OVER-DETERMINATION IN ACOUSTIC TWO-PORT DATA MEASUREMENT

Transcription

1 OVER-DEERMINAION IN ACOUSIC WO-POR DAA MEASUREMEN Sry Allm, Hns Bodén nd Mts Åom he Mrcus Wllenerg Lortory for Sound nd Virtion Reserch Dept. of Aeronuticl nd Vehicle Engineering, KH, SE-0044 Stockholm, Sweden. Astrct Mesurement of plne wve coustic trnsmission properties, so clled two-port dt, of flow duct components is importnt in mny pplictions. It is n importnt tool for instnce in the development of mufflers for IC-engines. Mesurement of two-port dt is difficult when the flow velocity in the mesurement duct is high ecuse of the flow noise contmintion of the mesured pressure signls. he plne wve coustic two-port is x mtrix contining 4 complex quntities t ech frequency. o erimentlly determine these unknowns the coustic stte vriles on the inlet nd outlet side must e mesured for two independent test cses. he two independent test cses cn e creted y: chnging the coustic lod on the outlet side leding to the so-clled two-lod technique or y using one coustic source on the inlet side nd one coustic source on the outlet side leding to the so-clled two-source technique. In the ltter cse the independent test cses re creted y first using the source on the inlet side nd then the source on the outlet side. As pointed out y Åom it is lso possile to run oth sources simultneously to crete more thn two independent test cses. his over-determintion could e used to improve the mesurement results for instnce if the dt is contminted y flow-noise. In this pper over-determintion is tested y pplying up to 5 different test cses. his procedure hs een pplied to single orifice test oject.. INRODUCION here re severl prmeters tht descrie the coustic performnce of muffler nd/or its ssocited piping. hese include noise reduction (NR), insertion loss (IL) nd trnsmission loss (L). he NR is the sound pressure level difference cross the muffler. hough the NR cn e esily mesured, it is not prticulrly helpful for muffler design. he IL is the sound pressure level difference t point, usully outside the system, without nd with the muffler present. hough the IL is very useful to industry, it is not so esy to clculte since it depends not only on the muffler Eds.: J. Eerhrdsteiner, H.A. Mng, H. Wuke

2 S. Allm, H. Bodén, nd M. Åom geometry itself ut lso on the source impednce nd the rdition impednce. he L is the difference in sound power level etween the incident nd the trnsmitted sound wve when the muffler termintion is nechoic. It is property of the duct element under test only so it is helpful for instnce in muffler design. In mny cses the coustic properties such s trnsmission nd insertion losses cn not e determined nlyticlly, owing for instnce to the complex geometry or the presence of men flow. herefore erimentl techniques must e used. he stndrd technique tody for mesuring coustic plne wve properties in ducts, such s sorption coefficient, reflection coefficient nd impednce is the two-microphone method (MM) [], []. he sound pressure is decomposed into its incident nd reflected wves nd the input sound power my then e clculted. rnsmission loss cn in principle e determined from mesurement of the incident nd trnsmitted power using the MM on the upstrem nd downstrem side of the test oject provided tht fully nechoic termintion cn e implemented on the outlet side. It is however very difficult, to design n nechoic termintion tht is effective t low frequencies. An cousticl element, like muffler, cn lso e modelled vi its twoport dt relting the coustic stte vriles on the inlet nd outlet sides [], [4]. Using the two-port prmeters, the trnsmission loss of muffler cn e redily clculted. Furthermore, if the source impednce is known, the two-port dt prmeters of the muffler cn e used to predict the insertion loss of the muffler system [4]. he erimentl determintion of the two-port dt hs een investigted y mny reserchers. he most usfull method is tht propsed y Doige nd Munjl [5], the two different sttes vriles required to clculte n coustic -port re otined y chnging the source loction, with the rest of the system kept unchnged. As demonstrted in reference [5] the two-source method typiclly gives etter results compred to the two-lod method nd it does not ffect on the men flow field, since the geometry of the system is kept unchnged [5]. Åom [6], [7] presented nd tested method for mesuring the two-port dt in the form of scttering-mtrix, descriing the reltionship etween the trveling wve mplitudes of the pressure on either side of the test oject. his technique cn esily e extended to the cse of n ritrry numer of ports. He lso suggested the ide of over-determintion y running oth sources simultneously nd therey creting more independent coustic test cses. A method to suppress disturing flow noise ws lso descried in reference [7], using reference signl correlted with the coustic field. he im of this work is to test this over-determintion technique for improving the mesurement results for instnce if the dt is contminted y flow-noise.. HEORIICAL BACKGROUND A two-port is liner system with n input nd output. he properties of cousticl two-ports cn e determined either y theoreticl models or y mesurements. he reltion etween the input nd the output sttes of time-invrint, liner nd pssive two-port cn, in the frequency domin, e written: X Y ()

