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On the study of the active attenuation of noise in an L-formed duct
Applied Acoustics 34 (1991) 181-191
On the Study of the Active Attenuation of Noise in an L-Formed Duct
Jiluo Zhou, Tielin Shi Department of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, People's Republic of China
& Shuqi Lu Department of Mechanical Engineering, Shaanxi Institute of Mechanical Engineering, Xi'an, People's Republic of China (Received 26 November 1990; revised version received 25 March 1991; accepted 26 March 1991)
A BSTRA CT On the basis of analysis of the characteristics o f sound waves propagated in a duct, this paper puts forward a new proposal related to the location of the sound sources. The primary source which is usually located at the duct end is now at the end o f a branch perpendicular to the main duct, and the secondary source which is usually located on the duct wall is now at the main duct end. Such a shaped duct is named an L-formed duct. Theory and practice have verified that the sound which is emitted from the secondary source at the duct end exhibits fairly good amplitude and phase response characteristics, and shows an excellent working directionality as well. This results in an improvement of the working capacity of the system and a reduction of the feedback effect o f the secondary sound on the primary sound detector. The latter guarantees an active noise control system working with high stability. Test results show that the active noise control system in an L-formed duct is capable of considerable noise reduction, and is more effective in comparison with a sbnilar system in an ordinary straight duct. Therefore, it is very efficient in practical situations. 181 Applied Acoustics 0003-682X/91/$03.50 © 1991 Elsevier Science Publishers Ltd, England. Printed in Great Britain
182
Jiluo Zhou. Tielin Shg Shuqi Lu
1 INTRODUCTION The heart of the matter for establishing an active noise control system is to reproduce, exactly, a secondary sound with waves of equal amplitude and opposite phase to those of the primary sound, so that they counteract each other. Whether the basic requirement above can be satisfied is mainly dependent on the following two factors: the first is to detect precisely the primary sound signal; the second is to reproduce exactly, the sound waves from a secondary source with equal amplitude and opposite phase to those of the primary sound waves. It is not difficult to realize the demands of the former, as a high sensitive sound detector is adopted and the secondary source has no feedback effect on the primary sound field. The latter has been realized, as a high quality system with functions for reversing phases simultaneously has been successfully designed and manufactured. However, it is difficult to satisfy the demands of the latter criterion. According to the working capacity of the system for processing the primary sound signals and for inverting the phase of the signals as well as obtaining the necessary accuracy of the inverted phase, a definite phase error must be produced in the noise attenuation process of the system. Therefore, the noise frequency control will inevitably be limited to a definite range, and in the final analysis results in a restricted noise attenuation effect. In order to improve the processing capacity of the system for primary sound signals and to improve the accuracy of the inverted signal phase, research on the active noise control system has in recent years shifted from a complicated multipolar system to a monopole system, which consists of only a few elements, and is therefore very simple in structure. This results in a rapid decrease in the influence of characteristic errors of the system elements on that of the whole system. Further research has been carried out for improving the charadteristics of the whole noise control system. Chaplin, t Warnaka and Tichy, 2 Ross, 3 etc., who were engaged in research on systems using digital filter techniques and adaptive control techniques, and Zhou and Shi 4'5 who devoted themselves to research using analogue compensating techniques. All of this research work achieved remarkable success, but the analogue compensating monopole system may have a notable advantage in practical uses, owing to its simple structure, low cost and ease of application. Another way of improving the capacity of the active noise control system in ducts is aimed at the disposition of the sound sources. An L-formed duct is therefore proposed in this paper. As shown in Fig. 1, the primary source L 1 is situated at the end of a branch, which is orthogonally connected with the main duct, and the secondary source L2 is situated at the main duct end. The sound detector Mic 1 is used for primary sound detection, and the sound detector Mic 2 is used for inspecting the residual sound in the duct. It can be
183
Active attenuation of noise in an L-formed duct Primary sou r o e
Primary
__T
sound
detector
I Sound level meter
,
~ ~ Mic 2
Secondary source Sounder box
Fig. I.
II
Residual sound
detector An L-formed duct with its active noise attenuation monople system.
proved that such unusual disposition of sound sources shows a much better emission from the secondary source and a much better working directionality of the primary sound detector. This results in a stable active noise control system without any special design on the system stability. Test results show that an analogue compensating monopole system working in the L-formed duct achieves a remarkable noise attenuation effect, which is better than if it were in an ordinary straight duct. Therefore, it is recommended for practical application.
