Topology Optimization of Suction Muffler for Noise Attenuation

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1 Purdu Univrsity Purdu -Pubs Intrnational Comprssor Enginring Confrnc School of Mchanical Enginring 2012 Topology Optimization of Suction Mufflr for Nois Attnuation Jin Woo L jinwool@ajou.ac.kr Dong Wook Choi Follow this and additional works at: L, Jin Woo and Choi, Dong Wook, "Topology Optimization of Suction Mufflr for Nois Attnuation" (2012). Intrnational Comprssor Enginring Confrnc. Papr This documnt has bn mad availabl through Purdu -Pubs, a srvic of th Purdu Univrsity Libraris. Plas contact pubs@purdu.du for additional information. Complt procdings may b acquird in print and on CD-ROM dirctly from th Ray W. Hrrick Laboratoris at Hrrick/Evnts/ordrlit.html

2 1437, Pag 1 Topology Optimization of Suction Mufflr for Nois Attnuation Jin Woo LEE 1 *, Dong Wook CHOI 2 1 Ajou Univrsity, Division of Mchanical Enginring, Suwon, Gyonggi-do, Rpublic of Kora ( , , jinwool@ajou.ac.kr) 2 Ajou Univrsity, Division of Mchanical Enginring, Suwon, Gyonggi-do, Rpublic of Kora ( , , stynr04@ajou.ac.kr) * Corrsponding Author ABSTRACT A topology optimization mthod is dvlopd to optimally dsign suction mufflrs in rciprocating comprssors. Suction mufflrs should b dsignd for high nois rduction. Th suction mufflrs ar not asy to systmatically dsign bcaus thir outr shap is so complicatd and th cntr axs of th inlt/outlt do not coincid. Mufflr rsarchrs in industry hav dsignd th intrnal configuration of suction mufflrs intuitivly and xprintially. Howvr, sinc our proposd mufflr dsign mthod is not rstrictd to location of th inlt and outlt and to th outr shap of suction mufflr, it could b applid to suction mufflr dsign problms. A topology optimization problm is formulatd for a finit lmnt modl simulating a suction mufflr for a rciprocating comprssor. Transmission loss valu at a targt frquncy is slctd as an objctiv function and partition volum is constraind. Dsign variabls chang continuously from zro to on during optimization procss. Th matrial filling on lmnt is an intrmdiat matrial btwn and solid in ach itrativ calculation and bcom or rigid body at a final convrgd stag dpnding on th valu of dsign variabls. Rigid body lmnts build up partitions or flow path to incras transmission loss. Th proposd mufflr dsign mthod is applid to a suction mufflr, which has bn introducd at an intrnational confrnc. 1. INTRODUCTION A ractiv mufflr is placd around th rfrigrant suction part of a rciprocating comprssor to rduc low frquncy nois (L t al., 2002). Th ractiv mufflr is calld as a suction mufflr. Sinc th volum of th suction mufflr is dtrmind aftr othr componnts ar dsignd, its outr shap is complicatd and th axs of its inlt and outlt do not coincid with ach othr in many cass. Thrfor, convntional mufflr dsign mthods (Slamt and Radaivich, 1997, Slamt and Ji, 1999), which hav bn introducd so far, ar not asy to apply to suction mufflr dsign problms. Many rciprocating comprssor dvloping companis hav difficulty in dsigning th intrnal configuration of a suction mufflr to incras its nois attnuation prformanc in a targt frquncy rang. In many cass, nw suction mufflrs, which hav bn rportd in th Intrnational Comprssor Enginring Confrnc at Purdu, rflct dsignrs intuition and xprinc, and rquir a lot of tim and many trials and rrors. Hnc, a nw mufflr dsign mthod is rquird to figur out th currnt difficultis in comprssor companis. Topology optimization has bn widly usd in structural dsign problms (Bndsø and Sigmund, 2004). Th topology optimization dsign mthod has a lot of advantags ovr shap and siz optimizations. Th utmost advantag among thm is that th topology optimization dsign mthod dos not dpnd on dsignrs intuition and Intrnational Comprssor Enginring Confrnc at Purdu, July 16-19, 2012

