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The Use of Acoustic Waveguides in Sound Detecting Systems "THE USE OF ACOUSTIC WAVEGUIDES IN SOUND DETECTING SYSTEMS" A Thesis submitted for the Degree of DOCTOR OF PHILOSOPHY in the UNIVERSITY OF LONDON by BRYAN WOODWARD, M.Sc., D.I.C., A.Inst.P. Department of Physics Imperial College of Science and Technology South Kensington LONDON, S.W.7. NOVEMBER, 1968. 2 ABSTRACT The study of the mechanisms by which a reverberant tank of water induces stress waves in semi-immersed, cylindrical, elastic waveguides has been carried out to provide information for the design of a safety device for the incidence of boiling in a nuclear reactor. At each tank resonance there is a distinct distribution of acoustic pressure throughout the volume of water, and it has been shown that - these pressure fields can actuate longitudinal vibrations in semi- immersed rods (and tubes). The vibration amplitude depends directly on the rod length, and is a maximum at the resonant lengths of the rod. The accelerations of the upper ends of these rods were measured • by means of a calibrated accelerometer and an attempt has been made to relate this to the acoustic pressure at the lower immersed end. However, there is also a contribution to the vibrations created by the spatially-varying acoustic pressure developed along the curved side of the rods, although it appears that the end-face contribution is predominant. In order to investigate more explicitly this "end- contribution" the curved surface of a wave guide rod was isolated from the surrounding water by an enclosing concentric tube. Investigations were also made on the influence of the form and of the physical dimensions upon the response of the waveguides. 3 ACKNOWLEDGEMENTS It is a pleasure to record my gratitude to Dr. R. W. B. Stephens of the Physics Department, Imperial College, for providing me with the opportunity to work for a Ph.D. degree, for the interest he has taken in the supervision of this research and particularly for his patient reading and constructive criticism of the thesis. Many other people in the Physics Department have given me consid- erable assistance, notably Mr. A. Sutherland, Mr. M. Oakey (Acoustics Group), and Mr. F. Martin (Student's Workshop) in the design and construction of the waveguide support mechanism; the Main Workshop staff under the direction of Mr. W. Shand, in build- ing the support and traverse framework and Mr. M. Jackson in photographic services. To all these people I convey my thanks. I wish also to express my thanks to the United Kingdom 'Atomic Energy Authority, the sponsors of this research, and to Mr. A. J. Walton, Mr. I. D. MacLeod and Mr. F. Latham for their advice and suggestions during the initial stages of the project at U.K.A.E.A. Risley, Lancashire. The final presentation of this work would have been impossible without the incalculable efforts of Joy Dunning who typed the thesis in its entirety. To her I am extremely grateful. I extend this gratitude to the members of the Acoustics Group who have enlightened the past two years by their geniality- and with whom I have had the good fortune to work. Finally I wish to extend my thanks to my family for their unfailing help and encouragement throughout the years. B.W. 4 CONTENTS Page No ABSTRACT 2 ACKNOWLEDGEMENTS 3 CONTENTS 4 INTRODUCTION 9 CHAPTER 1 REVIEW OF RESEARCH RELEVANT TO THE PRESENT 15 PROBLEM 1.1. Introductory Review 15 1.2. Reverberant Sound Fields 18 1.3. Sound Radiation from Cylinders Immersed in 29 Fluids 1.4. Coupling of Plane Waves to a Semi-Immersed 31 Waveguide 1.5. Coupling of Spherical Waves to an Immersed 34 Waveguide CHAPTER 2 PRESSURE FIELDS IN RESONANT ENCLOSURES 39 2.1. Pressure Field Configuration in Rectangular 39 Enclosures 2.2. Pressure Field Configuration in Cylindrical 45 Tanks 2.3. Description of the Co-ordinate System used 50 in the Experiments 5 Page No. CHAPTER 3 EXPERIMENTAL SYSTEM 52 3.1. Plan of Research 52 3.2. Description of Apparatus 54 3.3. Method of Supporting Waveguides 59 3.4. Pressure Transducer Mountings 64 3.5. Vibration Isolation and Noise Reduction 65 3.6. Mounting of Accelerometers 66 3.7. Choice of Waveguides 69 3.8. Calibration of Apparatus 70 (a) Level Recorder 70 (b) Microphone Amplifier 71 (c) Accelerometers 71 (d) Pressure Probes 71 3.9. Experimental Errors 75 (a) Frequency Readings 75 (b) Positioning of Waveguides and Probes 75 (c) Calibration Procedure 76 (d) Reading Signal Levels on Level Recorder 76 Paper CHAPTER 4 PRELIMINARY INVESTIGATION OF ACOUSTIC 80 FIELDS IN THE EXPERIMENTAL TANK 4.1. Justification of Experiments 80 4.2. Finding the Natural Resonance Frequencies of 82 the Tank 4.3. Variation of Acoustic Pressure with Position 85 of Probe: Source Transducer in Fixed Position (a) Variation in the z-direction 85 (b) Radial Variation 86 (c) Angular (0) Variation at a Constant 88 Radius 6 Page No. CHAPTER 4 CONTINUED 4.4. Variation of Acoustic Pressure with Position 92 of Driving Transducer: Probe in Fixed Posi- tion (a) Variation in the z-direction 92 (b) Radial Variation 93 4.5. Concept of "Effective Vessel Radius" 98 CHAPTER 5 USE OF SOLID ROD WAVEGUIDES AS SOUND 101 DETECTORS IN THE EXPERIMENTAL TANK 5.1. 