ACOUSTIC ATTENUATION IN FULLY-FILLED PERFORATED DISSIPATIVE MUFFLERS WITH EXTENDED INLET/OUTLET

Transcription

1 ACOUSTIC ATTENUATION IN FULLY-FILLED PERFORATED DISSIPATIVE MUFFLERS WITH EXTENDED INLET/OUTLET Hluk Erol *, Özcn Ametolu Istnbul Tecnicl University, Fculty of Mecnicl Engineering, 34349, Gümü+suyu, Istnbul, Turkey. Abstrct Exust noise of IC engines is te min comonent of noise ollution of te urbn environment. To ttenute te exust noise, exnsion cmbers wit different configurtion s become n imortnt re of reserc nd develoment. Te resent study considers coustic crcteristics of circulr fully-filled erforted dissitive mufflers wit extended inlet/outlet. In ddition to te finite element metod, n exerimentl work is considered. Fiber mteril wit different rdii is resented nd discussed. Perfortion rtios of te ies re lso discussed in tis study. All rmeters vlidted wit exerimentl work wit rcticl designed muffler for obtining te trnsmission loss. Comrison wit te results obtined vi exerimentl mesurements justifies te roces used ere. INTRODUCTION Exnsion cmbers wit extended ies exibit desirble coustic ttenution erformnce s combintion of usully brodbnd domes of simle exnsion cmber nd te resonnt eks of qurter-wve resontor. Vrious selections of lengts of extended ducts cuse gret imrovement on te coustic beviour of silencers over wide frequency rnge. Furtermore, recent works in fiber roerties combined wit teir brodbnd coustic dissition crcteristics nd erforted ducts mke suc mufflers otentilly desirble for teir coustic crcteristics. Te coustic ttenution of te exust muffler is imortnt for utomotive engineers. Exust muffler designers often use fiber mterils nd erforted ies in dissitive mufflers in order to imrove te ttenution over wide frequency rnge. Eds.: H. Erol, O. Ametoglu

2 H. Erol, O. Ametoglu Different metods for modelling dissitive mufflers ve been studied reviously by te resercers. Xu et l. [1], by using two-dimensionl nlyticl roc, exmined te effect of fiber tickness, cmber dimeter nd mteril roerties on te coustic erformnce of dissitive silencers. An nlyticl roc ws roosed bsed on te solution of eigeneqution for circulr dissitive exnsion cmber. Te coustic ressure nd rticle velocity cross te silencer discontinuities were mtced by imosing te continuities of te velocity/ressure integrl over discrete zones t te exnsion/contrction. Kirby [], resented metod tt two-dimensionl finite element eigenvlue clcultion is combined wit oint colloction mtcing sceme in te inlet/outlet ducts for mufflers wit men flow nd erforted ie. Tis metod sowed good greement wit exerimentl mesurements. Selmet et l. [3], combined te beviour of extended ducts nd te effects of dissition of bsorbing mterils. A ybrid silencer ws studied bot by metods of boundry element metod nd multi-dimensionl roc to see te effects of vritions in te structure of te muffler. Finite element metod ws commonly discussed for modelling mufflers by mens of tking tree-dimensionl effects into ccount. Munjl [4], considered metods for solving Glerkin formultion nd lso Medizde et l. [5], imlemented tree dimensionl finite element metod to redict te trnsmission loss of muffler for wide frequency rnge. In tose studies, ybrid muffler wit erforted ies nd bsorbing mterils ws modelled for obtining trnsmission loss (TL) crcteristics by using finite element metods. Te results obtined vi numericl metods were comred wit exeriments wic tey d good greements. Severl exerimentl works were imlemented for different metods. Clculting four-ole rmeters is te most common wy of redicting trnsmission loss. Munjl et l. [6], wo roosed twosource metod for mesuring te four-ole rmeters of n coustic element or combintion of elements. In tis study, te im is to redict te coustic erformnce of fully-filled erforted dissitive mufflers wit extended inlet/outlet. In order to control qurter wve resontor frequencies, bsorbing mteril ositioned in te centrl region of te muffler. Finite element roc is lied to redict four ole rmeters for vrious different combintions of mufflers to obtin trnsmission loss crcteristics. Exerimentl studies re done to rovide results of te finite element metod roc. THEORY Te system to be delt wit in te resent study is sown digrmmticlly in Fig. 1. Let it be ssumed tt te rdius of te inlet nd outlet ies is r, weres te lengt nd rdius of te cmber is L nd R, resectively. Also, te tickness of te fiber mteril is t. Te liner wve eqution for erfect gs wit no dming, t P = c P (1)

