Comparison of Two Acoustic Waveguide Methods for Determining Liner Impedance

10 Pages·2001·0.66 MB·English

by  Jones, Michael G.

_33/2i
AIAA 2001-2266
Comparison of Two Acoustic Waveguide
Methods for Determining Liner
Impedance
Michael G. Jones, Willie R. Watson,
Maureen B. Tracy, and Tony L. Parrott
NASA Langley Research Center
Hampton, VA
7th AIAA/CEAS
Aeroacoustics Conference
May 28-30, 2001
Maastricht, The Netherlands
For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
1801 Alexander Bell Drive, Suite 500, Reston, VA 20191-4344
Comparison of Two Acoustic Waveguide Methods
for Determining Liner Impedance
Michael G. Jones,* Willie R. Watson, ¢Maureen B. Tracy,*and Tony L. Parrott §
NASA Langley Research Center
Hampton, VA
Abstract were observed. The two methods are then compared
for mean flow Mach numbers up to 0.5, and are
Acoustic measurements taken in a flow impedance
shown to give consistent results for both types of
tube are used to assess the relative accuracy of
test liners. The quality of the results indicates that
two waveguide methods for impedance eduction in
the Single Mode Method should be used when the
the presence of grazing flow. The aeroacoustic
environment is assumed to contain forward and measured acoustic pressure profile is clearly domi-
nated by a single progressive mode, and the Finite
backward-traveling acoustic waves, consisting of
Element Method should be used for all other cases.
multiple modes, and uniform mean flow. Both meth-
ods require a measurement of the complex acous-
Nomenclature
tic pressure profile over the length of the test liner.
The Single Mode Method assumes that the sound c sound speed in duct, m/s
pressure level and phase decay rates of a single pro- f frequency, Hz
gressive mode can be extracted from this measured H duct height, m
= ,/:-i
complex acoustic pressure profile. No a priori as- i
sumptions arc made in the Finite Element Method k free space wavenumber, m-1
regarding the modal or reflection content in the mea- k_ axial wavenumber for single progres-
sured acoustic pressure profile. The integrity of sive mode, m-1
each method is initially demonstrated by how well ky transverse wavenumber, m- 1
their no-flow impedances match those acquired in L length of FEM computational
a normal incidence impedance tube. These tests domain, m
were conducted using ceramic tubular and conven- L1, L2 distance from source plane to liner
tional perforate liners. Ceramic tubular liners were leading and trailing edges, respec-
included because of their impedance insensitivity tively, m
to mean flow effects. Conversely, the conventional M average Mach number across duct
cross-section
perforate liner was included because its impedance
is known to be sensitive to mean flow velocity ef- p(x, y) complex acoustic pressure, Pa
fects. Excellent comparisons between impedance Pref reference pressure, 20 #Pa
values educed with the two waveguide methods in SPL(x) sound pressure level, dB
the absence of mean flow and the corresponding val- x, y axial and transverse coordinates, re-
ues educed with the normal incident impedance tube spectively, m
xi wall measurement location, m
*Research Scientist, Structural Acoustics Branch, Aerody-
namics, Aerothermodynamics and Acoustics Competency
tSenior Research Scientist, Computational Modeling and Symbols:
Simulation Branch, Aerodynamics, Aerothermodynamics and ¢(X) measured phase, radians
Acoustics Competency, Member of AIAA P0 ambient density
_Research Scientist, Aeroacoustics Brafich, Aerodynamics, acoustic resistance, real component
Aerothermodynamics and Acoustics Competency
of
§Senior Research Scientist, Structural Acoustics Branch,
Aerodynamics, Aerothermodynamics and Acoustics Compe- w = 27r/, angular frequency
tency X acoustic reactance, imaginary com-
Copyright (_)2001 by the American Institute of Aeronau- ponent of
tics and Astronautics, hie. No copyright is asserted in the
United States under Title 17, U,S. Code. The U.S. Govern- + ix, normal incidence acoustic
ment has a royalty-free license to exercise all rights under the impedance, normalized by poc
copyright claimed herein for government purposes. All other
rights are reserved by the copyright owner.
