会議名称:The 28th International Congress and Exposition on Noise Control Engineering主催学会:INCE/US

Ito Makoto

Sekine Hidehisa

Terao Michihito

伊藤 誠

寺尾 道仁

関根 秀久

English

Article会議名称:The 28th International Congress and Exposition on Noise Control Engineering主催学会:INCE/USAconference pape

寺尾, 道仁

Terao, Michihito

関根, 秀久

Sekine, Hidehisa

伊藤, 誠

Ito, Makoto

KANAGAWA University Repository

Fort Lauderdale, Florida, USAinte,.noile 991999 December 06-08ACOUSTIC PERFORMANCE OF A SPLITTER DUCT SILENCERWITH ZIGZAG AIRWAYSM Terao, H Sekine and M. ItohKanagawa University, Rokkaku-bashi 3-27-1, Kanagawa-ku, Yokohama-shi, 221-8686, JapanINTRODUCTIONThe acoustic performance of a splitter duct silencer of the sound stream type with gourd-shaped absorbers wasstudied. Silencers of this type are applied to obstruct the transmission waves that pass directly through the straightairways when silencers of the parallel baffle type are used. These splitter duct attenuators are usually installed in aHVAC duct or an air passage of large sectional dimensions, and the lowest order several modes in it come into theimportant audible range. When the number of the far-field modes possible in all of the connecting straight ducts isM , the number of the transmission factors between every mode incidence and every mode transmission is amountto M squared. To determine these transmission factors, the incoming and outgoing wave pressures of N +1 modesat each interface must be decomposed generally from the sound pressures at 2(N + 1) positions around eachinterface for M independent sound field conditions. A significant preciseness is required in the sound pressureobservation to achieve this. Last year [1], we presented transmission factors obtained from sound pressures by ameasurement and a BEM numerical simulation at frequencies below second mode cutoff. The agreement of thesewas satisfactory. However, as the number of the possible far-field modes increases, difficulty increases in meetingthe preciseness in the pressure measurement. In this study, we carried out the numerical simulations rigorously toobtain precise sound pressures in the duct. Consequently, for 2D attenuators of a sound-stream type and a parallelbaffle type as shown in Figure 1, we attained the purpose to determine and to compare the transmission factorsbetween the incidence and transmission modes possible at frequencies below eighth mode cutoffDECOMPOSITION INTO TRAVELING WAVE PRESSURESTaking an interface, the coordinates and the origin (0,0) as shown in Figure 2 in the straight duct region of eachduct connected to the attenuator where evanescent modes from the discontinuities have died out, the soundpressure p(x, y) is represented asN Np(x,y) = LQ(n) exp(-jk~n)x)cos(k~n)y) + Lb(n) exp(+jk~n)x)cos(k~n)y) (1)n=O n=Owhere n(=0,1,2, ... ,N) represents the number of the pressure nodes in the y direction, and lV is the highestnumber of the propagating modes for the frequency of interest in the straight duct. The quantities k~n) = n1r / Wandk~n) = {(m/ c)2 - (k~n)2 }1/2 are the wave numbers of the nth mode in the y and x directions, respectively.The quantities Q(n) and ben) denote the outgoing and incoming plane wave pressures, respectively, of the nthmode at the origin. These traveling wave pressures can be determined by solving simultaneously a set of equations(1) corresponding to the sound pressures p(x, y) at 2(N + 1) positions. These sound pressures were observed byconducting a BE numerical simulation [2] for both types ofFigure 1 (a) and (b). Typical results of these are shown inFigure 3.579DETERMINATION OF CHARACTERISTIC FACTORSThe outgoing wave pressure, al(n) , of the nth mode on a interface f is represented by the superposition of thecontributions of the incoming waves, be'(n') ' of all of the modes n' of all of the interfaces f' asL NI.'af(n) = L L 7:fen) P.'(n·)bP.'(n') ' for f =I,ll"", L ,and n =0,1,2,"', N f (2)P.'= I n'= 0where N f. and N f' are the highest orders of the propagating modes in the f th and f' th straight duct sections,respectively, L denotes the number of the ducts connected to the attenuator, and 7:e(n)e'(n') represents thecharacteristic transmission (or reflection when f = f') factor between an incoming wave bf.'(n') and itscontribution to an outgoing wave aP.(n)' To determine these factors, M deferent cases of the sound fields weregenerated and measured, where M = NI +NIl +... + N L + L. Having and solving a set of M independentequations (2) for every f(n), we can determine the unknowns 7:l(n)l'(n') of total M without using anechoicterminations.TRANSMISSION FACTORSFigure 4 shows the amplitude of the transmission factors 7:11(0) 1(0) of the attenuators installed in a straight ductsection as shown in Figure 1. The glass fiber blanket of 32 kg 1m3 and the flow resistance of 8500 kg .s 1m3 wassupposed. The empirical formulae by Delany and Bazley [2] were employed to give the acoustic properties of theblanket. Since the attenuators have symmetry in shape and were installed in a straight duct section, the transmissionand reflection factors related to the non-zero order modes, though these results are omitted here, were negligiblyo-T ~~~V)i --1- '09'. .o . .