2 BASIC PRINCIPLES A N D T E S T S O F T H E S O U N D
P R O P A G A T E D IN A DUCT It is assumed that the sound waves are propagated in a duct of rigid structure, and that the dimensions of the duct are L=, Ly and L=, where L~-- oc (see Fig. 2), and that the sound wave propagated in the duct will not be influenced by sound reflections from the duct end.
S
Fig. 2. A straight duct showing dimensions L=, Ly and L~ with L: = ~.
Jiluo Z h o u , Tielin S h L S h u q i L u
184
Also, the sound source is located at the end of a duct, and the distribution of the vibration velocity at the transducer surface is: u = uA(.v,3'1 e i''
(t)
where ttA(.r,)" ) constant, then the sound waves propagated in the duct will only be plane waves, as the frequency is kept below the cut-off frequency of the associated duct. Under the above conditions, the sound pressure in the duct will be 6 =
P = PA eif°t -k::~
(2)
where PA is the sound pressure amplitude (under such conditions PA = • • constant); k. is a undetermined constant, which satisfies k;,, + k. 2r + k : " = k-;' k is the wave number, i.e. k = o)/c; and c is the sound velocity. It means that the sound pressure amplitude in the duct is independent of sound frequency. As for a circular sound source situated on the duct wall, the radiated sound pressure at a point _- under plane wave conditions can be expressed as."
7
P=
pcqircR2 Jt(kR) e A kR
ikl: - :il
(3)
where p is the density of air, q,. is the vibration velocity of source i, A is the cross-sectional are of the duct, R is the radius of the circular source. Jt(kR)is a Bessel function o f order one, and z; is the position o f the centre of source i. It can be seen from eqn (3) that the amplitude of the sound pressure p is a function of frequency except at lower frequencies, i.e. where k R << I, when the amplitude is then approximately independent o f the sound frequency. Therefore, from the viewpoint of the sound radiation characteristics, a sound source located at the duct end is preferable to that located on the duct wall. In the former situation, only a few factors influence the emitted sound waves in the duct. This is of advantage for improving the attenuation capacity o f the noise control system, and it is one o f the pecularities of the Lformed duct. Experiments were carried out in order to make a comparison of the sound characteristics produced by two different sound sources, one of which is situated on the duct wall, and the other which is located at the duct end respectively. Figure 3 shows the experimental set-up for this purpose. For measuring the phase response o f the power amplifier-loudspeakermicrophone open loop system (the P L M system) it is seen from Fig. 3 that white noise signals produced from a signal generator pass through the power amplifier, are then fed into the loudspeaker L1 or L2 alternatively, or are fed through the time delay segment, then into the channel B of the spectrum analyser. The noise signal picked up from the microphones Mic 1
Active attenuation of noise in an L-formed duct
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o
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e
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, amplifier ~ L
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185
A
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t
t
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-1
I
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:LtC
Fig. 3. The experimental set-up for comparison of the sound characteristics oftwo different sources, where one is located on the duct wall, and the other at the duct end.
or Mic 2 is fed into channel A of the spectrum analyser. The phase response of the P L M system is then measured and recorded in the spectrum analyser. The measurement of the sound pressure emitted from the loudspeaker L1 or L2 is simpler than that stated above. The white noise signals produced from the signal generator is fed through the power amplifier, then into the loudspeaker L1 or L2. The sound signal picked up is fed into the spectrum analyser for recording. It should be noted that the two different loudspeakers L1 and L2 as well as the two different microphones Mic ! and Mic 2 illustrated on Fig. 3 are actually one and the same. Their positions are interchangeable for different measurements, in order to eliminate the differences in characteristics of different loudspeakers and microphones. Figure 4 shows the test results of the frequency response of different sound sources individually located on the duct wall and at the duct end respectively. It is clearly seen from the figure that the frequency response of the sound emitted from a source located at the duct end is much more linear than that from a source located on the duct wall, especially for frequencies higher than 500 Hz. In other words, the sound emitted from a source situated e"
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Test results for comparison o f the sound frequency responses produced between (a) the sound source on the duct wall, and (b) the sound source at the duct end.