Introduction tracted from this measured acoustic pressure profile
data. The Finite Element Method (FEM) makes no
The continual improvement of acoustic liner de-
apriori assumptions regarding the modal content or
sign is a critical element in commercial aircraft noise the amount, of reflections in the measured data. The
emission control. To that end, it is becoming in-
integrity of each method is initially demonstrated by
creasingly important to achieve the optimum liner
showing agreement between their impedance values
impedance for each portion of the engine nacelle. educed in the absence of flow and those acquired in
To achieve this goal, test methodologies must be es-
a normal incidence impedance tube. The two meth-
tablished to accurately educe the normal incidence
ods are then compared for tests with up to Mach 0.5
acoustic impedance of test liners in the presence of mean flow.
mean flow. This knowledge can then be used to
The remainder of this paper is organized into four
improve the existing acoustic impedance prediction sections. The first section gives a description of the
tools, such that additional liner configurations can
waveguide and test liners, and describes the data
be confidently predicted without the need for costly acquisition system for the two impedance eduction
experimental tests. Typically, either in situ 1 or methodologies. The second section provides a brief
waveguide 2,3 methods are used to educe the acoustic discussion of the theory underlying the two wave-
impedance of test liners. guide methods. The third section contains a discus-
The in situ method requires the insertion of two sion of the results obtained after implementation of
microphones into the test liner. (Additional mi- the two impedance methodologies on data acquired
crophones are required for multi-layer liners.) The in the NASA Langley Flow Impedance Test Facility.
transfer function between the complex acoustic pres- Conclusions relevant to this paper are presented in
sures measured by these microphones is then used to the final section.
educe the acoustic impedance. This method is sim-
ple to implement; however, there are a few draw- Experimental Setup
backs. In addition to microphone installation ef-
Description of Test Liners
fects (local damage to the liner by microphone in- Two types of acoustic liners were used in the cur-
sertion and discontinuous surface impedance due to
rent study; ceramic tubular and conventional per-
a flush-mounted microphone in the liner), the in situ forate. The ceramic tubular material was chosen
method provides only local information. In order to because it is expected to be insensitive to mean flow
determine if the liner exhibits a uniform impedance,
effects. Sensitivity to mean flow velocity is expected
this method must be applied a number of times with to be significantly increased for the conventional per-
the microphones installed at various locations in the forate liner, for which the acoustic resistance is con-
liner. Regardless, because of its simplicity, the in centrated in the vicinity of the orifices. The two liner
situ method remains quite useful.
types, shown schematically in figure 1, are described
Waveguide methods, on the other hand, provide in detail here:
global results without the need for invasive measure-
ments within the test material. However, they typi- a) The ceramic tubular liner consists of "sinusoid-
cally require significantly more data than is needed shaped" parallel channels embedded in a ce-
for the in situ method. Depending on the complex- ramic matrix. These channels, with equivalent
circular diameters of 0.76 mm, run perpendicu-
ity of the chosen implementation, waveguide meth-
ods can be used to analyze uniform or variable lar to the exposed surface to provide a surface
impedance liners, sometimes with the same data ac- porosity of 65%. The channels are rigidly termi-
nated such that each is isolated from its neigh-
quisition sequence.
bor to ensure a locally reacting structure. The
The purpose of this paper is to assess the integrity
channel diameter is small enough that the flow
of two waveguide methods for determining the nor-
effects are minimal without the typical addition
mal incidence acoustic impedance in grazing flow.
of a cover sheet.
The aeroacoustic environment is assumed to contain
forward and backward-traveling acoustic waves, con- Three ceramic tubular configurations were
sisting of multiple modes, and uniform mean flow. tested. The first was a uniform-depth configu-
Both methods require a measurement of the complex ration, in which all channels were 77.5 mm deep.
acoustic pressure profile over the length of the liner. For convenience, this liner is labeled "CTI".
