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HDL-CR., 7-025-I • •0Ii-1
October 1978
Effect of Angle of Attack on Cavity Flow Oscillations
by
V. Sarohia and P, F. Massier
Prepared byJet Propulsior LaboratoryCalifornia Institute of Technology
! >. Pasadena, CA 911038 (JPL Publication 79-19)
iLz Under cuntract
/ • MIPR No. R-77-25
,V
U.S. Army Electronics Researchand Oevelopmernt Command
Harry Diamond Labo-mtoriesAdolphi, MD 20783
.-. .- - -..
SIS
The findings in this report are notto be construed as an official Departmentof the Army position unless so designatedby other authorized documents.
Citation of manufacturers' or tradenames does not constitute an official in-dorsemert or approval of the use thereof.
Destroy this report when it is nolonger needed. Do not return it to theoriginator.
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I I. iey WORDS (Continue on ,-tee..sid It n *eemy and Idene1ir by Nock number)
Jets, Wakes, and Viscid-Inviscid Flow Interactions
C2111 A T , AC? C=ae ,,,r- , e,,L 8 l y-, --. , by block mab)
4Separated subsonic flow over cavitie3s of several widths and depths locatedon fuze-nose and ellipsoidal axisynmmetric bodies have been i nyestigated experi-mentally at various angles of attack to the free-stream. Te'flu uatlng and meanvelocities and pressures inside the cavity were measured at various circumfer-enti Il locations. Large circumferential variations in the root mean square pres-sure luctuations were observed in the cavity at an angle of attack. The hot-wire measurements of velocity fluctuations showed that the circumferential..------
SUNCLASSIFIEDc I I CUmYYV CLASS1P1CATIOM OF THIS PA=E (9bm Duel talai.
- M -Fa-- . - -O-
UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE(naha Data Entetod)
20.
variations in cavity pressure oscillations were caused by the loss of spanwisecoherency of the large-scale structures around the cavity. Visualization ofthe flow further confirmed that the strength of the cavity pressure fluctuationswas closely related tothe presence of the large-scale organized fluctuations inthe cavity shear flow. he mean velocity measurements showed changes in growthrates, dO/dx, at various circumferential locations along the cavity shear layer,where 0 is the momentum t ickness, and x is the streamwise coordinate. High-speed Schlieren motion pictwres further showed that this growth of the shearlayer was accompanied by a process of the large-scale eddies engulfing the fluidinside the cavity. The engulfed fluid was subsequently carried by these eddiesinto the potential flow surrounding the cavity and remained unmixed downstreamfrom the cavity for many wavelengths of the convecting large-scale eddies.For the fuze-nose model, the upstream edge of the axisymmetric cavity should belocated at X0 > 1.25 in. for cavity flow to oscillate. At this location, forcavity widths > 0.25 in. and depths > 0.050 in., the cavity flow oscillationswere observed a-t free-stream velocities > 500 ft/s.
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............. . .
CONTENTS
1 INTRODUCTION ------------------------------------------------
2 EXPERIMENTAL ARRANGEMENT -------------------------------------------- 92.1 Model and Free-Jet Facility ----------------------------------------- 92.2 Instrumentation and Measurements ------------------------------------ 102.3 Flow Visualization -------------------------------------------------- 11
3 EXPERIMENTAL RESULTS ------------------------------------------------ 113.1 Visualization of Cavity Flow ---------------------------------------- 113.2 Cavity Pressure Fluctuations at Angle of Attack --------------------- 133.3 Growth of Cavity Shear Layer ---------------------------------------- 153.4 Minimum Depth for Oscillations
at Different Cavity Locations --------------------------------------- 16
4 DISCUSSION AND CONCLUSIONS ------------------------------------------ 17
NOMENCLATURE ------------------------------------------------- 19
REFERENCES ---------------------------------------------------------- 21
DISTRIBUTION LIST ------------------------------------------------ 53
............................ ................................................... 5
1 17
• --3-
4 -
Tables
Effect of Angle of Attack on Pressure OscillationsInside Cavity
1 Width, b = 0.3 in.; Depth, d = 0.1 in.;Location, ( - 00 - ----------------------------------------------------- 22
2 Width, b = 0.3 in.; Depth, d = 0.1 in.;Location, ( = 300 - --- --- ---- --- --- --- --- ---- --- --- --- --- --- --- -- 23
3 Width, b = 0.3 in.; Depth, d = 0.1 in.;Location, ý = 600 ----------------------------------------------------- 24
