Noise Suppression Spoiler for the Air Ring of a Large Polyethylene Film-Blowing Equipment
K. K. Botros, E. Clavelle, J. Geerligs, J. Marler, R. Raynard, D. Cust and B. Rehlau
NOVA Research & Technology Corporation.
Calgary, Alberta, Canada
ABSTRACT
This paper presents novel alterations of the design of large polyethylene film-blowing equipment that
resulted in significant suppression of the overall sound pressure level (SPL) generated when the machine
was operating close to its high output range. SPL suppression obtained was in the order of 27-29 dBA.
Analysis showed that the shallow cavity created between the adjustable chimney inner geometry and the
fixed chimney of the upper air ring is responsible for a discrete-tone noise around 119 dB. Two positions
of the adjustable chimney were found to be responsible for this high single-tone noise. The design
alterations responsible for noise suppression include modifications to the lip of the fixed chimney in the
form of stream-wise groves (saw-teeth spoiler) and sealing or minimizing the two rows of holes on the side
on the adjustable chimney. Noise excitation mechanism and means of alleviation were investigated by
acoustic analysis supported by SPL measurements on the full size equipment.
INTRODUCTION
A concern was raised that a high overall sound pressure level (OSPL), in the order of 104 dBA, was
recorded around the Macro Film Blowing Line (Model D10-1) when it was operating close to its high
output. Area and personnel noise samples taken indicated that an actual personal exposure over 6 hours
reached a level of 93.1 dBA and a projected exposure over 8 hours reached 94.5 dBA. The latter translates
to 893% dose based on the Alberta Occupational Exposure Limit of 85 dBA over an 8-hour period. This
high OSPL has also caused discomfort to personnel in offices adjacent to the area of the equipment, even
when adjacent firewalls were closed. OSPL measurements taken in an area of 90 m2 surrounding the
Macro Line also confirmed that the OSPL was around 90 - 104 dBA, which is quite high for continuous
exposure. The actual OSPL at source would be considerably higher than that measured away from source
according to the distance rule {20 log (R/Ro)}, where R and Ro are radii at measured and source locations,
respectively.
Subsequent measurements were taken with a handheld OSPL device, when the airflow to the Outer Bubble
Cooling ring was set at maximum. These measurements were taken during operation simulations (cooling
air blower operating, but no film being blown) and indicated a maximum noise level of 107 dBA at the
operator’s platform on the Macro Unit. The 107 dBA noise was distinguished as a discrete tone character,
while other noise generated during different operating conditions was of a broadband type. The Inner
Bubble Cooling (IBC) air was examined and did not generate any noise level of concern.
Measurements of SPL spectra taken at different position of the adjustable chimney of the outer air ring will
be presented, followed by brief description of the excitation mechanisms as related to two distinct positions
of the chimney. Computational fluid dynamic (CFD) analyses were performed to aid in the understanding
of the flow field between the two chimneys. Various ideas for design modifications to the outer ring were
investigated and supported by SPL spectral measurements on the full size equipment. Due to the size of
the Macro Line and the three dimensional space it occupies; it would be impractical, if not impossible, to
apply conventional sound enclosure methods to minimize noise. Even if it were feasible to enclose the
film line, the operator(s) would have to be inside the enclosure to operate the equipment, increasing their
overall noise exposure.
RELEVANT DATA
Figure 1 shows different view-angles of the subject Macro Film Line. Outer Bubble Cooling air is
diverted into two channels (lower chamber and upper chamber), as shown in Fig. 2. The main components
of the upper air chamber are: the deflector lip, the fixed chimney and the adjustable chimney. The
adjustable chimney is used to direct the airflow relative to the film bubble so as to maintain the frost line on
the bubble at a reasonably low location along the bubble length. Dimensions of the air ring assembly were
taken from actual measurements and the drawing shown in Fig. 2. Maximum air mean flow velocity in the
gap between the lip of the fixed chimney and the deflector ring was measured by a handheld anemometer
and was found to be around 40 m/s at a blower speed setting of 52%.
Figure 1: Photos of the Macro Film Line.
Figure 2: Schematic of the Air Ring at Normal Position.
Discrete-tone noise is generated when the lower chamber was throttled to minimum gap and most of the air
is diverted to the upper chamber. Table 1 gives the relevant data for the cooling air at this setting and the
blower speed of 52%.