3 1437, Pag 2 xprinc. Thrfor, a crativ optimal dsign can b obtaind by topology optimization. L and Kim (2009a, 2007a) formulatd acoustical topology optimization problms for acoustic dvic dsign. Espcially, thy (2009b, 2007b) showd that th topology optimization mthod can b applid to ractiv mufflr dsign problm: intrnal partitions should b optimally locatd in a mufflr to incras a transmission loss valu at a targt frquncy. In this work, L and Kim s suggstd mthod (2009b, 2007b) is xtndd to suction mufflr dsign problms. This papr is outlind as follows: first, a suction mufflr dsign problm is rformulatd as an acoustical topology optimization problm; thn th formulatd dsign problm is solvd at a singl targt frquncy for various partition volums; and futur work is discussd for practical application. Th suction mufflr, which has bn rportd prviously in othr confrnc (Svndsn and Møllr, 2005), is slctd as an analysis modl and is assumd as a 2 dimnsional modl for computation tim rduction. Th finit lmnt modl of th suction mufflr is mployd for acoustical analysis and optimization. On finit lmnt is filld with intrmdiat matrial btwn rigid body and, which is xprssd as a function of dsign variabls, during optimization procss. Dsign variabls ar updatd by using a gradint-basd optimization algorithm (Svanbrg, 1987). 2. REFORMULATION OF SUCTION MUFFLER DESIGN PROBLEM An acoustical topology optimization problm is formulatd for th 2-dimnsional suction mufflr in Figur 1. Th outr shap of th suction mufflr is obtaind from th 3-dimsional suction mufflr which Svndsn and Møllr (2005) usd for nois rduction. Rfrigrant ntrs th right nd of th mufflr and gos out into th uppr nd, and th outr shap is too complicatd to asily locat som partitions for transmission loss incras. Th intrnal ara in th suction mufflr is dividd into a dsign domain and a non-dsign domain. For rfrigrant passag, a non-dsign domain is assumd to b filld with rfrigrant during optimization. Som partitions, which ar built up during optimization, will b locatd optimally in th dsign domain. Figur 1: Suction mufflr with right-nd inlt/uppr outlt Intrnational Comprssor Enginring Confrnc at Purdu, July 16-19, 2012

4 1437, Pag 3 To rformulat th suction mufflr dsign problm, th acoustical topology optimization problm in L and Kim s mthod (2009b, 2007b) is rcalld. Th transmission loss valu at a targt frquncy is slctd as an objctiv function in Equation (1) and th volum ratio btwn partitions and th suction mufflr is constraind in Equation (2). Th dnsity and bulk modulus of on finit lmnt ar xprssd as functions of dsign variabls in Equation (3). Th dsign variabls chang continuously from 0 to 1. Th finit lmnt is filld with an intrmdiat matrial btwn rigid body and during optimization procss and pushd to rigid body or by th intrpolation functions in Equation (3). Th dsign variabls convrg 0 or 1 at a convrgd topology. Th transmission loss valu at ach itrativ calculation is calculatd by using th thr-point mthod (Wu and Wan, 1996) in Equation (4). Max TL f = ft χ whr TL rprsnts a transmission loss valu at a targt frquncy, variabl vctors. (1) f t is a targt frquncy, and χ is a dsign V dv χ / V V r (2) whr χ is a dsign variabl, V is th total volum of suction mufflr, and V r is th volum ratio btwn allowd partitions and th suction mufflr. 1/ ρ 1/ K ( χ ) = 1/ ρ + χ (1/ ρrigid 1/ ρ ) ( χ ) = 1/ K + χ (1/ K 1/ K ) rigid (3) 2 whr ρ is th dnsity and K is th bulk modulus ( K = ρc ). 1 p p TL = 20 log, 10 p jk x j 2k x πf k = (4) c whr p 1 and p 2 ar acoustic prssurs at two points in th inlt ara of Figur 1 and p 3 is an acoustic prssur at on point in th outlt ara. Symbols of x 12 and c ar th distanc btwn two points in th inlt ara and sound spd, rspctivly. To calculat transmission loss at a targt frquncy, finit lmnt mthod is mployd. Th finit lmnt analysis is implmntd by using Olsn t al. s mthod (2006). Dsign variabls ar updatd by th Mthod of Moving Asymptots (Svanbrg, 1987) during optimization procss. Th mthod is rquird th snsitivity analysis of th objctiv function and th constraint with rspct to ach dsign variabl. Th snsitivity analysis is prformd by th Adjoint mthod (Duhring t al. 2008). 3. OPTIMAL SUCTION MUFFLERS Th formulatd topology optimization problm for suction mufflr dsign is solvd at f t = 900 Hz for four diffrnt volum ratios ( V r = 0.01, 0.02, 0.05, ). Fluid passing through th suction mufflr is assumd to b air. Spcific valus in Tabl 1 ar usd in th optimization. Th dnsity and sound spd of rigid body ar dtrmind by using th critria suggstd by L and Kim (2009c). Figur 2 shows optimal mufflrs obtaind by solving th topology optimization problm. Black aras ar filld with rigid bodis, which build up th partitions. In all optimal mufflrs, partitions wr built up around an inlt and an outlt. Th partition locatd around th outlt hlps incrasing th transmission loss valu at th targt frquncy bttr than th partition locatd around th inlt. An Intrnational Comprssor Enginring Confrnc at Purdu, July 16-19, 2012

5 1437, Pag 4 intrsting point is that th partitions ar built up blow th non-dsign domain conncting th inlt and th outlt. Th location of th partitions could not b found without th topology optimization basd dsign mthod. Figur 3 compars th transmission loss curvs of th four optimal mufflrs with th rfrnc mufflr ( V r = ) Tabl 1: Spcific valus usd in th optimization Symbols Physical manings Spcific valus ρ Dnsity of kg / m ρ rigid body Dnsity of rigid body c Sound spd in 343 m / s rigid body 7 kg / m c Sound spd in rigid body 3430 m / s x 12 Distanc btwn two points in th inlt m H Hight of th mufflr m W Width of th mufflr 0.14 m 3 (a) V r = (b) V r = (c) V r = (d) V r = Figur 2: Optimal topologis Intrnational Comprssor Enginring Confrnc at Purdu, July 16-19, 2012