The Single Mode Method (SMM) is based on the For the other two configurations, labeled "CT2"
assumption that the sound pressure level and phase and "CT3", the channel depth was varied over
decay rates of a single progressive mode can be ex- a 50.8 mm length (1/8 th of total length) of
CT2-Staircase CT3-QuadraticResidue
Ceramic tubular
core
Rigid backplate
Perforated
facesheet
Honeycomb core
Rigid backplate
9.5 mm
38.1 mm 1 2 3 4 5 6 123 4 56 7 8 910111213
CT2Dimensions CT3Dimensions
Step Length Depth Step Length Depth
# (mm) (mm) # (mm) (mm)
Fig. 1. Sketch of test liners.
1 10.9 31.0 1,13 4.2 35.1
2 11.7 40.4 2,12 4.1 37.8
3 5.3 49.8 3,11 3.6 64.3
the liner. This pattern was repeated over the 4 6.3 58.9 4,10 3.6 43.9
5 3.4 68.8 5,9 4.2 48.0
entire length of the liner (8 cycles). The 6 13.2 77.5 6,8 3.6 74.4
dimensions for ttmse configurations are included 7 4.2 67.6
with the sketch in figure 2. A prediction code 4
was used with an optimization routine to de- Fig. 2. Sketch of "CT2" & "CT3" - 1 cycle.
termine the channel depths and "step" lengths
for the "CT2" liner (staircase pattern), with a
target impedance of p0c. A quadratic residue Test Apparatus and Data Acquisition
sequence 5 was used as a guide in the design of The input data used to educe the impedances of
the "CT3" liner. This design is commonly used each liner were obtained from measurements in the
in concert halls to improve listener response. NASA Langley Flow Impedance Test Facility. A
schematic of the flow impedance tube is provided in
Clearly, the impedance should vary along the
figure 3. This apparatus has a 50.8 mm×50.8 mm
length of the liner for the "CT2" and "CT3"
cross-section in which a controlled aeroacoustic en-
configurations, since the depth of each liner
vironment is achieved. The 50.8 mm-wide by
varies in the axial direction. Since a full cy-
406.4 mm-long liner is centered in a test section that
cle of depth variation occurs within a 50.8 mm
includes the region from the source plane (203.2 mm
length, which is less than thc shortest wave-
upstream of the liner leading edge) to the exit plane
length of interest, the impedance is assumed to
be "smeared" over the surface of the liner. It (203.2 mm downstream of the liner trailing edge).
should als9 be potedo laere that theFEM de-. The desired aeroacoustic environment in the test
scribed in this paper is capable of resolving this section is achieved with four 120 Watt electr0mag-
impedance variability. However, the amount of netic acoustic drivers, whose phase-matched outputs
data required increases as the impedance vari- are combined to generate discrete tones from 0.5 to
ability to be resolved increases. 3.0 kHz with sound pre_ure levels of 130 dB at the
liner leading edge. The mean flow is conditioned
b) The perforate liner consists of an aluminum by a specially designed plenum that allows flow to
facesheet bonded onto 9.5 mm-diameter hex- be combined with the sound field such that sound
cell honeycomb cavities that are 38.1 mm in transmission efficiency degradation is minimal. The
depth. The facesh_t has a porosity of 8.7%, uniform flow Mach number used to perform each
with 0.1 mm-diameter holes and a sheet thick- impedance eduction in this report was taken to be
hess of 0.64 mm. This liner is typical of the the average value of the Mach number profile meas-
type of material currently installed in commer- ured at the mid-liner axial plane (406.4 mm down-
cial aircraft engines for noise suppression. stream of the source plane). Tests were conducted
