acoustic absorption characteristics of an orifice with a
TRANSCRIPT
NASA Grant Report
GTRI Report A5004/2000-4
Acoustic Absorption Characteristicsof an Orifice With a Mean Bias Flow
K. K. Ahuja, R. J. Gaeta, Jr.. and M. D'Agostino
Georgia Institute of Technology, GTR1/A Z4SL
Acoustics and Aerospace Technologies Branch
Atlanta, Georgia 30332-0844
Grant NAG I- 1734
31 March 2000
Submitted to •
National Aeronautics and
Space Administration
Langley Research CenterHampton, Virginia 23681-0001
Fore_ord/Ackno_ledgments
This report was prepared by the Acoustics and Aerospace Technologies Branch of the
Aerospace. Transportation, and Advanced Systems Laborator? (ATASL) of Georgia Tech
Research Institute (GTRI) for NASA Langley Research Center. Hampton. Virginia. underGrant NAG 1-1734.
Mr. Mike Jones was the Project Manager lbr NASA kangle.v Research Center. GTRI's
Project Director was Dr. K.K. Ahuja.
This work was carried out to obtain data lbr validation of bias flow codes being developed b',
High Technology Corporation. Special thanks are due to Dr. Meelan Choudhari of High
Technolog5 Corporation for suggesting this ,,york. Note that this report is one of fix e separate
volumes prepared to document the work conducted b v GTRI under NASA Grant N.-\G1-
1734. The GTRI report numbers, authors, and titles ot'each report are listed in the tablebelow:
GTRI Report Number Authors TiHe
A5004/2000-1 Ahuja, K. K. and Gaeta, R.J. Active Control of Liner
Impedance bx Var:: ingPertbrate Orifice Geometrx
A5004/2000-2
A5004/2000-3
A5004/2000-4
A5004/2000-5
Ahuja, K. K., Munro. S. E. andGaeta, R. J.
Ahuja, K. K.. Gaeta, R. J. and
D'Agostino. M. S.
Ahuja, K. K., Oaeta. R. J. and
D'Agostino, M. S.
Ahuja, K. K. Cataldi. P. andGaeta, R. J.
Flow Duct Data tbr
Validation of Acoustic
Liner Codes for ImpedanceEduction
High Amplitude AcousticBehavior of a Slit-Orifice
backed b va Caxitv
.Acoustic .AbsorptionCharacteristics of an
Orifice With a Mean Bias
Flou,
Sound Absorption of a2DOF Resonant Liner v, ith
Negative Bias Flow
Table of Contents
Description Pave
Acknowledgments ............................................................................................................................ i
Table of Contents ............................................................................................................................ ii
List of Figures ................................................................................................................................. iii
Executive Summary. ...................................................................................................................... iv
1.0 Introduction ......................................................................................................................... 1
2.0 Experimental Facilities and Approach .............................................................................. 1
2. ! Normal Incidence Impedance Tube ...................................................................... I2.2 Bias Flow Supply .................................................................................................. 2..) ._,.o Anechoic Termination ............................................................................................ 22.4 Hot \Vire Measuren'tents ........................................................................................ 2
3.0 Data Acquisition and Reduction ........................................................................................ 2
4.0 Mean Flow Characterization Upstream of Orifice ......................................................... 3
5.0 Results ..............................................................................................................................
5.1 Absorption Coefficient ........................................................................................... 35.2 Normal Incidence Impedance ................................................................................ 4
6.0 Concluding Comments ....................................................................................................... 5
7.0 References ........................................................................................................................... (5
,Appendix A: Tabulated Orifice Velocities and Impedance Tube Velocit,,, Profiles ............... I g
Appendix B: Tabulated Orifice Acoustic ,Absorption Coefficient and Impedance .................. 20
Figure
List of Figures
Page
Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.
Figure 10.
Figure 11.
Experimental set-up for impedance measurements of single orifice underbias flow conditions. .................................................................................................... 7
Flow pattern for single orifice impedance tube measurements.. ............................... 8
Hot-Wire placement for upstream velocib profiles and orifice center velocit5measurements ............................................................................................................... 9
Measured orifice velocib versus bias volume flow rate with no acousticexcitation.. ................................................................................................................... 10
Bias flow mean velocity profiles approximately 2 inches upstream of orificein impedance tube. ..................................................................................................... 11
Effect of orifice bias flow Mach number on absorption coefficient.. ..................... 12
Nonlinearib' of orifice: Acoustic impedance as a function of orifice velocitywith NO bias flow present. ....................................................................................... 13
Effect of incident sound amplitude on absorption coefficient vdth bias flow. ....... 14
Effect of Strouhal number on absorption coefficient.. ............................................. 15
Effect of bias flov, Mach number on normalized resistance.. ................................. 16
Effect of bias flow Mach number on ........................................................................ 17
iii
Executive Summan"
The objective of the study' reported here ',,,as to acquire acoustic and tlo_v data tbr numericalvalidation of impedance models that simulate bias flow through perforates. The impedancemodel is being developed by' researchers at High Technology Corporation. This reportdocuments normal incidence impedance measurements a singular circular orifice v,ith mean flow
passing through it. All measurements are made within a 1.I2 inch (28.5 mm) diameterimpedance tube. The mean flow is introduced upstream of the orifice (with the flo_a and incidentsound wave travelling in the same direction) vdth an anechoic termination dov,nstream or" theorifice. Velocity' profiles are obtained upstream of the orifice to characterize the intlov,boundary" conditions. Velocity' in the center of the orifice is also obtained. .All \elocitxmeasurements are made with a hot wire anemometer and subsequently checked v,ith mass flox_measurements made concurrently. All impedance measurements are made using the Tx_o-Microphone Method. Although we have left the analysis of the data to the developers of theimpedance models that simulate bias flow through perforate, our initial examination indicatesthat our results follov+ the trends consistent x_ith published theory on impedance of pertoratesv,ith a steady bias flow.
