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Acoustic behavior of orifice plates and perforated plates with reference to low-frequency sound absorption
Journal ofSound
and Vibration
ACOUSTIC
(1990) 139(3), 361-381
BEHAVIOR
PERFORATED
PLATES
LOW-FREQUENCY
OF
ORIFICE
WITH SOUND
PLATES
REFERENCE
AND TO
ABSORPTION-+’
M. SALIKUDDINS Lockheed Aeronautical Systems Company, Marietta, Georgia 30063,
U.S.A.
(Received 27 February 1989, and in recised,form 14 August 1989)
Analyses of impulse time history data from acoustic transmission tests for conical nozzles attached to a pipe show that the internal reflections from the solid contraction and the open area tend to cancel. To gain understanding of the opposing reflections, tests were conducted by replacing the conical nozzles with orifice plates and perforated plates. The primary variable was the open-to-solid area ratio. Internal reflection coefficient data reveal that, for an area ratio of lo-12%, the low-frequency internal reflection is reduced from unity to about 0.2. On the basis of comparisons of far field and internal data, acoustic energy is not conserved. Results are presented for a complex reflection coefficient and the far field noise for a series of orifice and perforated plate configurations. 1. INTRODUCTION
During the past several years, research on the transmission of sound through various duct terminations has been carried out at Lockheed, Georgia Division [l-7]. Because of the extreme difficulty in experimentally separating incident from reflected acoustic waves for the purpose of determining internal acoustic energy from either periodic or broadband sources of continuous excitation, an acoustic impulse technique developed by Salikuddin et al. [8] was utilized. In this technique a high-intensity pulse generated by a spark discharge is used as the sound source. One interesting aspect of the test results, the cancellation of low-frequency reflections, was revealed upon examination of termination reflection coefficient data obtained for the conical nozzles. These spectral reflection coefficients are derived from the ratio of the reflected pulse spectrum to that of the incident pulse [ 1,8]. Examination of the temporal characteristics of the reflected wave from a slowly contracting conical nozzle reveals some interesting characteristics. In Figure 1 are shown the reflections from a straight open pipe, three typical conical nozzles, and a straight pipe with a plugged end. The ratio of the conical nozzle open areas to that of the pipe (contraction ratio, AR) to which they are attached are 0.37,0*25 and 0.0625. For the straight open pipe, the reflection occurs only at the exit, resulting in an inverted (expansion wave) pulse. For the conical nozzles, unlike the straight duct, two opposite types of reflections are observed. One is due to the nozzle contraction and is in phase with the incident pulse (compression wave), and the other one is due to the open termination and is out of phase with the incident pulse. For the straight pipe with a plugged end, the reflection is identical to the incident wave. Thus, the nozzles present the upstream with two reflections that are, in effect, out of phase with each other.
Whis work was sponsored by Lockheed’s IRAD program. A portion of this paper appeared in AIAA Paper 80-0991, presented at the 6th Aeroacoustic Conference, 1980. $ Current address: General Electric Aircraft Engines Company, Mail Drop A-304, 1 Neumann Way, P.O. Box 156301, Cincinnati, Ohio45215-6301, U.S.A. 361 0022-460X/90/120361
+21 $03.00/O
@ 1990 Academic
Press Limited
362
M.
Figure
1. In-duct
SAI_IKCII~I~IN
time histories for various conical
nozzle terminations
to a 10 cm diameter
duct.
When the actual spectra1 reflection coefficients are examined for the nozzles (see Figure 2), it can be seen that as the nozzle exit diameter decreases from 10 to 2.5 cm, the reflection coefficient amplitude for very low frequencies is decreased. On physical grounds, this decrease in reflection coefficient at low frequencies is apparently due to the cancellation of the low-frequency reflection from the nozzle contraction by that from the open end. Further examination of Figure 1 indicates that the reflection from the nozzle contraction occurs somewhat earlier than that from the open end. This time difference is attributed
Non-dimensional frequency kRD Figure 2. Effect of nozzle exit area on reflection coefficient for conical nozzle terminations to a 10 cm diameter duct: -, 10 cm diameter straight duct; - - - - -, 6.2 cm diameter conical nozzle; - - -, 5 cm diameter conical nozzle; --, 2.5 cm diameter conical nozzle; - - -, plugged end termination.
PERFORATE
LOW-FREQUENCY
SOUND
ABSORPTION
363
to two factors. First, the nozzle shoulder begins 20-37 cm upstream of the nozzle exit. Thus, the reflection from the solid nozzle contraction begins from the shoulder and continues until the pulse arrives at the exit. This portion of the reflection is in phase with the incident pulse, as shown in Figure 1. Second, it is well known that the open end reflection occurs slightly outside the nozzle exit plane [9] and it is out-of-phase with the incident pulase (i.e., expansion wave). Thus, the reflected expansion wave due to the nozzle open end appears after the completion of the nozzle contraction reflection. It should be noted that the small amount of reflection cancellation observed (see Figure 2) is possible only if the reflections of opposite phases do overlap. This is possible, in this case, due to non-linear propagation effects of the relatively high-amplitude pulses used in this study. When a high-intensity pulse (or any kind of sound wave) propagates through a duct it creates a finite pressure difference between the inside of the duct and outside. Therefore, the reflection from the nozzle contraction sees a pressure release through the nozzle opening: so a portion of this reflected compression wave escapes through the nozzle opening, and becomes overlapped with the reflected expansion wave from the nozzle exit. The low-frequency components of these two reflections are out of phase with each other. Therefore, the overlapping process causes some amount of low-frequency acoustic energy cancellation. In addition, some amount of acoustic energy could have been dissipated due to its conversion into vertical energy at the exit. Insignificant pressure difference exists between in-duct and free field due to low-intensity pulse (or sound wave) propagation. Therefore, the reflected compression wave propagates only along its reflected direction, which prevents overlapping between anti-phase reflections. As a result, acoustic energy loss due to reflection cancellation does not occur for linear level sound waves. Due to the low level of the pulse the conversion of acoustic energy into vertical energy at the nozzle exit becomes insignificant. For finite amplitude waves, more low-frequency cancellation should occur by increasing the in-phase reflection so that more of it would propagate along the pressure release direction (i.e., toward the nozzle opening). In this process, maximum cancellation would be obtained when the portion of in-phase reflection propagating in the pressure release direction becomes identical in magnitude to the open end reflection (i.e., optimum level). The amount of reflection cancellation would diminish by increasing or decreasing the in-phase reflection component from its optimum level. If an orifice plate is used to terminate the pipe instead of a nozzle, the solid body and open-end reflections can be caused to occur at approximately the same time (or location). Actually, a slightly inverted cone could be used to cause the two reflections to occur at precisely the same time. This would favor the release of in-phase reflection through the orifice opening. If the strength of each of these two reflection components (i.e., the in-phase and out-of-phase) can be related to the area from which the reflection occurs, then an optimized situation is envisaged whereby the low-frequency reflection is completely cancelled. To test this concept and to determine whether or not low-frequency acoustic energy is conserved between in-duct and far field measurements, a series of tests was undertaken using orifice plates, perforated plates, and conical nozzles as the duct termination, with the primary variable being the ratio, K, of the orifice open area to the solid area. The cont.raction ratio of the nozzle or the porosity of orifice plate or perforated plate, represented by A,, is related to K by A,=K/(l+K)=D:/D’,
K = D;/(D’-
D;),
(1,2)
where D is the inner diameter of the duct and DE is the equivalent diameter of the termination opening. For an orifice plate DE is the diameter of the hole. For a perforated
364
M. SALIKUDDIN
plate having
n holes with diameter
d,, the equivalent
diameter
DI. is expressed
as
D,. = d,,&.
2. EXPERIMENTAL 2.1.
THE
DUCT
SET-UP
(3)
AND
DATA
ANALYSIS
TERMINATIONS
A photographic view of all the duct terminations used in the present study is shown in Figure 3. The duct terminations include 12 orifice plates and ten perforated plates, with AR ranging from 0 to 1. The orifice plates are made of 0.635 cm thick aluminum plates. To eliminate the orifice hole thickness (depth) effect, the orifice plate surface is bevelled from the downstream side so that the edge of the orifice hole is sharp. The perforated plates are made of thin metallic sheets. The geometric parameters for orifice plates and perforated plates are listed in Tables 1 and 2, respectively. The nozzle configurations tested in this study include a straight 10 cm diameter duct and three conical nozzles with exit diameters of 6.2,5*0 and 2.5 cm. The test results presented in this paper are only for the no-flow condition. While the main emphasis is on the results for orifice and perforated plate terminations, some nozzle results are used for purposes of comparison.
Figure
3. The orifice plates
and perforated
TABLE
Geometric Serial number 1 2 3 4 5 6 7 8 9 10 11 12
D,
(cm)
0.0 1.27 1.905 2.54 3.404 4.572 5.08 5.904 6.2 7.23 1 8.349 10.16
parameters A, 0.0 0.01562 0.03516 0.0625 0.1111 0.2 0.25 0.333 0,372 0.5 0.667 1.0
plates
used as duct terminations.
1
.for orifice plates K 0.0 0.01587 0.03644 0.0667 0.125 0.25 0.333 0.5 0.5926 1.0 2.0 00
Remarks Closed
end
Straight open duct
PERFORATE
LOW-FREQUENCY TABLE
ABSORPTION
2
Geometric parameters for perforated plates
Serial
2.2.
SOUND
number
n
4
(mm)
DE
(cm)
AR
K
1
32
3.2
1.809
0.0313
2
54
3.2
2.351
0.0529
0.0323 0.0558
3
130
2.4
2.736
0.0716
0.077
4
968
1.6
4.978
0.237
0.3106
1
5
3820
1.0
6.18
0.3653
0.5756
6
968
2.1
6.533
0.4082
0.6899
7
107
6.4
6.566
0.4124
0.7019
8
1591
1.8
7.181
0.493
0.9722
9
1203
2.1
7.277
0.5065
1.0265
10
441
3.5
7.35
0.5166
1.06875
EXPERIMENTAL
CONFIGURATION
The experimental configuration shown in Figure 4 consisted of a spark noise source located on the centerline of a 10 cm diameter pipe about 6 m upstream of the duct exit termination inside an anechoi’c room. A pressure transducer, to measure the in-duct signals, was mounted through the wall of the pipe 76.2 cm upstream of the termination. Provision was made to mount various nozzle, orifice plate and perforated plate terminations. Far field signals were measured on a plate arc of 2.44 m radius with 0.635 cm diameter Briiel and Kjaer (B&K) microphones, extending from 0” to 120” from the jet downstream axis. Most of these microphones were placed at 10” intervals, but a few in the rear arc were placed at 5” intervals. 2.3.
