Sound Propagation in a Square Duct having an Inlet and Outlet Located on the Crossed Right Angle Face

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Interntionl Journl of Emerging Engineering Reserch nd Technology Volume 6, Issue 8, 018, PP 9-13 ISSN 349-4395 (Print) & ISSN 349-4409 (Online) Sound Propgtion in Squre Duct hving n Inlet nd Outlet

Deprtment of Control nd Informtion System Engineering, Ntionl Institute of Technology Kummoto College, Jpn.

1 Interntionl Journl of Emerging Engineering Reserch nd Technology Volume 6, Issue 8, 018, PP 9-13 ISSN (Print) & ISSN (Online) Sound Propgtion in Squre Duct hving n Inlet nd Outlet Locted on the Crossed Right Angle Fce 1 Sohei Nishimur, Yuy Nishimur 1 Deprtment of Mechnicl nd Intelligent System Engineering, Ntionl Institute of Technology Kummoto College, Jpn. Deprtment of Control nd Informtion System Engineering, Ntionl Institute of Technology Kummoto College, Jpn. *Corresponding Author: Sohei Nishimur, Deprtment of Mechnicl nd Intelligent System Engineering, Ntionl Institute of Technology, Kummoto College, Jpn. ABSTRACT A previous study discussed rectngulr sound proofing ventiltion unit hving n inlet nd n outlet locted on the opposite fce which results in reduced outlet re. As result, the ventiltion function is decresed. To improve this problem, squre one feturing n inlet nd n outlet which re locted on the crossed right ngle fce is proposed in this work. First, outlet sound pressure to the given inlet uniform velocity is obtined bsed on the wve eqution nd the boundry conditions. Next, the experimentl results re shown to be in resonble greement with our theoreticl predictions. Keywords: Wve eqution, sound propgtion, resonnce, higher-order mode INTRODUCTION Along with the remrkble economic development, in recent yers in developing countries environmentl problems including rod noise hve been getting worse in countries belonging to tropicl regions. Yno nd others [1] mesured rod trffic noise on the min rod of Vietnm for 4 hours nd reported tht noise level of more thn 75 db occurred lmost ll dy on the rod with the highest noise level. On the other hnd, ventiltion holes re widely used in countries in tropicl regions, which re instlled in the middle of the window nd the roof. However, the noise of the rod psses through the ventiltion hole nd propgtes to the living spce. As result, there is virtully no difference in the noise level between the room nd the outside, nd people living in n environment re incresingly uncomfortble with noise incresing yer by yer even though there re considerble fmilirity nd ptience. In recent houses, glss plte is indicted on the outside of the door ventiltion hole to provide sound proofing mesures. With this mesures indoors only ttenution levels of only 10 db - 15 db cn be obtined, but people re considerbly reduced discomfort to noise. However, most residentil houses in Southest Asi do not hve ir-conditioning equipment, therefore by closing the glss plte during the dy, the ventilte the room indoors cnnot be done. A previous study [] discussed rectngulr sound proofing ventiltion unit hving n inlet nd n outlet locted on the opposite fce which results in reduced outlet re. As result, the ventiltion function is decresed. To improve this problem, squre one feturing n inlet nd n outlet which re locted on the crossed right ngle confront is proposed in this work. There re for two sorts of wves inside the chmber, nmely the stnding wve tht propgtes in the xil direction nd the trverse wve tht propgtes in the rdil direction. The trverse wve occurs in the high frequency rnge. Regrding the circulr cylindricl chmber, the noise will hve tendency to increse in this frequency rnge, fr from decresing depending on the resonnce of the higher modes. In this pper, t first the outlet sound pressure to the given inlet uniform velocity is obtined bsed on the wve eqution nd the boundry conditions. Next, the experimentl results re shown to be in resonble greement with our theoreticl predictions. METHOD OF ANALYSIS Insertion Loss Insertion loss IL defined by [3] Interntionl Journl of Emerging Engineering Reserch nd Technology V6 I