4 Width, b = 0.3 in.; Depth, d = 0.1 in.;Location, t = 90 -. . . . ..----------------------------------------------- 25
5 Width, b = 0.4 in.; Depth, d = 0.1 in.;Location, = = 0° ---------------------------------------------------- 26
6 Width, b = 0.4 in.; Depth, d = 0.1 in.;Location, = 300 ----------------------------------------------------- 27
7 Width, b = 0.4 in.; Depth, d = 0.1 in.;Location, = 60 - ----------------------------------------------------- 28
8 Width, b = 0.4 in.; Depth, d = 0.1 in.;Location, q, = 90 -. . . . ..----------------------------------------------- 29
9 Width, b = 0.475 in.; Depth, d = 0.1 in.;Location, = 0 -.------------------------------------------------------ 30
10 Width, b = 0.475 in.; Depth. d = 0.1 in.;Location, = 30 - ----------------------------------------------------- 31
11 Width, b = 0.475 in.; Depth, d = 0.1 in.;Location, = 60 -. . . . ..----------------------------------------------- 32
12 Width, b = 0.475 in.; Depth, d = 0.1 in.;Location, = 900 ----------------------------------------------------- 33
13 Width, b = 0.475 in.; Depth, d = 0.225 in.;Location p 0* ------------------------------------------------------ 34
14 Width, b 0.475 in.; Depth, d = 0.225 in.;Location, p = 30 .----------------------------------------------------- 35
15 Width, b 0.475 in.; Depth, d = 0.225 in.;Location, ,p 60 .----------------------------------------------------- 36
16 Width, b 0.475 in.; Depth, d = 0.225 in.;Location, , 90° ----------------------------------------------------- 37
-4-
Figures
1 Cavity Oscillation Model with Pertinent Nomenclature ------------- 38
2 Axisymmetric Cavity Flow System ------------------------------------ 39
3 Diagnostics of Cavity Flow Oscillations ----------------------- 40
4 Visualization of Cavity Flow with b = 0.68 in., d = 0.75 in.,and U- = 60 ft/s ----------------------------------------- 41
5 Visualization of Cavity Flow with b = 0.68 in., d = 0.25 in.,and U- = 60 ft/s --------------------------------------------------- 42
6 Visualization of Cavity Flow with b = 0.68 in., d = 0.25 in.,and U- = 60 ft/s ----------------------------------------- 43
7 High-Speed Schlieren Motion Pictures Showing Large-Scale Structuresin Oscillating Cavity Flow at a = 0* with U- = 60 ft/s, b = 0.68in., and d = 0.25 in. (Time Between Frames = 0.2 ms.) ------------ 44
8 High-Speed Schlieren Motion Pictures Showing Large-Scale Structuresin Oscillating Cavity Flow at a = 3.5' with U- = 60 ft/s, b = 0.68in., and d = 0.25 in. (Time Between Frames = 0.18 ms.) ------------- 45
9 High-Speed Schlieren Motion Pictures Showing Large-Scale Structuresin Oscillating Cavity Flow at a = -3.5' with U- = 60 ft/s, b = 0.68in., and d = 0.25 in. (Time Between Frames = 0.18 ms.) ------------ 46
10 Influence of Angle of Attack on Cavity Pressure Fluctuationswith b = 0.475 in., d = 0.225 in., and U- = 341 ft/s --------------- 47
11 Effect of Angle of Attack on Cavity Pressure Fluctuationswith b = 0.475 in., d = 0.225 in., and U- = 341 ft/s --------------- 48
12 Influence of Angle of Attack on Cavity Pressure Fluctuationswith b = 0.475 in., d = 0.225 in., and U- = 585 ft/s --------------- 49
13 Effect of Angle of Attack on Cavity Pressure Fluctuations
with b = 0.475 in., d = 0.225 in., and LU = 585 ft/s --------------- 50
14 Inflence of Angle of Attack on Shear Layer Growth Rate ------------- 51
15 Flow Around Axisymnetric Cavity at Angle of Attack ----------------- 52
-5-- U . .-
1. INTRODUCTION
It has been observed by many investigators, e.g., East (Ref. 1), Karamcheti
(Ref. 2), Roshko (Ref. 3), Sarohia (Ref. 4), that a separated shear layer over
a cavity sustains oscillations over a wide range of Mach numbers and Reynolds
numbers, with both laminar and turbulent boundary layers and over a wide range
of length to depth ratios. Shadowgraph pictures of Sarohia and Massier (Ref. 5)
indicate the presence of organized large-vortex structures in the oscillating
flow over an axisymmetric cavity for both a laminar as well as a turbulent
boundary layer at the upstream cavity corner. These pictures, along with
detailed measurements taken in the cavity shear, layer under a wide range of
cavity configurations and flow conditions (Sarohia, Ref. 6), strongly indicate
that the cavity flow oscillation phenomenon results primarily from the inherent
instability of the mean velocity in the shear layer over the cavity. This
instability results from the presence of an inflection point in the profile,
which occurs for both laminar and turbulent separated flows over the cavity.