1.0 Introduction
Personnel at High-Technology Corporation in Hampton. VA. are developing computationalaeroacoustic codes to simulate the effecls of flow on the impedance of orifices. Flowthrough acoustic liners that incorporate perforates have the potential for high acousticattenuation as well as control of the frequency of attenuation j2. Acoustic data and
corresponding flow data to validate these codes do not exist and it is the objective of thisreport to prox'ide such data. In order to facilitate the numerical validation, GTRI's highintensity impedance tube was modified to provide an anechoic termination downstream ofthe orifice and provide measurements of xelocity profiles upstream of the orifice. Inaddition, velocities in the center of the orifice ,,,,ere also obtained. The stead,, flo'`', ',',assupplied by a suction device downstream of the orifice which created a negative bias flow(mean flow travelling in same direction as incident acoustic wave).
2.0 Exl_erimental Approach and Facilities
The beha`"ior of a single circular orifice under the influence of bias flo'`', was studied using anormal incidence impedance tube that had several unique features: I) The tube allov, ed tbr asource of air to enter upstream of the orifice [tra,,elling in the same direction as the incidentacoustic wave] as well as an exhaust port downstream of the orit'_ce; 2) it ,,',as prox ided v, ithan anechoic termination downstream of the orifice' and 3) it had a port that allowed a hot-'``"ire to be placed in the center of the orifice. The mean mass flow rate in the impedance tube',',as measutred with a venturi meter. A hot-'Mre anemometer ',',as used to measure mean flo'o,
profiles upstream of the orifice in the impedance tube. The anechoic termination assured thatthe measured impedance was due to the orifice (and surrounding plate) alone.
The orifice under consideration was circular (diameter = 0.1954 in.) and was placed in a 2.5-inch diameter aluminum plate that was approximately 0.032-inches thick. The orifice plate'`,,'as placed between flanges on the impedance tube at the measurement reference plane. Thecontrolled variables in this experiment were acoustic frequency, amplitude, and bias flo_velocity. Table I shows the test conditions covered in the present stud,,. For each case. thereflection coefficient, absorption coefficient and acoustic impedance '`',ere measured.
_Frequenc.v [Hz] Incident Amplitude [dB] Orifice Mach Number1000 II0, 120, 130, 145 0.00,0.05,0.10,0.15,0.202000 I10, 120, 130. t45 0.00,0.05,0.10.0.15,0.20
3000 110, 120, 130, 145 0.00,0.05,0,10,0.15.0.20
4000 I l0, 120, 130. 145 0.00, 0.05, 0. l 0, 0, 15, 0.20
5000 II0. 120 0.00, 0.05, 0.10, 0.15, 0.20
6000 I10. 120, 130, 145 0.00, 0.05.0.10, 0,15, 0,20
Table I. Test conditions for single orifice with bias flow.
2.1 Normal Incidence Impedance TubeThe normal incidence acoustic impedance measurements were r_ade using the T,_,.oMicrophone Method as originally described by Chung and Blaser 3 Our impedance tube '`',asa steel tube whose general specifications are detailed in reference 4. The tube's inner
diameter is 1.12 inches. Figure I shows the basic impedance tube set-up tbr the presentexperiments.
2.2 Bias Fio_, SupplyBias flow was supplied to the impedance tube via a suction device. An air amplifier, similarto the one described in the 2DOF tests of reference 2, was used to create negative pressure ina conduit. The conduit was attached to the impedance tube with two 0.375 i;_ch pressureports on the tube downstream of the orifice (see figure 1). Air was drawn in from the inletports near the acoustic driver, pushed through the orifice and out the tube to the air amplifier.A Flow-Dyne venturi flow meter was placed in-line to measure the mass flow rate in theimpedance tube. Figure 2 shows the impedance tube and the path of the bias flow.
2.3 Anechoic Termination
Elimination of acoustic reflection downstream of the orifice was accomplished by placing
sound absorbing material at the impedance tube's termination. An l 1-inch long wedge or"
Pyrell loam was followed by a large box filled vdth fiberglass (see Figure: l). Tests were
conducted to verify the extent of the reflection back to the reference plane where the orifice
was installed. Using a broadband noise as input, an absorption coefficient of 0.96 was
achieved at I000 Hz. Absorption coefficients of 0.99 were achieved above 1000 Hz with the
anechoic termination in place.
