of high vorticity generation and
exhibits some instability towards the end of the picture.
conditions which would be somewhere between these two Results such as these will be used in following sections to
temperatures. The variation of both the refractive index
discuss the primary instability mode of the shear layer
and the absorption coefficient with wavelength in the line produced by curved shocks.

191
˚
Fig. 4a–d. Adjusting the dye laser frequency using a propane flame NaCl. In the subsequent shots, the dye laser is tuned: b several mA
seeded with sodium. Image a shows the setup, with laser light from the sodium D-line; c near the edge of the D-line, and d near the
(coming from the right) illuminating a propane burner and casting its center of the D-line. Note how absorption increases as the laser is
shadow on a screen. Above the burner is a metal rod with crystallized tuned closer to the absorption peak
Unfortunately, while it is now clear that sodium metal
In the following sections, two effects of the wire on the
is better suited for the purposes of flow visualization than flow are discussed: the interactions of the wire with the
NaCl, it was used for only a few shots towards the end of bow shock of the model and the effects of the wire wake on
the study.
the flow.
4.1
Interaction between wire and shock
3.5
Limits in the range of applicability of SWSV
In order to seed specific areas of the flow and improve the
reliability of the technique, it was found that placing the
wire downstream of the bow shock of the model, directly
into the shock layer, produced the best results. This pro-
cedure means that at some point along its length, the wire
pierces the bow shock. Hence, the wire interacts with the
shock in two ways: the shock generated by the wire
interacts with the model shock and the wake behind the
wire locally disturbs the model shock.
The combination of these two interactions was found to
have an effect on some of the results obtained: in some
cases, entrainment of sodium spanwise into the wire wake
was observed. This was particularly evident when streaks
were produced in the vicinity of the intersection of the wire
with the shock and did not seem to depend significantly on
the angle of attack of the wire. By investigating this region
with SWSV, the critical region appeared to be localized to a
few wire diameters around the point of intersection. At
larger distances from the shock, the wire wake did not seem
to have an effect on the flow. Within the critical region,
While there are no clear upper limits to the maximum
enthalpy at which SWSV will work, the effectiveness of
using sodium to visualize flows at low enthalpy is limited.
For these flows, the width of the D-line is substantially
reduced compared to higher enthalpy conditions, so that
precise adjustment of the laser frequency becomes critical.
Moreover, the concentration of sodium in the flow is re-
duced at the lower temperatures, compounding the prob-
lem of detecting clear streaks in the flow. With our crude
flame-tuning method, it has not been possible to observe
streaklines at the lower enthalpy conditions (5 MJ/kg) in
our experiments.
4
The effect of the wire on SWSV results
A drawback of SWSV is that it does not permit the
investigation of the flow in a non-intrusive manner.
In a study focused on flow stability (for which SWSV
was originally developed), it is important to be able to
separate possible wire effects from the stability of the shear however, streaks may be entrained into the wake of the
layer itself. wire, even across the shock, as shown in Fig. 6.

192
Fig. 6. Entrainment of a streakline within the wire wake, above the
plane of the shock
Fig. 5. Comparison of sodium lumps versus NaCl in tagging the flow.
Top: wire setup before the shot. The sodium metal, pasted onto the
wire, is clearly visible above the model. The salt crystal on the wire is
to the left of the field of view. Bottom: shadowgraph of the flow over
the model. The increased concentration of sodium along the streak
generated by the metal lump is clearly evident when compared to the
streak produced by the NaCl (below)
Fig. 7. Streaklines through the shear layer
4.2
Effect of wire wake on flow
The effect of the wire on the flow is, of course, not
limited to its intersection with the shock. Since the wire
is essentially a cylinder in cross-flow, it may be
responsible for any structures observed in a streakline.
The geometry of the model and of the optical system
being known, quantitative measurements can be made
to verify whether any observed structures are, in fact,
shed by the wire or may be attributed to a different
source.
One of the clearest examples of the results of our
investigation that may be used to discuss this situation is
presented in Fig. 7. This shadowgraph shows the flow
over the blunted wedge, with a leading edge of 3.5 cm
radius (the wedge has a span of approximately 20 cm and
a half-angle of 30ꢀ. The cylindrical leading edge is
removable.) The wire is 0.61 mm in diameter and has
three sodium source points, spaced at 2.5-cm intervals,
spanning the shock layer from the body to the shock. The
bottom streakline is aligned with a streamline near the
stagnation point of the wedge; the center streakline is
aligned approximately with the streamline that passes
through the point of maximum vorticity generation
(i.e., the center of the shear layer); and the top streakline
is very close to the oblique (nearly straight) part of
the shock.