'>•iv -iv"-tal *esults (Ref. 6) showed that the organized flow disturbances
caused by these large-scale structures in the cavity shear layer are amplified
almost exponentially as they propagate downstream. Due to the strong influence
of the feedback from the downstream cavity corner, no merging or pairing of
these organized structures with each other occurred in the cavity mixing layer.
Such merging was observed, however, in free shear flows by Brown and Roshko
(Ref. 7), Winant and Browand (Ref. 8), and others. The presence of the large
organized structures in the flow' contributed to a larger growth of the cavity
shear layer than for a freely developing one. These large structures have
been shown to be greatly responsible for the pressure fluctuations inside the
cavity (Ref. 5).
-7 - ,",7
[
In Sarohia (Ref. 6), the signals detected by a reference hot-wire probe
were cross correlated with those detected by a second probe which was moved
circumferentially. These cross correlations showed that when the cavity was
aligned with the free-stream flow, the flow oscillations were axisymmetric.
The spark shadowgraphs of the cavity flow also showed that the large-scale struc-
tures associated with cavity flow oscillations were circumferentially coherent.
Since these oscillations result from strong feedback with the downstream cavity
corner, a comparatively large modification of this feedback behavior results.
Consequently, the cavity-flow oscillations are modified when the free-stream
velocity is at an angle of the attack with respect to the axis of the axisym-
metric cavity. Knowledge of the manner in which the cavity flow is modified
circumferentially at an angle of attack can lead to increased insight into the
mechanism of these self-sustained oscillations.
Fxperimental rnults of Willmarth et al. (Ref. 9) showed that pressure
oscillations inside an axisymmetric cavity were sensitive to the angle of the
cavity with respect to the free-stream. Willmarth et al. reported that velocity
and pressure flucutations, associated with cavity shear flow, varied largely as
the angle of the free-stream was varied with respect to the axis of the cavity.
Unfortunately, no detailed measurements of the flow field around the cavity were
made to determine the basic modification of cavity flow associated with '"he angle
of attack configuration.
The experiments conducted under the present investigation were performed
to advance the understanding of the manner in which initial flow conditions at
the upstream cavity corner influence the phenomenon of cavity flow oscillations.I
Flow visualization and detail measurements of cavity shear layer velocity and
pressure measurement inside the cavity were made to help gain further insight
-8-
-- . -- - -- - ,. - - - -
into the mechanism of oscillations in separated cavity flows. Due to the modi-
fication of the spanwise coherency of these organized large-scale structures
in the cavity flow, these measurements have also elucidated the role of spanwise
structures in the development of separated shear flows.
2. EXPERIMENTAL ARRANGEMENT
2.1 Model and Free-Jet Facility
The cavity model, as indicated in Figure 1, was mounted on a movable plat-
form. This platform allowed the model to be positioned at various angles up
to +100 with respect to the axis of tne free jet. The model, which had a diameter
D = 2.0 in., was tested in a 7-in.-diameter open-jet tunnel. A semicircular
arc ring of 10-in. diameter, which was large enough not to disturb the free-jet
flow, was constructed around the cavity model as shown in Figure 2. This ring
carried a hot-wire probe which could be positioned at various circumferential
locations around the cavity flow. The hot-wire probe could be moved accurately
along the streamwise direction, x, and across the flow, y, at various selected
circumferential locations with an accuracy of +0.001 in.
Two axisymmetric models were employed for this investigation. One had an
ellipsoidal nose shape and the other had a fuze nose. Both models had provision
for step variation of depth, d, together with a continuously adjustable width, b.