TEST
PROCEDURE
AND
DATA
ANALYSIS
The basic test procedure consisted located inside the duct, and measuring
of discharging the capacitor across the spark gap the resulting incident and reflected pressure pulses
Polar radius = 2.44 m
Far field microphones
plate Figure 4. In-duct
and far field measurement
configuration
366
M.
SALIKUDDIN
by the in-duct transducer and the transmitted pulse by the far field microphones. The in-duct and all the far field pulses were recorded simultaneously on a 2%track tape recorder. The subsequent analysis of each pulse was achieved conveniently on a dualchannel, digital FFT signal analyzer with transient capture facilities. The spectral contents of the incident, the reflected and the transmitted pulses were obtained from the Fourier transforms of the pulses produced by the FFT signal analyzer. The complex transfer function operation is also performed by the FFT analyzer. This operation between reflected and incident pulses is identically equal to the complex spectra1 power reflection coefficient of the termination. The incident power ( W, ) and the reflected power ( W,) are derived from the spectra1 content of the incident and reflected pulses. The transmitted power ( WT) is the difference between the incident and the reflected power. The complex reflection coefficient, a, is defined as c = ((+Iei* = (p,/p,) eig,
(4)
where p* and pi are the incident and reflected pressure magnitudes and 4 is the phase angle between the reflected and incident pressure amplitudes. However, the reflection coefficient amplitudes referred in this paper are actually the power reflection coefficient amplitudes on a decibel scale, and are expressed as a = 10 log,, (p;/p:). The normalized
radiation impedance 2, of the termination
(5) can be expressed as [lo]
(l+lale”)
(lI~E)(R+iX)=Z,=(l_lulei~). Therefore, 1 - (u(2
R’@=(1+]+2]o]
2(a( sin 4 X’PE=(1+]+2~cT~cosC$)3
cos 4)’
(7,g)
where (RIPE) and (X/FE) are the normalized radiation resistance and reactance, respectively. jj and E are the density and speed of sound, respectively. The incident power W, and reflected power W, are expressed (under the assumption of plane wave propagation) as (9)
W, = (&/P~P:,
W, = (&lPGf,
where AD is the cross-sectional area of the duct. The transmitted difference between the incident and the reflected power: W,- = (&liW(~;
power
W,
is the (10)
-pf).
Similarly, the transfer function of a far field pulse with respect to the incident in-duct pulse gives the transmission coefficient of the duct termination. The variation of far field sound pressure levels as a function of polar angle in the radiated field defines the directivity and is a function of frequency. The radiated sound power in the far field, W,, is calculated by the summation of the products of sound intensities measured by individual microphones and the corresponding elemental surface areas ASi. The sound intensities are derived from the far field sound pressure levels. Thus, WJ==& POCO
ASi =
4rRZ, sin (8i) sin (A0;/2), ~TRZ,[~-COS
(A8,/2)],
i (P:)iAS,, i=l
1<
i=l
i=n
i< n ,
i (11)
PERFORATE
LOW-FREQUENCY
SOUND
ABSORPTION
367
In these equations p,, and E0 are the mean density and speed of sound in the anechoi’c chamber, respectively. R, is the radius of the polar arc, 6i is the polar angle for the ith microphone measured from the downstream jet axis, A@, is the elemental angle for the ( pF), is the far field ith microphone, and n is the total number of far field microphones. pressure magnitude at 0,. The power loss, or power absorption, is the difference between the far field power U:, and the transmitted power WT. On a decibel scale, power absorption is defined as +r=lOlog,o(W,/W,)
3. IN-DUCT 3.1.
IN-.DUCT
TIME
HISTORIES,
REFLECTION
(12)
(dB).
RESULTS COEFFICIENTS
AND
RADIATION
IMPEDANCES
Tests were conducted for 12 orifice plates and ten perforated plates with open-area-tosolid-area ratios (i.e., K) ranging from 0 to CO.The intensity of the incident pulses used in these tests was of the order of 150 dB. Some of the in-duct time histories, showing both the incident and reflected pulses for orifice plates and perforated plates, are shown in Figures 5 and 6, respectively. For the closed and open termination reflections in Figures 5 and 6, the values of K are zero and infinity, respectively. For K = 0, the incident pulse is reflected as a compression wave identical to the incident pulse, whereas, for the open end (K = co), the incident wave is reflected as an expansion wave which is out of phase with the incident pulse. The reflections due to orifice plates and perforated plates range between the K = 0 and K = CO,and are a combination of in-phase and out-of-phase pulses with respect to the incident pulse. As discussed in the introduction, portions of these reflections were eliminated by cancellation due to non-linear propagation effects. As seen in Figures 5 and 6, the reflection due to the solid surface increases with increasing K, and vice versa. Reflection coefficients for orifice plates and perforated plates are plotted in Figures 7 and 8, respectively, as functions of non-dimensional frequency, kRo, where k is the wavenumber and RD is the duct radius. The reflection coefficient amplitudes for orifice plates (see Figure 7) decrease with decreasing K at low frequencies (i.e., kRD < 0.2). For K = 0.125 the reflection coefficient amplitudes at low frequencies are very low. If the value of K is decreased further (i.e., for K = O-067), the reflection coefficient amplitudes increase at low frequencies, indicating less cancellation at low frequencies. Therefore, an optimum value of K lies between 0.125 and 0.067 corresponding to maximum cancellation at low frequencies. The reflection coefficient phase decreases monotonically with decreasing K at low frequencies. A similar behavior is observed from the reflection coefficient plots for the perforated plates, as shown in Figure 8. In this plot, maximum low-frequency reflection cancellation is found to occur for K = O-0771. To illustrate the reflection cancellation phenomena clearly, the reflection coefficient amplitudes for orifice plates and perforated plates are plotted against log,, (K) for several kR D, in Figure 9. Examination non-dimensional frequencies, of Figure 9 indicates that a maximum cancellation of the low-frequency reflections occurs for log,,, (K) = -0.9 (i.e., K = 0.13). Furthermore, the highest cancellation is observed at the lowest frequency. The magnitude of this cancellation gradually decreases as the frequency increases. At higher frequencies (i.e., kRD > O-8), the reflection coefficient increases with decreasing values of K, as was seen in Figures 7 and 8. The radiation impedances for the orifice and perforated plate terminations were calculated by using equations (7) and (8). As an example, the radiation resistance and reactance
368
M. SALIKUDDIN
, b-2
rnsd Time
Figure
5. In-duct
time histories
for various
orifice plate terminations
to a 10 cm diameter
duct.
spectra for orifice plate terminations are presented in Figure 10. The radiation resistance, as well as the reactance values, increases with increasing K for orifice and perforated plate terminations for frequencies up to kR, = 2.5. The spectral shape for the orifice plate reactance is similar to that for the straight duct [lo]. The peak reactance value occurs at a frequency (i.e., kRD) which increases with decreasing K. The reactance spectra for perforated plate terminations do not exhibit any definite trend for smaller K values. However, for K greater than O-077 1 the reactance spectra look similar to those for orifice plate terminations. Beyond kRD = 2.5, the radiation impedance spectra for orifice plate as well as perforated plate terminations do not show any definite trend with respect to K. This is presumably due to the influence of the second order circumferential mode, which seems to be prominent in the reflected waves for lower values of K. 3.2.
INTERPRETATION
OF
REFLECTION
COEFFICIENT
RESULTS
results presented in section 3.1 indicate that a low-frequency “anechoi’c” termination at the no-flow condition is possible by using an orifice plate or a perforated plate with a suitable value of K. This idea of reflection cancellation is not new. In the late The
PERFORATE
LOW-FREQUENCY
SOUND
369
ABSORPTION
Time
Figure
6. In-duct
time histories
for various
perforated
plate terminations
to a 10 cm diameter
duct.
194Os, supersonic wind tunnel designers used the concept of a slotted wall to effect cancellation of the reflected shock wave (see the publication of Goethert [ 111 for a complete list of references). From theory, it was shown that the open-to-solid-area ratio to give “complete cancellation” should be O-5. However, experimental results showed a value between 0.1 and 0.2, which is in agreement with our result of O-13. The problem of acoustic transmission and reflection from an orifice have also been studied extensively inside the pipe and at the pipe termination. Davis [ 121 has given an excellent review and summary of work conducted prior to 1957. He treated the orifice termination on an infinite pipe and showed that the orifice acts as a low-pass filter. However, a tube downstream of the orifice has a significant influence on the reflection and transmission process. Miles [ 131 performed an analysis of the sound radiated from a circular tube terminated with an orifice in an infinite flange. He calculated the reflection coefficient for the situation for which the orifice was one-half the pipe diameter. Whereas the analysis produces the
370
M. SALIKUDDIN
Non-dimensional frequency, kRo Figure 7. Effect of exit orifice plate opening on reflection coefficient for orifice plate terminations diameter duct: -, K = co; - - - - -, K=2~O;---,~=l.O~-_--,~~O.5~-.---,~~O.~5~-__,~~O.~~5~ - - -, K = 0.067; - - -, K = 0.036; -, K = 0.016; - - -, K = 0 (plugged termination); data from Johnson and Schmidt [19]; A, K = 0.371; 0, K = 0.122; 0, K = 0.042.