The axi-symmetric cavity created by the inner space of the adjustable chimney and the top surface of the
fixed chimney (see Fig. 2) is characterized by the stream-wise length ‘L’, and an average depth ‘D’ in the
radial direction. Table 2 gives these two characteristic dimensions and the ratio ‘L/D’ at different positions
of the adjustable chimney. The ratio ‘L/D’ is an important parameter for discrete-tone generation as will be
seen later.
Table 1: Relevant Data at Blower Speed = 52%.
o
Air Temperature ( C)
3
Air Density (kg/m )
Speed of Sound (m/s)
Air Velocity at gap (m/s)
Diameter of Deflector Lip (mm)
Air Viscosity (Pa.s)
Average Reynolds number (based on
gap width between Fixed Chimney and
Deflector Lip of 10 mm)
Mean Air Stream Mach Number
15
1.086
339.4
38
330
1.79E-05
23,057
0.112
INITIAL MEASUREMENTS
Acoustic measurements were taken using a Bruel & Kjaer 2148 Dual Channel Portable Signal Analyzer. A
type 4134 B&K microphone was used with type 2669 cable connected to a ZN 0664 dual channel input
module. The microphone was calibrated with a B&K type 4220 Piston Phone. The measurement setup was
discrete channel 400 line auto-spectrum with A-weighting, 12.8 kHz frequency span, 16 linear averages,
and Hanning window time weighting. The microphone was firmly mounted on a stationary structure with
its sensing point located approximately 0.35 m horizontally from centerline of the Macro Line and 0.35 m
vertically above the plane of the deflector lip. At this location, the microphone is approximately 0.50 m
diagonally away from the center of the upper air ring.
The first SPL measurement was taken at a normal operation setting of the lower and upper air ring and with
maximum airflow and normal position of the adjustable chimney. The measured SPL spectrum is shown in
Fig. 3, which indicates that the noise generated is broadband with an overall SPL in the order of 84 dBA
and a maximum level of approximately 87 dBA.
140
Sound Pressure (rms- dBA)
Normal Operation
120
100
80
60
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Frequency - Hz
Figure 3: Measurements of SPL Spectra at Normal Operation (Cooling Air flowing in Both Lower
and Upper Chambers).
Subsequent tests were taken with the air ring set to apply maximum throttle to the lower ring, directing the
majority of the airflow to the upper ring. Operation of the film line with the air ring at this setting produced
the highest detected noise level. Several measurements were taken at different positions of the adjustable
chimney starting with the lower-most position (L = 0 mm) to the upper-most position (L = 46 mm), and
concluding with a measurement with the adjustable chimney removed. The results of these measurements
are shown in Figure 4 and a summary is given below in Table 2.
Sound Pressure (rms- dBA)
140
L = 0 mm
L = 5 mm
L = 12 mm
L = 19 mm
L = 21 mm
L = 23 mm
120
100
80
60
0
1000
2000
3000
4000
5000
Frequency - Hz
140
L = 31 mm
L = 39 mm
L = 40 mm
L = 46 mm
Chimney Removed
Sound Pressure (rms- dBA)
130
120
110
100
90
80
70
60
0
1000
2000
3000
4000
5000
Frequency - Hz
Figure 4: Measurements of SPL Spectra at Different Positions of the Adjustable Chimney.
It was found that the pattern of the SPL spectrum changes with the position of the adjustable chimney as
follows:
1.
2.
At L = 0, 5 and 12 mm the corresponding SPL spectrum is generally of a broadband nature with
maximum SPL around 86 dBA (see Table 3).
At L = 19, 21 and 23 mm a sharp peak started to developed which reached maximum of 119 dBA
at L = 21 mm and frequency = 1888 Hz along with its higher harmonics. These measurements
are consistent with the OSPL measurements at the floor level and at a distance of approximately
3.
4.
5.
4.0 m away from the center of the upper ring. This confirms the noise reduction due to distance of
20 log (4.0/0.5) = 18 dB.
Further increase in the position of the adjustable chimney resulted in bringing the spectrum back
to a broadband character as shown in Fig. 4, with the maximum SPL dropped to 92.8 dBA.
Further increase in the position of the chimney resulted in reappearance of a sharp peaks at L =
39-46 mm.
Finally, removing the adjustable chimney altogether produced a broadband noise at normal levels
of approximately 85 dBA.
Table 2: Summary of Peak SPL at Different Positions of the Adjustable Chimney.
