U.S. patent number RE31,275 [Application Number 06/266,715] was granted by the patent office on 1983-06-14 for zeno duct sound attenuating means.
This patent grant is currently assigned to Lockheed Corporation. Invention is credited to Leslie S. Wirt.
United States Patent |
RE31,275 |
Wirt |
June 14, 1983 |
Zeno duct sound attenuating means
Abstract
A broadband sound attenuating, acoustically lined, duct of
varying cross-sectional shape but in the usual case having a
constant cross-sectional area, and wherein the duct liner is
configured to maintain an essentially constant acoustic resistance
and scaled acoustic reactance throughout provided by means of
changes in the effective depth of the liner. Design tradeoffs
permit some variation in the cross-sectional area of the duct with
concomitant changes in liner properties. In all cases, the duct is
designed so that every section along its major axis is optimally
tuned to absorb most efficiently some part of the frequency
spectrum of interest. The device is particularly suitable for sound
suppression of jet aircraft engines.
Inventors: |
Wirt; Leslie S. (Newhall,
CA) |
Assignee: |
Lockheed Corporation (Burbank,
CA)
|
Family
ID: |
26951995 |
Appl.
No.: |
06/266,715 |
Filed: |
May 26, 1981 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
Reissue of: |
799953 |
May 24, 1977 |
04109750 |
Aug 29, 1978 |
|
|
Current U.S.
Class: |
181/224; 181/248;
181/252 |
Current CPC
Class: |
F01N
13/20 (20130101); F02K 1/827 (20130101); F02K
1/40 (20130101) |
Current International
Class: |
F01N
7/00 (20060101); F01N 7/20 (20060101); F02K
1/82 (20060101); F02K 1/00 (20060101); F02K
1/40 (20060101); F01N 001/04 () |
Field of
Search: |
;181/213,214,224,247,248,252,264,222 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Primary Examiner: Hix; L. T.
Assistant Examiner: Fuller; Benjamin R.
Attorney, Agent or Firm: Smith; Frederic P.
Claims
What is claimed is:
1. A sound attenuating duct operable over a frequency band spanning
a given intermediate frequency, comprising:
boundary means defining a liquid passage having a substantially
uniform cross-sectional area of the flow path therethrough, and
further having a first dimension transverse of the flow path at a
first location, which first dimension is that which provides
optimum sound attenuation at said given intermediate frequency, and
having second and third dimensions transverse of the flow path at
respective second and third locations spaced apart from said first
location, said second and third dimensions differing from said
first dimension so as to provide effective sound attenuation over
said absorption band; and,
sound absorbing liner means on at least a portion of an interior
wall of said boundary means at said first, second, and third
locations, said liner means having an essentially constant acoustic
resistance over said absorption band, and the ratio of the
effective depth of said liner means at each of said locations to
their respective transverse duct dimensions, being substantially
constant.
2. A sound attenuating duct as defined in claim 1 including:
a plurality of sound absorptive splitters each of which is located
at a respective one of said second and third locations.
3. A sound attenuating duct as defined in claim 1 wherein the
interior cross-sectional shape of said duct varies continuously
between said locations.
4. A sound attenuating duct as defined in claim 3 wherein the
cross-sectional shape of said duct is square at one end thereof and
elongate rectangular at the other end thereof.
5. A sound attenuating duct as defined in claim 3 wherein the
cross-sectional shape of said duct is circular at one end thereof
and rectangular at the other end thereof.
6. A sound attenuating duct as defined in claim 3 wherein the
cross-sectional shape of said duct is fluted at one end thereof,
and rectangular at the other end thereof.
7. A sound attenuating duct as defined in claim 3 wherein the
cross-sectional shape of said duct is circular at one end thereof
and fluted at the other end thereof.
8. A sound attenuating duct as defined in claim 3 wherein the
cross-sectional shape of said duct is circular at one end thereof
and oval at the other end thereof.
9. A sound attenuating duct as defined in claim 1 wherein said
boundary means comprises a conduit, and wherein said second
location is upstream of said first location and said third location
is downstream of said first location.
10. A sound attenuating duct as defined in claim 9 wherein the
dimension of said conduit normal to said first dimension remains
substantially constant throughout said flow path.
11. A sound attenuating duct as defined in claim 10 wherein the
thickness of said liner means varies substantially uniformly
throughout said flow path.
12. A sound attenuating duct as defined in claim 1 wherein said
liner means comprises a resistive facing sheet over a compartmented
air space.