3 ICSV13, July -6, 6, Vienn, Austri were P is te sound ressure nd c is te seed of sound. If eqution (1) is solved for corresonding boundry nd initil conditions in te time domin, it gives P s function of time nd sce. Figure 1 Muffler wit erforted ie nd orous mteril. Te sound ressure ssumed for time-rmonic solution is P i t = e. () Ten te liner wve eqution becomes Helmoltz s eqution s = k, (3) were is in te frequency domin. For mufflers wit orous mterils, te governing equtions become + k = in nd + k = in b (4) b b b were nd re te domins of ir nd bulk orous mteril resectively. Te boundry conditions re = 1, t te inlet, =, on rigid wlls, = ik, t te outlet. (5) n n One-dimensionl lne wve rogtion is ssumed t te inlet nd te outlet ies. Hence, t te outlet, te necoic boundry condition identified in eqution (5) is rter simle form of Robin boundry condition. Te norml velocity is continuous nd te norml ressure grdient is roortionl to density rtio t te interfce between ir nd orous mteril, tus reresented s u n u n. (6) b b = b b, = n n On te erforted ie, te bsic ssumtions for modelling erforted lte in n coustic field re continuous norml velocity nd discontinuous ressure troug te ie. Te simle reltion roosed by Sullivn nd Crocker [7] is considered sufficiently ccurte for usge in tis er. Te dimensionless trnsfer imednce Z t of erforted lte cn be roximted s follows

4 H. Erol, O. Ametoglu 1 Z = t (.4 i. f ) c +, (7) were is te rtio of te oen re to te totl re of te ie. Te ressure jum,, norml rticle velocity, u n nd norml sound ressure grdient reltion re clculted by following equtions, resectively. = cztun, = i un. (8) n Note tt eqution (7) is vlid only for erforted ie surrounded by ir, so nrrow ir g between te bsortion mteril nd te erforted ie is ssumed. At tis oint, following continuous sce of comlex functions must be introduced s { 1 1 Re Im : Re, Im } Z = = + i H H (9) were H 1 is te Hilbert sce. Te vritonl formultion of te roblem is to find Z suc tt ( ) ( b b b) b b k k + i ( ) ds + i ( ) ds Z Z 1 1 S1 t S t ik ds = S k d+ k d were S is te cross-sectionl re of te outut ie nd S 1 nd S re surfces of erforted lte. In eqution (1), volume integrls (te first two terms) governing ir nd orous mteril, surfce integrls (te next two terms) governing ressure jum troug erforted ie nd linked te ressure in bot sides nd te lst integrl surfce term is te Robin boundry condition for modelling necoic termintion t te outlet. Common Glerkin formultion metod is utilized for solving te eqution. Tree-dimensionl domin, is divided into K tetredrl elements. Te discreet roximtion sce, H K j= 1 (1) = (11) H, is defined s 1 1 { Re Im Re Im } : ( ), ( ) H = = + i P P (1) 1 j j were P re olynomils of degree two defined on ec tetredrl elements, j. Te globl bsis functions, ( X ) =, 1 & n, m & N, (13) n m nm