2.4 Hot-V,,'ire Measurements
Two sets of hot-wire measurements were made. A traverse of the floxv-field perpendicular to
the axis of the impedance tube upstream of the orifice characterized the approaching mean
flow profile. The hot-wire probe was placed in one of the microphone ports and traversed
across the tube. Measurements of the velocity in the center of the orifice were also made. A
special port was installed downstream of the orifice that allowed the hot-wire probe to enter
the tube to be placed in the orifice's center. Figure 3 shows how the hot-wire probe ,,',as
arranged in the impedance tube for velocity measurements.
3.0 Data Acquisition and Reduction
Acoustic impedance was determined using acoustic measurements from tv,o microphones
that were flush mounted near the reference plane _,here the oritice was placed (see Figure I ).
The cross spectral data from these signals were processed with an HP 3667A Signal Analx zer
and then used in the Chung and Blaser algorithm tbr the Two Microphone Method processed
on a Pentium II platform. A sinusoidal input from a function generator was supplied to the
JBL acoustic driver via a Carvin Amplifier. Acoustic impedance `.*,'as obtained with and
without bias flow present. All acoustic data was obtained with no hot-wire present in the
impedance tube. The amplitude of the discrete tone was fixed at constant incident sound
pressure levels prescribed in Table I. The incident amplitude was determined from the
measured impedance via the method outlined in Chung and Blaser. It took several iterations
before finding the correct driver voltage that produced the correct incident sound pressure
level, but once found, the voltage was matched for all bias fio`._, conditions.
The bias flow was controlled by adjusting the air amplifier supply pressure. In order to set
the bias flow magnitude to the values prescribed in Table I, a series of hot-`.viremeasurements were made with no acoustic excitation. The volume flow rate was determined
from pressure measurements made on the venturi using standard compressible flo_, theol.
Real time data was acquired with a kabView program that converted the pressure
measurementsinto avolume flow rate. With thehot-wireplacedin thecenterof theorifice.the bias flow rate wasadjusteduntil a relationshipbetweenflow rateand orifice velocitycould be determined. Thus, a given orifice Mach number corresponded to a specific mass
flow rate that could be set with the air amplifier. The Mach number was referenced to the
ambient temperature outside of the impedance tube. ligure 4 shows the relationship between
volume flow rate and orifice velocity. For comparison, the calculated orifice velocity from
continuity is shown as well. There is good agreement between the hot-wire and the
calculated values, with differences attributed to the unknown orifice discharge coefficient
and mass flow measurement accuracy.
4.0 Mean Flow Characterization Upstream of Orifice
Before acoustic impedance measurements ,.,,'ere made, the flow approaching the orifice x_astraversed to quantify the mean velocity profile. The hot-wire was traversed until it almosttouched the opposite ,,,,'all from its entrance point. However, in order to maintain a proper seal.the hot-wire could not be placed near the entrance ,,,.'all. In spite of this, almost 85% of the tubediameter was traversed with the probe. For the bias flow orifice Mach numbers indicated inTable I, mean flow profiles were obtained for boundary condition information for futurenumerical studies. Figure 5 shows these velocity profiles approximately 2 inches upstream ofthe orifice.
5.0 Results
5.1 Absorption CoefficientThe absorption coefficient was calculated from the measured reflection coefficient using therelationship:
o:=I- R 2
and plotted as a function of orifice bias flou, Mach number. The results are shown in I:igur, ,,.noting that a smooth curve was fit through the data points. Also note that data for 130 dB and145 dB at 5000 Hz cou[d not be obtained due to irregularity in the acoustic driver. Iigut_.,,, _,,_6d show data for 110 dB, 120 dB, 130 dB, and 145 dB, respectively.
One feature of the data is that, for the frequencies tested, there appears to be a relative minimaand maxima for a given frequency as the bias flow is increased. At 1000 Hz, the maximumabsorption occurs at M = 0.05 (- 17 m/s) and at 2000 Hz it occurs at M = 0. I (- 34 m/s) v, ith the."caveat that at 145 dB at these two frequencies, increasing bias flow diminishes the absorptionAs frequency is increased, the bias flow Mach number at which maximum absorption occursincreases.
Another feature of the absorption data is that it appears to be relatively3'ndependent of amplitudeof the incident wave. This can be more clearly seen by examining the nonlinearity of the orificewith no bias flow present, l.igure 7 shov_'s the normalized resistance and reactance of the ori fic_:as a function of the rms velocity in the center of the orifice. These velocities correspond toincident sound pressure levels listed in Table I. (Data for 5000 Hz is not shov,'n because the I 3_!dB & 145 dB cases were not obtained.) The impedance is relatively independent of theamplitudes tested when the orifice velocities ,,_,ere belo,x 10 m/s. Only 1000 Hz and 200_3 I I.,exhibit nonlinearity when the incident amplitude _as 145 dB. This is consistent x_ilh th,:
absorptiondatashownin I'igtLre6, andis evenmoreevidentin I.igmes8a throughNcthat showtheabsorptioncoefficientasa functionof incidentlevel tbr eachtYequency,respectively.