Jiluo Zhou, Tielin Shi, Shuqi Lu
186
at the duct end shows much reduced errors in amplitude and phase response, and therefore, has much greater capability of cancelling the noise in the duct.
E S T A B L I S H M E N T A N D ANALYSIS OF A M O N O P O L E SYSTEM FOR ACTIVE A T T E N U A T I O N OF NOISE IN AN L - F O R M E D D U C T The experimental set-up used for testing the performance of an active noise attenuation monopole system worked in the L-formed duct is shown in Fig. 5. The working principle of the experimental arrangement is clearly illustrated in the block diagrams of the figure, and it is unnecessary here to go into detail.
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g
soo. I
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-
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i1•
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level~__~ J~
I
D
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Fig. 5. The experimental set-up used for testing (a) the characteristics the sound emitted from the secondary source, (b) the working directionality of the secondary source, and (c) the accuracy of sound detector situated in the branch.
187
Actire attenuation o f noise in an L-formed duct
3.1 The emission characteristics of the source located at the main duct end in an L-formed duct It is well known that the emission characteristics of a sound source consist mainly of the amplitude and phase response. These are generally known as the frequency response. Figure 6(a) shows the test results of the frequency response o f the sound emitted from a source located at the main duct end. It is seen from the figure that the frequency response in a limited frequency range of 60-1060 Hz exhibits fairly good linearity, and in comparison with that shown in Fig. 4, is much better than that of a source located on the duct wall, but is lightly inferior to that o f a source located at a straight duct end in a definite frequency range, owing to the change of acoustic impedance at the corner of the L-formed duct.
3.2 The working direction of the secondary source and the detection accuracy of the primary sound detector in an L-formed duct The detection accuracy o f a sound detector is mainly dependent on its directionality. The better the directionality of the sound detector, the less the
,
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Fig. 6. Test results of the sound characteristics emitted from sources worked in an Lformed duct: (a) the frequency response of the sound emitted from the secondary source; (b) the working directionality of the sound emitted from the secondary source; (c) the working directionality of the primary sound detector.
188
Jiluo Zhou, Tielin Shi, Shuqi Lu
influence of the secondary sound feedback effect on it. "~It is clear that in the L-formed duct the major part of the sound energy emitted from the secondary source passes into the main duct. Therefore, the secondary sound shows a much better working directionality and has little influence on the primary sound field. This results in an improvement in the detection accuracy of the primary sound detector. In other words, it is possible to reduce the requirement on the directionality of the primary sound detector. This is the second peculiarity of an active noise control system working in an L-formed duct. Figure 6(b) shows the test results of the sound directionality emitted from the secondary source in an L-formed duct. It can be seen from the figure that the secondary sound pressure response (curve a) measured at point A in the main duct is distinctly higher than that (curve b) measured at point B in the branch (see Fig. 5(b)). In other words, the sound energy entering the main duct is distinctly higher than that entering the branch. So it can be concluded that the sound wave, which is emitted from the secondary source, propagates with an excellent working directionality in the main duct. This results in a contribution to the directionality of the sound detector for detecting the primary sound in the branch. Figure 6(c) shows the test results of the working directionality of a sound detector working in the branch of an L-formed duct. During tests, the primary source and the secondary source are each switched on in their proper order, and the sound level caused by the two sources at point D regulated to an equal sound level of 93 dB respectively (see in Fig. 5(c)). As shown in Fig. 6, curve c is the sound pressure response at point C, where only the primary source is switched on, and curve d is the sound pressure response at the same point, when only the secondary source is switched on. It is clear from the figure that the sound pressure response of curve c is much higher than that of curve d. The difference in the sound pressure responses represents the working directionality of the primary sound detector working in the branch of an L-formed duct. It shows approximately the same directional factor ~t ~ - 20 dB at different frequencies. It can be then assumed that the feedback effect from the secondary source has no influence on the primary sound detector. In other words, the active noise attenuation system in the Lformed duct is always stable, and there is no need for a special stability design in the system. 4 TEST R E S U L T S A N D ANALYSIS For testing the capacity of an active noise control system in an L-formed duct, a low-pass filter compensating monopole system in which a low-pass filter is used as a compensating element Ho(i~o) is adopted. 5
189
Acti~'e atten,~ation of noise in an L-formed duct
Low-pass
r:¢'l
J
Is,go= I lgenerat°rl
SpectrumI Janalyse~" I
Polished 1 "~--"-0 amplifier
Mic2
Sounder box
Fig. 7. The experimental set-up for testing the capacity of an active noise attenuation monopole system operating in the L-formed duct.
