650:422 AEROSPACE ENGINEERING LAB SECTION 12 MARCH 23, 2017
Supersonic Flow in a Wind Tunnel
Department of Mechanical and Aerospace Engineering
Rutgers University, Piscataway, New Jersey 08854
The objective of the supersonic wind tunnel
laboratory is to familiarize ourselves with the
physics behind Schlieren Imaging and to perform the
experimental setup of a blowdown in a supersonic
wind tunnel. The blowdown in conjunction with the
schlieren method will allow us to visually see the
shock waves formed around an object in the test
section. In this particular tunnel setup, we use the
Mach number 3.45 which is specific and cannot be
changed. A Schlieren camera is used to examine the
shock waves within the test section.
INTRODUCTION
A supersonic wind tunnel consists of a
closed environment in which air is drawn
through at supersonic speeds. The mach
number and flow are determined by the
geometry of the nozzle which are specific and
cannot be changed. The wind tunnel is used in
order to achieve a fixed flow pattern at a given
instant. The apparatus given to us is a tunnel
that includes a high quality schlieren imaging
system, LaVision digital camera, high
andwidth pressure transducers, an Ng-YAG
laser and a data acquisition within the tunnel.
The apparatus includes a small window
at the test section to observe the flow over an
object, in our experiment we used a pointed
structure. The purpose is to simulate,envision,
and examine how the flow over the abso
ed
object affects it. The visual flows that we see
over the object are called shock waves and are
produced by the deflection of supersonic flow
over the object. In our case, we witness an
attached shock due to the sharp structure used
and the low angle of attack.
Table 1. Wind Tunnel Specifics
Mach Number 3.45
Velocity 630 m/s
Stagnation Pressure 200 psia
Stagnation
Temperature
60 ∘ F
Test Section 6 x 6 in
Run Time 10 s
The Schlieren Imaging as discussed
efore is produced by the deflection of light
ays by the changes in the index of refraction
n. With n being the ratio of the speed of light
in a vacuum which is 3x 108 m/s to that of
the speed of light in the specific material.We
are given a Z-type schlieren system as seen
elow.
Figure 1. Z-type schlieren system
In our system here we have an LED light that
is reflected from one spherical mi
or and
passes through the test section where the light
ays may be bent from the transition through
the shock wave. Another spherical meets the
light at the other side and reflects it towards a
fixed point at the edge of a knife which
inte
upts the rays. These rays are reflected for
the third time and
ought to the image plane,
the LaVision camera which creates the visual
effects of the shock waves. Another image
created is that of the expansion fan(s) which is
a centered expansion about the pointed corner
which is the production of Mach waves. The
flow is accelerated at these fans.
RESULTS AND DISCUSSION
For the first part of our experiment we
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650:422 AEROSPACE ENGINEERING LAB SECTION 12 MARCH 23, 2017
test the Schlieren imaging on a table top. The
tools used are a candle, a razor blade, a
magnifying glass, and the mi
or for reflecting.
A light is shined through the candle flame and
y blocking a fragment of the light that
efracted from the density of the hot air we
may create an image of the contrasted hot air.
We blocked the light with the edge of a razor
lade and placed the magnifying glass
precisely at the focal point in order to create
the image.
Figure 2. Schematic of Schlieren System
To achieve a clear image, the focal length must
e 2 times the length as seen in the image
above but instead of being reflected towards a
camera, the image is reflected onto a white
piece of paper. Because of the use of a
spherical magnifying glass and mi
or, the
image will appear to be flipped.
In order to explain how Schlieren
images are made, we must first discuss the
properties behind refraction. Refraction takes
place when light rays pass from one medium
into the next. What makes the light bend is the
difference in refractive index (optical density).
If light enters a medium with a lower
efractive index than the previous one, then it
will speed up and vice versa. The schlieren
method has been used in order to visualize the
fluctuations in the optical densities.
Figure 3. Schlieren Imaging Table Top
Setup
Figure 4. Focused Schlieren Image
Next, we proceeded with the Schlieren
experiment using the supersonic wind tunnel.
