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NPS ARCHIVE 1997,O^ LIN, H. NAVAL POSTGRADUATE SCHOOL Monterey, California DISSERTATION AN ANNULAR THERMOACOUSTIC PRIME MOVER by Lin, Hsiao-Tseng September 1997 Thesis advisor: Anthony A. Atchley _ Thesis L640115 Approved for public release; distribution is unlimited. WJi OXLIBRARY OSTGRADUATESCHOOL ™n CA 03943-5101 ILEYKNI : OSTG'; UERF- REPORT DOCUMENTATION PAGE Formapproved OMB No.0704-188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate orany otheraspect ofthis collection ofinformation including suggestions for reducingthisburden,toWashingtonHeadquartersservices,DirectorateforInformationOperationsandReports, 1215JeffersonDavisHighway, Suite 1204,Arlington,VA22202-4302,andtotheOfficeofManagementandBudget,PaperworkReductionProject(0704-0188) Washington DC20503. 1.AGENCYUSEONLY (LeaveBlank) 2.REPORTDATE 3.REPORTTYPEANDDATES COVERED September 1997 Ph.D. Dissertation TITLEANDSUBTITLE FUNDINGNUMBERS 4. 5. ANANNULARTHERMOACOUSTIC PRIME MOVER AUTHOR(S) 6. Lin, Hsiao-Tseng PERFORMINGORGANIZATIONNAME(S) ANDADDRESS(ES) PERFORMING ORGANIZATION 7. 8. Naval Postgraduate School REPORTNUMBER Monterey, CA93943-5000 9.SPONSORING/MONITORINGAGENCYNAME(S)ANDADDRESS(ES) 10.SPONSORING/MONITORING AGENCYREPORTNUMBER SUPPLEMENTARY NOTES 11. The views expressed in this thesis are those oftheauthorand do notreflecttheofficial policy orposition ofthe DepartmentofDefense orthe U.S. Government. 12a.DISTRD3UTION/AVAILABILITYSTATEMENT 12b.DISTRIBUTIONCODE Approved forpublic release; distribution is unlimited. 13.ABSTRACT (Maximum 200words) The dissertation constitutes the first detailed theoretical and experimental investigation of a thermoacoustic prime mover with periodic boundary conditions. There are five significant aspects to this research: (1) using DeltaE to analyze an annular prime mover, (2) developing an entirely new analysis program using MATLAB, (3) designing, building, and experimentally investigating a single stack, annular prime mover, (4) experimentally investigating a constricted, single stack annular prime mover, (5) predicting the performance ofa two stack annularprime mover. The major conclusions are: (1) A single stack annular prime mover will not reach onsetbecause the eigenmodes ofthe system do not support thermoacoustic growth. (2) A constricted annular prime mover will reach onset because the constriction forces dominating boundary conditions that alter the eigenmodes. (3) A two stack prime mover is predicted to reach onset because one ofthe eigenmodes ofthe symmetric system does support thermoacoustics. 14.SUBJECTTERMS 15.NUMBER OFPAGES 249 Acoustics, Thermoacoustics, AnnularResonator, PrimeMover 16.PRICECODE 17.SECURITY CLASSIFI- 18.SECURITYCLASSIFI- 19.SECURITYCLASSIFI- 20.LIMITATIONOF CATIONOFREPORT CATIONOFTHIS CATIONOFTHIS ABSTRACT PAGE ABSTRACT UL Unclassified Unclassified Unclassified NSN7540-01-280-5500 StandardForm298 (Rev. 2-89) PrescribedbyANSIStd239-18 11 Approved for public release; distribution is unlimited. AN ANNULAR THERMOACOUSTIC PRIME MOVER Lin, Hsiao-Tseng Major, Republic of China Army B.S., Chung Cheng Institute of Technology in Taiwan, 1984 M.S., Naval Postgraduate School, 1989 Submitted in partial fulfillment of requirements for the degree of DOCTOR OF PHILOSOPHY IN ENGINEERING ACOUSTICS from the NAVAL POSTGRADUATE SCHOOL September 1997 7 AroWc PS 10 DUu: OXLIBRARY NJAVAi POSTGRADUATESCHOOL ABSTRACT The dissertation constitutes the first detailed theoretical and experimental investigation of a thermoacoustic prime mover with periodic boundary conditions. There are five significant aspects to this research: (1) using DeltaE to analyze an annular prime mover, (2) developing an entirely new analysis program using MATLAB, (3) designing, building, and experimentally investigating a single stack, annular prime mover, (4) experimentally investigating a constricted, single stack annular prime mover, (5) predicting the performance ofa two stack annularprime mover. The majorconclusions are: (1) A single stack annular prime mover will not reach onset because the eigenmodes of the system do A not support thermoacoustic growth. (2) constricted annularprime moverwill reach onset because the constriction forces dominating boundary conditions that alter the eigenmodes. A (3) two stackprime moveris predicted to reach onset because one of the eigenmodes of the symmetric system does support thermoacoustics. VI . .... TABLE OF CONTENTS INTRODUCTION I. 1 THEORY II. 11 A. REVIEW OFTHERMOACOUSTICS 12 B. COMPLEX EIGENFREQUENCY 19 C. THE ANNULAR GEOMETRY FOR A PRIMEMOVER 21 D COMPUTER SIMULATION OFTHE ANNULARPRIME MOVER 22 1 Problem Statement 23 2. DeltaE 24 MATLAB 3. Program 28 a. Approach 28 b. Description 32 c. Validation 33 E. END EFFECTS 44 1 Conformal Transformation Method 45 2 HigherOrderMode Method 46 . III. EXPERIMENTALAPPARATUS AND PROCEDURE 47 A. INTRODUCTION 47 B. EXPERIMENTAL APPARATUS 47 AnnularResonator System 47 1 2. Stack Assembly 49 3 Ambient HeatExchangerAssembly 50 4 Hot Heat Exchanger Assembly 51 . vn ..... 5 Stack/Heat Exchanger Assembly 59 6 Constriction 60 7 Microphones 62 8 Thermocouples Instrumentation 66 C. EXPERIMENTAL PROCEDURE 69 Resonator Setup 69 1 2 Determining Resonator Characteristic 70 . 3. DataCollection 71 IV. RESULTS AND DISCUSSION 73 A. ANNULAR PRIME MOVER 73 B. CONSTRICTED ANNULAR PRIME MOVER 91 C. TWO STACK ANNULAR PRIME MOVER 105 V. SUMMARY AND CONCLUSION 115 APPENDIX A. DELTAE INPUT FILE 117 APPENDIX A.l DELTAE INPUTFILE FORTHELOW MODE 117 APPENDIX A.2 DELTAE INPUT FILE FORTHE HIGH MODE 26 1 APPENDIX B. THE MATHEMATICA PROGRAM FOR THE LEAST SQUARE FIT TO THE FREQUENCY RESPONSE 135 APPENDIX C. THE MATLAB PROGRAM 137 APPENDIX D. PROPERTIES OF AF-45 GLASS .,..173 APPENDIX CONSTRUCTION DRAWINGS E. 175 vui