The experimental set-up is illustrated in Fig. 7. For eliminating the sound reflections from the termination of the branch to the primary sound field, a polished marble slab, which gives a very high sound reflection factor of y = 0.985--0-99 for frequencies at f_< 4000 Hz, is placed on the internal wall of the branch at an inclined angle of 42-5 °, and the secondary source is slightly inclined with a slope angle of 5° at the main duct end. The working process of the noise control system is easily understood from the block diagram shown in the figure, and it is unnessary here to elaborate. In order to make comparison of the effect of the noise control system between the two different duct forms, the L-formed duct and the ordinary straight duct, tests in the L-formed duct are performed under the same conditions as those imposed earlier in the ordinary straight duct. That is, tests are performed with the same random noise of 100, 250, 500 and 1000 Hz bandwidths and the same extremes of the different frequency bandwidths respectively. Figure 8(a) shows the test results obtained with a low-pass filter compensating monopole system working in an ordinary straight duct, 5 and Fig. 8(b) shows the present test results of the system working in an L-formed duct. It is seen from the figure that the system in an L-formed duct is more efficient than that in an ordinary straight duct, not only from the point of view of noise attenuation, but in the homogeneous noise reduction in the whole effective frequency range, especially for higher frequencies. Therefore, it can be stated that the noise control system in an L-formed duct is much more capable of noise reduction of wider as well as narrower bandwidths, and is practically very effective. Moreover, it should be noted that the flatness and roughness of the polished marble surface greatly influences the primary sound reflection, and therefore, inevitably, the noise attenuation.
Jiluo Zhou, Tielin Shi, Shuqi Lu
190
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Fig. 8. A comparison of the test results of a low-pass filter compensating monopole system for active attenuation of random noise of different band widths la) in an ordinary straight duct 5 and (b) in an L-formed duct, respectively. The upper line is with the system off and the lower line with the system on.
Active attenuation of noise in an L-fbrmed duct
191
5 CONCLUSIONS (1)
An L-formed duct used for active noise control can greatly improve the sound emission characteristics and the sound emission capacity of the secondary source in the main duct. That is, the secondary sound exhibits a much better linearity of frequency response and much better working directionality. (2) A much improved linearity of the secondary sound frequency response means that the active noise control system working in an L-formed duct can effectively decrease the reproduction errors of the secondary sound. This results in an improvement of the working capacity of the system. However, it should be noted that a certain change or deviation in the acoustic impedance owing to the passage at the corner of the L-formed duct leads to a reduction in the linearity of the frequency response in a certain frequency range. (3) A much better working directionality of the secondary source in the Lformed duct leads to an effective reduction of the influence of the feedback effect of the secondary source on the primary sound field. This results in a reduction of the requirement for working directionality and an improvement of the direction accuracy of the primary sound detector. Therefore, the system is always stable and there is no need for special design to cater for the system's stability. (4) A noise control system working in an L-formed duct is more capable of noise reduction than that working in an ordinary straight duct, especially at higher frequencies. Therefore, the L-formed duct is more effective in practice, but the duct structure is rather more complicated. REFERENCES 1. Chapin, B., The cancellation of repetitive noise and vibration. Proc. of InterNoise 80, Inst. of Noise Control Eng., USA, 1980, pp. 699-702. 2. Warnaka, G. E. & Tichy, J., Acoustic mixing in active attenuations. Proc. of InterNoise 80, Inst. of Noise Control Eng., USA, 1980, p. 683-8. 3. Ross, C. F., An adaptive digital filter for broadband active sound control. J. of Sound and Vibration, 80(3)(1982) 381-8. 4. Zhou, J. L. & Shi, T. L., A study of the analogue compensating monopole system for active attenuation of noise in a duct. Applied Acoustics, 28(3) (1989) 187-202. 5. Zhou, J. L. & Shi, T. L., A study of the low-pass filter compensating monopole system for active attenuation of noise in a duct. Applied Acoustics, 31(4) (1990) 281-93. 6. Du, G. H., etaL, Elementary Acoustics. Shanghai Science & Technology Press, People's Republic of China, 1981 (in Chinese). 7. Brengier, M. & Roure, A., Broadband active sound absorption in a duct carrying uniformly flowing fluid. J. of Sound and Vibration, 68(3) (1980) 437-49.