The ellipsoidal-nose model was used primarily for flow visualization and for
measurement of fluctuating and mean velocity components in the cavity shear layer.
Most of the pressure measurements iniside the cavity were made with the fuze-nose
shape model as shown in Figure 1. A depth of 0.1 in. was selected for which
the width was changed in steps having values of 0.3, 0.4, and 0.475 in. This
model had provision for inserting a pressure transducer at the base of the cavity.
For four selected free-stream velocities, U. = 341, 426, 514, and 585 ft/s,
-i--9-
fpressure fluctuations inside the cavity were measured at 0 = +2', +4W, +6',
and +10'. Selected cavitypressure flucutations also were measured for d = 0.225
in. and b = 0.475 in. Throughout the present experiments of the fuze-nose model,
the leading edge of the cavity was fixed at X0 = 2.1 in. from the leading edge
of the fuze nose.
Experiments were performed also on the fuze-nose cavity model to determine
the minimum depth, d min' needed for onset of cavity-flow oscillations. The value
of dmin was determined for three axial locations: X0 = 0.75, 1.25, and 2.10 in.
from the leading edge of the fuze nose.
2.2 Instrumentation and Measurements
Constant-temperature, hot-wire anemometry was used extensively to determine
the mean and the fluctuating velocity components of cavity-flow oscillations.
Two hot-wire probes were employed which could be moved individually along the
x and across the y directions of the cavity shear layer, The experimental setup
was constructed to provide circumferential motion of these two hot wires relative
to each other. The dc outputs of the hot wires, which are priportional to the
mean velocities, were recorded on an X-Y plotter. The ac output signals of the
hot wires, which are proportional to the velocity fluctuations in the cavity
shear layer, were analyzed on an all-digital, real-time spectrum analyzer. The
outputs of the two hot wires were cross correlated on a correlation and proba-
bility analyzer, which is an all-digital high-speed processing instrument and
provides real-time computation for auto correlations and cross correlations.
The output of the correlation was either displayed on an oscilloscope or plotted
on an X-Y plotter.
The pressure fluctuations of the flow inside the cavity were measured with
-10-
a 1/8-in. pressure transducer, which was flush-mounted on the base of the cavity.
The rise time of this transducer was 2 ps. The frequency response of the pressure
transducer was from 2 to 40,000 Hz. The output of the pressure transducer was
amplified 100 times and then passed through a filter to remove the component
of the signal caused by the vibration of the system. The root mean square (rms)
value of the pressure signal was measured on a time-averaging rms voltmeter.
The signal was also analyzed on a spectrum analyzer to determine frequency dis-
tribution. From this, the mean square pressure fluctuations at the frequency
of cavity flow oscillations were estimated as a function of cavity flow for each
cavity configuration.
2.3 Flow Visualization
Flow near the cavity was visualized by injecting a small amount of CO? gas
through the base of the cavity. Still shadowgraphs were taken with a spark
source that had a duration of approximately 1.0 I.ts. A two-mirror Schlieren System
was used as shown in Figure 3 to take high-speed motion pictures up to 7000
frames/s. The spark source, which had a duration of 0.3 ps, was triggered by
the camera. This time was short enough to "freeze" the motion of the cavity
flow field.
3. EXPERIMENTAL RESULTS
3.1 Visualization of Cavity Flow
The shadowgraph pictures of Figure 4 indicate the influence of angle of
attack, ct, of the free stream with respect to the axis of the axisyrinetric cavity
for values of b - 0.68 in., d 0.75 in., and U = 60 ft/s. At (i = 0, the or-
ganized large-scale structures in the cavity shear layer can be seen in this
-11-
shadowgraph to be circumferentially symmetrical. At a = 4', however, structures
were destroyed in the vicinity of the circumferential location, ( = 1800, i.e.,
at the lower side of the cavity. On the upper side of the cavity ((p 00), the
organized structures were not affected by the angle of attack. The circumfer-
ential distribution of the fluctuating velocity in the cavity shear layer in-
dicated that at an angle of attack the coherency of these structures was gradually
destroyed as the circumferential position changed from (p 0' to ( = 180'. Similar
behavior was evident for other cavity configurations, as Figures 5 and 6 indicate
for , = 40 and 6', respectively.