to a 10 cm
symbols for the
correct limiting value when the pipe terminates as an infinite flange (i.e., the orifice diameter equals the pipe diameter), it does not agree with the measured results in Figure 7. At zero frequency, Miles predicts a unity reflection coefficient, whereas the results presented by Davis [ 121 for an orifice in an infinite tube indicate a zero reflection coefficient. The actual result lies between these two extremes. Johnston and Schmidt [ 141 conducted an experimental study somewhat similar to that described here. Their primary interest was to validate a correlation technique whereby the reflection coefficient could be obtained from a broadband signal. In the process of satisfying their original objective, they conducted experiments with an unflanged pipe terminated with an orifice, similar to that reported here. Their reflection coefficient amplitudes for values of K = 0*042,0*122 and 0.371 are also shown on Figure 7. Of the three sets of reflection coefficient data, only that for K = 0.122 is comparable with our data. Even that is off by about 6 dB at the very lowest frequency. Even though the trend is similar, there is little basis for comparison between the Johnston and Schmidt data and the current results. Bechert [15], in examining Imelmann’s [16] data, concluded that a low-frequency “anechdic” termination exists for an orifice plate, but that the reflection cancellation was governed by a mean flow energy absorption mechanism. On the basis of the experimental data, Bechert hypothesized that the acoustic energy was converted into vertical energy in the jet flow. He showed that the minimum reflection was obtained when the area ratio
PERFORATE
‘j; t b 4 3 0 g
LOW-FREQUENCY
SOUND
371
ABSORPTION
60-
-60
-
-120
-
0
1
2 3 Non-dwnenslanal frequency, kRg
4
Figure 8. Effect of exit plate porosity on reflection coefficient for perforated plate terminations diameter duct: -, K = co; - - - - -, K = 1.02652; - - -, K = 0.5756; --, K = 0,311; -, K =0.0558;-- -,K =0.0323;- - -,K =0 (plugged termination). ---,
to a 10 cm
K = 0.0771;
of the orifice to the pipe was equal to the Mach number through the orifice (M -c-c1). His analysis and Imelmann’s data showed very little absorption at the zero Mach number. High-intensity pulses were used in deriving the results for the present study while low-intensity signals were used by Bechert [15] and Imelmann [16]. As discussed in references [17-191, since high-intensity sound generates a high enough particle velocity comparable to that of a very-low-velocity flow, a phenomenon similar to that which occurs in the presence of flow may take place when high-intensity sound propagates through the orifice, even in the absence of mean flow. In this situation, the low-frequency reduction of the reflection coefficient must be occurring in two stages. First, attenuation of reflection may be caused at the termination due to conversion of acoustic energy into vertical energy, as indicated in references [20,21], where the reflection coefficient amplitudes for a straight open-end duct were found to be lower for high-intensity sound propagation than for low-amplitude (i.e., linear) sound propagation. Second, the mutual cancellation of the two types of reflections (i.e., in phase and out-of-phase reflections) may be occurring at or near the duct exit. Maximum reflection cancellation may occur when the portion of in-phase reflection propagating in the pressure release direction is the same in magnitude as the out-of-phase open end reflection. This may be the reason that the reflection cancellation was reduced with further reduction of K, when the in-phase reftection in the
372
M.
-2.0
/
t
-1.6
-1.2
SALIKUDDIN
I
,
/
I
I
-0.8
-0.4
0
0.4
0.8
I.2
log ,o (K) Figure
9. Influence
duct terminations
of open-to-solid
on reflection
area ratio
( K ) for
orifice
plate (lines)
and perforated
plate (symbols)
coefficient.
pressure release direction becomes greater than the out-of-phase open end reflection. These non-linear effects should increase with increasing sound intensity, and are further studied in a companion paper. 4. FAR
FIELD
RESULTS
The primary purpose of this paper is presentation of the results showing the lowfrequency power absorption. However, for the sake of completeness and to lead to the power absorption results, the far field sound pressure levels and the power spectra are also presented here. 4.1.
TIME
HISTORIES
AND
NORMALIZED
SOUND
PRESSURE
LEVELS
Typical far field time histories for a few orifice plate terminations are shown in Figure 11. The main purpose of presenting these figures is to examine the narrowing or broadening of the pulses as a function of polar angle and open-to-solid area ratio, K. All the orifice plate and perforated plate terminations display narrower pulses at smaller polar angles compared to those at higher polar angles, indicating more high-frequency transmission at smaller angles. Decreasing the value of K does not appreciably change the pulse width, unlike what is observed with conical nozzles [6]. However, the peak levels of the pulses diminish rapidly with decreasing values of K, indicating less energy transmission. From the pulse time histories, far field sound pressure level spectra were evaluated and normalized with respect to the incident sound pressure levels. This normalized parameter is called the relative sound pressure level. Typical spectra for orifice plate terminations are shown in Figure 12. As observed from these figures, the sound spectral level for each termination increases at all polar angles with increasing value of K. This behavior indicates that the amount of sound radiated out is proportional to the open
PERFORATE
0
LOW-FREQUENCY
1
SOUND
2
Non-dlmenslonol
373
ABSORPTION
3
frequency, hRo
Figure IO. Effect of exit orifice plate opening on radiation impedance for orifice diameter duct: -, K = co; - - - - -, K=2.0;---,K=~.O;-_--,~=O.5;----_.~~O.25;-__--,~~O.,25; -_ _ , K =0.067; - - -, K =0.036; --, K ~0.016.
plate terminationsto a 10cm
K= 0.01507
Ims It Figure
11. Far field time histories
for various
Time orifice plate terminations
to a 10 cm diameter
duct.
374
M. SALIKUDDIN
Non-dimensional
frequency, kRD
Figure 12. Effect of exit orifice plate opening on far field sound pressure level spectra terminations to a 10 cm diameter duct at a number of polar angles (0): -O-,K=co;___~___,K=l.O; --A---, K =0.25; --+--, K=0~125;-.-_*-.--,K=0.O36;---_x----,K=0~016.
for orifice
plate
PERFORATE
LOW-FREQCJENCY
SOUND
ABSORPTION
375
area of the duct termination. The same behavior is also observed with perforated plate terminations. The far field sound pressure levels for orifice and perforated plate terminations decrease monotonically with decreasing values of K for all frequencies, as for conical nozzle terminations [17]. This behavior of sound pressure levels is not consistent with the observation made in the reflection coefficient plots shown in Figure 9, where the reflection coefficient amplitude decreases with decreasing K up to a certain value of K (i.e., K = 0.13) and then starts to increase. If the transmitted powers were simply the differences of the incident and the reflected powers then, depending on the reflection coefficient variation, the sound pressure level directivity patterns would have shown an increasing trend with increasing K up to around K =0*13 and then would have started to decrease. However, the observed sound pressure level directivity pattern indicates a possible energy loss (dissipation) at or near the termination. This can be further established by studying the variation of far field power and transmitted power with respect to frequency and K as discussed in the following section. 4.2.
FAR
FlELV
ACOUSTlC
POWER
On the basis of the reflection coefficient data presented in Figures 7-9 for orifice plates and perforated plates, it is shown that a low-frequency reflection cancellation is taking place at the duct termination. The cancelled acoustic energy is either transmitted out to the far field or is absorbed at the duct termination by some dissipative mechanism. To ascertain what happens to the energy when this low-frequency reflection cancellation occurs, the far field and transmitted acoustic powers for orifice plates and perforated plates were estimated from the measured data and are studied in this section. The effect of orifice plate and perforated plate openings on the transmission behavior can be studied, on an overall basis, by examining the far field acoustic power W, derived from far field sound pressure levels. Since the tests in this study were conducted with a spark discharge sound source, the incident power could have varied slightly from one test to another. Therefore, to compare the far field power spectra between several with respect to the termination configurations, far field powers W, were normalized corresponding incident power W,. On a decibel scale, this normalized far field power (I+!+1 is expressed as +, = 10 log,,( W,/ W, 1.
(13)
In Figure 13, the normalized far field acoustic power for a number of orifice plate terminations is plotted against a non-dimensional frequency based on the duct radius, RI_,, which is a fixed quantity. The spectral level, as shown in Figure 13, increases with increasing K, which emphasizes the fact that more acoustic power is radiated out to the far field through a large open area. Similar behavior is also observed with perforated plate results. Even at low frequencies, the normalized far field acoustic power increases monotonically with increasing K. A similar trend is also demonstrated in Figure 14, in which the values of the normalized far field acoustic power for orifice plate and perforated plate terminations at a number of values of kR, are plotted against log,,(K). 4.3.
POWER
ABSORPTION
RESULTS
power absorption spectra for the orifice plate and perforated plate terminations for different K are plotted in Figure 15. With increasing K (i.e., open area), the lowfrequency power loss decreases for these terminations. With increasing frequency the amount of power absorption reduces for each termination. The
376
M. SALIKUDDIN
0
2 Non-dimenslonal
1
3 frequency, kR,
4
5
Figure 13. Effect of exit orifice plate opening on far-field acoustic power for orifice plate terminations to a ~-,K=co;___~___,K~~.O;_--_n-_--,~~l.O;__+_-,~~O.~; 10 cm diameter duct: ----_*---, K=O.25; ---_x-----, K=O.l25; -V---_. KzO.667: --v-..---, KzO.036; -*-. K =0.016.
-it 3-
3-
I-
-4C )_2.0
. I
- A.6
Figure 14. Influence of open-to-solid duct terminations on far field acoustic
I
-1.2
I
-0.8
I
-0.4 log ,o (Kl
I
I
0
0.4
I
0.8
area ratio (K) for orifice plate (lines) and perforated power.
plate (symbols)
For the open duct termination, with no acoustic power dissipation anywhere, the far field and transmitted power spectra are expected to be identical (i.e., log,,[ W,/ W,] = 0 dB). But, as can be seen in Figure 15, the measured far field power is less than the estimated transmitted power at low frequency. This discrepancy can be due to one or more of the following factors. (1) The transmitted power is estimated by using equation (10) which involves the reflection coefficient amplitude: in our earlier work [8,20] it was
PERFORATE
LOW-FREQUENCY
SOUND
377
ABSORPTION
(a)
I
-40
u
1
I 2 Non-dimensional
frequency,
(b)
I 4
3
5
kR,
Figure 15. Effect of (a) exit orifice plate opening and (b) exit perforated absorptlon.(a~~C-,K=~(A,=1);---~---,K=1(A,=0~5~;--~---,K=0~25(A,=0~2); (AR =O.llll); ------+----, K =0.125 -.--_*-.--, K=0.0364 K =0.0159 (A, =0.0156); (b) -0-, K =‘x (A, = I); ---O---, _._._.---, K =0.311 (AR = 0.237); ---A----, -m--, K =0,0558 (A, =0.0529; --A ----, K =0.0323 (AH =0.0313).