5 ICSV13, July -6, 6, Vienn, Austri were N is te totl number of globl nodes in te model. X is te coordinte of ec nodes. By using globl bsis functions,, cn be N ( X) ( X) = ( X) (14) m m m= 1 were m = ( X m). Using eqution (14), exnd ll functions to vritionl formultion, te discretized eqution of liner systems of lgebric equtions suc tt A=f (15) were te coefficient mtrix A is srse symmetric mtrix, is te sound ressure mlitude vector of nodl vlues nd f is forcing function vector of nodl vlues. In tis eqution f is only non-zero vlue t te inlet ie ccording to Diriclet boundry conditions. All tese vlues re comlex numbers t ll nd cn be written (A Re+iA Im)( Re+i Im)=fRe + if Im (16) Eqution (16), cn be written in mtrix form s ARe AIm Re fre = (17) AIm -ARe -Im fim wic bove eqution is solved by severl itertive solvers develoed before. Te comonents of te coefficient mtrix A, A mn re A = k d+ k d mn ( m n mn) ( m n bmn) b b k k + i ( ) ds+ i ( ) ds m n n m n n Z 1 t Z S S t S ik ds m n Wen lying Eqution (18) to ec comonents to evlute te globl mtrix A, ll locl coordintes (x,y,z) trnsformed into globl coordinte system ( 1,, 3 ). For tetredrl elements, te coordintes of reference elements re functions of te elementl bsis functions, i ( 1 ). Te comonents of te elementl mtrix Â, Â ij for n internl element, cn be written s 1 Aij = [! J "! J " 3 3 i l j l J # l= 1 l x $# i= 1 l x $ 3 3 i l j l +! J "! J " # y $# y $ i= 1 l i= 1 l 3 3 i l j l J J ] d k J i jd i= 1 l z i= 1 l z +! "! " # $# $ (18) (19)

6 H. Erol, O. Ametoglu wic 1 & i, j & 1 intervl. Elementl integrtion is numericlly erformed by Gussin qudrture wic is defined on te reference element. In tis study, te finite element metod roc is done by MSc.Actrn tt is commercil ckge rogrm wic s wide librry of coustic elements nd mterils. Porous medi nd erforted ie cn be modelled in te rogrm. EXPERIMENTAL SETUP Te common rocedure for mesuring te trnsmission loss (TL) of muffler is to determine te incident ower by decomosition teory nd te trnsmitted ower by te lne wve roximtion ssuming n necoic termintion t te outlet. Unfortuntely, it is difficult to determine fully necoic termintion. Furtermore, tere re two lterntive mesurement tecniques wic re considered not require n necoic termintion: te two lod metod nd te two source metod. In tis er two-lod metod is lied. An cousticl element, like muffler, cn lso be modelled to obtin four-ole rmeters. Assuming lne wve rogtion t te inlet nd outlet, te four-ole metod is to relte te ressure nd velocity (rticle, volume or mss) t te inlet to tt t te outlet. Using te four-ole rmeters, te trnsmission loss of muffler cn lso be redily clculted. Te two-lod metod, wic is bsed on trnsfer mtrix metod, cn be modelled by its four-ole rmeters, s sow in Figure. Figure Four-ole rmeters for exerimentl setu. Te trnsfer mtrix is sown below * A1 ' -( ), * A ' ) & =! ") & () ( B1 % # + $ ( B % were -(),,(), +(), () re te four-ole rmeters; A 1 (), B 1 () nd A (), B () re te ressure nd velocities t te inlet nd outlet, resectively. Aliction is bsed on te trnsfer mtrix metod, wic muffler must be lced like in te Figure 3. Also, by cnging te end condition (coustic imednce) wit two serte mesurements. Generlly, two lods cn be two different lengt ies, single ie wit nd witout bsorbing mteril or even two different mufflers. In tis er, two lods metod were cieved by ie wit nd witout bsorbing mteril. Tus, trnsmission loss is clculted by TL = Log1 -( ) (1)