Several series of high-speed Schlieren motion picture frames showing the
effects of angle of attack on the formation of large-scale organized structures
at b = 0.68 in., d = 0.25 in., and U = 60 ft/s are shown in Figures 7, 8, and
9 at a = 00, 3.50 and -3.5', respectively. The cavity was oscillating in the
second mode with nondimensional frequency fb/U = 1.69, where f = 1785 Hz. At
a = 0 (Figure 7), the rollup ot an organized structure is evident from frame 1
onwards. As the rollup of this convecting large organized structure continued,
it engulfed the cavity fluid (which was made visible when a small amount of CO2
gas was injected) into the free-stream potential fluid. Some of the cavity fluid
engulfed 6y the free-stream potential fluid. Some of the cavity fluid engulfed
by the organ;ized large-scale cavity structure can be inferred in Figure 7, frame 4.
The cavity fluid, which i- carried by the large organized cavity structure, re-
mained unmixed with the free-stream fluid as far as three to four wavelengths
downstream from the downstream edge of the cavity. The wavelength is here de-
fined as that of the organized large eddies in the cavity shear layer, i.e.,
X U c /f,
At a 3.50, Figure 8 shows the cavity oscillations close to (p = 0. As
-12-
- -r
indicated in the instant spark shadowgraphs of Figures 4 to 6, ti;e high-speed
Schlieren motion picture frames shown in Figure 8 indicated thlat the cavity
flow was not altered significantly by the angle of attack. Closer examination
of these high-speed picture frames, however, revealed that the oscillations
around 0* = 0° were even more organized for 00 < a < 60 as compared with a 00.
For 60 < a < 10, these large-scale structures again became less organized.
The pressure fluctuations inside the cavity were accordingly modified by the
angle of attack (section 3.2). There seemed to be a very close relationship
of the coherency of organized structures in the caý_ity shear layer and the
pressure oscillations inside *he cavity.
Around 4 = 1800, on the. other hand, the organized large-scale structures
were very sensitive to the angle of attack. As shown in Figure 9, these
structures were almost destroyed at an angle of attack of -3.50. These results
are in accordance with the still shadowgraphs shown in Figures 4 to 6.
3.2 Cavity Pressure Fluctuations at Angle of Attack
The influence of angle of attack on pressure fluctuations inside the cavity
was determined for d = 0.1 in. and for b = 0.3, 0.4, and 0.475 in. at UCO = 426,
514, and 585 ft/s. Tests were performed also at the above free-stream velocities
e.. well as at U = 341 ft/s for b = 0.475 in. and d = 0.225 in. Pressure fluc-
tuations inside the cavity were measured at locations 4 Q01, 600, and 9g0. At
these cavity flow conditions and configurations, tests were conducted at a =
+20, +40, +60 and +10*. Because of the sVMnetry of the axisymmetric flow, the
above combinations of the values of 0 and a were sufficient to infer the pressure
o;rillations over the entire 3600 around the cavity. In all, 64 sets of data
were taken. The data are tabulated in Tables 1 to 16.
V>
-13-
The present results showed that the frequency of cavity-flow oscillations
was independent of the angle of attack for a given cavity configuration and
free-stream velocity.
The present results in Tables I to 16 indicate that the rms pressure
fluctuations inside the cavity are very sensitive to the angle of attack.
Figure 10 shows typical results of filtered rms pressure fluctuation, PFILTERED', U2
normalized with the free-stream dynamic pressure, (1/2) pUO , for b = 0.475 in
d = 0.225 in., and U = 341 ft/s. Results for four circumferential locations
4 = 00, 300, 600, and 900 are plotted in Figure 10. At a = 00 for =) 00, the
rms pressure fluctuations were about 1.4% of the free-stream dynamic pressure.
As a was increased further, the strength of the pressure oscillations due to
cavity flow oscillation decreased in magnitude. As one would expect, the magni-
tudes of the pressure fluctuations for 4 = 00, 300, 60', and 90' at a = 00 were
almost identical because the flow oscillations were circumferentially axisymmetric.
At an angle of attack for 4 = 30', 60°, and 90', the cavity pressure fluctuation
peaked around a = 20. Relatively, the rms pressure fluctuations for ) = 00, 30°,
600 and 90' for -10' < c < 0° were less sensitive to the angle of attack than for
00 < C < 100.
Figure 11 indicated the influence of the angle of attack on the filtered
pressure in terms of total cavity rms pressure fluctuations at b = 0.475 in.,
d = 0.225 in., and U = 341 ft/s. At 4 90° and a = 00, only about 43% of the
cavity rms pressure fluctuations was at cavity oscillation frequency. At about
Si = 40, most of the pressure fluctuations were at the cavity oscillation frequency.