13. A sound attenuating duct as defined in claim 1 wherein said
liner means comprises an acoustically resistive foam material.
14. A sound attenuating duct as defined in claim 1 wherein said
liner means comprises a fibrous sound absorber material.
15. A sound attenuating duct comprising:
means defining an elongate flow passage of substantially uniform
cross-sectional area throughout and a lesser transverse dimension d
which varies along the length of said flow passage; and,
sound absorptive means located within said passage defining means,
and wherein the acoustical resistance of said absorptive means
measured in rayls equals approximately 0.9 (df/c) pc, and the
acoustical reactance X of said duct measured in rayls equals
approximately -0.8 (df/c) pc, .Iadd.and the product df is kept
essentially constant, .Iaddend.where d equals the lesser transverse
dimension of said flow passage, f equals the frequency of local
maximum attenuation, c equals the speed of sound in the medium
within the duct, and p equals the density of said medium, whereby R
and X remain essentially constant throughout the length of said
flow passage.
16. A sound attenuating duct as defined in claim 15 wherein said
dimension d varies smoothly along the length of said duct.
17. A sound attenuating duct as defined in claim 15 wherein said
dimension d has at least three discrete values.
18. A sound attenuating duct comprising:
means defining an elongate flow passage having a transverse
dimension d which varies along the length of said flow passage;
sound absorptive means located within said passage defining means,
and wherein the acoustical resistance of said absorptive means
measured in rayls equals approximately 0.9 (df/c) .[.pc.].
.Iadd.pc/(1+M).sup.2.Iaddend., and the acoustical reactance X of
said duct measured in rayls equals approximately -0.8 (df/c)
.[.pc.]. .Iadd.pc/(1+M).sup.2 and the product df/(1+M).sup.2 is
kept essentially constant.Iaddend., where d equals the transverse
dimension of said flow passage, f equals the frequency of local
maximum attenuation, c equals the speed of sound in the medium
within the duct, .[.and.]. p equals the density of said medium,
.Iadd.and M is the Mach number of flow in said flow passage,
.Iaddend.whereby R and X remain essentially constant throughout the
length of said flow passage;
fluid flows through said passage at a local flow Mach number
M.sub.0 at a first location in said passage and at a local flow
Mach number M.sub.1 at a second location whichis displaced along
said passage from said first location, and wherein
said sound absorptive means has a finite local acoustic impedance
Z.sub.0 the value of which at said first location, and at a first
given frequency f.sub.0, is determined by the effective transverse
dimension of said passage d.sub.0 ; and,
at said second location having an effective transverse dimension
d.sub.1, where d.sub.1 .noteq.d.sub.0, the local acoustic impedance
Z.sub.1 is made to equal Z.sub.0, at a second given frequency
f.sub.1, where f.sub.0 .noteq.f.sub.1, by maintaining the following
relationship: ##EQU8##
19. A sound attenuating duct as defined in claim 18 wherein:
20. A sound attenuating duct as defined in claim 18 wherein the
effective transverse dimension varies continuously and smoothly
between said first and second locations.
21. A sound attenuating duct for the conduction of fluid flow
therethrough, comprising:
an axially extending passageway, said passageway being variable in
cross-sectional shape due to a variation in flow passsage width,
but remaining substantially constant in cross-sectional area;
and,
a sound absorptive liner within at least a portion of said
passageway and having variable acoustical properties such that the
normalized acoustical impedance thereof, as a function of the
wavelength of sound, expressed as Z(.lambda.)/pc, remains
essentially constant along said duct when determined at a frequency
for which .lambda.=d, where Z is acoustical impedance, .lambda. is
the wavelength of sound, p is the density of the medium within the
duct, c is the speed of sound in the medium, and d is the width of
the flow passage.
22. A sound attenuating duct as defined in claim 21 wherein:
##EQU9## wherein R(.lambda.)/pc is of the order of unity and
X(.lambda.)/pc is of the order of negative unity.
Description
BACKGROUND OF THE INVENTION
Various means have been proposed heretofore for reducing and
suppressing the noise in the exhaust duct of turbine engines, air
conditioning duct systems, and similar equipment. The most common
sound absorption technique of the prior art is the use of an
absorptive lining within the duct as shown, for example, in U.S.