Adjustable
Chimney
Position L
(mm)
0
5
12
19
21
23
31
39
40
46
Removed
Average
Cavity
Depth D
(mm)
20
19
18
17
16
15
14
13
12
12
no cavity
L/D
Peak rmsdBA
0.00
0.26
0.67
1.12
1.31
1.53
2.21
3.00
3.33
3.83
N/A
86.88
86.43
86.85
116.23
118.51
117.03
92.8
116.77
118.08
108.11
85.65
Frequency
at Peak
Amplitude
(Hz)
1664
3200
2112
2048
1888
1760
1728
1952
1920
1664
2592
Strouhal
Number
(fL/U)
0
0.421053
0.666947
1.024
1.043368
1.065263
1.409684
2.003368
2.021053
2.014316
The above test results are summarized in Table 2 and Fig. 5 in terms of peak SPL as function of L/D. It
indicates that there are two positions of the adjustable chimney where a peak discrete tone develops. This is
strikingly similar to that associated with self-excited oscillations of cavity flows where the excitation
mechanism is coupled to an acoustical resonance mode, a phenomenon that has been extensively studied
[1-10]. A review by Rockwell [1], in which 161 references are cited, summarizes recent advances to the
state of knowledge in this field. The following section discusses this phenomenon and its relationship to
the present problem in more detail.
Peak Sound Pressure (rms - dBA)
130
120
110
Adustable
Chimney
Removed
100
90
80
0
1
2
3
4
5
6
Cavity Length/Depth (L/D)
Figure 5: Measured Peak SPL vs. Position of Adjustable Chimney (L/D).
ANALYSIS
Self-sustaining cavity oscillation is a phenomenon that results from a strong coupling between the resonant
wave effects within the cavity and the flow field at the mouth of the cavity created by the shear layer
separating the primary flow over the cavity from the secondary flow inside the cavity. When L/D >1, the
cavity is termed a shallow cavity. Small perturbations at the leading edge of the cavity are amplified as
they travel downstream into vortical structures producing organized pressure and velocity fluctuations.
These fluctuations are drastically self-enhanced at selected frequencies if an impingement edge exists
downstream of the flow separation (e.g. the trailing edge of the cavity). The resulting pressure oscillations
can cause high vibration or noise problems as is shown in the present paper. Numerous investigations
(experimental and numerical) have been reported [1-10] which explain the mechanism and conditions for
the self-sustaining oscillations. Successful semi-empirical prediction of the frequencies of oscillation has
been given by Rockwell [2] Rossiter [6] Heller and Bliss [9] and Block [10]. In all of these investigations,
the prediction techniques have the same general form and require two empirical constants. They are based
on a simple description of the downstream movement of the shear-layer vortices and the internal cavity
acoustic field. Heller and Bliss [9] provide the most widely used formula for peak Strouhal number
(defining the frequency at peak SPL) as follows:
Stm =
f L
=
U
[
n − C1
k −1 2
M∞ / 1+
M∞
2
] + 1 / C2
The parameter (n) in the above equation refers to the mode number, where n = 1, 2, 3, 4 etc. The values of
C1 and C2 depend on the shear layer momentum thickness, flow Mach number, and L/D, among other
parameters. Rockwell [2] has found values of C1 = 0.25 and C2 = 0.56 at high values of L/D (e.g. >2).
Based on the above theory, the experimentally determined peak Strouhal number of the self-sustaining
oscillations within the Macro air ring assembly are plotted versus the positions of the adjustable chimney
where the peak SPL occurred (Fig. 6).
The theoretical predictions of the same (by Rockwell [2] and
Heller and Bliss [9]) are also shown as solid lines on the same Figure for the first four modes. It indicates
that the peak SPL observed around L = 21 mm corresponds to mode n=2, while the peak SPL observed
around the second position of L = 40 mm corresponds to mode n=4. The aforementioned observations
indicate that the shear-layer/acoustic field coupling mechanism is different for 21 mm and 40 mm positions
of the adjustable chimney. Information about the flow field over the cavity was needed, to discern the
nature of the difference between these two distinct positions, prompting a CFD simulation to be performed.
The results are given in the next section.
2.5
Peak Strouhal Number (fL/U)
n=4
2.0
n=3
1.5
n=2
1.0
n=1
0.5
0.0
0
1
2
3
4
5
6
Effective Cavity Length/Depth (L/D)
Figure 6: Comparison Between Measured Peak SPL Theory.
CFD SIMULATION
In order to examine the flow of air within and surrounding the air ring of the Macro Film Blowing Line, a
computational fluid dynamics (CFD) simulation was performed. The general idea is that the fundamental
equations of motion for a fluid are solved over a connected set of control volumes (or grid cells), which
together compose the geometry of interest. For the problem at hand, these equations include the
conservation of mass and momentum. The equations are solved to give either the steady-state or transient
velocity and pressure field everywhere within the simulated domain.
