Unsteady Wave Structure Near Separation in A Mach 5 Compression Ramp Interaction
Unsteady Wave Structure Near Separation in A Mach 5 Compression Ramp Interaction
Unsteady Wave Structure Near Separation in A Mach 5 Compression Ramp Interaction
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Introduction
For the two-dimensional compression ramp flows at supersonic speed, the generally accepted model of the flowfield is
sketched in Fig. 1. This was determined by Settles18 from pitot
pressure, static pressure, and total temperature surveys. These
measuring techniques have essentially zero frequency response, so this model represents a time-averaged picture. Since
the separation shock wave is unsteady,5 the question is raised
as to whether Fig. 1 is an accurate representation of the flow
structure, since it is the result of time-aver aging different
flowfields corresponding to different shock positions.
Kussoy et al.17 have addressed this question, for the
cylinder-flare interaction. In that study, simultaneous wallpressure fluctuations, high-speed shadow movies, and LDV
data were taken. Using a conditional sampling method, mean
streamlines were calculated for "shock-forward" and "shockback" positions and for the overall time-averaged cases. The
shock-forward and shock-back cases were defined as when
Ps(t) > Ps + aps andP 5 (0 < Ps - 0.5 c^, respectively.
Here, Ps(t) is the5instantaneous wall pressure, Ps the mean
value, and oPs the standard deviation, all measured at the
mean shock position. The results showed that the separated
bubble "expanded and contracted like a balloon." Gramann
and Dolling have observed a similar phenomenon in flows induced by circular cylinders19 and by unswept compression
ramps.9 In the latter studies, the instantaneous separation
point was determined to be at, or just downstream of, the instantaneous shock foot, showing that the separation process
itself is intermittent. The separation line determined by
3
Y.
6.
Received July 10, 1989; revision received Feb. 26, 1990. Copyright
1990 by the American Institute of Aeronautics and Astronautics,
Inc. All rights reserved.
*Graduate Student, Department of Aerospace Engineering and Engineering Mechanics. Student Member AIAA.
t Associate Professor, Department of Aerospace Engineering and
Engineering Mechanics. Associate Fellow AIAA.
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MAY 1991
Experimental Program
Wind Tunnel and Model
729
Flow Conditions
730
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0.75
t(ms)
I
0.0
1.0
2.0
3.0
4.0
5.0
Analysis Techniques
Standard time-series analysis techniques, and conditional
sampling and ensemble-averaging techniques have been used
to analyze the data. The latter techniques are discussed below.
Conditional Sampling
Wi-rZT,
AIAA JOURNAL
tion and is called the rise time (or "rise"). Similarly, when the
boxcar assumes a value of 0, this signifies a downstream shock
passage and is called the fall time (or "fall"). Hence, each
shock passage is characterized by a rise time and a corresponding fall time. These times are the only pertinent information in
the analysis of the separation shock motion.
In the current study, a third threshold T3 was introduced in
addition to Tl and T2. This third threshold is needed to determine the shock fall times more accurately. In prior analyses,
most of the separation shock statistics were calculated using
only the rise times, which are more easily determined than the
fall times. In the current study, however, an accurate measurement of the fall times is imperative, because they directly influence separation shock statistics. Since the rise time is used
to determine when the shock is at a specific position (this is
discussed in more detail in the next section), T3 was set equal
to T2 so that the fall time would correspond to exactly the
same shock position. In this case, T3 was used to monitor the
fall times as follows. Once a shock passage was detected using
T{ and T2, and an initial fall time was assigned, a counter was
then used to march backward in time until the instantaneous
value Pw(t) was found that was just below T3. The fall time
was then reassigned to this new value. The significance of this
improvement will be clearer later, when the statistics of the
upstream and downstream shock passages are compared.
Variable-Window Ensemble-Averaging
MAY 1991
731
-HCK
1.75
2.35
1.85
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1.35
T=O
T=0
t (ms)
t (ms)
T=0
____I___
T=0
1.78
P(T)
T(ms)
-0.4
-0.2
0.0
0.2
0.4
-0.4
-0.2
0.0
0.2
0.4
-0.4
-0.2
0.0
0.2
0.4 -0.4
-0.2
0.0
0.2
0.4
Discussion of Results
Basic Features of the Interaction
and downstream of S. This result is also seen in the zerocrossing frequency distribution that has a maximum value of
about 1.0 kHz at 7 0.5. In this flow, the length of the intermittent region is about 1.6 d0. It should be noted that the
streamwise distance has been expressed in terms of 50 for convenience, not because 50 is the appropriate scaling parameter.
Power spectra at five different positions in the interaction
are shown in Fig. 7. The normalized form, G(f) 'f/0pw, has
been used except for the incoming turbulent boundary layer
that is shown in dimensional form, G(f) -f, due to the difficulties of accurately measuring op^ . The incoming boundary
layer (curve 1) has a broadband spectrum; however, the coni
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
732
0.8
0.6
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0.2
0.0
-2.75
-2.25
-1.75
-1.25
-0.75
r's>
-HchI
0.75
I I I I I III
I I I I I III
,_ G(fH/a2Pw
j=1.00
0.25
0.00
0.75
0.50
0.25
0.00
0.20
x/80=-7.55
0.15
400-500 Hz, regardless of the position in the intermittent region. This dominance by the relatively low-frequency, highamplitude pressure fluctuations is preserved even at the downstream end of the intermittent region, where the highfrequency, high-amplitude pressure fluctuations of the turbulent shear layer are a larger fraction of the signal and begin to
contribute more to the variance. Even though the high-frequency content of the shear-layer fluctuations becomes more
and more dominant (curves 4 and 5), the low-frequency unsteadiness persists as far downstream as the compression ramp
corner.
