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: NPS ARCHIVE 1997^0 <o CKOE, S. NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS INVESTIGATION OF A CONSTRICTED ANNULARACOUSTIC RESONATOR by Choe, Seok Yun June, 1997 Thesis Advisor: Anthony A. Atchley Co-Advisor Ralph T. Muehleisen Thesis C448826 Approved for public release; distribution is unlimited. UDLEYKNOX LIBRARY JONTEREY CA 93943-5101 DUDLEY KNOXLIBRARY NAVAL POSTGRADUATESCHOOL MONTEREY, CA93943-6101 REPORT DOCUMENTATION PAGE FormApprovedOMBNo.0704-0188 Publicreportingburdenforthiscollectionofinformationisestimatedtoaverage 1 hourperresponse, includingthetimeforreviewinginstruction,searchingexistingdatasources, gatheringandmaintainingthedataneeded,andcompletingandreviewingthecollectionofinformation. Sendcommentsregardingthisburdenestimateoranyotheraspectofthis collectionofinformation,includingsuggestionsforreducingthisburden,toWashingtonHeadquartersServices,DirectorateforInformationOperationsandReports, 1215Jefferson DavisHighway,Suite1204,Arlington,VA22202^1302,andtotheOfficeofManagementandBudget,PaperworkReductionProject(0704-0188)WashingtonDC20503. 1. AGENCYUSEONLY(Leaveblank) 2. REPORTDATE 3. REPORTTYPEANDDATESCOVERED June 1997 Master's Thesis TITLEANDSUBTITLE FUNDINGNUMBERS INVESTIGATION OF A CONSTRICTED ANNULAR ACOUSTIC RESONATOR AUTHOR(S) Choe, Seok Yun 7. PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES) PERFORMING Naval Postgraduate School ORGANIZATION MontereyCA93943-5000 REPORTNUMBER 9. SPONSORING/MONITORINGAGENCYNAME(S)ANDADDRESS(ES) 10. SPONSORING/MONTTORING AGENCYREPORTNUMBER 11. SUPPLEMENTARYNOTES Theviews expressed inthis thesis are those ofthe author and do notreflectthe official policyorpositionoftheDepartmentofDefenseortheU.S. Government. 12a. DISTRIBUTION/AVAILABILrrYSTATEMENT 12b. DISTRIBUTIONCODE Approvedforpublicrelease; distributionis unlimited. 13. ABSTRACT (maximum 200words) One topic ofcurrent interest in thermoacoustic research is an annular prime mover [Lin et al., J. Acoust. Soc. Am, 100, 2846 (1996)]. The starting point for this research is an investigation of a constricted annular resonator. A literature search of the field resulted in surprisingly few references. The results of analytic, numerical, and experimental investigations are presented. Introducing a constriction into an annular resonator splits each longitudinal ductmode intotwo modes, one of a higher frequency with a pressure antinode at the constriction and one at a lower frequency with a velocity antinode near the constriction. The lower mode is more sensitive to changes in the length and porosity ofthe constriction than the highermode. Overall agreement between measured and predicted mode shapes and resonance frequencies is very good. It was found that it is necessary to include end corrections at the constriction to get accurate agreement between measured and predicted results. 14. SUBJECTTERMS 15. NUMBER OF acoustics: annularresonator,endcorrections,modesplitting PAGES88 16. PRICECODE 17. SECURITY CLASSIFICA- 18. SECURITY CLASSIFI- 19. SECURITY CLASSIFICA- 20. LIMITATION OF TIONOFREPORT CATIONOFTHISPAGE TIONOFABSTRACT ABSTRACT UL Unclassified Unclassified Unclassified NSN7540-01-280-5500 StandardForm298(Rev. 2-89) PrescribedbyANSIStd.239-18298-102 11 Approvedforpublic release; distribution isunlimited. INVESTIGATION OFACONSTRICTEDANNULARACOUSTIC RESONATOR Choe, SeokYun LieutenantCommander, KoreanNavy B.S., KoreanNavalAcademy, 1987 Submittedinpartialfulfillment oftherequirementsforthedegreesof MASTEROFSCIENCE INENGINEERINGACOUSTICS fromthe NAVALPOSTGRADUATE SCHOOL June 1997 'UULfcYKNO/LibKARY DUDLEY KNOX library 4AVALPOSTGRADUATESCHOO NAVAL POSTGRADUATE SCHOOL 10NTEREY CA 93943-5101 MONTEREY, CA 93943-5101 ABSTRACT One topic of current interest in thermoacoustic research is an annular prime mover [Lin et al., J. Acoust. Soc. Am, 100, 2846 (1996)]. The starting point for A this research is an investigation of a constricted annular resonator. literature search of the field resulted in surprisingly few references. The results of analytic, numerical, and experimental investigations are presented. Introducing a constriction into an annular resonator splits each longitudinal duct mode into two modes, one of a higher frequency with a pressure antinode at the constriction and one at a lower frequency with a velocity antinode near the constriction. The lower mode is more sensitive to changes in the length and porosity ofthe constriction than the higher mode. Overall agreement between measured and predicted mode shapes and resonance frequencies is very good. It was found that it is necessary to include end corrections at the constriction to get accurate agreement between measured and predicted results. VI TABLE OF CONTENTS INTRODUCTION I. 1 H THEORY 3 INTRODUCTION A. 3 SOLUTION FORA UNIFORM ANNULAR RESONATOR B. 3 PLANE WAVE THEORY C. 7 1. Uniform Cross Section Annular Resonator Constricted Annular Resonator 8 a. Undrivencase 8 b. Driven case 10 2. Constricted Annular Resonator 11 a. Frequency vs area ratio(no driver) 11 b. Mode shapes ofa constricted resonator 15 D. POLE-ZERO ANALYSIS 23 1. Analysis 23 E. THERMO-VISCOUS DAMPING 26 F. END EFFECTS 27 HI. EXPERIMENTAL APPARATUS AND PROCEDURE 29 A. INTRODUCTION 29 B. EXPERIMENTAL APPARATUS 29 1. Resonator and Driver 29 2. Microphone 31 a. Installation ofmicrophones 31 b. Calibration ofmicrophones 33 3. Constriction 35 4. Electronic Instrumentation 37 vii EXPERIMENTAL PROCEDURE C. 40 1. Resonator Setup 40 2. Determining Resonator Characteristics 40 3. Data Collection 41 IV. RESULTS AND DISCUSSION 43 A. RESONANCE FREQUENCIES 43 1. Comparison ofMeasured Resonance Frequency with Calculated Results without End Corrections 45 2. Comparison ofMeasured Resonance Frequency with Calculated Results with End Corrections 46 B. MODE SHAPES 48 SUMMARY AND CONCLUSIONS V. 55 APPENDIX DATA TABLE & MODE SHAPE 57 LIST OF REFERENCES 77 INITIAL DISTRIBUTION LIST 79 Vlll