plate
porosity
on acoustic
(A,=0,0352);
K = 1.0265 K = 0.771
power
----_x-----, (A, =0.5065); I A,
= 0.0716);
shown that the measured reflection coefficient for an open duct is slightly lower than that predicted by Levine and Schwinger [22] because of non-linear propagation effects; this reduction in the reflection coefficient should result in an apparent increase in transmitted power that would not be seen in the far field. (2) The far field power is calculated by using the measurements made at polar angles between 0” and 120” instead of o-180”; this would give a lower far field power (i.e., about 2-3 dB) at lower frequencies. (3) The calibrations between the far field microphones and the in-duct pressure transducer are difficult at very low frequencies because the impulse calibration technique used has greater error at low frequencies. To eliminate some of these discrepencies from the power absorption results, shown in Figure 15, it may be useful to express ( W,/ W,) for the terminations with respect to ( W,/ W,) for the open duct. This can be done by defining
378
M.
a power absorption
coefficient,
SALIKUDI~IN
n, as
‘4 = 10 log1,,[( w,/
W,),l(
W,l W,),l
f 14)
(db),
where ( W,-/ W,), is the power absorption for the test termination and ( W,/ W, 1,) is that for the open duct. The effect of the orifice plate and perforated plate openings on the power absorption coefficient is shown in Figure 16. At low frequencies, the power absorption coefficient decreases monotonically with decreasing K for both orifice plate and perforated plate terminations. So far, the spectral plots have been against the non-dimensional frequency based on the duct radius (i.e., R,,), which is a fixed quantity and does not correlate with termination geometrical parameters. Since the acoustic behaviors of the orifice plate and perforated plate terminations are very similar to those of conical nozzle terminations [6, 171, and the spectral plots for conical nozzles do collapse when plotted against a non-dimensional frequency based on the nozzle exit radius, an attempt was made to look into the orifice plate and perforated plate data on a similar basis. In this, a radius RF, which is the
-307
i 0
I 1
I
I
I
2
3
4
(b)
5
Non-dimensional frequency, kRo
Figure 16. Effect of (a) exit orifice absorption coefficient. (a) -U-,
plate opening and (b) exit perforated plate porosity on acoustic power K = 2 (AR =0.667);---e -- -, K = 1 (AR =0.5);--A--, K=O.S (A,=0.333); --+---, K=0.25 (A,=0.2); ---_*--, K=0.125 (A,=O.llll); x --, K = 0.0667 (A, = 0.0625); -V --, K = 0.0364 (AR = 0.0352); - - - v - - -, K = 0.0159 (A, =0.156); (b)-• --, K = 1.0687 (AR =0.5166);- -0 - - -, K = l.O265(A, =0.5065);--A---, K=0.702(A, =O-412);--+----, K=0.5756(A,=0.3653);---•_---,K =0.311 (A,=0.237);---_x-----, K =0.771 (AR =0.0716); -V---, K =0.558 (A,=0.0529);---v---, K =0.0323 (AR =0.0313).
PERFORATE
0
0.2
LOW-FREQUENCY
0.4 Non-dimensional
379
SOUND ABSORPTION
0.6 frequency,
0.8
1.0
kR,
Figure 17. Effect of (a) exit orifice plate opening and (b) exit perforated plate porosity on acoustic power absorption coefficient plotted against kR,, R, being the equivalent exit opening area (legend as Figure 16).
opening radius for orifice plates and the equivalent radius based on the open area for the perforated plates, was used for non-dimensional frequency. The spectral plot of the absorption coefficient for orifice plate and perforated plate terminations against the non-dimensional frequency kR, is shown in Figure 17. A reasonable collapse of the spectra for different K is observed in this figure. It should be noted that the power absorption coefficients for lower-porosity terminations have exceeded 0 dB (i.e., unity in linear scale) level, even for low kRE values. For these cases, low kR, corresponds to a much higher frequency, which exceeds the plane wave frequency limit of the 10 cm diameter duct. Even if the incident wave does not contain any appreciable amount of higher order modes the reflected wave may have significant contribution of higher order modes. The presence of these higher order modes, not accounted for in the absorption coefficient evaluation, may be the main reason for the apparent positive values. In addition, the reflected high-frequency components for lowporosity terminations are very low in magnitude. Some amount of error in the high frequency may have been caused by this poor signal-to-noise ratio. 5. CONCLUSIONS The acoustic behavior of orifice plate and perforated plate terminations is qualitatively similar to that of conical nozzle terminations. It has been shown that for an optimum
380
M. SALIKUI~I~IN
size of orifice plate or perforated plate termination, a low-frequency “anechoi’c” termination is possible, in which the two oppositely phased reflections cancel. On the basis of the observations of reflection coefficients, far field power, power absorption and power absorption coefficients presented in this paper, it can be concluded that some lowfrequency power for orifice plates and perforated plates is absorbed (or dissipated) at the duct termination. The absorption mechanism for this energy is not established in this paper. However, studies conducted by Ingard and Labate [23] in a smoke-filled standing wave tube indicated that non-linearities could be responsible for the energy loss. Some results presented in reference [17] indicate that the acoustic energy for finite amplitude wave propagation is dissipated in the form of vertical energy at the orifice plate and perforated plate terminations. This aspect of energy loss for orifice plate and perforated plate terminations has been studied extensively at Lockheed, Georgia, and the results are presented in a companion paper [24]. ACKNOWLEDGMENTS The author gratefully acknowledges the substantial contribution of Dr H. E. Plumblee, Jr in this work. The author also wishes to express his appreciation to Dr K. K. Ahuja and Dr H. K. Tanna for most helpful discussions and comments concerning this work.
REFERENCES 1. P. D. DEAN, M. SALIKUDDIN, K. K. AHUJA, H. E. PLUMBLEE, JR and P. MUNGUR 1979 NASA CR-159698, Volume 1. Studies of the acoustic transmission characteristics of coaxial nozzles with inverted velocity profiles. 2. M. SALIKUDDIN and H. E. PLUMBLEE, JR 1979 Lockheed-Georgia Company Engineering Report LG79ER0151. Effect of blow-in doors and centerbody plugs on the acoustic radiation characteristics of model supersonic inlets-an experimental study. 3. K. K. AHUJA, M. SALIKUDDIN, R. H. BURRIN and H. E. PLUMBLEE, JR 1980 NASA CR165133. A study of the acoustic transmission characteristics of suppressor nozzles. 4. M. SALIKUDDIN and H. E. PLUMBLEE, JR 1980 American Institute of Aeronautics and Astronautics 6th Aeroacoustics Conference AZAA Paper 80-0991. Low frequency sound absorption of orifice plates, perforated plates, and nozzles. 5. K. K. AHUJA, M. SALIKUDDIN and H. E. PLUMBLEE, JR 1980 American Institute ofAeronautics and Astronautics 6th Aeroacoustic Conference AZAA Paper 80-1027. Characteristics of internal and jet noise radiation from a multi-lobe, multi-tube suppressor nozzle tested statically and under flight conditions. 6. M. SALIKUDDIN and H. E. PLUMBLEE, JR 1980 Lockheed-Georgia Company Engineering Report LG80ER0204. Internal noise radiation characteristics of baffles, nozzles, orifice plates, and perforated plates used as duct terminations. 7. M. SALIKUDDIN, and K. K. AHUJA 1988 Journal of Sound and Vibration 123, 261-280. A device to generate high frequency noise from commercially available low frequency acoustic drivers. 8. M. SALIKUDDIN, P. D. DEAN, H. E. PLUMBLEE, JR and K. K. AHUJA 1980 Journal of Sound and Vibration 70,487-501. An impulse test technique with application to acoustic measurements. 9. P. M. MORSE 1948 Vibration and Sound. New York: McGraw-Hill. 10. M. SALIKUDDIN and P. MUNGUR 1983 Journal of Sound and Vibration 86,497-522. Acoustic radiation impedance of duct-nozzle system. 11. B. H. GOETHERT 1961 Transonic wind tunnel testing. New York: Pergamon Press. 12. D. D. DAVIS 1957 in Handbook of Noise Control, (C. M. Harris, editor) Acoustical filters and mufflers. New York: McGraw-Hill. 13. J. W. MILES 1948 Journal of the Acoustical Society of ,‘e+nerica 20(5), 652-664. Cylindrical tube coupled to a half-infinite space. 14. J. P. JOHNSTON and W. E. SCHMIDT 1976 American Znstitute of Aeronautics and Astronautics 3rd Aeroacoustics Conference AZAA Paper 76-538. Measurement of acoustic reflection from an obstruction in a pipe with flow.
PERFORATE
LOW-FREQUENCY
SOUND
ABSORPTION
,181
15. D. W. BECHERT 1980 Journal of Sound and Vibration 70, 389-405. Sound absorption caused by vorticity shedding demonstrated with a jet flow. 16. C. IMELMANN 1978 Diplomarbeir, Technische Uniuersitat, Berlin, Institutefir Technische Akustik. Einflufl der stromung auf den schalldurchgang durch rohmundungen (Influence of flow on the sound transmission through orifices). 17. M. SALIKUDDIN and K. K. AHUJA 1983 Journal ofSound and Vibration 91,479-502. Acoustic power dissipation on radiation through duct terminations-experiments. 18. A. CUMMINGS and W. EVERSMAN 1980 Lockheed-Georgia Engineering Report LG80ERO164. An investigation of acoustic energy loss in radiation from ducts to the far field at low frequencies. low Mach numbers, and high sound pressure levels. 19. A. CUMMINGS and W. EVERSMAN 1983 Journal @‘Sound and Vibration 91. 503-518. High amplitude acoustic transmission through duct terminations: theory. 20. M. SALIKUDDIN and W. H. BROWN 1986 Journal qf Sound and Vibration 106, 71-106. Non-linear effects in finite amplitude wave propagation through ducts and nozzles. H. BROWN,R. RAMAKRISHNAN and H. K.TANNA 1982 NASAC‘R21. M. SALIKUDDIN,~. 3656. Refinement and application of acoustic impulse technique to study nozzle transmission characteristics. 22. H. LEVINE and J. SCHWINGER 1948 Physical Review 75(4), 383-406. On the radiation of sound from an unflanged pipe. 23. U. INGARD and S. LABATE 1950 The Journal of the Acaustical Society of America 22( 21, 211-218. Acoustic circulation effects and the nonlinear impedance of orifices. 24. M. SALIKUDDIN and W. H. BROWN 1990 Journal oj’ Sound and Vibration 139, 383-405. Non-linear effects in finite amplitude wave propagation through orifice plate and perforated plate terminations.
and Vibration
ACOUSTIC
(1990) 139(3), 361-381
BEHAVIOR
PERFORATED
PLATES
LOW-FREQUENCY
OF
ORIFICE
WITH SOUND
PLATES
REFERENCE
AND TO
ABSORPTION-+’
M. SALIKUDDINS Lockheed Aeronautical Systems Company, Marietta, Georgia 30063,
U.S.A.