7 ICSV13, July -6, 6, Vienn, Austri Figure 3 Imednce Tube for exeriments to clculte trnsmission loss. RESULTS Exerimentl muffler s dimensions of simle exnsion cmber wit erforted ie nd coustic fiber lining of rock wool mteril. Te rdius of te inlet nd outlet ies is r =.7 cm, weres te lengt nd rdius of te cmber is L = 5 cm nd R = 1 cm, resectively. Also, te tickness of te rock wool is t = 3.5 cm. Te rock wool flow resistivity equls MKS ryls/m. Te frequency rnge of interest is between 1-3 Hz bot in numericl nd exerimentl evlutions. Te element size for te finite element domin ws cosen to rovide minimum 6 elements er wvelengt. It s 11 elements for cvity domin nd 6 elements for orous mteril domin. MSc.Actrn evlutes tis tye of muffler witin 17 minutes. Trnsmission Loss [db, ref= $P] erforted 64 oles (exerimentl) erforted 64 oles (numericl) Trnsmission Loss [db, ref= $P] exnsion cmber erforted 64 oles erforted 36 oles erforted 4 oles erforted 5 oles Frequency [Hz] Frequency [Hz] () (b) Figure 4 Trnsmission loss of mufflers wit erforted ie, () numericl nd exerimentl results, (b) different erfortion rtios. Trnsmission losses of mufflers wit nd witout orous medi re given in te Figure 4 nd 5, resectively. To rovide te FEM results, exerimentl clcultion is given wit tese figures. It cn be seen from figures tt te exerimentl nd numericl clcultions sows good greement bot for erforted mufflers nd erforted mufflers wit orous mteril. Some mismtc witin te trnsmission

8 H. Erol, O. Ametoglu loss vlues round 1.6 khz frequencies in Figure 5 cn be negligible becuse of mtemticl modelling. Te mtemticl model ssumes no bsortion in ir nd erfect reflection on te wlls wic is not ccurte. Anoter reson is tt, te orous mteril nd te erforted ltes re roximted by comlex coustic imednce evluted using rter simle emiricl reltions. Tis my exlin te errors in te results. Trnsmission Loss [db, ref= $P] orous medi 35mm tickness (exerimentl) orous medi 35mm tickness (numericl) Trnsmission Loss [db, ref= $P] orous medi tickness 35 mm orous medi tickness 3 mm orous medi tickness mm orous medi tickness 1 mm witout orous medi Frequency [Hz] Frequency [Hz] () (b) Figure 5 Trnsmission loss of mufflers wit erforted lte nd orous medi, () numericl nd exerimentl results, (b) different erfortion rtios. REFERENCES [1] Xu M.B., Selmet A., Lee I.J., Huff N.T., 4. Sound ttenution in dissitive exnsion cmbers, Journl of Sound nd Vibrtion, 7, [] Kirby, R., Trnsmission loss redictions for dissitive silencers of rbitrry cross section in te resence of men flow, J. Acoust. Soc. Am., 114, -9 (3) [3] Selmet, A., Lee, I. J., Huff, N. T., Acoustic ttenution of ybrid silencers, J. Sound Vib., 6, (3) [4] Munjl, M.L., Acoustics of Ducts nd Mufflers. (Wiley-Interscience, New York, 1987) [5] Medizde, O. Z., Prscivoiu, M., A tree-dimensionl finite element roc for redicting te trnsmission loss in mufflers nd silencers wit no men flow, Alied Acoustics, 66, (5) [6] Munjl, M.L. nd Doige A.G., Teory of two source-loction metod for direct exerimentl evlution of te four-ole rmeters of n erocoustic Element, J. Sound Vib., 141(), (199). [7] Sullivn J. W., A metod of modeling erforted tube muffler comonents, II. Alictions. J. Acoust. Soc. Am., 66, (1979).