6 Transmission Loss (db) 1437, Pag 5 70 V 60 r =0.00 V r = V r = V r = V r = Frquncy(Hz) Figur 3: Comparison of transmission loss curvs of four optimal mufflrs and th rfrnc mufflr. 4. CONCLUSIONS In this work, th topology optimization basd mufflr dsign mthod suggstd by L and Kim (2009b) was applid to a suction mufflr dsign problm. Optimal mufflrs wr obtaind for various volum ratios btwn partitions and mufflr. Th transmission loss valus at targt frquncy ar incrasd dramatically in th four optimal mufflrs compard with th rfrnc mufflr. Although th currnt approach was applid to twodimnsional mufflrs for rducing th computation tim, it could b applicabl to thr-dimnsional mufflr dsign problms without modification. REFERENCES Bndsø, M. P., Sigmund, O., 2004, Topology optimization-thory, mthods and applications, Springr, Nw York. Duhring, M. B., Jnsn, J. S., Sigmund, O., 2008, Acoustic Dsign by Topology Optimization, Journal of Sound and Vibration, vol. 317: p L, J. H., An, K. H., L, I. S., 2002, Dsign of th Suction Mufflr of a Rciprocating Comprssor, Procdings of Intrnational Comprssor Enginring Confrnc at Purdu, CD-ROM, C11-5. L, J. W., Kim, Y. Y., 2007a, Partition Hol Dsign for Maximizing or Minimizing th Fundamntal Eignfrquncy of a Doubl Cavity by Topology Optimization, Procdings of th 14th Intrnational Congrss on Sound and Vibration (ICSV14), CD-ROM. L, J. W., Kim, Y. Y., 2007b, Systmatic Dsign of an Expansion Chambr Mufflr Using a Topology Optimization Mthod, Procdings of Intr-nois 2007, CD-ROM. L, J. W., Kim, Y. Y., 2009a, Optimal Distribution of Hols in a Partition Intrfacing Two Cavitis for Controlling th Eignfrquncis by Acoustical Topology Optimization, Computr Mthods in Applid Mchanics and Enginring, vol. 198: p L, J. W., Kim, Y. Y., 2009b, Topology Optimization of Mufflr Intrnal Partitions for Improving Acoustical Attnuation Prformanc, Intrnational Journal for Numrical Mthods in Enginring, vol. 80: p L, J. W., Kim, Y. Y., 2009c, Rigid body modling issu in acoustical topology optimization, Computr Mthods in Applid Mchanics and Enginring, vol. 198: p Olsn, L. H., Okkls, F., Bruus, H., A High-Lvl Programming-Languag Implmntation of Topology Optimization Applid to Stady-Stat Navir-Stoks Flow, Intrnational Journal for Numrical Mthods in Enginring, vol. 65: p Intrnational Comprssor Enginring Confrnc at Purdu, July 16-19, 2012

7 1437, Pag 6 Slamt, A., Ji, Z. L., 1999, Acoustic Attnuation Prformanc of Circular Expansion Chambrs with Extndd Inlt/Outlt, Journal of Sound and Vibration, vol. 223(2): p Slamt, A., Radavich, P. M., 1997, Th Effct of Lngth on th Acoustic Attnuation Prformanc of Concntric Expansion Chambrs: an Analytical, Computational and Exprimntal Invstigation, Journal of Sound and Vibration, vol. 201(4): p Svanbrg, K., 1987, Th Mthod of Moving Asymptots: a Nw Modl for Structural Optimization, Intrnational Journal for Numrical Mthods in Enginring, vol. 24(2): p Svndsn, C., Møllr, H., 2005, Acoustic Optimization of Suction Mufflrs in Rciprocating Hrmtic Comprssors, Procdings of th 12th Intrnational Congrss on Sound and Vibration (ICSV12), CD-ROM. Wu, T. W., Wan G. C., 1996, Mufflr Prformanc Studis Using a Dirct Mixd-Body Boundary Elmnt Mthod and a Thr-Point Mthod for Evaluating Transmission loss, ASME/Journal of Vibration and Acoustics, vol. 118: p ACKNOWLEDGEMENT This rsarch was supportd by th Basic Scinc Rsarch Program through th National Rsarch Foundation of Kora (NRF) fundd by th Ministry of Education, Scinc and Tchnology (No ). Also, this rsarch was financially supportd by th Ministry of Knowldg Economy (MKE) and Kora Institut for Advancmnt of Tchnology (KIAT) through th Human Rsourc Training Projct for Stratgic Tchnology. Intrnational Comprssor Enginring Confrnc at Purdu, July 16-19, 2012