2 Sound Propgtion in Squre Duct hving n Inlet nd Out-let Locted on the Crossed Right Angle Fce IL = 10log W r W 0 = 0log U 1 U (1) Here, W r nd W 0 re the rdited power t one point in spce with or without the coustic element inserted between tht point nd the source. The rtio of U 1 /U is equl to the D prmeter of the four-pole prmeters, s fr s constnt velocity source be concerned. When three coustic elements connected in series, s the sectionl re of element 1 nd 3 re sufficiently smll to compre with those of element of the D prmeter of the whole system cn be described by the following pproximted eqution A B C D = A 1 B 1 A w B w A 3 B 3 C 1 D 1 C w D w C 3 D 3 D = (coskl 1 )(C w )(jz 3 sinkl 3 ) () where C w denoted the C prmeter of element. In order to obtin relible IL effect, D prmeter must be high enough. In other words, the design of element- to hve high enough prmeter C w is demnded. C w of squre SVU Model of the rectngulr soundproofing ventiltion unit which hs dimension of dis shown in Figure 1. Dimension of n input nd output re( i i1 ) (b i b i1 ) nd( 0 01 ) (d 0 ) they locted on the fce which hs section re of S b = nd S d = d, respectively. Figure1.Squre sound proofing ventiltion unit Wveeqution in terms ofvelocity potentil F is given by + + = 1 c t Φ (3) where c is the sound velocity. Let Φ = exp (jωt) (j = 1, ω = kc, k: wve number ) then the generl solution of Eq.(3) cn be given s = (Aexp μz + Bexp μz ) ( Csinαx + Dcosαx) Esin s α y + Fcos s α y (4) where μ = s k, A, B, C, D, E nd F re rbitrry constnts determinble from the boundry conditions, other symbols re constnts. Let /, / nd / zre the velocity component in the x, y nd z directions, respectively. Assuming the wlls of the cvity to be perfectly rigid nd the loss t the wll cn be neglected then boundry conditions re : [1] t x=0 =0 (5) [] t x= =0 (6) [3] t y=0 =0 (7) [4] t y= =V 0F 0 x, z (8) [5] t z=0 z =V if i x, z (9) [6] t z=d =0 (10) z where V i is the driving velocity t the input, F i (x, z)is defined s F ( x, y) i 1 x, b y b i1 i i1 i (11) 0 other res of x nd y Let = + b then / = / + b /, therefore we hve the following boundry conditions [1] t x=0 =0 (1) [] t x= =0 (13) [3] t y=0 [4] t y= =0 (14) =V 0F 0 x, z (15) [5] t z=0 =0 (16) z [1b] t x=0 =0 (17) [b] t x= =0 (18) [3b] t y=0 [4b] t y= =0 (19) =0 (0) 10 Interntionl Journl of Emerging Engineering Reserch nd Technology V6 I8 018

3 Sound Propgtion in Squre Duct hving n Inlet nd Out-let Locted on the Crossed Right Angle Fce [5b] t z=0 z =V if i x, z (1) Bsed on the bove boundry conditions becomes = 4 V i S b I m,n where I m,n = i m =0 n=0 cos nπy i i1 cosμ m,n (z d) μ m,n sinμ m,n d dx () cos y dy (3) i1 Similrly, b becomes b = 4 V 0 S d O m,n where O m,n = i m =0 n=0 i i1 cos nπy cos nπ d dx (z d) (4) cos nπ z d dy (5) i1 d The verge sound pressure on the output is found s P 0 = 1 S 0 = jk ρc S m =0 n =0 d 0 cosμ m,n z d d 0 cos nπ d d 0 P(x, b, z)dxdz 4 V i I m,n cos(nπ) S b μ m,n sinμ m,n d +4 V 0 O m,n S d β m,n tnβ m,n d z d dxdz dxdz (6) Where U i =V i S i is the volume velocity supplied from the input. Z 0 = ρc/s 0 is the chrcteristic impednce of the output. Expnding Eq.(6) with m=0 nd n=0 the bove eqution becomes P 0 = j4z 0 1 sinkd O 0,0U i + S 0 S d coskd U k U + 0 O m,n S d S 0 β m,n tn β m,n d I m,n O m,n cos(nπ) S d S 0 μ m,n sinμ m,n d U i (7) The Cw of SVU could be found from Eq. (7) s C w = U i P 0 RESULTS AND DISCUSSION (8) The verge of outlet sound pressure is derived from Eq. (7) in which the first term in the brcket represents the plne wve nd the second represents the higher order mode wve. First, with respect to the plne wve, the first term of Eq. (7), the sound pressure level is gret t the frequencies where the denomintor sin (kd) become zero. Nmely kd = ηπ f = η c d η = 1,, (9) Similrly, with respect to higher order mode wves, the second term of Eq. (7), the sound pressure level becomes gret t the frequencies given s follows: sinμ m,n d = 0 f m,n = c π = c + nπ m + n + η d η = 0, 1,, (30) The spectrum of plne wve nd higher order mode re showed in Figure. Note tht, in the cse of rectngulr SVU, the resonnce frequencies re f m,n = c π η = 0, 1,, (31) + nπ b From Eq. (30) nd Eq. (31), it is cler tht the number of resonnce frequencies generted inside the squre SVU is less thn those of rectngulr SVU. Verifying the theoreticl results As described bove, the wves in the SVU is Interntionl Journl of Emerging Engineering Reserch nd Technology V6 I