(Received 27 February 1989, and in recised,form 14 August 1989)
Analyses of impulse time history data from acoustic transmission tests for conical nozzles attached to a pipe show that the internal reflections from the solid contraction and the open area tend to cancel. To gain understanding of the opposing reflections, tests were conducted by replacing the conical nozzles with orifice plates and perforated plates. The primary variable was the open-to-solid area ratio. Internal reflection coefficient data reveal that, for an area ratio of lo-12%, the low-frequency internal reflection is reduced from unity to about 0.2. On the basis of comparisons of far field and internal data, acoustic energy is not conserved. Results are presented for a complex reflection coefficient and the far field noise for a series of orifice and perforated plate configurations. 1. INTRODUCTION
During the past several years, research on the transmission of sound through various duct terminations has been carried out at Lockheed, Georgia Division [l-7]. Because of the extreme difficulty in experimentally separating incident from reflected acoustic waves for the purpose of determining internal acoustic energy from either periodic or broadband sources of continuous excitation, an acoustic impulse technique developed by Salikuddin et al. [8] was utilized. In this technique a high-intensity pulse generated by a spark discharge is used as the sound source. One interesting aspect of the test results, the cancellation of low-frequency reflections, was revealed upon examination of termination reflection coefficient data obtained for the conical nozzles. These spectral reflection coefficients are derived from the ratio of the reflected pulse spectrum to that of the incident pulse [ 1,8]. Examination of the temporal characteristics of the reflected wave from a slowly contracting conical nozzle reveals some interesting characteristics. In Figure 1 are shown the reflections from a straight open pipe, three typical conical nozzles, and a straight pipe with a plugged end. The ratio of the conical nozzle open areas to that of the pipe (contraction ratio, AR) to which they are attached are 0.37,0*25 and 0.0625. For the straight open pipe, the reflection occurs only at the exit, resulting in an inverted (expansion wave) pulse. For the conical nozzles, unlike the straight duct, two opposite types of reflections are observed. One is due to the nozzle contraction and is in phase with the incident pulse (compression wave), and the other one is due to the open termination and is out of phase with the incident pulse. For the straight pipe with a plugged end, the reflection is identical to the incident wave. Thus, the nozzles present the upstream with two reflections that are, in effect, out of phase with each other.
Whis work was sponsored by Lockheed’s IRAD program. A portion of this paper appeared in AIAA Paper 80-0991, presented at the 6th Aeroacoustic Conference, 1980. $ Current address: General Electric Aircraft Engines Company, Mail Drop A-304, 1 Neumann Way, P.O. Box 156301, Cincinnati, Ohio45215-6301, U.S.A. 361 0022-460X/90/120361
+21 $03.00/O
@ 1990 Academic
Press Limited
362
M.
Figure
1. In-duct
SAI_IKCII~I~IN
time histories for various conical
nozzle terminations
to a 10 cm diameter
duct.
When the actual spectra1 reflection coefficients are examined for the nozzles (see Figure 2), it can be seen that as the nozzle exit diameter decreases from 10 to 2.5 cm, the reflection coefficient amplitude for very low frequencies is decreased. On physical grounds, this decrease in reflection coefficient at low frequencies is apparently due to the cancellation of the low-frequency reflection from the nozzle contraction by that from the open end. Further examination of Figure 1 indicates that the reflection from the nozzle contraction occurs somewhat earlier than that from the open end. This time difference is attributed
Non-dimensional frequency kRD Figure 2. Effect of nozzle exit area on reflection coefficient for conical nozzle terminations to a 10 cm diameter duct: -, 10 cm diameter straight duct; - - - - -, 6.2 cm diameter conical nozzle; - - -, 5 cm diameter conical nozzle; --, 2.5 cm diameter conical nozzle; - - -, plugged end termination.
PERFORATE
LOW-FREQUENCY
SOUND
ABSORPTION
363
to two factors. First, the nozzle shoulder begins 20-37 cm upstream of the nozzle exit. Thus, the reflection from the solid nozzle contraction begins from the shoulder and continues until the pulse arrives at the exit. This portion of the reflection is in phase with the incident pulse, as shown in Figure 1. Second, it is well known that the open end reflection occurs slightly outside the nozzle exit plane [9] and it is out-of-phase with the incident pulase (i.e., expansion wave). Thus, the reflected expansion wave due to the nozzle open end appears after the completion of the nozzle contraction reflection. It should be noted that the small amount of reflection cancellation observed (see Figure 2) is possible only if the reflections of opposite phases do overlap. This is possible, in this case, due to non-linear propagation effects of the relatively high-amplitude pulses used in this study. When a high-intensity pulse (or any kind of sound wave) propagates through a duct it creates a finite pressure difference between the inside of the duct and outside. Therefore, the reflection from the nozzle contraction sees a pressure release through the nozzle opening: so a portion of this reflected compression wave escapes through the nozzle opening, and becomes overlapped with the reflected expansion wave from the nozzle exit. The low-frequency components of these two reflections are out of phase with each other. Therefore, the overlapping process causes some amount of low-frequency acoustic energy cancellation. In addition, some amount of acoustic energy could have been dissipated due to its conversion into vertical energy at the exit. Insignificant pressure difference exists between in-duct and free field due to low-intensity pulse (or sound wave) propagation. Therefore, the reflected compression wave propagates only along its reflected direction, which prevents overlapping between anti-phase reflections. As a result, acoustic energy loss due to reflection cancellation does not occur for linear level sound waves. Due to the low level of the pulse the conversion of acoustic energy into vertical energy at the nozzle exit becomes insignificant. For finite amplitude waves, more low-frequency cancellation should occur by increasing the in-phase reflection so that more of it would propagate along the pressure release direction (i.e., toward the nozzle opening). In this process, maximum cancellation would be obtained when the portion of in-phase reflection propagating in the pressure release direction becomes identical in magnitude to the open end reflection (i.e., optimum level). The amount of reflection cancellation would diminish by increasing or decreasing the in-phase reflection component from its optimum level. If an orifice plate is used to terminate the pipe instead of a nozzle, the solid body and open-end reflections can be caused to occur at approximately the same time (or location). Actually, a slightly inverted cone could be used to cause the two reflections to occur at precisely the same time. This would favor the release of in-phase reflection through the orifice opening. If the strength of each of these two reflection components (i.e., the in-phase and out-of-phase) can be related to the area from which the reflection occurs, then an optimized situation is envisaged whereby the low-frequency reflection is completely cancelled. To test this concept and to determine whether or not low-frequency acoustic energy is conserved between in-duct and far field measurements, a series of tests was undertaken using orifice plates, perforated plates, and conical nozzles as the duct termination, with the primary variable being the ratio, K, of the orifice open area to the solid area. The cont.raction ratio of the nozzle or the porosity of orifice plate or perforated plate, represented by A,, is related to K by A,=K/(l+K)=D:/D’,
K = D;/(D’-
D;),
(1,2)
where D is the inner diameter of the duct and DE is the equivalent diameter of the termination opening. For an orifice plate DE is the diameter of the hole. For a perforated
364
M. SALIKUDDIN
plate having
n holes with diameter
d,, the equivalent
diameter
DI. is expressed
as
D,. = d,,&.
2. EXPERIMENTAL 2.1.
THE
DUCT
SET-UP
(3)
AND
DATA
ANALYSIS
TERMINATIONS
A photographic view of all the duct terminations used in the present study is shown in Figure 3. The duct terminations include 12 orifice plates and ten perforated plates, with AR ranging from 0 to 1. The orifice plates are made of 0.635 cm thick aluminum plates. To eliminate the orifice hole thickness (depth) effect, the orifice plate surface is bevelled from the downstream side so that the edge of the orifice hole is sharp. The perforated plates are made of thin metallic sheets. The geometric parameters for orifice plates and perforated plates are listed in Tables 1 and 2, respectively. The nozzle configurations tested in this study include a straight 10 cm diameter duct and three conical nozzles with exit diameters of 6.2,5*0 and 2.5 cm. The test results presented in this paper are only for the no-flow condition. While the main emphasis is on the results for orifice and perforated plate terminations, some nozzle results are used for purposes of comparison.
Figure
3. The orifice plates
and perforated
TABLE
Geometric Serial number 1 2 3 4 5 6 7 8 9 10 11 12
D,
(cm)
0.0 1.27 1.905 2.54 3.404 4.572 5.08 5.904 6.2 7.23 1 8.349 10.16
parameters A, 0.0 0.01562 0.03516 0.0625 0.1111 0.2 0.25 0.333 0,372 0.5 0.667 1.0
plates
used as duct terminations.
1
.for orifice plates K 0.0 0.01587 0.03644 0.0667 0.125 0.25 0.333 0.5 0.5926 1.0 2.0 00
Remarks Closed
end
Straight open duct
PERFORATE
LOW-FREQUENCY TABLE
ABSORPTION
2
Geometric parameters for perforated plates
Serial
2.2.
SOUND
number
n
4
(mm)
DE
(cm)
AR
K
1
32
3.2
1.809
0.0313
2
54
3.2
2.351
0.0529
0.0323 0.0558
3
130
2.4
2.736
0.0716
0.077
4
968
1.6
4.978
0.237
0.3106
1
5
3820
1.0
6.18
0.3653
0.5756
6
968
2.1
6.533
0.4082
0.6899
7
107
6.4
6.566
0.4124
0.7019
8
1591
1.8
7.181
0.493
0.9722
9
1203
2.1
7.277
0.5065
1.0265
10
441
3.5
7.35
0.5166
1.06875
EXPERIMENTAL
CONFIGURATION
The experimental configuration shown in Figure 4 consisted of a spark noise source located on the centerline of a 10 cm diameter pipe about 6 m upstream of the duct exit termination inside an anechoi’c room. A pressure transducer, to measure the in-duct signals, was mounted through the wall of the pipe 76.2 cm upstream of the termination. Provision was made to mount various nozzle, orifice plate and perforated plate terminations. Far field signals were measured on a plate arc of 2.44 m radius with 0.635 cm diameter Briiel and Kjaer (B&K) microphones, extending from 0” to 120” from the jet downstream axis. Most of these microphones were placed at 10” intervals, but a few in the rear arc were placed at 5” intervals. 2.3.