tube used in this study was designed to be operated
with source frequencies below the cut-on frequency
of higher-order modes. Also, the cross-section of the
tube is such that the insertion of probes causes con-
cerns regarding blockage effects. To eliminate the
1 2
7 8 need to install transverse probes, the experiment was
carefully designed to minimize higher-order mode ef-
1. High pressure air line fects at the source and exit planes. However, higher-
order mode effects cannot be avoided in the liner
2. Traversing microphone
3. Acoustic drivers region. These higher-order modes, as well as re-
4. Plenum flections, are generally present in the vicinity of the
5. Reference microphone leading and trailing edges of the specimen.
6. Test section with liner To avoid the need for a transverse probe, the
7. Termination source plane was located 203.2 mm upstream of the
8. To vacuum pumps leading edge of the test specimen in the hardwall sec-
tion of the duct, and the source frequency was kept
Fig. 3. LaRC Flow Impedance Tube. below the cut-on frequency of higher-order hardwall
modes. Higher-order mode effects caused by the in-
stallation of the test specimen are expected to decay
for centerline Mach numbers of 0.0, 0.1, 0.3 and 0.5.
upstream of the leading edge of the test specimen.
Acoustic waves propagate from left to right in fig- Therefore, the source pressure at each point along
ure 3, traversing the surface of the test specimen, the source plane is set to the value measured at the
and into a termination section designed to mini-
upper wall source location.
mize reflections over the frequency range of interest.
A similar procedure is applied at the exit plane.
Two 6.35 mm condenser-type microphones are flush
The exit plane is located 203.2 mm downstream
mounted in the test section; a reference microphone
of the trailing edge of the test specimen, also in
at the test specimen leading edge on the side wall
the hardwall section of the duct. A rotating two-
and a traversing microphone on an axial traverse
microphone plug was installed in the duct side-
bar, which forms a portion of the upper wall of the
wall near the exit ,plane, and the switched two-
test section. A 13.0 mm-wide precision-machined
microphone method u was used to obtain the exit
slot in the top wall of the flow impedance tube al-
impedance. Because the exit plane is 4 duct heights
lows this axial traverse bar to traverse the test sec-
downstream of the trailing edge of the liner, higher-
tion length by means of a computer-controlled digi-
order modes generated by the installation of the liner
tal stepping motor. The data acquisition program
are not expected to carry appreciable acoustic en-
automatically positions the traversing microphone
ergy to the exit plane. Thus, the exit impedance
at pre-selected locations, x,, from 203.2 mm up-
values at all points in the exit plane are assumed
stream of the leading edge to 50.8 mm downstream
identical.
of the trailing edge of the liner. At each mea-
surement location, a transfer function between the
Acoustic Waveguide Methods
traversing and reference microphones is used to de-
termine the sound pressure level SPL(xi) and phase
Single Mode.Method [SMM)
¢(x,) relative to the fixed microphone location. The
The SMM uses an infinite-waveguide model to
complex acoustic pressure at a given axial wall loca-
educe the impedance of the test liner from the mea.
tion is determined from the equation
sured wall complex acoustic pressure profile for a
single, unidirectional propagating mode. 2 The max-
p(x_, H) = PreflOSPL(x')/20e i¢(x') (1)
imum frequency tested was 3.0 kHz, which is typ-
where the reference pressure, Pref, is 20 #Pa. It ically below the cut-on frequency of higher-order
should be noted that an e_ time convention is used hardwall modes for the flow duct used in this study.
throughout this paper. The one exception to this is for Mach 0.5 mean flow,
The source-plane acoustic pressure and exit-plane for which the cut-on frequency is reduced to approxi-
impedance are typically functions of location in mately 2.9 kHz. At this Mach number, data acquired
these planes. Therefore, transverse probe micro- at 3.0 kHz can potentially contain one higher-order
phones should be used to measure this data with mode in the hardwall section. Exploratory tests con-
the test liner installed. However, the flow impedance ducted at higher frequencies, however, have previ-
4
"T
SPL ....... Phase, ¢
14°r Liner LE UnerTE _,__, , , _
H
I I
I Uniform Mean Flow, uo I
SPL, [ "* : \ I_._ _ ", I; tad
I " "l "', li o I D=,, I
I I
If///'/" .*f/'/'///'/.//'A /
L_ _ L2
Source Unknown impedance, _(x)
plane e
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
DistancefromSource Plane,m
Fig. 5. Geometry and coordinate system
Fig. 4. Sample SPL _ phase profiles. for FEM. (Not to scale)
impedance of the liner can then be determined using
ously indicated that this higher-order mode is not
carrying significant energy. Thus, potential higher-
order mode effects in the hardwall region were ig-
nored for this study.