The absorption of sound by the orifice with a bias flow jet has been treated analytically bvHowe- m the form of a bias flow through a rigid perforated screen with no backing caxitv..Howe showed that for a given level of bias flov,-, the absorption coefficient maximizes as theStrouhal number [S, = codo/12_] tends towards zero. He found that for normal incidence, themaximum absorption occurs when
O"_=1
Mo
where o" is the perforate porosity and Mo is the bias flow Math number. Furthermore. ',',hen thisratio is unity., the maximum absorption coefficient that can be achieved is shown to be 0.5 for aperforated screen with bias flow. For values _/3.1o greater than or less than unit),, the maximumabsorption is less than the value at _/ .1,to =1. At a given _J 3,/o, the absorption coefficientdecreases rapidly as the Strouhal approaches unit,,.'. Howe explains this behavior as follov, ss:When the vorticity length scale [-U¢,co] is small, velocities induced by successive vortex ringsmostly cancel, except in the vicinity of the orifices. At low Strouhal numbers, the vorticitiv ofone sign can stretch man}' orifice diameters downstream and produces a strong et'fect on _heflow. Thus. Howe concludes that vorticitv production at very high frequencies has a negligibleinfluence on the fluctuating flow.
In the present experiments, a single orifice rather than a perforate is used and the highest ratio ofporosity to bias flow Math number is 0.6 [___= 0.03 Mo = 0.05]. However, the trends that Hox_epredict are evident in the present data as shown in Figures % through Od, which sho`.,, the
absorption coefficient as a function a Strouhal number and Mo. Note, as 3,to tends tov, ardunit}', the absorption levels increase. Also, the rapid decrease in absorption coefticient as theStrouhal number approaches one is evident. It should be noted that not enough data x_ercobtained at the low Strouhal number region at the lowest bias flow Math number tested and at
the high bias flow Math number not enough data were obtained in the higher Strouhal numberregion to "'flesh out" the trend. However, the trend exhibited b v the __!./o = 0.3 cu_'es in t i_urc,,% throu,_'h 9d, are indicative of Howe's prediction. It is also evident that absorption coefficientsabove 0.5 were measured, which are greater than predicted.
We hope that these data will se_'e a useful purpose in validating other's theoretical models.
5.2 Normal Incidence ImpedanceTogether, tigures 10 and I I show the normalized impedance of the single orifice under theinfluence of a steady bias flow by displaying normalized resistance and reactance, respectivel._.as a function of bias flow Math number. These data were used to compute the retlectioncoefficient and thus the absorption coefficient data. Note that the resistance, in general.increases with increasing bias flow Math number. As the frequency increases, the bias Ilo`.,,Mach number at which the minimum reactance occurs increases. This is consistent `._ith the
trend in the absorption coefficient data (see Figure t_). Recall that the as the frequency increased.the value of bias flow Mach number at ,o,hich maximum absorptionoccurred increased lhcabsorption coefficient is large when the normalized impedance of the orifice plate is closest Iomatching the impedance of air Q_c)
6.0 Concluding Comments
Note that the purpose of acquiring the data presented here ',,,as to provide it to High TechnologyCorporation researchers for validating numerical models being de',eloped by them. The da_a hasbeen provided to them and NASA Langley Technical monitor tbr use by others.
7.0 References
!. Dean, P. D. & Tester, B. J. Duct I_'all Impedance Control as an Advanced Concept /i)rAcoustic Suppre.vsion, NASA Contractor Rept. CR- 1.34998, Nov. 1975
2. Cataldi, P., Ahuja, K. K. , and Gaeta, R. J. , Enhanced Sound Absorption thr_ough .VegativeBias Flow. AIAA Paper No. 99-1879, Presented at the 5_h AIAA/CEAS AeroacousticsConference. May 10-1 _ 1998, Seattle, WA.
, Chung, J. Y. and Blaser, D..4.. TransJer Function .I[ethod qf Measuring hT-Duct ,4toutticProperties: L Theot_v Journal of the Acoustic Society of America, Volume 68, No. 3, Sept..1980.
4. Gaeta, R, J. Liner Impedance Modification b._' !.'arving Perforate Or!rice Ge, ometrv Ph.DThesis, Georgia Institute of Technology, 1998.
5. Howe, .M.S. Acoustics o fFh¢id-Structure Interactions Cambridge Universit.-, Press.Cambridge. UK. 1998.
Pair of B&K 1/4 inch microphones, Type 4187(s = 0.78 inch, t= 2.08 inch)
Air InletEight 1/8 inch diameter hole t
equispaced around tube \19.875 inch from orifice X', s ,
al ',
I 6.375
19.875
21.625Acoustic driver
JBL 2446J
21.625 inches from orifice
Orifice Plate
0.032 inches thick
0.1954 inch diameter round orifice
centered inside tube
All Dimensions in Inches
17.375
1.000
Impedance TubeInner diameter 1.12 inch
... Anechoicv
Termination
Fiberglassfilled box
Air Outlet
Two 3/8 inch diameter hole,;
on opposite sides of the tube12.5 inches from orifice
Foam Wedge
II inch long
Tapered from diameter of tube down to flat 2D p,,',lnt
I Figure 1. Experimental set-up for impedance measurements or'single oritice under bias lloxv condition:,
Figure2. Flowpatternfor singleorifice impedancetubemeasurements.
Traversing
Direction Orifice
Hot Wire [0.7 in
Hotwire Placement for Velocity Profile Hot-wire Placement In Orifice Center
tFigure 3. Hot-Wire placement for upstream velocity profiles and orifice center velocity measurements.