TEST
PROCEDURE
AND
DATA
ANALYSIS
The basic test procedure consisted located inside the duct, and measuring
of discharging the capacitor across the spark gap the resulting incident and reflected pressure pulses
Polar radius = 2.44 m
Far field microphones
plate Figure 4. In-duct
and far field measurement
configuration
366
M.
SALIKUDDIN
by the in-duct transducer and the transmitted pulse by the far field microphones. The in-duct and all the far field pulses were recorded simultaneously on a 2%track tape recorder. The subsequent analysis of each pulse was achieved conveniently on a dualchannel, digital FFT signal analyzer with transient capture facilities. The spectral contents of the incident, the reflected and the transmitted pulses were obtained from the Fourier transforms of the pulses produced by the FFT signal analyzer. The complex transfer function operation is also performed by the FFT analyzer. This operation between reflected and incident pulses is identically equal to the complex spectra1 power reflection coefficient of the termination. The incident power ( W, ) and the reflected power ( W,) are derived from the spectra1 content of the incident and reflected pulses. The transmitted power ( WT) is the difference between the incident and the reflected power. The complex reflection coefficient, a, is defined as c = ((+Iei* = (p,/p,) eig,
(4)
where p* and pi are the incident and reflected pressure magnitudes and 4 is the phase angle between the reflected and incident pressure amplitudes. However, the reflection coefficient amplitudes referred in this paper are actually the power reflection coefficient amplitudes on a decibel scale, and are expressed as a = 10 log,, (p;/p:). The normalized
radiation impedance 2, of the termination
(5) can be expressed as [lo]
(l+lale”)
(lI~E)(R+iX)=Z,=(l_lulei~). Therefore, 1 - (u(2
R’@=(1+]+2]o]
2(a( sin 4 X’PE=(1+]+2~cT~cosC$)3
cos 4)’
(7,g)
where (RIPE) and (X/FE) are the normalized radiation resistance and reactance, respectively. jj and E are the density and speed of sound, respectively. The incident power W, and reflected power W, are expressed (under the assumption of plane wave propagation) as (9)
W, = (&/P~P:,
W, = (&lPGf,
where AD is the cross-sectional area of the duct. The transmitted difference between the incident and the reflected power: W,- = (&liW(~;
power
W,
is the (10)
-pf).
Similarly, the transfer function of a far field pulse with respect to the incident in-duct pulse gives the transmission coefficient of the duct termination. The variation of far field sound pressure levels as a function of polar angle in the radiated field defines the directivity and is a function of frequency. The radiated sound power in the far field, W,, is calculated by the summation of the products of sound intensities measured by individual microphones and the corresponding elemental surface areas ASi. The sound intensities are derived from the far field sound pressure levels. Thus, WJ==& POCO
ASi =
4rRZ, sin (8i) sin (A0;/2), ~TRZ,[~-COS
(A8,/2)],
i (P:)iAS,, i=l
1<
i=l
i=n
i< n ,
i (11)
PERFORATE
LOW-FREQUENCY
SOUND
ABSORPTION
367
In these equations p,, and E0 are the mean density and speed of sound in the anechoi’c chamber, respectively. R, is the radius of the polar arc, 6i is the polar angle for the ith microphone measured from the downstream jet axis, A@, is the elemental angle for the ( pF), is the far field ith microphone, and n is the total number of far field microphones. pressure magnitude at 0,. The power loss, or power absorption, is the difference between the far field power U:, and the transmitted power WT. On a decibel scale, power absorption is defined as +r=lOlog,o(W,/W,)
3. IN-DUCT 3.1.
IN-.DUCT
TIME
HISTORIES,
REFLECTION
(12)
(dB).
RESULTS COEFFICIENTS
AND
RADIATION
IMPEDANCES
Tests were conducted for 12 orifice plates and ten perforated plates with open-area-tosolid-area ratios (i.e., K) ranging from 0 to CO.The intensity of the incident pulses used in these tests was of the order of 150 dB. Some of the in-duct time histories, showing both the incident and reflected pulses for orifice plates and perforated plates, are shown in Figures 5 and 6, respectively. For the closed and open termination reflections in Figures 5 and 6, the values of K are zero and infinity, respectively. For K = 0, the incident pulse is reflected as a compression wave identical to the incident pulse, whereas, for the open end (K = co), the incident wave is reflected as an expansion wave which is out of phase with the incident pulse. The reflections due to orifice plates and perforated plates range between the K = 0 and K = CO,and are a combination of in-phase and out-of-phase pulses with respect to the incident pulse. As discussed in the introduction, portions of these reflections were eliminated by cancellation due to non-linear propagation effects. As seen in Figures 5 and 6, the reflection due to the solid surface increases with increasing K, and vice versa. Reflection coefficients for orifice plates and perforated plates are plotted in Figures 7 and 8, respectively, as functions of non-dimensional frequency, kRo, where k is the wavenumber and RD is the duct radius. The reflection coefficient amplitudes for orifice plates (see Figure 7) decrease with decreasing K at low frequencies (i.e., kRD < 0.2). For K = 0.125 the reflection coefficient amplitudes at low frequencies are very low. If the value of K is decreased further (i.e., for K = O-067), the reflection coefficient amplitudes increase at low frequencies, indicating less cancellation at low frequencies. Therefore, an optimum value of K lies between 0.125 and 0.067 corresponding to maximum cancellation at low frequencies. The reflection coefficient phase decreases monotonically with decreasing K at low frequencies. A similar behavior is observed from the reflection coefficient plots for the perforated plates, as shown in Figure 8. In this plot, maximum low-frequency reflection cancellation is found to occur for K = O-0771. To illustrate the reflection cancellation phenomena clearly, the reflection coefficient amplitudes for orifice plates and perforated plates are plotted against log,, (K) for several kR D, in Figure 9. Examination non-dimensional frequencies, of Figure 9 indicates that a maximum cancellation of the low-frequency reflections occurs for log,,, (K) = -0.9 (i.e., K = 0.13). Furthermore, the highest cancellation is observed at the lowest frequency. The magnitude of this cancellation gradually decreases as the frequency increases. At higher frequencies (i.e., kRD > O-8), the reflection coefficient increases with decreasing values of K, as was seen in Figures 7 and 8. The radiation impedances for the orifice and perforated plate terminations were calculated by using equations (7) and (8). As an example, the radiation resistance and reactance
368
M. SALIKUDDIN
, b-2
rnsd Time
Figure
5. In-duct
time histories
for various
orifice plate terminations
to a 10 cm diameter
duct.
spectra for orifice plate terminations are presented in Figure 10. The radiation resistance, as well as the reactance values, increases with increasing K for orifice and perforated plate terminations for frequencies up to kR, = 2.5. The spectral shape for the orifice plate reactance is similar to that for the straight duct [lo]. The peak reactance value occurs at a frequency (i.e., kRD) which increases with decreasing K. The reactance spectra for perforated plate terminations do not exhibit any definite trend for smaller K values. However, for K greater than O-077 1 the reactance spectra look similar to those for orifice plate terminations. Beyond kRD = 2.5, the radiation impedance spectra for orifice plate as well as perforated plate terminations do not show any definite trend with respect to K. This is presumably due to the influence of the second order circumferential mode, which seems to be prominent in the reflected waves for lower values of K. 3.2.
INTERPRETATION
OF
REFLECTION
COEFFICIENT
RESULTS
results presented in section 3.1 indicate that a low-frequency “anechoi’c” termination at the no-flow condition is possible by using an orifice plate or a perforated plate with a suitable value of K. This idea of reflection cancellation is not new. In the late The
PERFORATE
LOW-FREQUENCY
SOUND
369
ABSORPTION
Time
Figure
6. In-duct
time histories
for various
perforated
plate terminations
to a 10 cm diameter
duct.
194Os, supersonic wind tunnel designers used the concept of a slotted wall to effect cancellation of the reflected shock wave (see the publication of Goethert [ 111 for a complete list of references). From theory, it was shown that the open-to-solid-area ratio to give “complete cancellation” should be O-5. However, experimental results showed a value between 0.1 and 0.2, which is in agreement with our result of O-13. The problem of acoustic transmission and reflection from an orifice have also been studied extensively inside the pipe and at the pipe termination. Davis [ 121 has given an excellent review and summary of work conducted prior to 1957. He treated the orifice termination on an infinite pipe and showed that the orifice acts as a low-pass filter. However, a tube downstream of the orifice has a significant influence on the reflection and transmission process. Miles [ 131 performed an analysis of the sound radiated from a circular tube terminated with an orifice in an infinite flange. He calculated the reflection coefficient for the situation for which the orifice was one-half the pipe diameter. Whereas the analysis produces the
370
M. SALIKUDDIN
Non-dimensional frequency, kRo Figure 7. Effect of exit orifice plate opening on reflection coefficient for orifice plate terminations diameter duct: -, K = co; - - - - -, K=2~O;---,~=l.O~-_--,~~O.5~-.---,~~O.~5~-__,~~O.~~5~ - - -, K = 0.067; - - -, K = 0.036; -, K = 0.016; - - -, K = 0 (plugged termination); data from Johnson and Schmidt [19]; A, K = 0.371; 0, K = 0.122; 0, K = 0.042.