where
For this method, that portion of the measured
complex acoustic pressure profile which is over the
liner but away from the liner leading and trailing ky 1- [(1- M2)(_) + M] 2 (4)
edges is used. For the current study, this distance k (i - M 2)
was typically set. at approximately 50.8 mm, or one
Finite Element Method {FEM)
duct height. Thus, only the measured upper-wall
Figure 5 depicts the applicable geometry and co-
acoustic pressure profile which was over the cen-
ordinate system used to model the flow duct test
tral portion (approximately 305 ram) of the liner
section for the FEM. This method is described in de-
was used in the aaalysis. Figure 4 displays sound
tail elsewhere 3 and only sufficient detail is presented
pressure level (SPL) and phase (¢) data measured
here for completeness. The version of the FEM used
along the upper wall of the NASA Langley Flow
in this study incorporates the assumptions that the
Impedance Tube. The standing wave patterns in
mean flow profile is uniform and only plane acoustic
the SPL data near the leading and trailing edges of
waves exist in the spanwise direction (not shown in
the liner indicate that reflections and/or high-order
the sketch). The maximum frequency (3.0 kHz) is
mode effects are contaminating that portion of the
below the cut-on frequency for higher-order modes
data. For the central portion of the data, however,
in a hardwall region for all but the highest Mach
the SPL and phase decay with easily identifiable lin-
number (M=0.5) tested. In the lined section, the
ear slopes. This is an indication that a single, pro-
two side walls are rigid; thus, the assumption of no
gressive mode is dominant over the central portion
higher-order modes in the spanwise direction is rea-
of the liner. The SMM uses data from the central
sonable for the frequency range of interest.
portion of the curve to educe the impedance of the
The regions upstream (x = 0 to L1) and down-
test liner, assuming a single progressive mode.
stream (x = L2 to L) of the liner contain rigid walls.
The details of the SMM are provided in detail
As described earlier, the complex acoustic pressures
elsewhere. 2 For convenience, the elements necessary are measured at each of the measurement locations
to use the method are repeated here. First, the axial located along the upper wall (at x = 0,xl, x2, ...x,)
wavenumber (k,) for the dominant progressive mode using a microphone flush-mounted in the traversing
is computed from the measured portion of the data bar.
that has a constant slope using The FEM finds the solution to the steady-state
form of the convected wave equation,
k, - de(x) + i dSPL(x) (2)
dx 20Loglo(e) dx
(1 - M2)-_x2 + .0._2yP202-p2ik M _x + k2p = 0 (5)
In our selected time convention (ei_t), the signs of The source plane acoustic pressure boundary condi-
tion is
and _ are assumed to be negative for
right moving waves. The normal incidence acoustic p(O, y) = p_(y) (6)
J t
where p_(y) is the acoustic pressure profile in the
I+i .,T osMM[] EMI
transverse direction at the source plane. Because
only plane waves are assumed at the source plane, 4
p_(y) is set to the constant value measured with
the traversing microphone positioned in the source
3
plane.
The exit plane boundary condition is
e 2
Op(L, y) = -ikp( L, y) (7) _ m
cOx M --_ _exit (Y) 1
$ :h ±
which is derived from the requirement that the exit
0 , , d I _ , , I I I , J l I
impedance, _exit(Y), must equal the ratio of the
acoustic pressure to the axial component of acous- 2
tic velocity in that plane. Since only plane acoustic
waves are assumed at the exit plane, _exit is taken 1
to be the constant value determined using flush-
mounted meas-urements and plane wave analysis. 6
The boundary conditions at all rigid walls are given )C o m
a,s
-1
=0 (8)
Oy
, , , I , , , , I _ , , , I
which indicates that the normal component of acous-
1 2 3
tic particle velocity vanishes at a rigid wall. Finally,
the boundary condition for the lined region of the Frequency, kHz
duct (from x = L1 to x = L2 in figure 5) is given
by3
Fig. 6. Ceramic liner "CTI" - no flow.