~ .... . ... .~I -/:';\ /2\ /2\I~·_·- 300 ----~I(a) Sinusoidal sound-stream typeooN1I••••••••••••••• 1I················ '1• ea ••••••••• ea •••~250----.j(b) Parallel baflle typeTooN1Fig.! Splitter duct attenuators studiedb ~::::,/ ,,::::/" '\::::7 b ++- aal(O)~ 1(0) :-••••••• '" ~ ••.-.>~ "-.:../.<'> ..'x.Y ",. II(O) II(O)PI(1) ++--: 00II(............. . .. .•. 't1I(0)1(0) _-.-.- ••••••~ ~2·· ·· ..·.....~)(O)I(O) .::::: 0 0 : : : : 0 •••••••••••••••• ••PI(4) • .~ b 1(1) :::::::::::: ::: .•0. :::. ~ •a1(1) ._--.--------··.~I(l)I(1j! A'~.'~II(1)I(1) b......··_····~ alI(l)A-\-\-- ~ .. _.. IIO)A--\-\-PII(1)lPII (4)W=200 mmGlass Wool (32 kg/m3,Flow resistivity 8500 kg·s/m2 ) (O'i~"---700 .1-- 300 -I- 700 • ~xFig.2 Pressures, traveling wave pressures and transmission factors580(c) Parallel baffle type 6000Hz (2 W/'A=7.06)Fig.3 Pressure (in dB) and net-intensity distributions around absorberssmall compared with those for the fundamental mode incidence and the fundamental mode transmission, 'fII(O) 1(0)and 'fI(O) 1(0). The frequency of the maximum transmission loss of the fundamental mode (the least attenuationmode) for the parallel baffle attenuator of finite length is higher than that given by the Scott's theory [3] for infinitelength liners. The obstruction effect of the zigzag airway on the passing-through transmission shows a tendency to becancelled out by the sound waves passing through the absorbers of the sound-stream attenuator. This passing-through transmission in the absorbers is interrupted significantly by a plate inserted in a absorber as shown in theFigure 5.5818 ~2WI'A.764~I:~~p 20 't 11(0)1(0) --.............~ ~<3 ~----~ 30II c:::::Jbl(O)~~ -.. --- .. ---~------------.---> I-tt-~ an(o)I I:':.:'H :·;.:I 't 11(0)1(0);1__. ! .__. --I.r::::=:::J....;.;...;...;.'. ;...;... . ..;.;.';;.; ..;1. '~__-'----_r£Cl.!0~ 40d0'r;;Cl.!'8 50Cl.!d~~60CI.!"Cl.!o~ 40s::o'r;;Cl.!'8 50Cl.!d~~ 60 '---_--'--_--'-__1--.-_--1--_---'-__"'--_--'-----'1000 2000 3000 4000 5000 6000 7000 1000 2000 3000 4000 5000 6000 7000Frequency [Hz] Frequency [Hz](a) Parallel baffle type (b) Sinusoidal sound-stream typeFig.4 Characteristic transmission factors (oth mode incidence and oth mode transmission)bl(OIl-. .'Y'JV --;I ~OO ia I(Or*I~...·.:.I_vv:\ II with plate I~ 0~~---~2----;-1-3----.--14---oI-S-2-W;-'I'A.-,~ I V).ZV I4+++ Y"'\J\:..~!~ I••••••••.,..".. •••••• I w.o.plate I" -:\l j ·.:..•..•..••·.."~~·-.j~~~10e~::20b.OooNI 30CI.!'"Cl.!o~s:: 40o'r;;Cl.!·s 50CI.l~~601::..- ---'- -L...-__---'- ~~ 0 1 2 4 IS 2WI'A.::~ -t~::I-I+-~2-10 '" I \J\J§ ~ i /\./V\. IP 't1l(0)1(0) .~\ ~ /w.o.plate'020 '. ~ _____130 \···· ·7 ····· ..~. ! \.A..£:J ! ··•·..·v..·~40 bl«()F ~ ~I~all(OIo I I.~ I /\J\J\. I.~ 50 with plate I~r= 60c=..-__-L-__----L ....I.-__-----''--__---LI1000 2000 3000 4000 5000 1000 2000 3000 4000 5000Frequency [Hz] Frequency [Hz](a) Transmission factors (b) Reflection factorsFig.5 Effect of insertion of a plate on charastristic transmission and reflection factors(oth mode insidence and Othmode transmission)CONCLUSIONSThe transmission and reflection coefficients of splitter duct attenuators of a parallel baffle type and a sound-streamtype were determined for the incidence and transmission modes possible at frequencies below eighth mode cutoff ineach connecting ducts. It was found that the frequency of the maximum transmission loss of the fundamental modefor the parallel baffle attenuator of finite length was higher than that given by the Scott's theory for infinite lengthliners. The obstruction effect of the zigzag airways on the passing-through transmission shows a tendency to becancelled out by the sound waves passing through the absorbers of the sound-stream attenuator.REFERENCES1. "On characteristic transmission and reflection coefficients of splitter duct attenuators," M. Terao and H. Sekine, Proceedings of Internoise98, Christ church, New Zealand, 1998.2. "Acoustical properties of fibrous acoustical materials," M.E. Delanyand E.N. Bazley, Applied acoustics, 3,10S-116(1970).3. "The propagation of sound between walls of porous material," R.A Scott, Proceedings ofthe Physical Society 58, 3S8-368(1946).582

ACOUSTIC PERFORMANCE OF A SPLITTER DUCT SILENCER WITH ZIGZAG AIRWAYS

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ACOUSTIC PERFORMANCE OF A SPLITTER DUCT SILENCER WITH ZIGZAG AIRWAYS

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