to a 10 cm
symbols for the
correct limiting value when the pipe terminates as an infinite flange (i.e., the orifice diameter equals the pipe diameter), it does not agree with the measured results in Figure 7. At zero frequency, Miles predicts a unity reflection coefficient, whereas the results presented by Davis [ 121 for an orifice in an infinite tube indicate a zero reflection coefficient. The actual result lies between these two extremes. Johnston and Schmidt [ 141 conducted an experimental study somewhat similar to that described here. Their primary interest was to validate a correlation technique whereby the reflection coefficient could be obtained from a broadband signal. In the process of satisfying their original objective, they conducted experiments with an unflanged pipe terminated with an orifice, similar to that reported here. Their reflection coefficient amplitudes for values of K = 0*042,0*122 and 0.371 are also shown on Figure 7. Of the three sets of reflection coefficient data, only that for K = 0.122 is comparable with our data. Even that is off by about 6 dB at the very lowest frequency. Even though the trend is similar, there is little basis for comparison between the Johnston and Schmidt data and the current results. Bechert [15], in examining Imelmann’s [16] data, concluded that a low-frequency “anechdic” termination exists for an orifice plate, but that the reflection cancellation was governed by a mean flow energy absorption mechanism. On the basis of the experimental data, Bechert hypothesized that the acoustic energy was converted into vertical energy in the jet flow. He showed that the minimum reflection was obtained when the area ratio
PERFORATE
‘j; t b 4 3 0 g
LOW-FREQUENCY
SOUND
371
ABSORPTION
60-
-60
-
-120
-
0
1
2 3 Non-dwnenslanal frequency, kRg
4
Figure 8. Effect of exit plate porosity on reflection coefficient for perforated plate terminations diameter duct: -, K = co; - - - - -, K = 1.02652; - - -, K = 0.5756; --, K = 0,311; -, K =0.0558;-- -,K =0.0323;- - -,K =0 (plugged termination). ---,
to a 10 cm
K = 0.0771;
of the orifice to the pipe was equal to the Mach number through the orifice (M -c-c1). His analysis and Imelmann’s data showed very little absorption at the zero Mach number. High-intensity pulses were used in deriving the results for the present study while low-intensity signals were used by Bechert [15] and Imelmann [16]. As discussed in references [17-191, since high-intensity sound generates a high enough particle velocity comparable to that of a very-low-velocity flow, a phenomenon similar to that which occurs in the presence of flow may take place when high-intensity sound propagates through the orifice, even in the absence of mean flow. In this situation, the low-frequency reduction of the reflection coefficient must be occurring in two stages. First, attenuation of reflection may be caused at the termination due to conversion of acoustic energy into vertical energy, as indicated in references [20,21], where the reflection coefficient amplitudes for a straight open-end duct were found to be lower for high-intensity sound propagation than for low-amplitude (i.e., linear) sound propagation. Second, the mutual cancellation of the two types of reflections (i.e., in phase and out-of-phase reflections) may be occurring at or near the duct exit. Maximum reflection cancellation may occur when the portion of in-phase reflection propagating in the pressure release direction is the same in magnitude as the out-of-phase open end reflection. This may be the reason that the reflection cancellation was reduced with further reduction of K, when the in-phase reftection in the
372
M.
-2.0
/
t
-1.6
-1.2
SALIKUDDIN
I
,
/
I
I
-0.8
-0.4
0
0.4
0.8
I.2
log ,o (K) Figure
9. Influence
duct terminations
of open-to-solid
on reflection
area ratio
( K ) for
orifice
plate (lines)
and perforated
plate (symbols)
coefficient.
pressure release direction becomes greater than the out-of-phase open end reflection. These non-linear effects should increase with increasing sound intensity, and are further studied in a companion paper. 4. FAR
FIELD
RESULTS
The primary purpose of this paper is presentation of the results showing the lowfrequency power absorption. However, for the sake of completeness and to lead to the power absorption results, the far field sound pressure levels and the power spectra are also presented here. 4.1.
TIME
HISTORIES
AND
NORMALIZED
SOUND
PRESSURE
LEVELS
Typical far field time histories for a few orifice plate terminations are shown in Figure 11. The main purpose of presenting these figures is to examine the narrowing or broadening of the pulses as a function of polar angle and open-to-solid area ratio, K. All the orifice plate and perforated plate terminations display narrower pulses at smaller polar angles compared to those at higher polar angles, indicating more high-frequency transmission at smaller angles. Decreasing the value of K does not appreciably change the pulse width, unlike what is observed with conical nozzles [6]. However, the peak levels of the pulses diminish rapidly with decreasing values of K, indicating less energy transmission. From the pulse time histories, far field sound pressure level spectra were evaluated and normalized with respect to the incident sound pressure levels. This normalized parameter is called the relative sound pressure level. Typical spectra for orifice plate terminations are shown in Figure 12. As observed from these figures, the sound spectral level for each termination increases at all polar angles with increasing value of K. This behavior indicates that the amount of sound radiated out is proportional to the open
PERFORATE
0
LOW-FREQUENCY
1
SOUND
2
Non-dlmenslonol
373
ABSORPTION
3
frequency, hRo
Figure IO. Effect of exit orifice plate opening on radiation impedance for orifice diameter duct: -, K = co; - - - - -, K=2.0;---,K=~.O;-_--,~=O.5;----_.~~O.25;-__--,~~O.,25; -_ _ , K =0.067; - - -, K =0.036; --, K ~0.016.
plate terminationsto a 10cm
K= 0.01507
Ims It Figure
11. Far field time histories
for various
Time orifice plate terminations
to a 10 cm diameter
duct.
374
M. SALIKUDDIN
Non-dimensional
frequency, kRD
Figure 12. Effect of exit orifice plate opening on far field sound pressure level spectra terminations to a 10 cm diameter duct at a number of polar angles (0): -O-,K=co;___~___,K=l.O; --A---, K =0.25; --+--, K=0~125;-.-_*-.--,K=0.O36;---_x----,K=0~016.
for orifice
plate
PERFORATE
LOW-FREQCJENCY
SOUND
ABSORPTION
375
area of the duct termination. The same behavior is also observed with perforated plate terminations. The far field sound pressure levels for orifice and perforated plate terminations decrease monotonically with decreasing values of K for all frequencies, as for conical nozzle terminations [17]. This behavior of sound pressure levels is not consistent with the observation made in the reflection coefficient plots shown in Figure 9, where the reflection coefficient amplitude decreases with decreasing K up to a certain value of K (i.e., K = 0.13) and then starts to increase. If the transmitted powers were simply the differences of the incident and the reflected powers then, depending on the reflection coefficient variation, the sound pressure level directivity patterns would have shown an increasing trend with increasing K up to around K =0*13 and then would have started to decrease. However, the observed sound pressure level directivity pattern indicates a possible energy loss (dissipation) at or near the termination. This can be further established by studying the variation of far field power and transmitted power with respect to frequency and K as discussed in the following section. 4.2.
FAR
FlELV
ACOUSTlC
POWER
On the basis of the reflection coefficient data presented in Figures 7-9 for orifice plates and perforated plates, it is shown that a low-frequency reflection cancellation is taking place at the duct termination. The cancelled acoustic energy is either transmitted out to the far field or is absorbed at the duct termination by some dissipative mechanism. To ascertain what happens to the energy when this low-frequency reflection cancellation occurs, the far field and transmitted acoustic powers for orifice plates and perforated plates were estimated from the measured data and are studied in this section. The effect of orifice plate and perforated plate openings on the transmission behavior can be studied, on an overall basis, by examining the far field acoustic power W, derived from far field sound pressure levels. Since the tests in this study were conducted with a spark discharge sound source, the incident power could have varied slightly from one test to another. Therefore, to compare the far field power spectra between several with respect to the termination configurations, far field powers W, were normalized corresponding incident power W,. On a decibel scale, this normalized far field power (I+!+1 is expressed as +, = 10 log,,( W,/ W, 1.
(13)
In Figure 13, the normalized far field acoustic power for a number of orifice plate terminations is plotted against a non-dimensional frequency based on the duct radius, RI_,, which is a fixed quantity. The spectral level, as shown in Figure 13, increases with increasing K, which emphasizes the fact that more acoustic power is radiated out to the far field through a large open area. Similar behavior is also observed with perforated plate results. Even at low frequencies, the normalized far field acoustic power increases monotonically with increasing K. A similar trend is also demonstrated in Figure 14, in which the values of the normalized far field acoustic power for orifice plate and perforated plate terminations at a number of values of kR, are plotted against log,,(K). 4.3.
POWER
ABSORPTION
RESULTS
power absorption spectra for the orifice plate and perforated plate terminations for different K are plotted in Figure 15. With increasing K (i.e., open area), the lowfrequency power loss decreases for these terminations. With increasing frequency the amount of power absorption reduces for each termination. The
376
M. SALIKUDDIN
0
2 Non-dimenslonal
1
3 frequency, kR,
4
5
Figure 13. Effect of exit orifice plate opening on far-field acoustic power for orifice plate terminations to a ~-,K=co;___~___,K~~.O;_--_n-_--,~~l.O;__+_-,~~O.~; 10 cm diameter duct: ----_*---, K=O.25; ---_x-----, K=O.l25; -V---_. KzO.667: --v-..---, KzO.036; -*-. K =0.016.
-it 3-
3-
I-
-4C )_2.0
. I
- A.6
Figure 14. Influence of open-to-solid duct terminations on far field acoustic
I
-1.2
I
-0.8
I
-0.4 log ,o (Kl
I
I
0
0.4
I
0.8
area ratio (K) for orifice plate (lines) and perforated power.
plate (symbols)
For the open duct termination, with no acoustic power dissipation anywhere, the far field and transmitted power spectra are expected to be identical (i.e., log,,[ W,/ W,] = 0 dB). But, as can be seen in Figure 15, the measured far field power is less than the estimated transmitted power at low frequency. This discrepancy can be due to one or more of the following factors. (1) The transmitted power is estimated by using equation (10) which involves the reflection coefficient amplitude: in our earlier work [8,20] it was
PERFORATE
LOW-FREQUENCY
SOUND
377
ABSORPTION
(a)
I
-40
u
1
I 2 Non-dimensional
frequency,
(b)
I 4
3
5
kR,
Figure 15. Effect of (a) exit orifice plate opening and (b) exit perforated absorptlon.(a~~C-,K=~(A,=1);---~---,K=1(A,=0~5~;--~---,K=0~25(A,=0~2); (AR =O.llll); ------+----, K =0.125 -.--_*-.--, K=0.0364 K =0.0159 (A, =0.0156); (b) -0-, K =‘x (A, = I); ---O---, _._._.---, K =0.311 (AR = 0.237); ---A----, -m--, K =0,0558 (A, =0.0529; --A ----, K =0.0323 (AH =0.0313).