400
35O
300
->' 250
C,
> 200
U
.'E',- 150
100
5O
005
Volume FIo_ Rae [CFM]
Figure 4. Measured orifice velocity, versus bias volume flow rate with no acoustic excitation.
I0
1.1
i
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.10 0.5 ! 1.5 2 2.5
Mean Velocit3'(m/s)
Figure 5. Bias flow mean velocity profiles approximately 2 inches upstream of orifice in impedance tube. ]
11
0.8
0.6
=
'F 0.4
0.2
0
0.8
0.6
t=
..= o..t
I=,,O
0.2
SPL = 110 dB SPL = 120 dBi i
• ! ' _ ' ! ' _l I , I r [
,_.-o-,ooo.zl........ i ill i iii iiiiiil;il_,ooo............................................................. HZ
! _ i --.o-zooo ttz I "1 --_ 2oo,_I1,,................... !.................... i..................... i -'-0--3000 Hz | ........ _ 0.8 _ 3()0LI Ii,, |i i _:l--.,.-4ooo.,n _ -----4oooH,,
I"r., 0.6 --l" Gi""' It,'| •
L,
== 0.4
.g_ O,l
, s ] i 0 t0 0.05 0.1 0,15 0.] 0.2_ 0 0.05 0.1 0.1._ 0,2
U /(TRT _)o.._b-Melm amo
a. SPL,=II0
SPL = 130 dBL , / I
k...................._...................._...................:t-°--,ooo.,!.....i i !l.-o-,.ooo H, I
....................! ....................':...................._1_ 3000 Hz I ......"1 o.s
..........._ ..............i....................__---_ooo.zl .....J _
_ 0.4
._ o.2
o0 0.05 0.] 0.15 0.2 0.25
U b.m=./(TRTm_)°_
SPL, -- 130c.
l'b_,_l_, /(yRT b)°'_
I b. SPL==I20 1
SPL = 145 dBi _ t ' J ' I
i.................._!....................i.....................i_,ooo.,• ; ! ---o--2) i i i t
.................... i.................... i..................... : "¢-- 3/_O0 Ils
'....................i....................i......................-'.- 4000.,
0 0.(p3 0.1 0. IS 0:
U b-m../(7RT.,,,b )°''_
d. SPL, = 145 II
I
!
._J
o :F
o 2t
Figure 6. Effect of orifice bias flou. Mach number on absorp_on coefficient.
]'3
C,.
_e
ca
El
z
l0
o 1000 Hz[
o 2000 Hz
• 3000 Hz
• 4000 Hz
• (H)O0 tts o
0 • :
0 0
•
0,| .... A,,,I ........ t ........ i ........ i
0.001 0.01 0. I I 10
Orifice R_.IS _elocity ]m/s}
a. Normalized Resistance
O.
"-[[
¢a
ra
_e
Eo
Z
10
ii::ii:i il8 ---e--3000 Hz4000 Hz
--e- 6000 Ill
........................,................................t ...............:._...................! ..................
' iiiiliiiiiiiiiiiiiiiiiiiiiillii:iillliiilliiiiill.i1.11.....iliLi,_z .................................................................................................,....._ .....
0 ........ i ' ' ' e .... n ........ I ........ 1 , , ,
0.001 0.01 0.1 1 I0
Orifice RMS veioci_' Im/sl
I b. Normalized Reactance
I Figure 7. Nonlinearit)' of'orifice: Acoustic impedance as a t'unction of orifice velocit2: v_ith NO bias tlox_ pre,c_t
0.8
E 0.6
. 0.4
_ 0.2
00
f= I000 Hz f = 2000 Hz
't .................................................!l J • -'°--S L = I 0dB 7
......................................................... "-o--SPI. =llOdB i "-_--SI[': I.OdB J
= 145 dB __
................................ "............................... 7
_o, ............. .j
, i , i i , / o , t , ,0.05 0.1 0.15 0.2 0.25 0 0.0_ 0.1 0.15 0.2 o :Y
U / .... 0.5b- ",,le, n (Yl_'/amb) U _4e,,,/l',"RT,mb 1°"
E
g:
.2
s_
$.<
0.8
0.6
0.4
0.2
f = 3000 Hz
..................... . ................... i............. "-'<_SPL--,,0dBI! ! --°-'5PI. = 120dill
]-.-SrL, : ,3odS[................... !.................... _:............. "-_--SPL = 14'q de...................i.................................I - I
: _
0.05 0.1 0.15 0.2 0.25
U b.,_l,,=/(yRT b)O.._
f = 4000 HzI
g_@
i ................ ........ t'-'°--SPL, = II0dB
0.8 ................... :.................... +............ t --":'--- 4Pl , 120 d13 '
: _ t _4Pl. 130 dB !
_SPL 145dB0.6i
0.4
0 0.05 0.I 0,15 02 u.2._
U /('/RT )o.,
_-_,lean arab
.,=
E
0.8
0.6
f = 6000 Hz
"°--SPL i = 110 dB
-=°--SPL, 120 dB i .
"-*--" SPI. 130rib ! _
_SPL i 145dB I ....