Due to a superimposed random signal on the cavity pressure fluctuations, PFILTERED/
PTOTAL 1 was observed at the other transducer locations. Also as indicated
in Figure 11, due to disorganized cavity fluctuations at t 00, 300, 600,
-14-
and 900 for a < 00, only a small fraction of the cavity rms pressure
fluctuations was observed at the cavity oscillation frequency.
Figures 12 and 13 show cavity pressure oscillations as in Figures 10
and 11, but for UJ. 585 ft/s. Similar deductions as drawn above apply to
these results. Tables 1 to 16 list cavity pressure fluctuations for other
flow speeds and cavity configurations.
3.3 Growth of Cavity Shear Layer
Recently, the growth of free-shear flows has been closely linked to the
presence of the large-scaie organized structures in them (Ref. 7 and 8). The
velocity fluctuations in the oscillating cavity shear flow are organized because
of the strong f2edback resulting from th- shear flo', interaction with the
downstream cavity cornet. Such organized cavity flows have been shown to
grow very rapidly (Ref. 5 and 6).
This section presents the results pertalnina to the influence of the
angle of attack on the growth of tht cavity shear layer zt various spanwise
locations. Mean velocities in the cavity flow were obtained experimentally
to determine the growth irate of the cavity shear layer. Detailed meisure-9
ments were made with a fixed upstream Reynolds number Ree 0 = 1.38 x 10 fixed
width b/O 0 = 185, and fixed depth d/O 0 = 50. From these mean velocity pro-
files, the momentum thickness, 6, was dEtermin~e:
C O ¢o f U~ (1- d
Inside the cavity, the integration was terminated where U(y) was approxi-
mately 5% to 7% of the mean free-stream velocity. In this region, the accuracy
of the hot-wire measurements is doubtful. The growths of the cavity shear
-15-
- -- '-- .---
layer for a = 00 and 30 at • = 0' are indicated in Figure 14. Also shown
are the growth rates, do/dx, which represent the entrainment rates of the
shear layer. The increased entrainment rate for c = 30 seems to result from
locally enhanced periodic velocity fluctuations in the cavity shear layer.
This increase, in turn, also results in increased pressure fluctuations inside
the cavity as shown in Figures 10 to 13.
3.4 Minimum Depth for Oscillations at Different Cavity Locations
The minimum cavity depth for onset of cavity oscillations was determined
at three axial locations: X0 = 0.75, 1.25, and 2.10 in. from the leading
edge of the fuze-nose cavity model. The depth was increased in steps of
0.010 in. for a fixed width. The free-stream velocity was varied from 0 to
700 ft/s. If no cavity flow oscillations were observed at velocities up to
700 ft/s, the depth was increased further up to 0.060 in.
For cavity location 0.75, no cavity oscillations were observed up to
U = 700 ft/s and depths up to 0.60 in. for two widths, 0.2 and 0.3 in. How-
ever, a cavity located at 1.25 with b = 0.25 in. began to oscillate at dmin -
0.050 in. and at U t 500 ft/s. Then for a cavity location at 2.10 in. for
width 0.325 in., no oscillations up to U., = 7W. ft/s were observed for d
0.020, 0.030, and 0.040 in. At this location of 2.10 in., oscillations did
not occur until d min = 0.050 in. and U, : 420 ft/s.
From the results it was concluded that, for the fuze-nose model, the
upstream edge of the axisymmetric cavity should be located at X0> 1.25 in.
The cavity flow will oscillate around U > 500 ft/s with b > 0.25 in. and
d >0.050 in.
-16-
".
. - - .- -
4. DISCUSSION AND CONCLUSIONS
A sketch of a fuse nose at an angle of attack is shown in Figure 15.
