The Correlation of the Performance of Duct Lining Materials with Their Normal Incidence Properties

Transcription

1 Purdue Univerity Purdue e-pub Publication of the Ray W. Herrick Laboratorie School of Mechanical Engineering The Correlation of the Performance of Duct Lining Material with Their Normal Incidence Propertie J Stuart Bolton Purdue Univerity, bolton@purdue.edu Jeong-Woo Kim Taewook Yoo Jonathan H. Alexander 3M Corp. Follow thi and additional work at: Bolton, J Stuart; Kim, Jeong-Woo; Yoo, Taewook; and Alexander, Jonathan H., "The Correlation of the Performance of Duct Lining Material with Their Normal Incidence Propertie" (005). Publication of the Ray W. Herrick Laboratorie. Paper 4. Thi document ha been made available through Purdue e-pub, a ervice of the Purdue Univerity Librarie. Pleae contact epub@purdue.edu for additional information.

2 The Correlation of the Performance of Duct Lining Material with Their Normal Incidence Propertie Purdue Univerity Jeong-Woo Kim Taewook Yoo J. Stuart Bolton 3M Jonathan H. Alexander

3 Background Car door ytem Porou material are often ued to line channel Quetion: Doe the normal incidence aborption of channel lining correlate with the attenuation they produce at grazing incidence?

4 Approach Calculate attenuation in duct lined with elatic porou medium Confirm by experiment Then: conider two lining i treatment that have the ame normal incidence id aborption coefficient One with reitive t membrane e that partially a fill duct One without membrane that ha the ame ma/unit area but completely fill duct

5 Preure and Stre Field of Porou Material in Duct Sytem -D Model of Lined Duct Y y yx Air x xy Solid phae xy x Stre in olid Porou yx X y Solve for propagation characteritic in the x- direction Fluid phae Stre in fluid

6 Diplacement and tre olution for porou media All expreed in term of ix unknown coefficient Solid Diplacement Fluid Diplacement k jkxx C1 C 1 C 1 3 C 4 ty jkx x ux jkxe e e e e j e C 5e C6e k1 k1 k k kt jk yy jk yy jk yy jk yy jktyy jktyy k k k k k uy je Ce Ce Ce Ce j Ce Ce jkxx 1y jk1yy 1y jk1yy y jkyy y jkyy x jkxx jktyy jktyy e 5 6 k 1 k 1 k k k t C C C C k Ux jk b e b jkxx 1 jk1yy jk1yy 3 jkyy 4 jkyy ty jkx jk x tyy jktyy xe 1 1 e b e b e e jg C 5e C6e k1 k1 k k kt k x 1y jk1 y k1y jk1 y ky jk y k y jk k x jkxx Uy je b1 Ce 1 b1 Ce b Ce 3 b Ce 4 jg e Ce 5 Ce 6 k1 k1 k k kt jk x y y y y y jkty y jkty y Solid Normal Stre Fluid Normal Stre Solid Shear Stre k k k y N A bq Ce N A bq C e N A bq C e k k k 1y jk1yy 1y jk1yy y jkyy k k k N Ab Q C e N C e C e k y jk yy x ty jktyy jktyy jkxx e kt jk1yy jk1yy jkyy jkyy jk x x [ QbR Ce QbR C e Qb R C e Qb R C e ] e kk kk k k xy N Ce C e C e C e N C e C e e k k k x 1y jk 1 y y jk 1 y y x y jk y y jk y y x ty jk t y y jk t y y jk xx ( 1 ) ( 3 4 ) 5 6 t t t

7 Boundary condition: fully-lined model Y Y= d k y -D porou formulation of the free-wave olution in a lined duct. Y= -d k x X Rigid wall boundary condition Solve for k x at y d (1) u 0 () u 0 at y d (4) u 0 () (5) u 0 x( ymm) x( ymm) The characteritic diperion y( ymm) (3) U 0 y( ymm) G flxfl 0 y( ymm) (6) U 0 y( ymm) equation det( G fl ) 0 fl X fl C C C * * * T

8 Modeling of perforated membrane X P1 P P1 P S Y Pore (fluid) Volume Velocity Continuity (1) v (1 ) jw jw y1 t po () v (1 ) j W j W y t po Equation of Motion (3) P P ( v v ) R m j v 1 po t t t (1 ) Rt (4) P P ( v v ) hjv 1 po t 0 po v y W W t : : R : po p S : : : : R R / S T p olid Velocity of ound field Surface poroity of membrane Flexural motion of olid part Flexural motion of fluid part Frequency Flow reitivity of pore Area of one pore and olid Actual flow reitivity