0.2
i , I L , I
0 0.05 0.1 0.15 0.2 0.25
_'_ Ub ,_!,= /(yRT=mb )°'s
Figure 8. Effect of incident ,,ound
amplitude on absorption coel/icvcnlwith bias-flow.
1..1
;PL = llOdBi i
..................................._..............................--o-o ,_,o=0.6 I................................. = ............................. I -'°"_ M' = 0"3 I"
...................................i...............N ......-.-_,°=0: i
...................................i.................._..\..---o,,,o--O.,_!.
:............................ 55 ..........................,f...........7T,-,,,I..........FT],-;_V ........................;!
O.OI O,t I 10
0.9
0.8
0."
_ 0.6
0.._
0.4
'_ 0.3
_ 0.2
0,1
0
St = fd/UO O
I a. SPLI=I10dB
0.9
0.8
.__ 0.'_
0.6
@
_' 0.5
"'= O.4
0.3
0.2
0.1
o0.01
SPL i = 120 dB
........................................................ "°-" (_ M =0.6 -_v
............................................................... _ M = I).3 .
.................................._..............._ .......--dy M, = 11.2
...................................;............... "-q'-"o" M ° = 0.15
o.I 1 I0
St = fd :L'O O
b. SPLI =120dB 1
0 ........ l ........ I ........
0.01 0.1 I 10
.i
C@
L_@
I
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
00,ff
SPL = 145 dB
(_ _,1 = 0.6
............................................................._ M : 03
.................................................. "-*--_ ',1 : o.2
...................................................._c M = 0.15\ °
0.1 I
St=fd/U St=fd/Uo o o o
4
I0
Figure 9. Effect of Strouhal number on absorvion coefficient ]
IO
_g
i 0,1
E
Z
0.01
SPL _ ll0dB
! ! ! •
o.zl
/ ! .I_ 2oooH,Ii _1-*- ._oooHz I
.................., .........................................1_..._4ooo._ I .I '-'=-- _1to011,,II -4-- t,,,,,,, I t,' I
, I , I 1
0 0.0._ 0.1 0,1,_ 0.2
[b.,_l,, /l'(RT mb )O''c
a. SPLw=I10dB
0.2_
SPI. = 120 dBI
_- 10
1 [--_-=-_
__.__z
----,t---
0.1 'o 0.05
I1)01! !t z
2tm*l It/
3tPlO IIz
4000 tt z
51)till I1,'
o.1 o,15 o2
U /(yRT . )o.._b-Mean mind
0.:,_
I b. SPLI= 120 dB ]
qo
¢g
_e
Oz
10
o.I
SPL = 130 dB
.................... i ........................................ i .................................
_1000 Hz
I "-'o-- 2000 IIz
, /7"-"""'1.''0 0.05 0.1 0.15 0.2 0.25
U_M,._/(7RT ,=b)°'s
c. SPL_ = 130 dB I
SPL = 145 dB
i
l0
7,ee
_ 100(3 llz
;-_ e 2001) II/_ 3110t1 I1,"
--4000 Ilz
Z _ ¢_111)(tlit
0.10 0.05 o,I o.15 o.-'
U b.,,i,./(7RT =,b) °_
d. SPLI = 145 dB
I Figure 10. Effect of bias flov, ,Math number on normalized resistance.
!P<
w
_e
im
[07"
10
SPL = llOdB
-2-1ooo._| '-'0-- 2000 Ill I" ......... : .................... ! .................... i ...................
_3000 IIz| :-"_" 4000 Hz [ ............................::....................!...................
,--4m,,-,,-{_l)ltq) I / ![ ........................I .........i..... ] . .
0.05 i j t , ,0 I 0.1_ 0,2 0.2_
U bHein/(¥RTm b)°_
a. SPLt = 110 dB I
C,.
|
8qw
I
E{P
Z[
SPI. = 120 dB
I0, ' ' ' ' ' _ i_ .--.o--]000 H z I
II_-'--:'1oo._ I ..........: ...................................................J_-.--3ooo "'1 _ -lH"_.*°°° .zi ..........::.................i....................................!H "--e-- 5000 tlz i ........ i .................... !.................... ..............-_
10 , , i . . t . .,i ,
O' 0.0._ 0.1 0.15 I1 2 , 2_
L: t(','RT i °'_b--%|ea n ' amb
b. SPLj=I2OdB 1
!
d
tgtqwt.#
r,_e
tm
@z[
SPL = 130 dB
,iI:.::::,l............:.........................................................
o, , "........i.................................................,i J0 0.05 0.1 0.15 0.2 0.2.q
Ub.m,,,,/(yRT,,,b)°'s
10
8
|
fwe_f4D
"" 4
"IP
[ :@
Z
_;PL - 145 dB
II -.o-- 'ooo it, / : ..................:.........["1-- 3o00 llz I .... {....................:..........LI--"00° HzI
............ 2 ....................................... : ......