On the Study of the Active Attenuation of Noise in an L-Formed Duct
Jiluo Zhou, Tielin Shi Department of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, People's Republic of China
& Shuqi Lu Department of Mechanical Engineering, Shaanxi Institute of Mechanical Engineering, Xi'an, People's Republic of China (Received 26 November 1990; revised version received 25 March 1991; accepted 26 March 1991)
A BSTRA CT On the basis of analysis of the characteristics o f sound waves propagated in a duct, this paper puts forward a new proposal related to the location of the sound sources. The primary source which is usually located at the duct end is now at the end o f a branch perpendicular to the main duct, and the secondary source which is usually located on the duct wall is now at the main duct end. Such a shaped duct is named an L-formed duct. Theory and practice have verified that the sound which is emitted from the secondary source at the duct end exhibits fairly good amplitude and phase response characteristics, and shows an excellent working directionality as well. This results in an improvement of the working capacity of the system and a reduction of the feedback effect o f the secondary sound on the primary sound detector. The latter guarantees an active noise control system working with high stability. Test results show that the active noise control system in an L-formed duct is capable of considerable noise reduction, and is more effective in comparison with a sbnilar system in an ordinary straight duct. Therefore, it is very efficient in practical situations. 181 Applied Acoustics 0003-682X/91/$03.50 © 1991 Elsevier Science Publishers Ltd, England. Printed in Great Britain
182
Jiluo Zhou. Tielin Shg Shuqi Lu
1 INTRODUCTION The heart of the matter for establishing an active noise control system is to reproduce, exactly, a secondary sound with waves of equal amplitude and opposite phase to those of the primary sound, so that they counteract each other. Whether the basic requirement above can be satisfied is mainly dependent on the following two factors: the first is to detect precisely the primary sound signal; the second is to reproduce exactly, the sound waves from a secondary source with equal amplitude and opposite phase to those of the primary sound waves. It is not difficult to realize the demands of the former, as a high sensitive sound detector is adopted and the secondary source has no feedback effect on the primary sound field. The latter has been realized, as a high quality system with functions for reversing phases simultaneously has been successfully designed and manufactured. However, it is difficult to satisfy the demands of the latter criterion. According to the working capacity of the system for processing the primary sound signals and for inverting the phase of the signals as well as obtaining the necessary accuracy of the inverted phase, a definite phase error must be produced in the noise attenuation process of the system. Therefore, the noise frequency control will inevitably be limited to a definite range, and in the final analysis results in a restricted noise attenuation effect. In order to improve the processing capacity of the system for primary sound signals and to improve the accuracy of the inverted signal phase, research on the active noise control system has in recent years shifted from a complicated multipolar system to a monopole system, which consists of only a few elements, and is therefore very simple in structure. This results in a rapid decrease in the influence of characteristic errors of the system elements on that of the whole system. Further research has been carried out for improving the charadteristics of the whole noise control system. Chaplin, t Warnaka and Tichy, 2 Ross, 3 etc., who were engaged in research on systems using digital filter techniques and adaptive control techniques, and Zhou and Shi 4'5 who devoted themselves to research using analogue compensating techniques. All of this research work achieved remarkable success, but the analogue compensating monopole system may have a notable advantage in practical uses, owing to its simple structure, low cost and ease of application. Another way of improving the capacity of the active noise control system in ducts is aimed at the disposition of the sound sources. An L-formed duct is therefore proposed in this paper. As shown in Fig. 1, the primary source L 1 is situated at the end of a branch, which is orthogonally connected with the main duct, and the secondary source L2 is situated at the main duct end. The sound detector Mic 1 is used for primary sound detection, and the sound detector Mic 2 is used for inspecting the residual sound in the duct. It can be
183
Active attenuation of noise in an L-formed duct Primary sou r o e
Primary
__T
sound
detector
I Sound level meter
,
~ ~ Mic 2
Secondary source Sounder box
Fig. I.