Figure 7: CFD Model Grid.
Figure 7 shows the geometry of the near air ring region and its associated computational grid. The flow is
solved in an axi-symmetric co-ordinate system to reduce the computation domain and time. Several cases
were simulated to determine the effect of the adjustable chimney position. In all cases the deflector lip was
in its lowest position preventing all flow to the lower ring. Figures 8 and 9 show plots of velocity vectors
for the 21 mm and 40 mm adjustable chimney position, respectively. In both cases the tortuous fluid path
directs the fluid to form a jet issuing from the deflector lip (as opposed to being centered between the fixed
chimney and deflector lips). This jet, with its associated shear layer, then passes over the cavity formed by
the adjustable chimney. The position of the adjustable chimney strongly influences the direction of the jet
in relation to the lip of the chimney downstream. In Fig. 8, it is shown that the jet is diverted away from
the lip, rather than impinging on it. Therefore, the fact that a high level of noise was observed in this case,
it would have to do with an excitation mechanism that is coupled to a different acoustic resonance mode
than that existing in a mere shallow cavity (e.g.. amplification of certain frequencies of the general flow
noise, matching the resonance condition of the cavity/holes/guide assembly). In Fig. 9, however, the jet is
shown to impact the chimney lip at its trailing end; hence this position is akin to a conventional selfsustaining oscillation generated by the shallow cavity.
Figure 8: CFD of the Steady State Velocity Vectors for Adjustable Chimney Position L = 21 mm.
Furthermore, in the 40 mm position, it can be seen that the flow circulation in the cavity is akin to a closedbottom shallow cavity (i.e. without the holes), which indicates that the presence of the holes in this position
does not alter the characteristics of the cavity, as is the case at 21 mm position. For the relatively low
aspect ratio 21 mm chimney position, however, this situation does not exist, in that neither a clear presence
of a circulation, nor an impinging jet on the trailing edge prevails. This supports the conviction that
discrete noise generated at the 21 mm position is an acoustic resonance of the system surrounding the
cavity rather than the result of self-sustaining oscillation as would be the case in the 40 mm chimney
position of. This information explains why the discrete noise disappears at mid-span of the adjustable
chimney and then reappears as L increases to the next position, and why the modes of self-sustaining
oscillations are different.
Figure 9: CFD of the Steady State Velocity Vectors for Adjustable Chimney Position L = 40 mm.
TESTING OF NOISE ABATEMENT TECHNIQUES
The aforementioned measurements, analysis and CFD results indicate that there are two different noise
generation mechanisms that depend on the position of the adjustable chimney:
1.
The lower position is akin to self-excited oscillations coupled to acoustic resonance of a system
comprising the cavity, holes, outer guides and gaps between the guides. This is indicated by:
• the cavity at this position has L/D ≈ 1.0, hence it is neither a shallow nor a deep cavity; and
• the jet does not impinge on the trailing edge of the cavity giving rise to acoustic
communication to the outer field; and
• the diameter of the two rows of holes is large enough not to confine a resonance condition
in a now unbound cavity.
2.
The upper position is akin to a conventional self-sustaining oscillation created by flow passing a
shallow cavity and a feedback mechanism of impinging jet on the downstream lip of the cavity.
At chimney positions not matching the above two conditions, self-excited oscillations are not sustained,
resulting in lower SPL levels as shown in Fig. 5.
In order to suppress the noise of the second mechanism above, the literature offers various methods and
techniques, which are elegantly summarized by the review of Rockwell [2]. These noise suppression
methods encompass variations in the leading or trailing edge geometry of the cavity to destroy the feedback
mechanism of the self-sustaining oscillation phenomena to occur. The disruption of the first noise
mechanism (as listed above) was rather challenging, requiring variations of the system geometry in an
attempt to interrupt the acoustic characteristics of the system and destroy its coupling to the separated flow
at the lip. To determine the impact of noise disruption techniques on the aforementioned noise
mechanisms, the following techniques were investigated: (note: all tests were conducted with cooling air
blowing only – there was no polymer film blowing through the equipment).
•
•
•
•
•
•
Roughened (or spoiled) the leading edge of the cavity (i.e. the lip of the fixed chimney).
Spoiling was completed by pasting a Velcro tape on the lip to create stream-wise grooves on the
edge (see Fig. 10).