3 ICSV, July -6, 006, Vienn, Austri where, X/Y re the stte vectors t the input/output nd is [ ]-mtrix, which is independent of Y. o determine, from mesurements four unknown must e determined. o mke complete erimentl determintion of the properties of n cousticl two-port, two independent tests must e crried out. Mic. Mic. Mic. 4 Mic. 6 Acousticl wo-port S Loud speker A L est Oject L X Loud speker B Figure. Blck ox relting two pirs of stte vriles x nd y Any pir of stte vriles, i.e. stte vector, elonging to two-port defines liner D stte-spce. his mens tht from given stte vector n infinite set of lterntive stte vectors cn e generted y liner trnsformtions. Acoustic -port model is then n pproprite formlism nd common choice of stte vriles is the plne wve coustic pressure p nd volume velocity q. he trnsfer-mtrix form uses the coustic pressure p nd the volume velocity q, i.e. X [ p, q ] nd Y [ p, q ], here nd represent two different ducts crosssection. If there re no internl sources inside the two-port element the trnsfer-mtrix could e written in the following form [7]: where, nd q q p p () q q ( i k L ) p ( i k L ) p p A ( p i k L p i k ρ c p A ρ c { ( ) ( L ) )} ( i k L ) p ( i k L ) p {( p ( i k L ) p ( i k L ) )} () (4) In order to clculte the trnsfer mtrix, the trnsfer function etween reference signl nd trveling wve mplitudes in positive nd negtive direction see Figure is required, the electric signl driving the externl source, e, is chosen. By using the ssumptions in references [6], [7], the pressure mplitudes in positive nd negtive directions in side cn e written s:

4 S. Allm, H. Bodén, nd M. Åom H H e ( i k s ) H e ( i k s ) ( i k s ) e ( i k s ) H e ( i k s ) ( i k s ) (5) Due to the devition from the idel cse, which introduces mplitude nd phse shifts, reltive clirtion of the microphone mesurement chin is therefore needed. It sufficient to mesure the trnsfer function etween the used microphones nd reference microphone sy microphone, then the clirted trnsfer function cn e presented s: cl H rm H rm H m, where m is the microphone numer nd r refers to the reference side. By using the clirted trnsfer function, eqution (5) gives: H H ( i k s ) H ( i k s ) ( i k s ) ( i k s ) H ( i k s ) ( i k s ) At oth testes we determine the pressure nd volume velocity spectr using twomicrophone method, nd the unknown two port mtrix is determined from the mtrix eqution p p p p (7) q q q q where, nd refers to the mesured dt when the signl comes from the upstrem nd downstrem side respectively. he trnsfer mtrix cn e solved for if eqution (7) is stisfied, i.e. hen the trnsfer mtrix cn e clculted from: (6) p p (8) det 0 q q p q p q p q p q (9) If more thn two independent coustic test cses re creted the unknown two port mtrix is determined from the following mtrix eqution: 4

5 ICSV, July -6, 006, Vienn, Austri N N (0) N N he trnsfer mtrix cn e clculted from:... N N N N... (). ES PROCEDURE Experiments were crried out t room temperture using the flow coustic test fcility t he Mrcus Wllenerg Lortory (MWL) for Sound nd Virtion reserch t KH. he test duct used during the eriments consisted of stndrd steel-pipe with wll thickness of mm, duct inner dimeter 57 mm nd overll length of round 7 meters. he test oject ws single diphrgm orifice with concentric holes nd dimeter of 0 mm. Four loudspekers were used s externl coustic sources. he loudspekers were divided eqully etween the upstrem nd downstrem side s shown in Figure. he distnces etween the loudspekers were chosen to void ny pressure minim t the source position. Six flush mounted condenser microphones (B&K 498) were used, three upstrem nd three downstrem of the test oject giving two microphone seprtions mm nd 8 mm pproximtely covering frequency rnges Hz nd Hz.. he cut-on frequency of the first higher order mode in circulr duct is: f cut on.84c ( M ) πd, where d is the duct dimeter, or round 400 Hz in this cse. he flow speed ws mesured upstrem of the test section using smll pitot-tue connected to n electronic mnometer t distnce of 000 mm from the upstrem loudspekers section. D. A. System S.C. S.C. Mic. Mic. Mic. Mic.4 Mic.5 Mic.6 M Dmper S est Oject L Dmper Loud Speker S Loud Speker Figure. Mesurement configurtion for plne wve decomposition t MWL. 5