II
Residual sound
detector An L-formed duct with its active noise attenuation monople system.
proved that such unusual disposition of sound sources shows a much better emission from the secondary source and a much better working directionality of the primary sound detector. This results in a stable active noise control system without any special design on the system stability. Test results show that an analogue compensating monopole system working in the L-formed duct achieves a remarkable noise attenuation effect, which is better than if it were in an ordinary straight duct. Therefore, it is recommended for practical application.
2 BASIC PRINCIPLES A N D T E S T S O F T H E S O U N D
P R O P A G A T E D IN A DUCT It is assumed that the sound waves are propagated in a duct of rigid structure, and that the dimensions of the duct are L=, Ly and L=, where L~-- oc (see Fig. 2), and that the sound wave propagated in the duct will not be influenced by sound reflections from the duct end.
S
Fig. 2. A straight duct showing dimensions L=, Ly and L~ with L: = ~.
Jiluo Z h o u , Tielin S h L S h u q i L u
184
Also, the sound source is located at the end of a duct, and the distribution of the vibration velocity at the transducer surface is: u = uA(.v,3'1 e i''
(t)
where ttA(.r,)" ) constant, then the sound waves propagated in the duct will only be plane waves, as the frequency is kept below the cut-off frequency of the associated duct. Under the above conditions, the sound pressure in the duct will be 6 =
P = PA eif°t -k::~
(2)
where PA is the sound pressure amplitude (under such conditions PA = • • constant); k. is a undetermined constant, which satisfies k;,, + k. 2r + k : " = k-;' k is the wave number, i.e. k = o)/c; and c is the sound velocity. It means that the sound pressure amplitude in the duct is independent of sound frequency. As for a circular sound source situated on the duct wall, the radiated sound pressure at a point _- under plane wave conditions can be expressed as."
7
P=
pcqircR2 Jt(kR) e A kR
ikl: - :il
(3)
where p is the density of air, q,. is the vibration velocity of source i, A is the cross-sectional are of the duct, R is the radius of the circular source. Jt(kR)is a Bessel function o f order one, and z; is the position o f the centre of source i. It can be seen from eqn (3) that the amplitude of the sound pressure p is a function of frequency except at lower frequencies, i.e. where k R << I, when the amplitude is then approximately independent o f the sound frequency. Therefore, from the viewpoint of the sound radiation characteristics, a sound source located at the duct end is preferable to that located on the duct wall. In the former situation, only a few factors influence the emitted sound waves in the duct. This is of advantage for improving the attenuation capacity o f the noise control system, and it is one o f the pecularities of the Lformed duct. Experiments were carried out in order to make a comparison of the sound characteristics produced by two different sound sources, one of which is situated on the duct wall, and the other which is located at the duct end respectively. Figure 3 shows the experimental set-up for this purpose. For measuring the phase response o f the power amplifier-loudspeakermicrophone open loop system (the P L M system) it is seen from Fig. 3 that white noise signals produced from a signal generator pass through the power amplifier, are then fed into the loudspeaker L1 or L2 alternatively, or are fed through the time delay segment, then into the channel B of the spectrum analyser. The noise signal picked up from the microphones Mic 1
Active attenuation of noise in an L-formed duct
P
o
w
e
r
, amplifier ~ L
Signal
185
A
[
t
t
_lTime-d~l~
-1
I
a
Channel S JSpectr~m I
qana,y,, " I
:LtC
Fig. 3. The experimental set-up for comparison of the sound characteristics oftwo different sources, where one is located on the duct wall, and the other at the duct end.
or Mic 2 is fed into channel A of the spectrum analyser. The phase response of the P L M system is then measured and recorded in the spectrum analyser. The measurement of the sound pressure emitted from the loudspeaker L1 or L2 is simpler than that stated above. The white noise signals produced from the signal generator is fed through the power amplifier, then into the loudspeaker L1 or L2. The sound signal picked up is fed into the spectrum analyser for recording. It should be noted that the two different loudspeakers L1 and L2 as well as the two different microphones Mic ! and Mic 2 illustrated on Fig. 3 are actually one and the same. Their positions are interchangeable for different measurements, in order to eliminate the differences in characteristics of different loudspeakers and microphones. Figure 4 shows the test results of the frequency response of different sound sources individually located on the duct wall and at the duct end respectively. It is clearly seen from the figure that the frequency response of the sound emitted from a source located at the duct end is much more linear than that from a source located on the duct wall, especially for frequencies higher than 500 Hz. In other words, the sound emitted from a source situated e"
.9 el
o
\
~.! ,
o
.