Roughened (or spoiled) the trailing edge of the cavity, (i.e. the lip of the adjustable chimney),
using Velcro tape.
Roughened (or spoiled) the lip of the deflector ring using Velcro tape.
Altered the acoustic resonance by sealing the holes on the adjustable chimney. This disrupted
the radial resonance mode (see Fig. 11).
Sealed the circumferential gap between the adjustable chimney and the inner guide. This
disrupted the axial resonance mode within circumferential gap (see Fig. 12).
Insertion of pads in the gap between the adjustable chimney and the inner guide. This disrupted
the circular resonance mode (see Fig. 13).
Saw Teeth Lip
Figure 10: Roughened (Spoiled) the Leading Edge of the Cavity.
Figure 11: Altered The Acoustic Resonance By Sealing The Holes On The Adjustable Chimney.
Figure 12: Disrupted the Axial Resonance Mode In The Guide Gap.
Figure 13: Disrupted the Circular Resonance Mode in Guide Gap.
All of the above noise suppression techniques were tested at various positions of the adjustable chimney
during 52% flow and maximum throttle of the lower ring. Spoiling the fixed chimney lip with stream-wise
grooves created by the Velcro tape did not produce any noise suppression at the lower position (L ≈ 21
mm) as shown in Fig. 14. This reinforces the supposition that the discrete frequency excitation
observed is caused by the separated jet oscillation coupled to an acoustic mode occurring outside the
cavity. When the two rows of holes were sealed with duct-tape, the system comprising the cavity, holes
and outer guide was eliminated, destroying the acoustic mode responsible for sustaining the jet instability
and/or amplification. This theory is confirmed with the test results of Fig. 15, where a significant noise
reduction of the order of 29 dB is demonstrated by just sealing the holes.
140
Sound Pressure (rms- dBA)
L = 21 mm (with Lip Spoiler)
120
100
80
60
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Frequency - Hz
Figure 14: Measured SPL Spectrum at L = 21 mm With Lip Spoiler Only.
140
Sound Pressure (rms- dBA)
L = 21 mm (with Closed Holes)
L= 21 mm (Original Design)
120
100
80
60
0
1000
2000
3000
4000
5000
Frequency - Hz
Figure 15: Measured SPL Spectrum at L = 21 mm With Holes Closed.
For the upper position of the adjustable chimney (around L ≈ 40 mm), roughening the leading edge of the
cavity (i.e. the lip of the fixed chimney) was effective in noise reduction of the order of 26.5 dB as
demonstrated by the comparison in Fig. 16. All other methods were less effective in noise reduction at this
position. It was also noted that, sealing the holes appeared to have little effect on noise reduction at the 40
mm position because the cavity L/D ratio was increased and the porosity created by the holes was
minimized.
140
Sound Pressure (rms- dBA)
L = 39 mm (with Closed Holes and Lip Spoiler)
L = 39 mm (Original Design)
120
100
80
60
0
1000
2000
3000
4000
5000
Frequency - Hz
Figure 16: Measured SPL Spectrum at L = 39 mm With Closed Holes and Lip Spoiler.
DISCUSSION OF THE ABATEMENT METHODS
The above argument, supported by measurements and analyses, clearly support that spoiling the leading
edge of the cavity by roughening the lip of the fixed chimney of the Big Mac Film Line is effective in noise
abatement at the upper position (L ≈ 40 mm). The development of a spoiler on the leading edge of the
cavity could be easily achieved using standard single-path machine knife tools, EDM (Electrical Discharge
Machining) methods or other machining techniques. Based on discussions with the manufacturer (Macro)
sealing the perforation on the adjustable chimney to suppress the high level of noise when the chimney is at
the lower position (L ≈ 21 mm) is an undesirable solution. The manufacturer (Macro) believed that sealing
the holes would result in polymer bubble instability, as the main purpose of these holes is to equalize
pressure in the cavity and/or to draw ambient air through an ejector effect. A less stringent solution was
then suggested to reduce the size of these holes to a point where the acoustic mode is disrupted enough
while maintaining the air flow to cavity through an ejector effect for bubble stability purposes.
In an attempt to gauge film bubble stability, film blowing tests were conducted with holes uncovered, and
then with holes covered at adjustable chimney position of L = 21 mm and maximum air at 52% (see Fig.
17). Data indicates that closing the holes resulted in a significant reduction in the SPL level, as was clearly
audible to personnel around the equipment during the test. Bubble stability was, however, a subjective
parameter that requires a method be developed to establish it in a more quantitative manner.