Pat. No. 3,542,152, granted to Arthur P. Adams et al. It is also
well known in the art to reduce the noise generated by
appurtenances coming into contact with the air stream, such as flow
splitters, guide vanes, fan blading, and the like, by reducing the
wake emanating thereby through the utilization of boundary layer
control. A prior art reference disclosing this approach is the
literature publication, "Quiet Engine Nacelle Design," M. Dean
Nelson, NASA SP-311, Aircraft Engine Noise Reduction, 1972. Other
flow-duct noise abating means are shown in U.S. Pat. No. 3,503,495
to Kobayashi et al, U.S. Pat. No. 3,511,336 to Rink et al, U.S.
Pat. No. 3,820,638 to Hanson. Still another approach to noise
reduction is that suggested in U.S. Pat. No. 3,033,494 to Tyler et
al, wherein noise reduction of jet engine exhaust may be provided
by means of shaping the jet engine exhaust duct. The use of
wedge-shaped bodies for the dissipation of high frequency vibratory
energy is disclosed in U.S. Pat. No. 3,058,015 to Nesh.
A practical limitation of all of the aforementioned prior art
devices is the limited frequency spectrum over which they can
effectively function. There exists a need for a broadband sound
absorber of comparable efficiency. Classical acoustic theory
indicates that for any given duct there is a given acoustic
impedance spectrum of the duct liner which would provide the best
possible attenuation at all frequencies. However, there are no
known practical materials capable of providing an acoustic
impedance which is the optimum function of frequency. Resistance
which increases with frequency has been attained, but a reactance
which becomes more negative as the frequency increases has not been
attained in any practical way. Thus, the attenuation attained in
real ducts falls far short of theoretically attainable values,
except for a single frequency.
SUMMARY OF THE INVENTION
The present invention relates to an acousticallly lined duct
designed so that acoustical resistance and scaled reactance remain
essentially constant along the major axis or flow passage of the
duct. One way in which this may be achieved is by varying the
cross-sectional geometry without varying the cross-sectional area.
This design approach may be embodied in various ways including a
tapering duct construction, a fluted or cruciform construction, or
an annular construction with splitter vanes of progressively
changing dimensions therein. The acoustical lining material for
certain of the walls of such ducts is designed to present varying
thickness or gradually taper so as to assist in maintaining
cross-sectional area equivalencies, and at the same time be capable
of handling a broad range of noise frequencies. Inasmuch as there
is no reduction in the cross-sectional area of the duct along its
major axis, there is no significant flow penalty.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a perspective view of a conventional (prior art) square
cross-sectional flow duct, useful in the exposition of the
invention;
FIG. 2 is a chart illustrating the performance of the apparatus of
FIG. 1 wherein sound attenuation is plotted as a function of
frequency;
FIG. 3 is a cross-sectional elevation view of a first embodiment of
the invention;
FIG. 4 is a chart graphically illustrating the performance of the
apparatus of FIG. 3 wherein sound attenuation is plotted as a
function of frequency;
FIG. 5 is a perspective view of a second embodiment of the
invention which is square at one end and rectangular at the
other;
FIG. 6 is a perspective view of a third embodiment of the invention
wherein one end of the duct is circular and the other end is
rectangular;
FIG. 7 is a perspective view, partially in section, illustrating a
modification of the embodiment of the apparatus described in
connection with FIG. 3;
FIG. 8 is another embodiment of the invention having a circular
opening at one end and a cruciform opening at the other; and
FIG. 9 is a chart graphically comparing the performance of the
present invention with that of a typical prior art device, wherein
attenuation is plotted as a function of frequency.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
While the invention is particularly applicable for use in turbine
engine exhaust ducts, it is to be understood that the device has
applications in many other kinds of sound-generating apparatus,
particularly where the source of sound is in communication with a
fluid stream. The fluid stream may be either gas or liquid, since
the applicable physical laws apply equally for either fluid.
Typical examples of such applications are to be found in air
conditioning ducts, turbine inlets, ducted fans, and the like.
There is shown in FIG. 1 a section of a simple rectangular duct 1,
comprising side walls 2-5, constructed of any suitable and well
known material. The duct 1 has a uniform cross-sectional geometry,
generally of rectangular or square configuration. The duct 1 may be
lined on one or more of its interior walls with a sound absorptive
liner such as indicated at 6 and 7. The liner may comprise a
resistive facing sheet over a compartmented air space, or
acoustical foam, or other suitable material. The active or working
areas of the duct are those so treated with the resistive material.
It is well known that an acoustically lined duct, such as that
shown in FIG. 1, produces an attenuation spectrum, for sounds
propagated along the major axis thereof, which first rises with
increasing frequency, attains a maximum, and then declines in value
in a manner which resembles a resonance curve. Such a curve is
indicated at 8 in FIG. 2.