.
•
.
.
.
.
500 Frequency f (Hz) (a)
Fig. 4.
)
,
.
lOOO
i
o
*
i
500 Frequency f (Hz)
•
t
.
1ooo
(b)
Test results for comparison o f the sound frequency responses produced between (a) the sound source on the duct wall, and (b) the sound source at the duct end.
Jiluo Zhou, Tielin Shi, Shuqi Lu
186
at the duct end shows much reduced errors in amplitude and phase response, and therefore, has much greater capability of cancelling the noise in the duct.
E S T A B L I S H M E N T A N D ANALYSIS OF A M O N O P O L E SYSTEM FOR ACTIVE A T T E N U A T I O N OF NOISE IN AN L - F O R M E D D U C T The experimental set-up used for testing the performance of an active noise attenuation monopole system worked in the L-formed duct is shown in Fig. 5. The working principle of the experimental arrangement is clearly illustrated in the block diagrams of the figure, and it is unnecessary here to go into detail.
L1
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187
Actire attenuation o f noise in an L-formed duct
3.1 The emission characteristics of the source located at the main duct end in an L-formed duct It is well known that the emission characteristics of a sound source consist mainly of the amplitude and phase response. These are generally known as the frequency response. Figure 6(a) shows the test results of the frequency response o f the sound emitted from a source located at the main duct end. It is seen from the figure that the frequency response in a limited frequency range of 60-1060 Hz exhibits fairly good linearity, and in comparison with that shown in Fig. 4, is much better than that of a source located on the duct wall, but is lightly inferior to that o f a source located at a straight duct end in a definite frequency range, owing to the change of acoustic impedance at the corner of the L-formed duct.
3.2 The working direction of the secondary source and the detection accuracy of the primary sound detector in an L-formed duct The detection accuracy o f a sound detector is mainly dependent on its directionality. The better the directionality of the sound detector, the less the
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188
Jiluo Zhou, Tielin Shi, Shuqi Lu
influence of the secondary sound feedback effect on it. "~It is clear that in the L-formed duct the major part of the sound energy emitted from the secondary source passes into the main duct. Therefore, the secondary sound shows a much better working directionality and has little influence on the primary sound field. This results in an improvement in the detection accuracy of the primary sound detector. In other words, it is possible to reduce the requirement on the directionality of the primary sound detector. This is the second peculiarity of an active noise control system working in an L-formed duct. Figure 6(b) shows the test results of the sound directionality emitted from the secondary source in an L-formed duct. It can be seen from the figure that the secondary sound pressure response (curve a) measured at point A in the main duct is distinctly higher than that (curve b) measured at point B in the branch (see Fig. 5(b)). In other words, the sound energy entering the main duct is distinctly higher than that entering the branch. So it can be concluded that the sound wave, which is emitted from the secondary source, propagates with an excellent working directionality in the main duct. This results in a contribution to the directionality of the sound detector for detecting the primary sound in the branch. Figure 6(c) shows the test results of the working directionality of a sound detector working in the branch of an L-formed duct. During tests, the primary source and the secondary source are each switched on in their proper order, and the sound level caused by the two sources at point D regulated to an equal sound level of 93 dB respectively (see in Fig. 5(c)). As shown in Fig. 6, curve c is the sound pressure response at point C, where only the primary source is switched on, and curve d is the sound pressure response at the same point, when only the secondary source is switched on. It is clear from the figure that the sound pressure response of curve c is much higher than that of curve d. The difference in the sound pressure responses represents the working directionality of the primary sound detector working in the branch of an L-formed duct. It shows approximately the same directional factor ~t ~ - 20 dB at different frequencies. It can be then assumed that the feedback effect from the secondary source has no influence on the primary sound detector. In other words, the active noise attenuation system in the Lformed duct is always stable, and there is no need for a special stability design in the system. 4 TEST R E S U L T S A N D ANALYSIS For testing the capacity of an active noise control system in an L-formed duct, a low-pass filter compensating monopole system in which a low-pass filter is used as a compensating element Ho(i~o) is adopted. 5