cop(xo,)
-- ikp(x,O) +2MO [P(x,O)]
COy =" ¢(x) L ¢(x) J signs) for each of the liners at frequencies of 0.5 to
M 2 02 rp(x,0)] (9) 3.0 kHz, in steps of 0.5 kHz. Each of these liners
ik COxL2¢(x) j was then mounted in the flow impedance tube and
tested with no mean flow. The acquired data were
Equations (5)-(9) constitute a boundary value analyzed using the SMM and FEM, and the results
problem that can be solved to obtain the upper wall are included in fignres 6 and 7.
pressure when the impedance of the liner, _(x), is For the ceramic liner, the SMM and FEM results
known. The goal of the FEM is to determine the (depicted with circles and squares, respectively) are
unknown liner impedance, _(x), from the measured well matched to the corresponding NIT results. The
boundary data. The procedure consists of iterating same comparison holds for ttm perforate liner, ex-
through the solution to the boundary value problem cept at 0.5 kHz. While the acoustic reactances are
described by equations (5)-(9), and obtaining a set still well matched at this frequency, the acoustic re-
of upper wall acoustic pressures for each impedance sistances are significantly different. Diagnostic tests
function. As each new set of wall pressures is com- are planned to try to resolve the discrepancy at
puted, it is compared to the measured values until this frequency. Similar tests with other liner con-
convergence is achieved within an acceptable error figurations (not included in this report for the sake
range. of brevity) provided further confirmation that the
SMM and FEM educe the correct impedance spec-
Results and Discussion
tra in the absence of mean flow.
The initial acoustic waveguide method assessment Next, all four liners (three ceramic and one per-
was conducted using the uniform-depth ceramic and forate) were tested in the flow impedance tube at
perforate liners. These liners were first tested with centerline Mach numbers of 0.1, 0.3 and 0.5. The
the NASA Langley Research Center normal inci- results are provided in fig_lres 8, 9, 10 and 11. As
dence impedance tube (NIT). 7 Figures 6 and 7 con- expected, the acoustic resistance sensitivity to mean
tain the acoustic impedances (denoted with "+" flow velocity is less for the ceramic liners than for the
I+ NIT O SMM [] FEM I M=0.1 M=0.3 M=0.5
].U ISMM A © []
0.8 [] 4 V 0 '_
0.6 3 I I
O FEM
0
0.4
{)2
0.2
+ 1
0.0 J I i I i I I I I i I I i I [] O
2 0 i I I ]
2
0
1
8
-2 Z0 []
+
-1 v
-4 i I I , I i , , i I , I I I I
0 1 2 3 -2 , ,A, , I _ _ T i I , I I I
0 1 2
Frequency, kHz
Frequency, kHz
Fig. ?. Perforate liner - no flow.
Fig. 8. Ceramic liner "CTI" with flow.
rll
perforate, except at 0.5 kHz (see earlier discussion).
Also, the acoustic resistance is sensitive to mean flow 4
velocity for the uniform-depth ceramic liner near the I FEM v 0
anti-resonance (2.2 kHz). 3
There were some conditions where the SMM was
not appiicaloIe because a region of linear decay of
SPL and phase could not be extracted from the data. 0 2
For the remaining data, the SMM and FEM results
are typically well matched. 1
Fignres 8, 9 and 10 contain educed impedances
for the three ceramic tubular liner configurations. 0 1 i I , I , i i _ I , , i , I
The "CTI" (uniform depth) impedance spectrum 1
- @
is typical of a "quarter-wavelength" liner, with a
resonance near 1 kHz and an anti-resonance near 0
2 kHz. At 0.5 kHz, the SMM could not be im-
plemented because of significant reflections in the -1
upper-wall acoustic pressure profile. The FEM re- _ -2 - V
sults at this frequency vary significantly with mean
flow Mach number. As stated earlier, further stud- -3
ies are planned to better understand this result. It 0
should be noted, however, that this discrepancy at. -4 I
0.5 kHz does not occur for all tests. One possible 0 I 2 3
explanation for the discrepancy is that the sensi-
Frequency, kHz
tivity to mean shear flow is increased at low fre-
quencies for highly reflective conditions. 8 The- S-_I=M
Fig. 9. Ceramic liner "CT2" with flow.
and FEM results are well matched for the other fre-
| t
quencies tested, except near the anti-resonance fre-
quency. This difficulty at anti-resonance is typical
4
for impedance eduction techniques.