The value of the peak attenuation and the frequency at which it
occurs are a function of the duct width between the confronting
liners 6 and 7, (d), the duct length, (L), and the acoustic
impedance of the duct liner, (Z=R+JX), plus some additional
complications if flow is present.
Neglecting flow, the greatest attenuation occurs at each frequency
provided the resistance and reactance are a particular function of
the frequency.
R=0.91 (df/c) pc rayls
X=-0.77 (df/c) pc rayls
where p=density of the sound transmitting medium and c=the speed of
sound in the medium. The centimeter-gram-second (cgs) unit of
acoustic resistance is called the rayl.
Thus, for any given duct, there is a particular Z (f) which would
provide the best possible attenuation at all frequencies. However,
this optimum attenuation also shows a distinct peak near the
frequency f for which the duct width d is one wave length .lambda.
and the available attenuation rolls off at about 6 decibels (dB)
per octave at higher frequencies. There are no known prior art duct
lining materials capable of providing an acoustic impedance which
is the optimum function of frequency. Although a resistance which
increases with frequency is obtainable in practical materials, a
reactance which becomes more negative as frequency increases has
not heretofore been attained in any practical way. It is for this
reason that the attenuation attained in ducts of the type shown in
FIG. 1 falls far short of theoretically obtainable values except
that it may be attained at a single frequency by careful design of
the materials to provide optimum R and X at that frequency.
The greatest attenuation peak is attained if this design frequency
is that for which d=.lambda. with R=0.91 pc, X=-0.77 pc.
It should be noted that these conditions for optimum attenuation
are scalable; for example, if a first duct is made with d=30
centimeters (cm), R=0.91 pc, X=.Badd..[.0.77.]..Baddend..Iadd.-0.77
.Iaddend.pc at 1100 hertz (Hz) and 120 cm long, and a second duct
with d=15 cm, R=0.91 pc and X=.Badd..[.0
0.77.]..Baddend..Iadd.-0.77 .Iaddend.pc at 2200 Hz, 60 cm long, the
ducts will provide the same optimum value of attenuation at 1100
and 2200 Hz, respectively, and similarly also for any other scaling
factor. Note that R remains constant, and that the reactance has
also remained constant because the product df remains constant. For
most materials, this means that the thickness of the liner material
has been halved as the duct width d was halved. Advantage of this
property is taken by the present invention to obtain attenuation
closely approaching the theoretical optimum at all frequencies of
interest.
There is shown in FIG. 3 a first embodiment of the invention
comprising a flow duct 9 bounded by walls 11 and 12 on one side,
and a pair of confronting orthogonal walls (not shown) on the other
side. Thus, the cross-sectional configuration is rectangular. The
interior of the duct is provided with a central flow splitter 13, a
pair of intermediate flow splitters 15 and 16, and confronting wall
liners 17 and 18. The flow splitters 13-15, and wall liners 17 and
18 are fabricated from a sound absorptive material, such as
acoustical foam. Assume that the first section of the duct, along
its major axis, has a length L.sub.1 and has an effective internal
width d.sub.1, and provides optimum attenuation A.sub.1 at
frequency f.sub.1 with a liner having a thickness t.sub.1. Further
assume that the next section of the duct has a length L.sub.2 which
equals 1/2 L.sub.1 and is provided with a single splitter 13 having
a half thickness t.sub.2 which equals 1/2t.sub.1. Also assume that
the next section of the duct L.sub.3 has a length which equals
1/2L.sub.2 and 1/4L.sub.1, and is provided with three flow
splitters of sound absorptive material, each having a half
thickness t.sub.3 ; the half thickness t.sub.3 of the absorptive
splitter equals 1/2t.sub.2,=1/4t.sub.1, etc.
Because the thickness t scales to thinner values, both the exterior
size of the duct and the cross-section available to flow remain
constant. Optimum attenuation A.sub.1 =A.sub.2 =A.sub.3 =A.sub.n is
provided at f.sub.1, f.sub.2, f.sub.n for as many sections as are
provided. The attenuation of the three-section duct absorber of
FIG. 3 is shown by curves 48-50 in FIG. 4. The total length,
however, never attains 2L.sub.1 because L=L.sub.1 +1/2L.sub.1
+1/2.sup.n-1 L.sub.1 <2L.sub.1 for finite n. The design provides
essentially constant optimum attenuation from f.sub.1 to f.sub.n.
If the desired attenuation varies as a function of frequency, the
lengths L.sub.1 . . . L.sub.n may be varied accordingly.