'Introduction to Experiments with Solid Rods 101 5.2. Direct Measurements of Longitudinal Reson- 104 ance Frequencies of Solid Cylindrical Wave- guides 5.3. Identification of Peaks on Spectra for 110 Semi-Immersed Waveguides 5.4. Variation of Waveguide Response with Position 112 of Waveguide: Transducer in Fixed Position (a) Variation in the z-direction 112 (b) Radial Variation 113 5.5. Variation of Waveguide Response with Position 119 of Source Transducer: Waveguide in Fixed Position (a) Variation in the z-direction 119 (b) Radial Variation 120 5.6. Significance of Rod Dimensions 127 (a) Rods of the same Length but Different 127 Diameters (b) Dependence on Rod Length 130 5.7. Investigation of Energy Transfer Mechanism 139 between Acoustic Medium and Waveguide (a) Contribution of Plane End-Face of a 139 Rod (b) Contribution of Cylindrical Boundary 141 of rod Page No. CHAPTER 5 CONTINUED 5.8. Effect of Bending a Waveguide 148 5.9. Comparison of Responses for Similar Waveguides 151 off Stainless Steel, Copper, Brass and Dural- umin 5.10. Dependence of Probe and Waveguide Response on 153 Power of Source 5.11. Effect of Variation of the Angle of Immersion 155 CHAPTER 6 FURTHER QUALITATIVE EXPERIMENTS 159 6.1. Introduction 159 6.2. Comparison of Responses for Rods and Tubes 160 of the same length and material 6.3. Response of Finned Tube Waveguides 164 6.4. Use of an Accelerometer to Investigate Tank 168 Wall Vibration 6.5. Spiral Waveguide Characteristics 171 (a) Experimental Procedure 171 (b)Discussion 172 CHAPTER 7 INTERPRETATION OF RESULTS AND GENERAL 180 CONCLUSIONS 7.1. Forced Vibrations in a Semi-Immersed Wave- 180 guide (a) Discussion of the Problem 180 (b) Mechanism of Driving Force 181 (c) Damping 184 (d) Equation of Motion for Forced 184 Vibrations (e) Rate of Energy Supply to the Waveguide 186 8 Page No. CHAPTER 7 CONTINUED 7.2. Correlation of Acoustic Pressure and Wave- 188 guide Acceleration 7.3. Proposals for Further Study 191 1. Wire Waveguides 191 2. Phase Measurements 192 3. Horn Adaptor 192 4. Further Investigation of Energy 192 Transfer Mechanism 5. Pulse Propagation in Waveguides 193 6. Practical Design 193 APPENDIX I CALCULATION OF TANK RESONANCE FREQUENCIES 194 APPENDIX II PROGRAM TO COMPUTE "EFFECTIVE VESSEL RADIUS" 206 APPENDIX III PROGRAM TO COMPUTE YOUNG'S MODULUS AND 'Qs' 209 FOR WAVEGUIDES APPENDIX IV ACCELEROMETERS AND TRANSDUCERS 219 GLOSSARY 230 LIST OF SYMBOLS 231 REFERENCES 235 BIBLIOGRAPHY 239 9 INTRODUCTION The objective of this research was to provide information for designing an acoustical safety device to be used in the Proto- type Fast Reactor (PFR) under construction at Dounreay, in Caithness, Scotland. The PFR is a 250 Megawatt reactor due to be operational by 1971 and will act as a forerunner to reactors of perhaps 1000 MW or more which will be commissioned in the 1980s. In such a reactor the cooling agency is liquid sodium which has a normal working temperature between 400°C (at the inlet) and 600°C (at the outlet) but localized boiling may occur if there is a loss of coolant flow or if there is a power surge due to some perturbation of the nuclear reactivity. In order to avert a poss- ible fuel melt-down and subsequent release of fission products, various safety features must be incorporated, and it has been proposed that among these should be an acoustic waveguide acting as a detector of the signals produced by liquid boiling. The signals could then activate a Boiling Noise Detection System (BONDS) to shut down the reactor or operate a warning system. Unfortunately there is likely to be a significantly high level of background noise generated by sodium pumps and by cavitation nucleation and collapse. The low frequency pump noise may be fil- tered out but there remains the difficulty of distinguishing boiling noise from cavitation noise. Since both have essentially broad-band "white noise" spectra it is desirable to eliminate the cavitation noise which would otherwise occur all the time and activate the detection system. If this is possible the boiling noise alone can be detected 10 when the reactor becomes overheated. Wood (1963) has invest- igated this cavitation problem using carefully designed pumps with transparent casing so that the bubbles were visible. Experiments at Oak Ridge in the United States by Huntley et al (1966) and by MacPherson (1967) revealed that owing to its high tensile strength and surface tension, sodium does not boil without superheating it well above its, saturation temper- ature.
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