A separate system is provided to us on a bigge
scale than that of the table top but consisting
of the same method. They are placed in a way
to result a high resolution image via a camera
on one end. The goal is to obtain the schlieren
images at different angles of attack.
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650:422 AEROSPACE ENGINEERING LAB SECTION 12 MARCH 23, 2017
Figure 5. Schematic Design of Supersonic
Wind Tunnel (NASA)
Figure 6. Initial startup of wind tunnel
As described, the image from figure 6
epresents the visual schlieren image from the
test section of the tunnel during start up. As
one could see, the air in the tunnel seems to be
flu
ying around without an orderly manner.
Around the tip of the structure one can start to
detect the formation of a constant streamline
and what is to be predicted. At the moment we
get this glimpse of weak waves entering the
section.
Figure 7. Wind tunnel at full speed
The next figure is the image of the
wind tunnel at its full speed. One can see the
shock waves forming in parallel patterns at
diagonals. From here we can associate the
term “attached shock” and “Prandtl-Meyer
expansion fan” which are noticed at the tip and
the shoulder of the structure, respectively. One
may also detect the Mach lines that are a result
of imperfections or dents on the structure.
Thanks to the schlieren setup we can capture
these images of the streamlines and shock
waves. Otherwise, in person, it appears as
though nothing is really happening within the
wind tunnel.
Figure 8. Shut down of wind tunnel
At the shutdown of the wind tunnel we
can see from figure 8 the remaining diagonal
shock waves that linger; as the top portion of
the image begins to look like a flu
y of smoke
as in the startup image.
Under the theory that the half angle of
the cone model used was 11 degrees, we may
calculate the shock angle:
[1]
where, β -shock angle
θ -half angle of cone
M 1 -Mach numbe
γ = 1.4 (air)
By using figure 9 below, we made estimate the
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650:422 AEROSPACE ENGINEERING LAB SECTION 12 MARCH 23, 2017
shock angle to be about 20 degrees for a half
angle of 11 degrees.
Figure 9. NACA Technical Memorandum
1135 shock angle vs. cone half-angle
Figure 10. Supersonic flow encountering a
wedge and is deflected, forming an oblique
shock
From equation 1 we calculate the shock angle
for a half
Static pressure can be measured by
ecording its movement along the fluid
element at the same velocity. In our case, we
must work backwards from the stagnation
pressure in order to achieve the static pressure.
The stagnation pressure is simply the opposite,
it measured when the flow has come to a stop
isentropically. The static pressure can be
calculated by the following formula:
[2]
where, pt -stagnation pressure
p-static pressure
M-mach numbe
Through plug and chug, static pressure came
out to be 2.816 psia. As for static temperature,
we may simply use the relation:
[3]
where, T t -stagnation temperature
T-static temperature
Again, through plugging in previously given
numbers and the result for static pressure, we
may solve for static temperature. Static
temperature came to be 17.75 ∘ F.
ERROR ANALYSIS
Since the specifications were given and
the wind tunnel was handled by a professional
that leaves less room for e
or in this
experiment. That does not mean there was no
e
or at all. The wind tunnel itself was
established in the mid-1990s and has been
unning for nearly 3 decades. E
or may come
from age of the tunnel or even the deflections
from dents on the cone model that may not be
taken into consideration for the shock angle.
Because, this environment is very much
maintained at certain specifications, e
or will
e miniscule, otherwise human-related or due
to outdated equipment. Another source of e
or
may pertain to a fluctuation of temperature and
thus producing vapor content.
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650:422 AEROSPACE ENGINEERING LAB SECTION 12 MARCH 23, 2017
CONCLUSIONS
This experiment employed a supersonic
(M>1.0) wind tunnel with known criterion in
that allowed for the study of flow over a
pointed structure at a zero angle of attack. This
process was examined using the schlieren
technique/images. Through examination it may
e concluded that as the angle of attack on the
structure increases, the shock angle will
decrease.
REFERENCES
http:
www.physicsclassroom.com/class
efrn/Less
on-1/The-Cause-of-Refraction
https:
en.wikipedia.org/wiki/Stagnation_pressure
https:
en.wikipedia.org/wiki/Oblique_shock
650:433 Supersonic Wind Tunnel Lab Manual
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