In the foregoing discussion it has been assumed that there is no
flow within the duct. However, it is recognized that in certain
practical cases there will be flow within the duct and such action
may be conveniently specified by means of a local Mach number (M).
It should be noted that M is positive if flow through the duct and
sound travel in the same direction, but M is taken negative if flow
opposes the sound direction. If the effects of flow are included,
the optimum wall impedance is: ##EQU1## where
.lambda.=wavelength
M=Mach number of the flow in the duct
If the flow cross-sectional area of the duct is held constant then
##EQU2## Assume that at one end of the duct, which, for example,
may be the entrance, the width is d.sub.o and the lowest frequency
for which large attenuation is needed is f.sub.o then one may solve
for R.sub.opt and X.sub.opt and design a lining to provide this
value of impedance at frequency f.sub.o. Now, freeze the numerical
value of both R.sub.opt and X.sub.opt, call then R.sub.o and
X.sub.o.
In the case of an embodiment of the invention built with splitters,
as one passes from the first section having width d.sub.o the
passage abruptly narrows to width 1/2d.sub.o. It follows that for
frequency 2f.sub.o :
and all conditions are still optimum for absorption of frequency
2f.sub.o into the splitters. This process may be continued as often
as desired.
In the case of a continuously tapering duct the same argument
applies. A fixed value of R=R.sub.o and X=X.sub.o is optimum at any
frequency such that the product df is constant:
It is to be understood that:
R=R.sub.o a constant at any frequency f
X=X.sub.o where X is reckoned at frequency f at the point in the
duct where the duct width is d.
The manner in which this scaling is accomplished depends upon the
type of lining or sound absorptive treatment. Consider first a
resistive facing sheet over a compartmented air space.
For a linear facing sheet:
R=constant independent of frequency. Select a facing so that
R=R.sub.o
For an air space: ##EQU3## where t is the depth of the
airspace.
Thus, simply vary t along the duct such that
where t.sub.o had been originally selected such that: ##EQU4##
Even though the flow cross-section of the apparatus of FIG. 3 does
not vary along the major axis of the duct, for certain aerodynamic
considerations the use of flow splitters 13-16 may be
objectionable. Accordingly, there is shown in FIG. 5 a functionally
equivalent embodiment of the invention in which no flow splitters
are present. This embodiment comprises upper and lower walls 21 and
22, respectively, and side wals 23 and 24. The width of walls 21
and 22 continuously increases from one end to the other, while the
width of walls 23 and 24 decreases from one end to the other as
viewed in the same direction. These complementary tapers of the
orthogonally disposed walls result in a duct geometry in which one
end has a square cross-section and the other end has an elongate
rectangular cross-section. The taper or flare of the walls is
selected to hold the internal cross-section area constant. The
interior surfaces of walls 21 and 22 are faced with absorptive
linings 25 and 26, respectively. It is to be understood that the
linings 25 and 26 may comprise any suitable sound absorptive
treatment. The height between treated surfaces d decreases and the
width w increases at the rate necessary to hold the cross-section
area constant. The acoustic resistance R of the lining (25, 26) is
held constant near 0.91 pc and the thickness t is varied to keep
X=-0.77 pc. In other words, usually t/d=constant. This
configuration is the functional equivalent of that of the
previously described embodiment shown in FIG. 3.
There is shown in FIG. 6 still another embodiment of the invention
in which the first end of the duct, which may be either the inlet
or the outlet, has a circular cross-sectional geometry and the
other end of the duct 28 has an elongate rectangular cross-section
geometry. The duct 29 is provided with an absorptive interior wall
treatment 31-32.
The design procedure used to obtain the construction shown in FIGS.
3, 5 and 6 is to design a series of constant cross-section units of
lengths L.sub.1, L.sub.2, L.sub.3, etc. to provide the desired
values of A.sub.1, A.sub.2 . . . A.sub.n. In the embodiments of
FIGS. 5 and 6, the discontinuous sections (L.sub.1 . . . L.sub.n)
are smoothed into the continuously varying shape. In this way, any
desired attenuation spectrum can be obtained in an optimum way by a
minimum length duct.
The essence of the invention is a sound attenuating acoustically
lined duct of axially varying cross-section geometry, the liner or
interior acoustic treatment being so chosen that the acoustic
resistance R remains essentially constant and the ratio of
effective depth to the distance of the treated surfaces t/d remains
essentially constant. Resistance is always kept invarient while
scaling, and all dimensions L, d, etc., are inverse to frequency.