4.3
The cylinder in cross-flow
The nominal free-stream conditions of Fig. 7 correspond
to condition 1 in Table 1. Using the actual T5 reservoir

conditions recorded during the shot1. as input to a non-
equilibrium nozzle flow program (see Lordi et al. 1966),
better estimates of the flow conditions at the exit plane of
the nozzle can be computed. This free-stream flow is then
used as input into a computational fluid dynamics code for
hypersonic flows in thermochemical non-equilibrium
(Candler 1988), which computes the steady-state flow over
the blunt wedge and provides estimates for the flow con-
ditions downstream of the shock near the region where the
wire seeds the flow. The code used here was selected based
on a history of successful simulation of T5 flows, see e.g.,
Wen (1994) and Wen and Hornung (1995). Thus, the
conditions corresponding to Fig. 7 are listed in Table 2.
The viscosity used for the wire Reynolds number
calculation in Table 2 is computed using a formulation
described by Blottner et al. (1971).
The cylinder in cross-flow is known to produce peri-
odic oscillations in the wake of the cylinder over a large
range of Reynolds numbers. The dimensionless frequency
of these oscillations, the Strouhal number, is given by
Table 2. Local flow conditions at the source point of the three
streaklines seen in Fig. 7
Streakline
U (m/s)
M
T (K)
P (kPa)
Re
top
middle
bottom
2,850
2,400
1,500
2.4
1.9
0.9
4,400
5,160
5,900
108
107
182
1,200
800
630
happens to the stability of the flow in the wake of a
cylinder at Mach numbers greater than 1.
193
The cylinder in supersonic flow
Hot-wire studies in the wake of cylinders in supersonic
flows have looked specifically at this problem (Behrens
1966). In these studies, the width of the outer wake behind
the wire was measured and the spectrum of frequencies of
instability was determined. The main instability mode, for
given wire diameters, was found to occur in the far-wake
of the cylinder in hypersonic flows (meaning in that region
of the flow far from the coalescing free shear layer
produced by the boundary layer separating around the
cylinder and downstream from the wake shock). These
instabilities developed over several hundred diameters
downstream of the cylinder. It would appear therefore that
the structures observed here cannot be due to an
instability of the far-wake of the wire either, since
they appear in the shadowgraph much closer to the
wire.
fd
S ¼
;
ð1Þ
U
1
where f is the shedding frequency of the structures ob-
served downstream of the cylinder and d is the cylinder
diameter. The value of the Strouhal number for flows over
cylinders has been verified by many independent studies
to remain approximately constant at S=0.2 for Reynolds
numbers above Re=200 to as high as Re=107 (White 1991).
Additional studies on flow over yawed cylinders (Van Atta
1968) have shown that this result is also applicable to
cylinders inclined with respect to the flow if the Strouhal
number is formed with the component of velocity normal
to the cylinder.
Since the flow geometry and properties of Fig. 7 have
been identified, a wire wake analysis may be performed to
determine if the wavelength observed can indeed be due to
the wire. The component of velocity normal to the wire is
used to calculate the Strouhal number. Substituting the
values pertaining to the middle streakline of Fig. 7 into
Eq. 1, we get Sꢀ0.08, well below the expected value for
vortices shed from a cylinder. Furthermore, we observe
that the two streaks emanating from above and below the
center streak (corresponding to the center of the shear
layer) do not exhibit the large structures present in the
center streak. The variation in U across the shear layer,
responsible for variation in Reynolds number computed in
Table 2, is not enough to vary that parameter outside the
range for which the Strouhal number is constant. This
suggests the hypothesis that the structures observed in
the center streak are due to the instability of the shear
layer.
Wire vibration effect
Another possible source for the vortices observed in Fig. 7
is a vibration of the wire itself, which might cause the
vortex shedding to lock into this frequency. The natural
frequency of such a wire is given by
pffiffiffiffiffiffiffiffiffiffiffiffi
p
ðT=dÞ
xn ¼
;
ð2Þ
L
where T is the tension in the wire, d is the mass per unit
length of the wire, and L is the length of the wire.