4 Sound Propgtion in Squre Duct hving n Inlet nd Out-let Locted on the Crossed Right Angle Fce composed of plne wve nd higher order mode wve. In order to mximize the soundproofing bility of the SVU, it is necessry to reduce the sound pressure level or to prevent those wves from even occurring. sin(kd) become zero. Nmely kd = ηπ f = η c d η = 1,, (33) Similrly, with respect to higher order mode wves, the second term of Eq. (3), the sound pressure level becomes gret t the frequencies given s follows: sin(μ m,n d/) = 0 () 0Log P 01 f m,n = c π + nπ = c m + n + η d (b) sinh(m,0 d) Frequency (Hz) sinh(m 4,0 d) 0Log P 0 0Log P 04 frequency(hz( Frequency (Hz) Figure. Resonnce frequencies pper in the SVU. Resonnces will occur when the denomintor of Eq.(7) become zero. () plne wve component. (b) higher order mode wve component. When we locte the center of the outlet t z = d / Eq. (7) becomes η = 0, 1,, (34) From the bove equtions we cn understnd tht the sin (kd) nd sin(μ m,n d)of P 0 in Eq. (31) becomes sin (kd/) nd sin(μ m,n d/), respectively. This results in hlving of the number of resonnce frequencies generted inside the SVU. Figure 3 shows the experiment results to prove this fct. The dotted line is the mesured result when the microphone ws locted on the position of z=d. The solid line is the mesured result when the microphone ws locted on the position of z=d/. Note the mesurement method ws bsed on reference [4]. P 0 = j4z 0 1 sin ( kd ) O 0,0 U i + S 0 S d coskd cos ( kd ) U k U + 0 O m,n S d S 0 β m,n tn β m,n d I m,n O m,n cos(nπ) S d S 0 μ m,n sinh ( μ m,nd ) (3) With respect to the plne wve, the first term of Eq. (3), the sound pressure level is gret t the frequencies where the denomintor sin (kd/) U i Figure3. Mesured result (=0.14m, d=0.7m). Dotted line nd solid line re the output locted t d nd d/, respectively. CONCLUSION The presented here is the sound propgtion in the squre SVU feturing n inlet nd outlet is 1 Interntionl Journl of Emerging Engineering Reserch nd Technology V6 I8 018

5 Sound Propgtion in Squre Duct hving n Inlet nd Out-let Locted on the Crossed Right Angle Fce locted on crossed right ngle fce. The outlet position ws improved by plcing it on the lrger fce of the SVU to increse the ventiltion effect. In ddition, the outlet is locted in the center of the SVU to void the resonnce of plne wve sound pressure. REFERENCES [1] H.Y.T. Phn, T. Yno, H.A.T. Phn, T. Nishimur, T. Sto, Y. Hshimoto, Community response to rod trffic noise in Hnoi nd Ho Chi Minh City, Applied Acoustics, Vol. 71, 010, pp [] Y. Nishimur, S. Nishimur, T. Nishimur, T. Yno, Sound propgtion in soundproofing csement windows, Applied Acoustics, Vol. 70, 009, pp [3] Y. Nishimur, S. Nishimur, T. Nishimur, Acoustic chrcteristics of rod trffic noise nd csement windows in Vietnm, Journl of Temporl design in rchitecture nd the environment, Vol. 1, 013, pp [4] S. Nishimur, T. Nishimur, T. Yno, Acoustic nlysis of ellipticl muffler chmber hving perforted pipe, Journl of Sound nd Vibrtion, Vol. 97, 006, pp [5] M. Abom: Derivtion of four-pole prmeters for including higher-mode effects for expnsion chmber mufflers with extended inlet nd outlet, Journl Acoustic Society of Americ 137, pp , [6] J. G. Ih: The Rective Attenution of Rectngulr Plenum Chmbers, Journl of Sound nd Vibrtion, 171, pp. 93-1, 199. [7] T. M. Whlen: The behviour of higher order mode shpe derivtives in dmged, bem-like structure, Journl of Sound nd Vibrtion, 309, pp , 008. [8] T. Nishimur, T. Iked: Four-pole-prmeters for n ellipticl chmber with men flow, Electronics nd Communiction in Jpn, 81, pp. 1-9, [9] T. Nishimur, T. Ando, T. Iked: Resonnce of ellipticl muffler chmber hving nonuniformly perforted pipe, Electronics nd Communiction in Jpn, 85, pp. -8, 00. [10] R. Glv, P. L. Regud, M. Abom: Study of folded resontor including the effects of higher order modes, Journl of Sound nd Vibrtion, 73, 7, pp , 004. [11] Z.H. Wng, C.K. Hui, C.F. Ng: The coustic performnce of ventilted window with qurterwve resontors nd membrne bsorber, Applied Acoustics, 78, pp. 1-6, 014. Cittion: Sohei Nishimur, Yuy Nishimur, (018). "Sound Propgtion in Squre Duct hving n Inlet nd Outlet Locted on the Crossed Right Angle Fce", Interntionl Journl of Emerging Engineering Reserch nd Technology, 6(8), pp Copyright: 018 Sohei Nishimur, et l. This is n open-ccess rticle distributed under the terms of the Cretive Commons Attribution License, which permits unrestricted use, distribution, nd reproduction in ny medium, provided the originl uthor nd source re credited. Interntionl Journl of Emerging Engineering Reserch nd Technology V6 I

Investigation of the Inlet and Outlet Location on the Soundproofing Ventilation Unit

Investigation of the Inlet and Outlet Location on the Soundproofing Ventilation Unit Send Orders for Reprints to reprints@enthmscience.e The Open Acoustics Journl 14 7 1-7 1 Open Access Investigtion of the Inlet nd Outlet oction on the Soundproofing Ventiltion nit Nsu Tsunetoshi 1 nd Nishimur