120
120
PE Film Blowing Run at L = 21 (With Holes Closed)
PE Film Blowing Run at L = 21 mm (Exisiting Design)
110
Sound Pressure (rms- dBA)
Sound Pressure (rms- dBA)
110
100
90
80
90
80
70
70
60
100
0
1000
2000
3000
Frequency - Hz
4000
5000
60
0
1000
2000
3000
4000
5000
Frequency - Hz
Figure 17: Measured SPL Spectrum at L = 21 mm During Actual Polyethylene Film Blowing
(Comparison Between Original Design and Holes Closed).
SUMMARY AND CONCLUSIONS
SPL spectra measurements taken at the Macro Film Blowing Line at various positions of the adjustable
chimney of the upper air ring clearly identified two positions where the noise generated was of a discretetone type. The peak amplitude of such noise reached 119 dBA. The shallow cavity created between the
adjustable chimney and the fixed chimney of the upper air ring along with system resonance was found to
be responsible for this discrete-tone noise generation. Two modes of high SPL levels were discerned. At
the lower position of the adjustable chimney, the high SPL level appears to be caused by amplification of a
resonating system, comprising an axi-symmetric cavity, perforation and an outer region bounded by the
guide shield. At the upper position, high SPL noise is generated through a conventional self-sustaining
oscillation in a shallow axi-symmetric cavity. The measured Strouhal numbers and peak amplitudes
coincide very well with theory for such flows and for two different oscillation modes of the 21 and 40 mm
positions of the adjustable chimney.
It is recommended to slightly alter the design of the lip of the fixed chimney such that a saw-teeth shaped
edge is incorporated to act as a shear-layer spoiler. This should not affect the mean airflow characteristics,
nor should it adversely impact the effectiveness of the outer bubble cooling. For the lower position of the
adjustable chimney, it is recommended that the holes are covered, or redesigned to be smaller in diameter.
Sealing (or smaller holes) have been shown to reduce the SPL level to 88 dBA (i.e. 29 dB reduction), while
maintaining the required airflow Bubble stability was a disputed and subjective parameter, and it is
recommended that a method to quantitatively determine bubble stability be developed to quantify the
effects of sealing holes on the lower adjustable chimney.
References
1.
Rockwell, D. and Naudascher, E. “ Review – Self-Sustaining Oscillations of Flow Past Cavities”,
ASME Journal of Fluids Engineering, Vol. 100, June 1979, pp.152- 165.
2.
Rockwell, D.: ”Prediction of Oscillation Frequencies for Unstable Flow Past Cavities”, ASME
Journal of Fluids Engineering, Vol. 99, 1997, pp. 294-300.
3.
Rockwell, D.: ”Oscillations of Impinging Shear Layers”, AIAA Journal, Vol. 21, No. 5, May
1983, pp.645-664.
4.
Tam, K.W.T.: “The Acoustic Modes of a Two-Dimensional Rectangular Cavity”, Journal of
Sound and Vibration, 49(3), 1976, pp.353-364.
5.
Tam, K.W.T. and Block, P. J. W.: “On the Tones and Pressure Oscillations Induced by Flow Over
Rectangular Cavities”, J. Fluid Mechanics, Vol. 89, part 2, 1978, pp.373-399.
6.
Bilanin, A and Covert, E.: “Estimation of Possible Excitation Frequencies for Shallow
Rectangular Cavities”, AIAA Journal, Vol. 11, No. 3, March 1973, pp.347-351.
7.
Hardin, J.C and Mason, J.P: “Broadband Noise by a Vortex Model of Cavity Flow”, AIAA
Journal Vol. 15, No. 5, May 1977, pp.632-637.
8.
Komerath, N.M., Ahuja, K.K and Chambers, F.W.: “Prediction and Measurement of Flows Over
Cavities – A Survey”, AIAA 25th Aerospace Science Meeting, Reno, Nevada, January 12-15,
1987.
9.
Heller, H.H. and Bliss, D.B.: “The Physical Mechanism of Flow Induced Pressure Fluctuations in
Cavities and Concepts for Their Suppression”, AIAAPaper 75-491, Hampton, VA., March 1975.
10. Block, P. J. W.: “Noise Response of Cavities of Varying Dimensions at Subsonic Speeds”,
N.A.S.A. Tech Note D-8351, 1976.
11. Ziada, S., Buhlmann, E.T. and Bolleter, U.: “ Flow Impingement as an Excitation Source in
Control Valves”, Journal of Fluids and Structures, Vol 3, pp. 529-549, 1989.