plate
porosity
on acoustic
(A,=0,0352);
K = 1.0265 K = 0.771
power
----_x-----, (A, =0.5065); I A,
= 0.0716);
shown that the measured reflection coefficient for an open duct is slightly lower than that predicted by Levine and Schwinger [22] because of non-linear propagation effects; this reduction in the reflection coefficient should result in an apparent increase in transmitted power that would not be seen in the far field. (2) The far field power is calculated by using the measurements made at polar angles between 0” and 120” instead of o-180”; this would give a lower far field power (i.e., about 2-3 dB) at lower frequencies. (3) The calibrations between the far field microphones and the in-duct pressure transducer are difficult at very low frequencies because the impulse calibration technique used has greater error at low frequencies. To eliminate some of these discrepencies from the power absorption results, shown in Figure 15, it may be useful to express ( W,/ W,) for the terminations with respect to ( W,/ W,) for the open duct. This can be done by defining
378
M.
a power absorption
coefficient,
SALIKUDI~IN
n, as
‘4 = 10 log1,,[( w,/
W,),l(
W,l W,),l
f 14)
(db),
where ( W,-/ W,), is the power absorption for the test termination and ( W,/ W, 1,) is that for the open duct. The effect of the orifice plate and perforated plate openings on the power absorption coefficient is shown in Figure 16. At low frequencies, the power absorption coefficient decreases monotonically with decreasing K for both orifice plate and perforated plate terminations. So far, the spectral plots have been against the non-dimensional frequency based on the duct radius (i.e., R,,), which is a fixed quantity and does not correlate with termination geometrical parameters. Since the acoustic behaviors of the orifice plate and perforated plate terminations are very similar to those of conical nozzle terminations [6, 171, and the spectral plots for conical nozzles do collapse when plotted against a non-dimensional frequency based on the nozzle exit radius, an attempt was made to look into the orifice plate and perforated plate data on a similar basis. In this, a radius RF, which is the
-307
i 0
I 1
I
I
I
2
3
4
(b)
5
Non-dimensional frequency, kRo
Figure 16. Effect of (a) exit orifice absorption coefficient. (a) -U-,
plate opening and (b) exit perforated plate porosity on acoustic power K = 2 (AR =0.667);---e -- -, K = 1 (AR =0.5);--A--, K=O.S (A,=0.333); --+---, K=0.25 (A,=0.2); ---_*--, K=0.125 (A,=O.llll); x --, K = 0.0667 (A, = 0.0625); -V --, K = 0.0364 (AR = 0.0352); - - - v - - -, K = 0.0159 (A, =0.156); (b)-• --, K = 1.0687 (AR =0.5166);- -0 - - -, K = l.O265(A, =0.5065);--A---, K=0.702(A, =O-412);--+----, K=0.5756(A,=0.3653);---•_---,K =0.311 (A,=0.237);---_x-----, K =0.771 (AR =0.0716); -V---, K =0.558 (A,=0.0529);---v---, K =0.0323 (AR =0.0313).
PERFORATE
0
0.2
LOW-FREQUENCY
0.4 Non-dimensional
379
SOUND ABSORPTION
0.6 frequency,
0.8
1.0
kR,
Figure 17. Effect of (a) exit orifice plate opening and (b) exit perforated plate porosity on acoustic power absorption coefficient plotted against kR,, R, being the equivalent exit opening area (legend as Figure 16).
opening radius for orifice plates and the equivalent radius based on the open area for the perforated plates, was used for non-dimensional frequency. The spectral plot of the absorption coefficient for orifice plate and perforated plate terminations against the non-dimensional frequency kR, is shown in Figure 17. A reasonable collapse of the spectra for different K is observed in this figure. It should be noted that the power absorption coefficients for lower-porosity terminations have exceeded 0 dB (i.e., unity in linear scale) level, even for low kRE values. For these cases, low kR, corresponds to a much higher frequency, which exceeds the plane wave frequency limit of the 10 cm diameter duct. Even if the incident wave does not contain any appreciable amount of higher order modes the reflected wave may have significant contribution of higher order modes. The presence of these higher order modes, not accounted for in the absorption coefficient evaluation, may be the main reason for the apparent positive values. In addition, the reflected high-frequency components for lowporosity terminations are very low in magnitude. Some amount of error in the high frequency may have been caused by this poor signal-to-noise ratio. 5. CONCLUSIONS The acoustic behavior of orifice plate and perforated plate terminations is qualitatively similar to that of conical nozzle terminations. It has been shown that for an optimum
380
M. SALIKUI~I~IN
size of orifice plate or perforated plate termination, a low-frequency “anechoi’c” termination is possible, in which the two oppositely phased reflections cancel. On the basis of the observations of reflection coefficients, far field power, power absorption and power absorption coefficients presented in this paper, it can be concluded that some lowfrequency power for orifice plates and perforated plates is absorbed (or dissipated) at the duct termination. The absorption mechanism for this energy is not established in this paper. However, studies conducted by Ingard and Labate [23] in a smoke-filled standing wave tube indicated that non-linearities could be responsible for the energy loss. Some results presented in reference [17] indicate that the acoustic energy for finite amplitude wave propagation is dissipated in the form of vertical energy at the orifice plate and perforated plate terminations. This aspect of energy loss for orifice plate and perforated plate terminations has been studied extensively at Lockheed, Georgia, and the results are presented in a companion paper [24]. ACKNOWLEDGMENTS The author gratefully acknowledges the substantial contribution of Dr H. E. Plumblee, Jr in this work. The author also wishes to express his appreciation to Dr K. K. Ahuja and Dr H. K. Tanna for most helpful discussions and comments concerning this work.
REFERENCES 1. P. D. DEAN, M. SALIKUDDIN, K. K. AHUJA, H. E. PLUMBLEE, JR and P. MUNGUR 1979 NASA CR-159698, Volume 1. Studies of the acoustic transmission characteristics of coaxial nozzles with inverted velocity profiles. 2. M. SALIKUDDIN and H. E. PLUMBLEE, JR 1979 Lockheed-Georgia Company Engineering Report LG79ER0151. Effect of blow-in doors and centerbody plugs on the acoustic radiation characteristics of model supersonic inlets-an experimental study. 3. K. K. AHUJA, M. SALIKUDDIN, R. H. BURRIN and H. E. PLUMBLEE, JR 1980 NASA CR165133. A study of the acoustic transmission characteristics of suppressor nozzles. 4. M. SALIKUDDIN and H. E. PLUMBLEE, JR 1980 American Institute of Aeronautics and Astronautics 6th Aeroacoustics Conference AZAA Paper 80-0991. Low frequency sound absorption of orifice plates, perforated plates, and nozzles. 5. K. K. AHUJA, M. SALIKUDDIN and H. E. PLUMBLEE, JR 1980 American Institute ofAeronautics and Astronautics 6th Aeroacoustic Conference AZAA Paper 80-1027. Characteristics of internal and jet noise radiation from a multi-lobe, multi-tube suppressor nozzle tested statically and under flight conditions. 6. M. SALIKUDDIN and H. E. PLUMBLEE, JR 1980 Lockheed-Georgia Company Engineering Report LG80ER0204. Internal noise radiation characteristics of baffles, nozzles, orifice plates, and perforated plates used as duct terminations. 7. M. SALIKUDDIN, and K. K. AHUJA 1988 Journal of Sound and Vibration 123, 261-280. A device to generate high frequency noise from commercially available low frequency acoustic drivers. 8. M. SALIKUDDIN, P. D. DEAN, H. E. PLUMBLEE, JR and K. K. AHUJA 1980 Journal of Sound and Vibration 70,487-501. An impulse test technique with application to acoustic measurements. 9. P. M. MORSE 1948 Vibration and Sound. New York: McGraw-Hill. 10. M. SALIKUDDIN and P. MUNGUR 1983 Journal of Sound and Vibration 86,497-522. Acoustic radiation impedance of duct-nozzle system. 11. B. H. GOETHERT 1961 Transonic wind tunnel testing. New York: Pergamon Press. 12. D. D. DAVIS 1957 in Handbook of Noise Control, (C. M. Harris, editor) Acoustical filters and mufflers. New York: McGraw-Hill. 13. J. W. MILES 1948 Journal of the Acoustical Society of ,‘e+nerica 20(5), 652-664. Cylindrical tube coupled to a half-infinite space. 14. J. P. JOHNSTON and W. E. SCHMIDT 1976 American Znstitute of Aeronautics and Astronautics 3rd Aeroacoustics Conference AZAA Paper 76-538. Measurement of acoustic reflection from an obstruction in a pipe with flow.
PERFORATE
LOW-FREQUENCY
SOUND
ABSORPTION
,181
15. D. W. BECHERT 1980 Journal of Sound and Vibration 70, 389-405. Sound absorption caused by vorticity shedding demonstrated with a jet flow. 16. C. IMELMANN 1978 Diplomarbeir, Technische Uniuersitat, Berlin, Institutefir Technische Akustik. Einflufl der stromung auf den schalldurchgang durch rohmundungen (Influence of flow on the sound transmission through orifices). 17. M. SALIKUDDIN and K. K. AHUJA 1983 Journal ofSound and Vibration 91,479-502. Acoustic power dissipation on radiation through duct terminations-experiments. 18. A. CUMMINGS and W. EVERSMAN 1980 Lockheed-Georgia Engineering Report LG80ERO164. An investigation of acoustic energy loss in radiation from ducts to the far field at low frequencies. low Mach numbers, and high sound pressure levels. 19. A. CUMMINGS and W. EVERSMAN 1983 Journal @‘Sound and Vibration 91. 503-518. High amplitude acoustic transmission through duct terminations: theory. 20. M. SALIKUDDIN and W. H. BROWN 1986 Journal qf Sound and Vibration 106, 71-106. Non-linear effects in finite amplitude wave propagation through ducts and nozzles. H. BROWN,R. RAMAKRISHNAN and H. K.TANNA 1982 NASAC‘R21. M. SALIKUDDIN,~. 3656. Refinement and application of acoustic impulse technique to study nozzle transmission characteristics. 22. H. LEVINE and J. SCHWINGER 1948 Physical Review 75(4), 383-406. On the radiation of sound from an unflanged pipe. 23. U. INGARD and S. LABATE 1950 The Journal of the Acaustical Society of America 22( 21, 211-218. Acoustic circulation effects and the nonlinear impedance of orifices. 24. M. SALIKUDDIN and W. H. BROWN 1990 Journal oj’ Sound and Vibration 139, 383-405. Non-linear effects in finite amplitude wave propagation through orifice plate and perforated plate terminations.