In the incompressible turbulent separated flow experiments
of Kiya and Sasaki,23'24 the characteristic Strouhal number, St
( =fLs/Uw), of the separation bubble unsteadiness was 0.12,
where Ls is the bubble length, U^ the freestream velocity, and
/the center frequency of the spectrum of the wall-pressure signal. In the current experiment, the Strouhal number, formed
the same way, is about 0.03. If the maximum zero-crossing
frequency is used instead of the center frequency, then the
value is about 0.06. In Refs. 23 and 24, the Strouhal number
of the low-frequency unsteadiness was less than about 0.2 with
a peak of 0.12 as stated above. In the current experiment, in
which the shock and bubble frequencies are less than 3-4 kHz,
the corresponding Strouhal numbers are about 0.18-0.24.
However, it should be noted that at this stage there is little evidence to suggest that in the high-speed case, /, and Ls are appropriate normalizers. More work under different flow conditions is needed to evaluate this.
Separation Shock Wave Strength as a Function of Position
jt/80=-0JS
0.50
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0.10
0.05
0.00
0.30
0.25
0.20
0.15
0.10
0.05
0.00
1.00
G(f)'f[xl04](psia2)
0.75
x/80=-3.38
0.50
Y=0.00
0.25
0.1
0.2
0.5
10
20
'50
100
-0.4
-0.3
-0.2
-0.1
0.1
0.2
0.3
0.4
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MAY 1991
upstream of channels n, n + 1, and n + 2. Since r = 0 corresponds essentially to the "freezing" of the shock at channel n,
the ensemble-averaged pressure value at r = 0 at station n + 1
can be used to define the separation shock strength at position
n. Hence, separation shock strength at station n, (APs1)?, is
defined as the difference between the ensemble-averaged pressure at T = 0 on channel n +1 and the pressure of the undisturbed boundary-layer component of the signal as measured by the same channel, n + \. Defining the shock strength
in this way avoids any ambiguities with respect to whether the
shock has actually crossed the transducer and eliminates any
transducer zero-shift and temperature drift problems that may
occur. This process can also be carried out for the shock moving in the downstream direction. It should be noted that, with
this definition, (APs1)? includes not only the pressure rise due
to the separation shock, but also the small increase in pressure
due to any compression between the separation shock and the
next transducer downstream.
In Fig. 9, shock strength (APs1)? for both upstream and
downstream motions of the separation shock is plotted vs the
normalized distance x/b0 from the corner. The importance of
the third threshold T3 should now be clear, because if it were
not introduced, the shock position at fall times would have
been slightly different than that at rise times. However, this is
not the case using T3, and the separation shock strength for
upstream motion can be compared directly with that of downstream motion. Also shown in Fig. 9 are the average intermittency values at each station. At low 7, the separation shock
strength increases rather gradually, but is followed by a more
rapid increase at higher intermittencies. Overall, the separation shock strength increases by about 50% as the shock
moves from the lowest 7 to the highest. This result is independent of the direction of motion of the shock.
Ensemble-Averaged Compression Structure in Intermittent Region
-Uh-
0.95
_ (APs)n! (psia)
-Z25
-2.00
-1.75
0.00
0.55
0.36
-2.50
733
-1.50
734
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-0.4
-0.3
-0.2
-0.1
Fig. 12 Ensemble-averaged pressure histories in the intermittent region for upstream and downstream shock motions (simultaneous data
in Fig. 13).
PE/A(^=O) (psia)
-3.5
-3.0 -2.5
-2.0
0.0
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MAY 1991
Conclusions
Fluctuating wall-pressure measurements have been made
upstream of the corner in a separated Mach 5 compression
ramp interaction. The objective was to examine the unsteady
compression wave structure near separation and its influence
on the pressure levels and histories under the separated shear
layer. The results can be summarized as follows.
1) The separation shock wave strength is a function of position in the intermittent region and increases with increasing inter mittency. This result is independent of the direction of motion of the separation shock wave.
2) The flow structure in the intermittent region is not that of
a single shock front undergoing random motion, as speculated
in earlier work. In this region, the separation shock wave is
followed by compression waves whose strength decreases with
distance from the shock foot. Further, the compression following the separation shock becomes stronger as the shock
moves downstream. This structure is also independent of the
direction of motion of the separation shock.
3) Ensemble-averaged pressure distributions show how the
mean flowiield is generated through the time-averaging of the
different flowfields corresponding to different shock positions. Ensemble-averaged pressure distributions for shockupstream and shock-downstream cases resemble typical mean
pressure distributions for large- and small-scale separated
flows, respectively.
4) Finally, there is a correlation between the separation
shock motion and the ensemble-averaged pressure histories
under the separated shear layer. The separation bubble
pressures rise and fall as the separation shock moves downstream and upstream, respectively, showing that the separation shock motion correlates with the low-frequency pressure
fluctuations of the separated bubble.
Acknowledgments
Support from AFOSR under Grant 86-0112, monitored by
L. Sakell, is gratefully acknowledged.
References
Bogdonoff, S. M., "Some Experimental Studies of the Separation
of Supersonic Turbulent Boundary Layers," Kept. 336, Aero. Eng.
Dept., Princeton Univ., Princeton, NJ, June 1955.
2
Chapman, D. R., Kuehn, D. M., and Larson, H. K., "Investigation of Separated Flows in Supersonic and Subsonic Streams with Emphasis on the Effect of Transition," NACA TN 3869, March 1957.
3
Kistler, A. L., "Fluctuating Wall Pressure Under Separated Super-
735