Further embodiments of this invention may take the form shown in
FIGS. 7 and 8.
Referring to FIG. 7 there is shown a flow duct 33 of circular
cross-section of uniform external dimension along its major axis.
Circular splitters 34, 35 and 36 of cylindrical shape, are
coaxially disposed within the duct 33 and carried by spiders 37 and
38, or any other suitable support means. The interior wall of duct
33 is provided with a sound absorptive treatment 39 which varies in
thickness along its length in conformance with the opposing
splitters (34-36).
There is shown in FIG. 8 an embodiment of the invention in which
the first end 41 of the duct 42 is of circular cross-section, and
the other end 43 is of cruciform cross-section. The interior walls
are lined with acoustic treatment 44 and 45 having a thickness
which varies along the major axis of the duct 42. That is, the
thickness of liner 44, for example, will be greater at end 41 than
at end 43.
There is shown in FIG. 9 actual measurements of the attenuation of
a sound absorber constructed in accordance with the invention as
compared with the sound absorption of a square duct such as that
shown in FIG. 1. As can be seen in FIG. 9, frequency in hertz is
plotted along the abscissa and attenuation in decibels is plotted
along the ordinate. The attenuation as a function of frequency for
the apparatus of FIG. 1 is shown by curve 48. Similarly, the
attenuation as a function of frequency obtained from the present
invention as constructed in accordance with FIG. 5, is shown by
curve 49. Both ducts from which these data were obtained are 46 cm
long and have a constant inside cross-sectional area of 232
cm.sup.2. The apparatus constructed in accordance with FIG. 1 is
lined on two sides with a commercial sound absorptive material,
called "Scottfelt," 1.2 cm thick with its density adjusted so that
its throughflow resistance is about 1 pc. The duct constructed in
accordance with the embodiment of FIG. 5 has an interior
cross-section which varies smoothly from a 15.times.15 cm square at
one end to a 3.8.times.58.5 cm rectangle at the other end. Two
opposing interior side walls are treated with Scottfelt. The
Scottfelt varies from 1.27 cm at the square end to 0.32 cm at the
rectangular end such that the thickness is always in the same
proportion to the local duct height. The density of the Scottfelt
is adjusted such that the local throughflow resistance is
maintained at 1 pc.
The attenuation of the two ducts was measured on a side by side
comparison basis and the results are shown in the graph of FIG. 9.
The attenuation spectrum of the control duct, FIG. 1, is exactly
that which would be expected from classical square duct theory, a
22 dB peak at 2500 Hz dropping rapidly and smoothly to 5 dB at 10
KHz. The attenuation of the duct constructed as shown in FIG. 5 is
also exactly as expected, 18 dB at 2500 Hz rising to a very broad
peak of 25 dB at 4 KHz and still showing 15 dB at 10 KHz. This
broad peak or hump in the curve can be shifted downward in
frequency by at least two octaves by use of thicker absorptive
lining material. It will be seen from the FIG. 9 graph that
substantial noise reduction over an extended frequency spectrum is
obtained by the apparatus of the present invention.
In summary, the invention may be described as follows: A lined duct
having a plurality of different duct widths such as d.sub.o,
d.sub.i the liners being scaled to provide substantially the same
values of acoustic resistance and acoustic reactance at different
frequencies, such as f.sub.o f.sub.1 where
In the most general case, the cross-sectional area need not remain
constant. If the cross-section area varies, the Mach number will
vary. ##EQU5## Note that the ratio of R.sub.opt to X.sub.opt is
always the same at any point in the duct and freuency f regardless
of the local Mach number.
Then instead of holding R constant adjust R as follows: ##EQU6##
Similarly, adjust X along the duct such that ##EQU7## In this way,
an optimum broadband lined diffuser can be designed. This is the
most general case.
Other duct geometries are more difficult to analyze formally. For
example, the exact scaling process for a round to .[.alliptical.].
.Iadd.elliptical .Iaddend.or round to oval or round to rectangular
duct is beyond such easy analysis, however, the analysis of the
equivalent square duct will always be approximately correct if the
value for equivalent d is judiciously chosen. For example, let
d=minor axis of an ellipse or the width of an oval. The object of
such approximations is the same, a duct every section of which is
optimally tuned to absorb most efficiently some part of the
frequency spectrum of interest. Many practical embodiments of the
inventions, in addition to those specifically shown and described
herein, may be made by those versed in the art by following the
teaching herein.
* * * * *