On the upper side (4 = 00), the free-stream flow along the model accelerates;
consequently, the flow over the cavity in this vicinity is in a region
of favorable pressure gradient. Cavity flow oscillations have been reported to
be very pronounced when the cavity is located in the favorable (negative)
pressure gradient (Ref. 5). This might have been one of the reasons
for strong pressure fluctuations inside the cavity at 4 ! 0' and at a = 2'
to 60 as observed in Figures 10 to 14. In contrast, however, it can be inferred
that the flow around the lower side (4 = 180') is in an adverse pressure
gradient region. Such flows over cavities tend to suppress cavity flow
oscillations. Still shadowgraphs in Figures 4 to 6 and high-speed motion
pictures in Figure 9 clearly indicate a disorganized flow over the cavity
located in an adverse pressure gradient. This disorganization explains theI
loss of periodic pressure fluctuations inside the cavity as indicated in Figures 10
to 14 for a < 00 at ý = 0', 30', 60', and 900
The experimental results of flow visualization pictures indicate a close rela-
tionship of organized cavity flow oscillations to the pressure fluctuations inside
the cavity. Due to the variation of circumferential coherency of these large-
scale structures at an angle of attack, there were associated circumferential
variations in the periodic cavity pressure fluctuations (Figures 10 to 13 and
Tables 1 to 16). These data illustrate that the production of cavity pressure
fluctuations results from the interaction of these organized large-scale
structures with the downstream corner of the cavity. Also, pressure fluctuations
inside the cavity are generated "locally" by the interaction of the cavity shear flow
-17-
--
[
with the downstream corner.
From the results of pressure measurements presented in Tables 1 to 16,
for an oscillating cavity flow at an angle of attack, strong oscillations
are always present in certain circumferential regions of the axisymmetric
cavity.
The enhanced growth of the cavity shear layer at an angle of attack as
indicated in Figure 14 indicates that the organized large-scale structures
are important in its growth. These organized eddies engulf the cavity fluid
and carry it into the potential flow surrounding the cavity. This engulfed
fluid remains unmixed for many wavelengths of the convecting large-scale
structures downstream from the cavity.
Because of the differential pressure imposed on the axisymmetric cavity
flow at an angle of attack, there is circumferential fluid motion inside the
cavity. This fluid motion can influence cavity flow oscillations and may
have been the cause of loss of the magnitude of the cavity pressure fluctuations
at large angles of attack, i.e., as shown in Tables 1 to 16. The role of this
cross flow both around the axisymmetric body and inside the cavity need further
attention.
S~-18-
_ _ _ _ _ _
"1" NOMENCLATURE
b Cavity width (Figure 1)
d Cavity depth (Figure 1)
D Outside diameter of axisymmetric body (Figure 1)
f Frequency in hertz
"2p 4p' Root mean square pressure fluctuations
R Outside radius of axisymmetric body (Figure 1)
ReD Reynolds number based on diameter (Figure 1)
Reo0 Reynolds number based on momentum thickness
S Distance along the axisymmetric body (Figure 1)
U(y) Mean velocity in x direction
U c Propagation speed of disturbances in the cavity shear layer
U. Free-stream velocity
x Streamwise coordinate from upstream cavity corner
X Streamwise distance (Figure 1)
X0 Location of upstream cavity corner (Figure 1)
y Transverse cnordinate
-19-
• !.
a Angle of attack between free-stream flow and cavity axis(see insert in Figure 10)
Circumferential location of transducer (see insert in
Figure 10)
Wavelength of propagating disturbance in shear layer
pCQ Density of ambient air
Shear layer momentum thickness
a 0 Shear layer momentum thickness at separation where x =0
fbf- Nondimensional frequency
Subscripts
)min Conditions for onset of cavity oscillations
( )FILTERED Filtered signal at cavity oscillation frequency
( )TOTAL Total output signal
-20-
,,4 , ..
REFERENCES
1. L. F. East, "Aerodynamic Induced Resonance in Rectangular Cavities,"
J. Sound and Vibrations, Vol. 3, March 1966, pp. 277-287.
2. K. Karamcheti, "Sound Radiated from Surface Cutouts in High-Speed Flows,"
Ph.D. Thesis, California Institute of Technology, June 1956.
3. A. Roshko," Some Measurements of Flow in a Rectangular Cutout." National
Aeronautics and Space Administration TN-3488, 1955.
4. V. Sarohia, "Experimental Investigation of Oscillations in Flows over
Shallow Cavities," AIAA Journal, Vol. 15, July 1977, pp. 984-991.
5. V. Sarohia and P. F. Massier, "Investigation of Pressure Oscillations in
Axisymmetric Cavity Flows," HDL-CR-025-1, September 1977.
6. V. Sarohia, "Experimental and Analytical Investigation of Oscillations
in Flows over Cavities," Ph.D. Thesis, Dept. of Aeronautics, California
Institute of Technology, Pasadena, CA, March 1975.