For the case of Fig. 7, Lꢀ28 cm and dꢀ2.3 g/m. The
tension in the wire, due to the drag of the flow and the lift
of the prongs supporting it (they are at a 1ꢀ angle of attack
with respect to the flow in this figure), is estimated at
approximately 20 N. Substituting these values into Eq. 2,
rad
xn ꢀ 1000
;
s
which corresponds to a period of 6 ms. This frequency is
more than an order of magnitude lower than that required
to explain the structures observed in Fig. 7 and therefore
cannot be accountable for them. Structures caused by the
wire vibrating in the flow would also be expected to affect
all three streaklines, not just one as shown in Fig. 7.
Finally, we note that the component of velocity per-
pendicular to the wire in all of these streaks is only mar-
ginally subsonic for the center streak and supersonic for
the top streak. It is important to consider, therefore, what
4.4
An experimental control study
In a further effort to investigate the effect of the wire on
the structures observed, a control experiment was carried
out. The goal of this control experiment was to isolate the
role of the wake of the wire in flows similar to those of
1Required specifically are the reservoir pressure and the reservoir
temperature. The former is measured directly, while the latter may be
computed from an equilibrium calculation across the reflected shock,
performed here using a code written by McIntosh (1969)

194
Fig. 8. Sharp leading-edge setup for wire control study in T5. Note
that the wire is fitted through the leading edge, so that the angle
between the wire and the surface of the wedge is comparable to that of
the experiment
interest here from that of the shock-produced shear layer
by using a sharp wedge which produces a straight attached
shock and therefore does not generate vorticity.
The test configuration of this experiment was similar to
the one discussed so far and the flow condition was the
same. The setup is shown in Fig. 8. With this configuration,
shock curvature effects are eliminated from the flow and
any streakline structure can only be caused by the effect of
the wire. Wires of different diameters are used, so that flows
over a range of wire Reynolds numbers can be compared.
The results of this experiment are shown in Fig. 9. They
do not suggest that a significant broadening of the streak
occurs as a result of the wire wake, nor do they exhibit a
preferred scale of wake structures. As before (Fig. 7 top
streak), the streaks exhibit turbulence in the wire wake.
This is thought to be the turbulence usually observed in
supersonic cylinder wakes close to the symmetry plane.
The wavelength of structures that would be shed by a cyl-
inder at a Strouhal number of 0.2 is included (to scale) in
these figures. There does not appear to be a correlation with
the wire diameter in any of the three shots in this figure,
suggesting that no regular vortex shedding typical of in-
compressible flows over cylinders occurs, but that the flow
is similar to the observations of Behrens (1966), who noted
that instabilities did not develop until much further
downstream in supersonic flow. This further supports our 5
Fig. 9. Test of the wire wake instability. All three shots use
condition 1 listed in Table 1. This test examines the effect of wire
diameter. It is 0.5 mm in the top picture; 1.0 mm in the middle and
2.0 mm in the bottom frame. The corresponding (expected)
wavelength is shown to scale in the figures. Clearly, no structures
of the expected scale occur
shadowgraph, the three streaks have completely mixed
together. Also, the bottom streak (closest to the body),
which is not in a region of high shear in the flow, remains
relatively undisturbed for most of its trajectory.
hypothesis that the structures observed in Fig. 7 are due to Summary of results from SWSV
an instability in the shear layer that is produced by the
curved shock.
Streakline visualization was used in more than 50 runs
with models of three different nose radii (19, 35, and
63.5 mm) at the three free-stream conditions of Table 1. In
Contrary to a free shear layer, which tends to grow
rapidly in a direction normal to the flow, the shear layer approximately one-third of the cases, a preferred scale of
produced by the curved shock is constrained on one side structures could be measured clearly (category A). In
by the body surface and on the other by the shock, thus another third, a preferred scale was evident in only two
limiting its spatial growth. Nevertheless, by the end of the structures or had only small amplitude (category B). In the

curved shocks. The technique uses the absorption and
enhanced refractivity properties of sodium near one of the
D-lines to visualize the streaklines. The effect of the wire
on the flow was investigated and found to be unimportant
to the purpose of the investigation.
SWSV was used in a series of experiments using hem-
icylindrically blunted wedges and showed that the shear
layer produced by curved shocks may become unstable at
sufficiently high density ratios and disturbance level. The
preferred wavelength of the structures that develop in the
shear layer is comparable to one-half of the leading edge
radius of the wedge. The results obtained were corrobo-
rated in a numerical study published separately.
195
References
Behrens FW (1966) Flow field and stability of the far wake behind
cylinders at hypersonic speeds. PhD thesis. California Institute of
Technology, Pasadena, Calif.
