Table Of Content:
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
