Study of the Effect of Grazing Flow on the Performance of Microperforated and Perforated Panels

Transcription

1 Purdue University Purdue e-pubs Pubiations of the Ray W. Herri Laboratories Shoo of Mehania Engineering Study of the Effet of Grazing Fow on the Performane of Miroerforated and Perforated Panes J Stuart Boton Purdue University, boton@urdue.edu Arun Viswanathan Foow this and additiona wors at: htt://dos.ib.urdue.edu/herri Boton, J Stuart and Viswanathan, Arun, "Study of the Effet of Grazing Fow on the Performane of Miroerforated and Perforated Panes" (013). Pubiations of the Ray W. Herri Laboratories. Paer 90. htt://dos.ib.urdue.edu/herri/90 his doument has been made avaiabe through Purdue e-pubs, a servie of the Purdue University Libraries. Pease ontat eubs@urdue.edu for additiona information.

2 Study of the Effet of Grazing fow on the Performane of Miroerforated and Perforated Panes Arun Viswanathan and J. Stuart Boton Ray W. Herri Laboratories Shoo of Mehania Engineering Purdue University

3 Sime Exansion Chamber FEM mode Inet (unit ressure) Anehoi termination Mirohone ositions (Charateristi ate Z) Anaysis Detais: Commeria Finite Eement ode ABAQUS is used. Domain disretization with Aousti Eements (AC3D4) Steady State Dynami anaysis with omex resonse outut he rea and imaginary art of ressure data in the frequeny domain is ost-roessed to obtain the ransmission Loss (L) 9/11/013

4 MPP as an equivaent orous materia he erforated faings are modeed as orous media omosed of identia yindria erforations of iruar ross-setion. he equivaent aoustia arameters are: Comex Density (Johnson et a.) ~ s ( ) 0 j j Comex Bu Moduus (Chamoux and Aard) ~ K ( ) ( 1) 1 P 0 / j8 C 0 1 j C Jaouen and Béot foowed o this aroah by haraterizing ate the radius of the erforations and the erforation rate as the aoustia arameters. 9/11/013 3

5 Absortion Coeffiient Correation of FEM resuts with Jaouen and Béot resuts MPP with 00 mm avity baing Sound ressure inet Mirohone ositions MPP Fuy refeting end ie onstraints is used to onnet the dissimiar MPP and Imedane tube meshes. MPP roerties: Porosity = 1.8% hiness = 0.35 mm Fow resistivity = 1.41x10 6 N s m 3 Perforation hoe radius = 7.61x10-5 m MPP an be modeed effetivey in Finite Eement Methods by using the equivaent orous materia Johnson-Chamoux-Aard (JCA) mode.

6 ransmission Loss of Exansion Chamber with MPP Cross setion view Exansion Sae MPP Main dut Exansion Chamber: Exansion ratio = 4 Exansion ength = 0. m Inet & Outet diameter = 0.1 m Magnified view Exansion sae MPP Main dut 9/11/013 5

7 Effet of grazing fow on MPP and PP roerties 9/11/013 6

8 . Resistane and Reatane of MPP with orretions due to grazing fow he normaized resistane and reatane for iruar hoed ates (Guo) r Re 1 j t J 1( j ) R 1 j J ( j ) 0 s Im j t 1 j J 1 ( j ) J j 0( ) 1 where d / 4 (dimensioness shear wave number) R s 0.5 (surfae resistane) Corretions due to grazing fow Resistane additive orretion = (onstant)(m/ σ) Rie suggested a vaue of 0.30 for the onstant whie Enady suggests a vaue of 0.50, and Munja suggested he vaue suggested by Munja is used here. Reatane subtrative orretion = δ/(1+305m 3 ) δ is the mass end orretion given by (0.85d) where d is the diameter of hoe. 9/11/013 7

9 Resistane and Reatane of PP with the effet of grazing fow Munja roosed the foowing equations as a genera emiria formua for the resistane and reatane terms of the imedane of the erforated ane by inuding the effets of the thiness, hoe diameter, orosity and grazing fow. R (1 7.3M ) / X [ f (1 51.0t)( d h )] / where M is the grazing fow Mah number, is the orosity, f is the frequeny in Hz, t is the thiness of the erforated ate in m, and d h is the diameter of the hoes in m. Vaidity range: 0.05 M 0.; ; 1 t 3 mm; 1.75 d h 7 mm. 9/11/013 8

10 Formuation of MPP and PP roerties from imedane data 1 A 1 R B ρ ρ By using ane wave theory, the Refetion and ransmission Coeffiients are: j j R sin os sin j e j sin os j sin os j sin os 9/11/013 9

11 Four oe arameters in terms of R and oeffiients For an aoustia eement in a dut, the transmission and refetion oeffiients in terms of four oe arameters are: 1 jd e 0 R Symmetry and reiroity roerties give: By maniuating equations for and R, the two unnown four oe arameters 1 and 1 an be exressed in terms of and R as shown: jd ( ) ( R 1) e 1 jd e 1 ( R 1 ( ) 1 ) e jd e jd 9/11/013 10

12 FEM Aoustia materia roerties from four oe arameters he Comex wave number and Comex harateristi Imedane an be found by: 1 os 1 ( 11) Z t he Comex Density and Comex Bu Moduus an then be found by: 1 1 Z Z hese roerties are used to mode MPP and PP with grazing g fow effets in FEM. 9/11/013 11

13 Correation of Noise Redution for PP with Grazing fow Noise redution of an extended inet and outet muffer based on a ase desribed by Munja. he muffer was tested with a mean fow of M = 0.. Dimensions: L 1 = 98 mm L =750 mm L 3 = 700 mm d 1 = d 3 =43.5 mm d = 19.4 mm a = b = 400 mm = 8 mm Porosity = 3.87% he deviations may be due to the fat that the FEM mode does not tae into aount the fow noise that ourred during the exeriment. 9/11/013 1

14 Effet of mean fow and grazing fow on MPP roerties MPP roerties: Porosity = 1.8% hiness = 0.35 mm Perforation hoe radius = 7.61x10-5 m Fow roerties: Mah number = 0. he effet of grazing fow on MPP roerties is negigibe. he L with no fow MPP roerties derived from imedane using the reations resented is simiar to L redited using the JCA mode. his orroborates the vaidity of the formuation. 9/11/013 13

15 Effet of mean fow and grazing fow on PP roerties PP roerties: Porosity = 4.1 % hiness = 1.59 mm Perforation hoe radius = 1.75 mm Fow roerties: Mah number = 0. It an be seen that grazing g fow has onsiderabe effet on the roerties of PP and thereby affets the ransmission Loss erformane of PP. 9/11/013 14

16 Conusions Perforated and miroerforated eements of muffer systems an be modeed as equivaent orous regions he effet of grazing fow on erforated sheets is nown and an be inororated into exressions for the transfer imedane of the eements From the transfer imedanes inuding fow effets, the harateristi imedane and wave number of the equivaent orous ayer an be dedued hose vaues may then be used to mode the effet of fow on the erformane of erforated muffer eements At the ow Mah numbers tyia of automotive HVAC systems, the effet of fow on the transfer imedane of miroerforated eements is negigibe Fow has some effet on the transfer imedane of erforated eements he major effet of fow at ow Mah numbers resuts from the atered waveengths in the u and downstream diretions 9/11/013 15

17 Questions? 9/11/013 16