7. R. L. Brown and A. Roshko, "On Density Effects and Large Scale Structures
in Turbulent Mixing Layer," J. Fluid Mechanics, Vol. 64, Part 4, 1974,
pp. 775-816.
8. C. D. Winant and D. F. Browand, "Vortex Paring: The Mechanism of Turbulent
Mixing-Layer Growth at Moderate Reynolds Number," J. Fluia Mechanics,
Vol. 63, 1974, pp. 237-255.
9. W. W. Willmarth, et al., "Management of Turbulent Shear Layers in
Separated Flows," J. Aircraft, Vol. 15, July 1978, pp. 385-386.
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-41-
U
a) ANGLE OF ATTACK a= 00
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FIGURE 5. VISUALIZATION OF CAVITY FLOW WITH b = 0.68 in., d =0.25 in.. and Ub, 60 ft/s
-42-
I,,
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FIGURE 6. VISUALIZATION OF CAVITY FLOW WITH b 0.68 in., d 0.25 in., and U, 60 ft/s
-43-
S. .. l
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- 43
FIGURE 7. HIGH-SPEED SCHLIEREN MOTION PICTURES SHOWING LARGE-SCALE STRUCTURESIN OSCILLATING CAVITY FLOW AT a = 0° with Uc, = 60 ft/s, b 0.68in., AND d 0.25 in. (TIME BETWEEN FRAMES 0.2 ms.)
-44-
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FIGURE 8. HIGH-SPEED SCHLIEREN MOTION PICTURES SHOWING LARGE-SCALE STRUCTURESIN OSCILLATING CAVITY FLOW AT a = 3.50 with U,, = 60 ft/s, b = 0.68in., AND d = 0.25 in. (TIME BETWEEN FRAMES :O0.8 mns.)
-45-
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FIGURE 9. HIGH-SPEED SCHLIEREN MOTION PICTURES SHOWING LARGE-SCALE STRUCTURESIN OSCILLATING CAVITY FLOW AT a = 3.5° U,, 60 ft/s, b =0.68in., AND d :0.25 in. (TIME BETWEEN FRAMES =0.18 "is.)
i -46-
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DISTRIBUTION LIST
Address
Defense Documentation Center, ATTN: DDC-TCA, Ca eron Station, Alexandria,Virginia 22314 (12 copies)
HDL Library, Harry Diamond Laboratories, 2800 Powder Mill Road, Adelphia,Maryland 20783 (3 cop>ýs)
Editorial Committee (Chairman), Harry Diamond Laboratories, 2800 Powder MillRoad, Adelphia, Maryland 20783
HDL Branch 013, Harry Diamond Laboratories, 2800 Powder Mill Road, Adelphia,Maryland 20783
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Lyndon J. Cox, Program and Plans Office, Harry Diamond Laboratories, 2800 PowderMill Road, Adelphia, Maryland 20783
David L. Overman, S and A Devices, Branch 420, Harry Diamond Laboratories, 2800Powder Mill Road, Adelphia, Maryland 20783
James K. O'Steen, Naval Surface Weapons Center, White Ok Laboratory, SilverSpring, Maryland 20910
Fred Sachs, U.S. Anry Atmiaments Research and Development Coinnand, PicatinnyArsenal, Dover, New Jersey 07801
James Murray, U.S. Army Research Office, P. 0. Box 12211, Research Triangle Park,North Carolina 27709
Robert E. Singleton, Engineerirg Science Division, U.S. Atmvy Research Office,P. 0. Box 1211, Research Triangle Park, North Carolina 27709
D. Rockwell, Professor of Mechanical Engineering, Department of MechanicalEngineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015
-53-
California Institute of Technology, Graduate Aeronautical Laboratory, Pasadena,California 91109
M. V. Morkovin, Department of Mechanical and Aerospace Engineering, IllinoisInstitute of Technology, Chicago, Illinois 60619
A. Roshko, Mail Stop 205-50, Department of Aeronautics, California Instituteof Technology, Pasadena, California 91125
Fazle Hussain, Director and Professor of Mechanical Engineering, Aerodynamicsand Turbulence Laboratory, Cullen College of Engineering, Houston, Texas 7700l4
K. Karamcheti, Professor of Aeronautics, Department of Aeronautics arid Astro-nautics, Stanford Univerisity, Stanford, California J4305
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