. 1 i I
o.o._ o.I o.i._ 02
L" I(7RT )o_b-%lrlin mb
r Figure I I. Effect of bias flow Math number on normalized reactance,
17
Appendix A
Tabulated Orifice Velocities and Impedance Tube Velocity Profiles
Measured Orifice Mean Velocities and
Mo Vol. Flow Uo
] CF:< [ ft,s]
3.O_SOOO 3.16900 56.5C
0.!0CCO 1.2200 113.00
$.15000 2.0000 169.50
0.20000 3.0500 226.00
Volume Flow Rates
Mean Velocity Profiles Measure2 2.08
"!,D
_'_5080
O. ! 4 _0 3
0.17600
0.21100
?.24600
0.28100
C.31600
0 35298
O 39700
S 45_00
O 49236
52-30
C.5}_SC
3.E3303
_.66883
-0383J •
_.73_08
S. _7430
0.89900
0.84439
Xo = 0.05
0.020CO0
8. :1000
0.28000
29 _ :_
0.37800
0.45090
0,49900
0. s_vO_
0. 57000
9.58000
0,68000
O. 6O8OO
0. 62000
0.62000
0.62000
0. 61000
3. 61300
_. 60000
:3. 60000
9.58000
0.57000
0.56000
0.52000
0.51000
0.45000
Xo = 3.'3 X: =
O 2 _ ....
0. ( 4 Z C"
C._-[ZS
O. 96000
368S
i i000
1 u�_
1 i!0C
! lOCO
i I000
1 0700
i O9C:C
090 _
I lOCC
" iOCO
1.0880
1.0800
1.0500
1.04C0
0.980C0
] . } ?3 .'Z
i.z130
i. 4 Z ,,."0
" .4 }ZO
" ,5200
i. =_,200
".5-30
i.5"00
.5 ?30
- a_-,r
:.- ?:o.. :_1. _
l. 5ESS
i.=_133
:nches Upstream
Mo = 3,2.?
3. E4"i'_00
1.34C2
I .6200
1.9300
1.94C "
2 .C2 _
2. C:=CO..
; C503
2 " 200
2 ' 300
2 12, CO
2 15C0
2 "400
2 " 500
2 ' 602
2 " 6OC,.., . 63C
2 162C
2.i£Z:
2 i _
2. 3800
..... 2.4'_
Iq
Appendix B
Tabulated Orifice Acoustic Absorption Coefficient and Impedance
-:e_ency = 580 H.z
SPLi = ii0 dB
Ahsorp:ion
Xo Cceffisien: R'p= k P-
" -..... _6 a_ 3 61139 _'-:. , < _b,,o _,._v .v ......
0.850000 0.7C960 2.7742 !.15--
,?.!0C00 3.4-960 5.2139 -.-!!2
0.20000 0.2Z660 9.9433 5.9379
SPLi = 122 dB
Ahsorp:ion
Ms Coefficient F,pc
C.3C[0 0.314-3 _.6}25-
7.C5$3CC 3.71420 2._96_
:,i-::23 :,.4E4_: 5.'1:{9
: i_3:3 3.3E82C _ E3_:
3.20:,3: S.2_vC " 9.4-3-
;( p-2.33{_5
1 - L_-
C , . _ -
SPL± = "3:3 dR
Mc Cceffi:ient _ PC X PcO.O@CO 8, 3(520 0.75_-: 2. }£_:3
C.05C'C30 0.74990 1.343_ 1.1563
v.10@00 $.49470 _ 74_4 _ -:_
0.15000 _,."____=920 -.E_92 3.2121
:3.20000 0.255_0 9.:489 6.:'99-
.... e ..... =.,, F, pc X'P:
3.33{.;3 O. 64-63 2. 5199 i. "919
_53:09 O 59E30 2 9109 _ -=s:....... - .... - '-9:.0_ ,..,, O •_ =-U 4 .4 S.' _ ",
• s__u, 3 373SC _ " _- 3. 1{79
9. 29000 3.25200 9.554_ ,:.}43a
Frequency = .....
SPLi = ii? dB
Absoro:isn
Xc Coef fic:ent R,,ps ]( p-
n .... 0.'_02? £ _:--_ "-,_._=""'-"
%,, , ......
C .!OO00 " .4 _4Z3 4 .2263 2 .7_49
v.i =_,,,_, ._._.._s_ 6.3}-4 ......_::--
SPLi = 120 dB
Absorption
Ho Coefficient P.p: X P:
9.C0C'3 9.'9278 3.941ff2 2.9-12
0.C:5C03} 0.41393 1.4926 2._£4_
C,.IOOCC 3.4_692 4.-4_ f.-}-5
0.i_338 2.3_10'0 6.2969 }.[£-9
'3.20232 _.2-998 _.52[ _ i.4s]@
SPLL = 13'[ gBA£sc_u::n
0 8ff30C2 0 37340 , -_ _ _'a-
_. J_C 0 5_8 _ - 2.6545r, i0 ..... • _ _0 ].5790
SmL" = 142 ZB
A_ssrpz=sn
..... e ..... e..z p: X Pc
:.3]23 0.4952C 3.3_e_ i. 9_32
Cs<._ 0.45-'J ] 7861 - -'-'*
""-'_ 3 4_640 3 89 _ 2 -9"-
0.209u0 9.25790 _.7858 _._6-7
Effluent7 = 2_ u-
£FLi = "i0 dB
Abs¢_. __D_icz
" OOOO 0 '_'Q_'_''
0. 050000 0 .._7n10_ 0 .88270 4 .14£__
u.;;u_O _ 4zlCU 3.2371 ].5729
3. 15000 0. 356_0 5. 1122 4 .46-2
O. 20,300 0. 26180 6. 9628 6. =.=.69
S_L= = -sr_v dB
Absorption
Mo Ccefficien= R,'p: X Pc_.$2t[: 0.093300 0.68280 [.1424
" i_ "'_ 0.41_20 3 229- _ ;'::
_,i_:330 3.3[_40 5.13_9 4,4][4
.......__[ 0.2(260 7.0!9'. <"....=;'.