I FEM v <>
I By comparison, the impedance spectra for the
_ "CT2" (staircase geometry) and the "CT3"
(quadratic residue geometry) are relatively
e2 frequency-independent. These geometries were
designed to try to achieve an acoustic resistance
of unity and an acoustic reactance of zero over
i
the entire frequency range of interest. Clearly, the
impedance spectra demonstrate that the design
o
procedure was successful. Again, as expected, all
I three ceramic liners are observed to be relatively
insensitive to mean flow Mach number. Thus,
o
the ceramic tubular liner results provide a useful
baseline for the evaluation of acoustic waveguide
-i
methods, since the results acquired with a normal
_-2 incidence impedance tube can be directly compared
V
with those acquired with a flow impedance tube.
-3 Finally, the impedance spectrum for the perfo-
rate liner is provided in figure 11. As expected, the
-4 , i , _ , , I 4 , , , I acoustic resistance increases uniformly with increas-
I 2 3 ing mean flow Mach number, while the acoustic re-
actance is relatively insensitive to changes in mean
Frequency, kHz
flow Mach number. Because of the separation be-
tween the acoustic resistance results for the differ-
Fig. 10. Ceramic liner "CT3" with flow.
ent flow Mach numbers, the excellent comparison
between SMM and FEM results is especially clear
M=0.1 M=0.3 M=0.5 I for this liner. At frequencies of 1.5 kHz and higher,
I
SMM A © []
4 the acoustic reactance is almost completely a func-
FEM V <> @
tion of the cavity depth and is virtually independent
3 of mean flow velocity. Because of high reflections at
0.5 and 1.0 kHz, the SMM could not be implemented
at a flow Mach number of 0.5. Thus, no comparisons
e2
can be made at these frequencies at Mach 0.5.
0
X
1 Conclusions
_ _ 0 0
Based on the results of this work, the following
0 I I I specific conclusions are drawn:
2
. In the absence of mean flow, both acoustic
1
wavegnide methods educe impedance spectra
that are almost identical with those acquired
0
with a normal incidence impedance tube.
X. 1
. The waveguide methods confirm that
-2 impedance spectra for the ceramic tubular
liners are less sensitive to mean flow effects
-3 , I .... I , , , , I than is the case for the perforate liner.
0 1 2 3
As was expected from their design features, the
.
Frequency, kHz
impedance spectra of the variable depth ceramic
liners are relatively independent of frequency
Fig. 11. Perforate liner with flow. and mean flow velocity effects. This insensi-
tivitytoflowvelocitymakestheselinersuseful
forevaluatioonfacoustiwcaveguidmeethods.
4.WhentheSMMcanbeexercised(i.e.,linear
SPLandphasedecayratescanbedetermined),
itprovidensearlyidenticailmpedancetosthose
educedwiththeFEM.
5.Becauseof its relativesimplicity,the SMM
shouldbeusedwhenthepropagationdatais
clearlydominatebdyasinglemode.TheFEM
kspreferrefdorallothercases.
References
iphillips, B., "Effects of High Value Wave Amp-
litude and Mean Flow on a Helmholtz Resonator,"
NASA TMX-1582, 1967.
2Armstrong, D.L., Beckemeyer, R.J. and Olsen,
R.F., "Impedance Measurements of Acoustic Duct
Liners With Grazing Flow," Paper presented at the
87th Meeting of the Acoustical Society of America,
New York, NY, 1974.
3Watson, W.R., Jones, M.G., and Parrott, T.L.,
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