´
Belanger J (1993) Studies of mixing and combustion in hypervelocity
Fig. 10. Correlation between the wavelength of the structures
flows with hot hydrogen injection. PhD thesis. Graduate
Aeronautical Laboratories, California Institute of Technology,
Pasadena, Calif.
observed in the shear layer and the nose radius
Blendstrup G, Bershader D, Langhoff P (1979) Recent results of
resonant refractivity studies for improved flow visualization.
In: Lifshitz A, Rom J (eds) Proceedings of the 12th International
Symposium on Shock Waves, 1979, Jerusalem, Israel, pp 258–265
Blottner FG, Johnson M, Ellis M (1971) Chemically reacting viscous
flow program for multi-component gas mixtures. Technical
Report SC-RR-70–754. Sandia Laboratories, Albuquerque, N. M.
Candler G (1988) The computation of weakly ionized hypersonic
flows in thermo-chemical nonequilibrium. PhD thesis. Stanford
University, Stanford, Calif.
Cummings EB (1995) Laser-induced thermal acoustics. PhD thesis.
Graduate Aeronautical Laboratories, California Institute of Tech-
nology, Pasadena, Calif.
Fric TF, Roshko A (1994) Vortical structures in the wake of a trans-
verse jet. J Fluid Mech 279:1
last third, only one or two structures could be discerned
(category C). In this application, the method does not
produce particularly clean streaks and the central wake
turbulence can obscure regular structures. If an instability
of the shear layer produced by the curved shock does
occur, the size of the structures has to scale with the nose
radius, since, for the inviscid flow, this is the only char-
acteristic length. To test this, the measured scale is plotted
against the nose radius in Fig. 10.
The overall trend of these data shows an increase of
wavelength with nose radius, but the scatter of the data
that results from the error in measuring the wavelength, is
too large to make conclusions about proportionality.
Nevertheless, the dotted line of best fit suggests that the
instability in the shear layer is most susceptible to dis-
turbance wavelengths of about one-half of the leading edge
radius.
Germain P (1994) The boundary layer on a sharp cone in high-
enthalpy flow. PhD thesis. Graduate Aeronautical Laboratories,
California Institute of Technology, Pasadena, Calif.
Goddard VP, MacLaughlin JA, Brown FNM (1959) Visual supersonic
flow patterns by means of smoke lines. J Aero/Space Sci 26:761–
762
While the results presented here are suggestive of an
instability of the kind expected, they are not sufficiently
convincing to draw firm conclusions. In part, this may be
connected to the fact that the highest normal-shock
density ratio achievable in T5 nozzle flows is approxi-
mately 12, whereas the work of Hornung and Lemieux
(2001) has shown that the shear layer becomes unstable
to small-amplitude disturbances within a few nose radii
only when this density ratio is 14 or greater. The fact
that we observe the instability in nozzle flows at all may
be related to the disturbance amplitude in T5 nozzle
flows. The wavelength of the instability observed by
SWSV is in line with the results of Hornung and
Lemieux (2001).
Hayes WD, Probstein RF (1966) Hypersonic flow theory, 2nd edn.
Academic Press, New York
Hornung HG, Lemieux P (2001) Shock layer instability near the
Newtonian limit of hypervelocity flows. Phys Fluids 13:2394
Lordi JA, Mates RE, Moselle JR (1966) Computer program for the
numerical solution of nonequilibrium expansions of reacting gas
mixtures. Technical Report NASA CR-472. NASA, Washington,
D.C.
Lukasiewicz J (1973) Experimental methods of hypersonics. Marcel
Dekker, New York
McIntosh MK (1969) A computer program for the numerical calcu-
lation of equilibrium and perfect gas conditions in shock tunnels.
Technical Note CPD 169. Australian Defense Scientific Service,
Canberra, Australia
Thorne AP (1988) Spectrophysics. Chapman & Hall, London
Atta CW Van (1968) Experiments on vortex shedding from yawed
circular cylinders. AIAA J 6:931
Wen CY (1994) Hypervelocity flow over spheres. PhD thesis. Graduate
Aeronautical Laboratories, California Institute of Technology,
Pasadena, Calif.
Wen CY, Hornung HG (1995) Non-equilibrium dissociating flow over
spheres. J Fluid Mech 299:389
White FM (1991) Viscous fluid flow, 2nd edition. McGraw-Hill, New
York
6
Conclusion
A technique for visualizing streaklines in hypervelocity
flows, named SWSV, was developed for the purpose of
investigating the stability of shear layers produced by