_,b$c r£-. " :.-.
Y.c Coefficient _ P-- X P"_];.3800 _' n =-_" :.,=,.,,_'
..3e_Ou) ,..''.,._2490 0._339 .... :
....._ 0.40090 3.03 _ 3, 4
0. 150CO 0.3_60 5. !272 4 .4"[69
0.20':00 0.26300 ".2392 _._.._"_ '_
SPLi = i45 dB
Ahscrp:ion
Xo Ccefficient R/pc X"P-._ ..... 0.12850 S _ -r _ .....
0.'3[0C;03 0.
SPLi = ii0 dBAbsorption
Mo Coefflcient0.0000 0.3ff'�CO3.0 _ .._,000 O nlO330
......... 3.ZE253
O 15000 ; _'s_"
0.20000 0.2428C
? pc0.44660
0.38-503
3.2717
4.6012
Z P=
ff.F2_-
4.142ff
7.-614
6.6423
SPL: = II2G dB
}1o Coe_ fl_ient
0. OOCO ,_". 3520C0
,x_ C, • "_0.1 0,_. ,_ 0 257!_
R'ps
0.440<<
0.22730
i.<i3T
3.ffff_
4,_412
Z pc_._423
4]?if
#" - -
SZLi = "33 d_
Azssr_=ion
Ms Cceff!:ient B,pc _ p-
O.CO00 0.0_3500 3,456-[ _.{_9-
0.023000 0.047930 _.39_43 5.59"_
O._nOOO 0 ?_ ". '......... i 526_ _ 51_6
0.15000 v'.2i170 3.2160 4._4 &_
0.20080 0,24420 4._43 _.62_
SPLL = 14ff dB
:,:o Coefficien: - pc X pc
OC,'_ ...... _ .-68 " : £}6Z• _.. ;.: c_4uC 3 8u
" _:'"_- . _64.0 0.7793 % ;c_
..... _r '3 13220 " 939=_ " 4 }4-4
. 5-3C 0.31420 2.58-'4 4.4 =_-''."
200o _ _ 25620 4 6384 _ _-_
_4
Yrequen=y = 5000 Hz
W_I =
Absorpt ion
.No Coefficient P pc ;( p"
0.00,30 0.069500 0.498C8 :-.O_6O
0.058000 O. _a'_ ......_,-u._ 0.63140 :.J_.=
0. ! 0_300 0. 11380 0. 69130 4 .=.}_2
15000 ......_,_,_=,_ 1 7!9 = 4 5_6_
0.20000 0.26630 2. 6973 5. 19:9
SfLi =
Mo
O.OOOO
0.355000
0.13291
O.!_fO2
0.29000
!20 dB
Absorption
Coefficient
0.049800
0.27100
0.259-3
0. }25}- _
2.6?3"
, - _ . -
4. }694
7:equenc'] = _S:3D H=
SPLi = 125 aB
Abscrpuion
Mo Coefficien: _'p: X'p:
).0C00 2.10790 $.42[30 4._6f-
U.050000 9.1290$ 8.96=-Z0 5.1C=-2
}.!00$0 0.093780 3.4=-f96 4.1-_,
0.1=-200 3.2=-2-:7 1.4440 4.12_9
0 2 n'_ _ . • ' -.• _,.,0_ 0 31420 2 3=-4£ _.'52;
Sfli = 120 dBA_,_,-,_w_ : _
Xo Coeffizier.: _ p: Z pc
$.[__10 9.'892C 4.62"22 4.=-69"
• '..... . 0.9393: ....O 35._0 0 12450 =-.-,,:
o 19300 _ 15_4 _ _ 64--' ...._,, ,
'2.1E3C0 3,2=-9d: 1,4_:7 4.7_11
S.Z:30C 3._1441 2.:-9- 4.11?-
SPLi =
Mo
O.O0OO
0.053000
0.i0000
0.15000
0.20000
lfO dB
Absor_t:on
Ccefficzen:
3.127"C
O ! _
0.!44 0
0.255 O
0.313 C
._ p:
3. }_f-C
C, -3=_iC
_ .:_397
2. C=_3C
ZP:4,_26f
5.g_27
4.!584
4.1952
4.10(2
SFL: = 14=,, ,13
AbsorpU.cn
:-:c Cce f ficien:
:. 30,:2 ,,'_. 3Q73''. ,:,,_
._.. .... _,,_ 0 _!60 _• _ ,,g
#' _ _COO 0 7 1"160
- " = _ ",'-' 0.19_40
"v._.')9"200 0 .,_9690
._,pc0. =-39C:
0 , - 9=-4 -
823=-
XP:4.44-9
4,?:f?
4. ]}9:,
4. ?_a31
_6