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The experimental set-up is illustrated in Fig. 7. For eliminating the sound reflections from the termination of the branch to the primary sound field, a polished marble slab, which gives a very high sound reflection factor of y = 0.985--0-99 for frequencies at f_< 4000 Hz, is placed on the internal wall of the branch at an inclined angle of 42-5 °, and the secondary source is slightly inclined with a slope angle of 5° at the main duct end. The working process of the noise control system is easily understood from the block diagram shown in the figure, and it is unnessary here to elaborate. In order to make comparison of the effect of the noise control system between the two different duct forms, the L-formed duct and the ordinary straight duct, tests in the L-formed duct are performed under the same conditions as those imposed earlier in the ordinary straight duct. That is, tests are performed with the same random noise of 100, 250, 500 and 1000 Hz bandwidths and the same extremes of the different frequency bandwidths respectively. Figure 8(a) shows the test results obtained with a low-pass filter compensating monopole system working in an ordinary straight duct, 5 and Fig. 8(b) shows the present test results of the system working in an L-formed duct. It is seen from the figure that the system in an L-formed duct is more efficient than that in an ordinary straight duct, not only from the point of view of noise attenuation, but in the homogeneous noise reduction in the whole effective frequency range, especially for higher frequencies. Therefore, it can be stated that the noise control system in an L-formed duct is much more capable of noise reduction of wider as well as narrower bandwidths, and is practically very effective. Moreover, it should be noted that the flatness and roughness of the polished marble surface greatly influences the primary sound reflection, and therefore, inevitably, the noise attenuation.
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Active attenuation of noise in an L-fbrmed duct
191
5 CONCLUSIONS (1)
An L-formed duct used for active noise control can greatly improve the sound emission characteristics and the sound emission capacity of the secondary source in the main duct. That is, the secondary sound exhibits a much better linearity of frequency response and much better working directionality. (2) A much improved linearity of the secondary sound frequency response means that the active noise control system working in an L-formed duct can effectively decrease the reproduction errors of the secondary sound. This results in an improvement of the working capacity of the system. However, it should be noted that a certain change or deviation in the acoustic impedance owing to the passage at the corner of the L-formed duct leads to a reduction in the linearity of the frequency response in a certain frequency range. (3) A much better working directionality of the secondary source in the Lformed duct leads to an effective reduction of the influence of the feedback effect of the secondary source on the primary sound field. This results in a reduction of the requirement for working directionality and an improvement of the direction accuracy of the primary sound detector. Therefore, the system is always stable and there is no need for special design to cater for the system's stability. (4) A noise control system working in an L-formed duct is more capable of noise reduction than that working in an ordinary straight duct, especially at higher frequencies. Therefore, the L-formed duct is more effective in practice, but the duct structure is rather more complicated. REFERENCES 1. Chapin, B., The cancellation of repetitive noise and vibration. Proc. of InterNoise 80, Inst. of Noise Control Eng., USA, 1980, pp. 699-702. 2. Warnaka, G. E. & Tichy, J., Acoustic mixing in active attenuations. Proc. of InterNoise 80, Inst. of Noise Control Eng., USA, 1980, p. 683-8. 3. Ross, C. F., An adaptive digital filter for broadband active sound control. J. of Sound and Vibration, 80(3)(1982) 381-8. 4. Zhou, J. L. & Shi, T. L., A study of the analogue compensating monopole system for active attenuation of noise in a duct. Applied Acoustics, 28(3) (1989) 187-202. 5. Zhou, J. L. & Shi, T. L., A study of the low-pass filter compensating monopole system for active attenuation of noise in a duct. Applied Acoustics, 31(4) (1990) 281-93. 6. Du, G. H., etaL, Elementary Acoustics. Shanghai Science & Technology Press, People's Republic of China, 1981 (in Chinese). 7. Brengier, M. & Roure, A., Broadband active sound absorption in a duct carrying uniformly flowing fluid. J. of Sound and Vibration, 68(3) (1980) 437-49.