6 S. Allm, H. Bodén, nd M. Åom he flow speed ws mesured in the middle of the duct nd efore nd fter ech coustic mesurement nd the verge ws used. o generte over-determintion y independent coustic test cses, the two sources were first used one t time, then oth sources were used simultneously, the phse ws then chnged 80 degrees on the upstrem side nd then on the downstrem side. his produced five independent test cses. o e le to test the efficiency of the technique y hving resonly low signl-to-noise-rtio rndom noise excittion ws used nd 00 verges were mde. 4. RESULS AND DISCUSSIONS he coustic two port, of single diphrgm orifice, hs een determined using overdetermintion s descried in eqution () with up to five independent coustic test cses. he signl-to-nose rtio ws resonly low s shown in Figure. he computed results hve een compred with results from the originl two source loction method. he new procedure gives etter result compred to the theoreticl results s shown in Figure 4. he theoreticl result hs een clculted using D FEM softwre FEMLAB [0] nd the impednce of the orifice hs een modelled using the tested Buer formul []. An improvement of the results cn e otined y using the sme procedure with higher input source level (S/N) Rtio (db) Frequency (Hz) Figure. Signl to noise rtio t reference microphone when the signl comes from upstrem side. 6

7 ICSV, July -6, 006, Vienn, Austri sources Mesurements 4 Mesurements 5 Mesurements Prediction rnsmission Loss (db) Frequency (Hz) Figure 4. Effect of numer of over-determintion using dditionl coustic test cses on the mesured trnsmission loss compred to theoreticl results for single orifice. 5. SUMMARY AND CONCLUSIONS o erimentlly determine coustic two-port mtrices for flow duct components the coustic stte vriles on the inlet nd outlet side must e mesured for two independent test cses. In the so-clled two-source loction technique the independent test cses re creted y first using source on the inlet side nd then source on the outlet side. It ws pointed out y Åom [7] tht it is lso possile to run oth sources simultneously to crete more thn two independent test cses. his overdetermintion could e used to improve the mesurement results for instnce if the dt is contminted y flow-noise. A technique for creting numer of independent test cses hs een suggested in the present pper nd tested, on single orifice test oject, with up to 5 different test cses. he results show tht significnt improvement of the erimentl results cn e otined using this technique. 7

8 S. Allm, H. Bodén, nd M. Åom REFERENCES [] ISO054-:996, Acoustics Determintion of Sound Asoring Coefficient nd Impednce in Impednce ues, Prt I: Method Using Stnding Wve Rtio. [] ISO 054-:998, Acoustics Determintion of Sound Asorption coefficient nd Impednce method in Impednce ues, Prt II: rnsfer Function method. V. B. Pnicker nd M.L. Munjl 98 Journl of Sound nd Virtion 77(4), Impednce ue echnology for flow Acoustics. [] M.L. Munjl 987. Acoustics of Ducts nd Mufflers, New York: Wiley- Interscience. [4] A.G. Doige nd M.L. Munjl. 988 Proceeding of Noise control 88, An Improved Experimentl Method for Determining rnsfer Mtrices or Pipe Line Elements with Flow. [5] M.L. Munjl, nd A.G. Doige 990 Journl of Sound nd Virtion 4(), -. heory of wo Source-loction Method for Direct Experimentl Evlution of the Four-Pole Prmeters of n Aerocoustic Element. [6] M Åom 99 Journl of Mech. System nd Signl Proceeding 5 (), Mesurement of the Scttering-Mtrix of Acousticl wo-ports. [7] M. Åom (99) Journl of Sound nd Virtion, 55 (), A note on the Experimentl Determintion of Acousticl wo-port Mtrices [8] Sry Allm nd Mts Åom (005) Journl of Sound nd Virtion. Investigtion of Dmping nd Rdition using Full Plne Wve Decomposition in Ducts. [9] FEMLAB., COMSOL Multiphysics User s Guide Copyright [0] B. Buer, Impednce theory nd mesurements on porous coustic liners, J. Aircrft 4, (977). [] Eswrn nd M.L.Munjl 99 Journl of the Acoustic Society of Americ 90(4), 6-7. rnsfer Mtrix Modeling of Hyperolic nd Prolic Ducts with Incompressile Flow. 8