9 Comparion of predicted and meaured normal incidence TL for the perforated membrane To obtain material propertie of the reitive creen TL meaured by impedance tube hp [ m] R m p / S 600[MKS Rayl] [kg/m ] Eight layer Four layer Meaurement 8 layer 4 layer layer 1 layer TL (db) 8 4 Two layer One layer Prediction Rp/S = 600 * N N=1,,4, Frequency (Hz)

10 Boundary condition: partially-filled with perforated membrane model (FPMA) Y X Y=L Y=L 1 Y=0 k y k x G X 0 p p C C C C C C Air: A1,A Porou C1 C6 A A W W W p t p po The characteritic diperion equation det( G p ) 0 p Perforated membrane X T at y 0 (1) ux 0 () uy 0 (3) U 0 y at y L 1 (4) (1 ) jw jw (5) uy Wt (6) Uy Wpo (1 ) Wt y t po p hp 1 Wt (7) ux Wp x (8) mw yx p p (9) (1 ) (1 ) ( ) ' p p y j Wpo Wt Rp j kx yx p p mw t ' pp j Wpo Wt Rp 0 php1wpo (10) ( ) at y L (11) 0 y h

11 Model FPMA: Yellow gla fiber, 100 Hz 100 F:\Reearch\Kx_reult5\Rtube_yellow_FPMA\FPMA_Fbae_S100.mat Y mm Air Real (kx) mm Yellow g/f Model FPMA X Imag (kx)

12 FPMA: Root trajectorie Real (kx) Imag (kx)

13 Square duct ytem and gla fiber layer 0.5m 4-microphone tranfer matrix method ued to meaure attenuation at grazing incidence

14 Gla fiber and membrane propertie Gla fiber (yellow) Em=3360 in vacuo bulk Young' modulu N/m eta=0.35 in vacuo lo factor ve= 0.4 bulk poion' ratio igma= teady tate, macrocopic flow reitvity - MKS Rayl/m epil_ =1.1 geometrical tructure factor OMp= poroity ro1=6.6 bulk denity of olid phae Perforated membrane: modified by the equivalent normal aborption performance hp1=0.5e-3 thickne of membrane m=0. ma/area for perforated membrane (kg/m ) OM=0.95 urface poroity Rpm=350 effective flow reitvity (MKS Rayl/m 3 )

15 Comparion of meaured and predicted reult Attenuation rate can be calculated from the imaginary part of axial wave number k ( f) j ( f) x P Lp f db m 1 0log 0log ( ) [ /(0.5 )] ( f ) P e 00 5 mm gla fiber layer w/o crim 5 mm gla fiber layer with crim 00 in db/0.5m Atte enuation ratio Mode 7 80 Mode 1 Meaurement Frequency enc in Hz in db/0.5m Atte enuation ratio i 160 Mode Meaurement 40 Mode Frequency in Hz

16 Normal aborption coefficient x R c 1 x y Comparion how imilar aborption performance between F and FPM model 1 65 mm F: Total ma/area: 0.49 kg/m coefficient F FPM R c 1 x y Norm mal aborption mm FPM: Total ma/area: kg/m h [ m] p1 3 p / S 350[MKS Rayl/m ] R m [kg/m ] Frequency in Hz

17 Attenuation Rate of yellow gla fiber Y Fully lined duct how much higher attenuation performance than partially filled duct 65 mm k x X 150 F FPMA 5mm 40 mm F: Total ma/area: 0.49 kg/m Y Air k x X FPMA: Total ma/area: kg/m hp [ m] Rp / S 350[MKS Rayl] m 0. [kg/m ] 0.95 Attenuation n ratio in db/ /m Frequency in Hz Normal incidence aborption i not a good prediction of grazing incidence performance

18 Summary Formulated lined duct model featuring air pace, reitive crim and poro-elatic layer. Performed experimental meaurement of lined duct attenuation rate. Showed good agreement between prediction and meaurement for partially-lined duct cae. Calculation of normal aborption coefficient for a ingle porou layer and layer with perforated crim. Find the equivalent ma/area and flow reitivity for the perforated membrane to have imilar normal incidence aborption performance to the fully lined model. Reult how attenuation performance in axial direction i much lower for the layer + crim cae than for the treatment that fill the duct