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Nonlinear Propagation of High-Frequency Energy from Blast Waves”, in Innovations in Nonlinear Acoustics, ISNA 17, Edited by A

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Nonlinear Propagation of High-Frequency Energy from Blast Waves”, in Innovations in Nonlinear Acoustics, ISNA 17, Edited by A The Pennsylvania State University The Graduate School NONLINEAR PROPAGATION OF HIGH-FREQUENCY ENERGY FROM BLAST WAVES AS IT PERTAINS TO BAT HEARING A Thesis in Acoustics by Alexandra Loubeau °c 2006 Alexandra Loubeau Submitted in Partial Ful¯llment of the Requirements for the Degree of Doctor of Philosophy December 2006 The thesis of Alexandra Loubeau was reviewed and approved¤ by the following: Victor W. Sparrow Associate Professor of Acoustics Thesis Advisor, Chair of Committee Thomas B. Gabrielson Professor of Acoustics John S. Lamancusa Professor of Mechanical Engineering Anthony A. Atchley Professor of Acoustics Head of the Graduate Program in Acoustics ¤Signatures are on ¯le in the Graduate School. Abstract Close exposure to blast noise from military weapons training can adversely a®ect the hearing of both humans and wildlife. One concern is the e®ect of high- frequency noise from Army weapons training on the hearing of endangered bats. Blast wave propagation measurements were conducted to investigate nonlinear ef- fects on the development of blast waveforms as they propagate from the source. Measurements were made at ranges of 25, 50, and 100 m from the blast. Par- ticular emphasis was placed on observation of rise time variation with distance. Resolving the ¯ne shock structure of blast waves requires robust transducers with high-frequency capability beyond 100 kHz, hence the limitations of traditional mi- crophones and the e®ect of microphone orientation were investigated. Measure- ments were made with a wide-bandwidth capacitor microphone for comparison 1 with conventional 3.175-mm ( 8 -in.) microphones with and without ba²es. The 3.175-mm microphone oriented at 90± to the propagation direction did not have su±cient high-frequency response to capture the actual rise times at a range of 50 m. Microphone ba²es eliminate di®raction artifacts on the rise portion of the measured waveform and therefore allow for a more accurate measurement of the blast rise time. The wide-band microphone has an extended high-frequency re- sponse and can resolve shorter rise times than conventional microphones. For a source of 0.57 kg (1.25 lb) of C-4 plastic explosive, it was observed that nonlinear e®ects steepened the waveform, thereby decreasing the shock rise time, from 25 to 50 m. At 100 m, the rise times had increased slightly. For comparison to the measured blast waveforms, several models of nonlinear propagation are applied to the problem of ¯nite-amplitude blast wave propagation. Shock front models, such as the Johnson and Hammerton model, and full-waveform iii marching algorithms, such as the Anderson model, are investigated and compared to experimental results. The models successfully predict blast wave rise times at medium distances in a homogeneous atmosphere, although rise time predictions are shorter than what was measured in an inhomogeneous atmosphere. Atmospheric turbulence, absent in the models, may be the primary cause of this di®erence in rise times at longer distances. Results from the measurements and models indicate that bats located within approximately 200 m of the detonation of 0.57 kg of C-4 will be exposed to audible levels of high-frequency energy, but whether those levels could be damaging to bat hearing cannot be established at this time. iv Table of Contents Chapter 1 Introduction 1 1.1 Introduction ............................... 1 1.2 Endangered Bats ............................ 2 1.3 Explosions Overview .......................... 3 1.3.1 Gun Muzzle Blast Versus Explosion of a Charge . 4 1.4 Shock Rise Time De¯nition ...................... 6 1.5 Propagation of Blast Noise ....................... 8 1.5.1 Nonlinear Propagation ..................... 8 1.5.2 Previous Blast Wave Experiments . 10 1.5.3 Outdoor Sound Propagation . 11 1.5.3.1 Geometrical Spreading . 12 1.5.3.2 Atmospheric Absorption and Dispersion . 12 1.5.3.3 Ground Impedance . 13 1.5.3.4 Atmospheric Refraction and Sound Speed Variability 13 1.5.3.5 Atmospheric Turbulence . 14 1.6 Modeling Techniques for Nonlinear Wave Propagation . 14 1.6.1 Hydrodynamic Models ..................... 14 1.6.2 The Burgers Equation ..................... 15 1.6.3 Shock Front Models ....................... 15 1.6.4 Full Waveform Models ..................... 21 1.7 Research Objectives ........................... 23 Chapter 2 Preliminary Shock Width Model 24 2.1 Plane Wave Rise Time Model ..................... 24 2.2 Spherical Wave Shock Width Model . 26 2.2.1 Spherical Wave Shock Width Model Applied to Blast Waves 28 2.3 Summary of Preliminary Model Results . 29 v Chapter 3 Experimental Setup 31 3.1 Experimental Objective ........................ 31 3.2 Chronology of Field Experiments ................... 31 3.3 Microphone Equipment ......................... 34 1 3.3.1 3.175-mm ( 8 -in.) Microphones . 34 3.3.1.1 Unba²ed Con¯guration . 34 3.3.1.2 Ba²ed Con¯guration . 34 3.3.1.3 Di®raction Calculations . 35 3.3.2 Wide-bandwidth Capacitor Microphone . 37 3.4 Experimental Con¯guration ...................... 39 3.5 Meteorological Conditions ....................... 41 Chapter 4 Experimental Results 43 4.1 Spectrographic Analysis ........................ 45 4.2 Typical Measured Waveforms ..................... 45 4.3 Rise Time Comparisons ........................ 48 4.4 Sound-Exposure Levels (LE) ...................... 51 4.4.1 LE Measurements ........................ 52 4.5 Di®raction Corrections ......................... 56 Chapter 5 Computational Models of Blast Wave Propagation 61 5.1 Johnson and Hammerton Model Predictions . 61 5.1.1 Model Equations ........................ 61 5.1.2 Implementation ......................... 63 5.1.3 JH Model Results ........................ 65 5.1.4 Comparison to Polyakova et al. Model Predictions . 68 5.2 Anderson Model Predictions ...................... 68 5.2.1 Model Equations ........................ 68 5.2.2 Implementation ......................... 69 5.2.2.1 Absorption and Dispersion . 71 5.2.2.2 Step Size ....................... 72 5.2.2.3 Usage ......................... 73 5.2.3 Anderson Model Results .................... 74 5.2.4 Comparison to Shock Front Model Predictions . 78 vi Chapter 6 Comparison of Experimental Results to Model Predictions 80 6.1 Rise Time Comparisons ........................ 80 6.2 Atmospheric Turbulence E®ects on Rise Times . 83 6.3 Comparison to Bass et al. Predictions . 83 6.4 Histograms ............................... 87 6.5 Comparison to Preliminary Shock Width Model . 87 Chapter 7 Potential E®ects of Blast Waves on Bat Hearing 91 7.1 Rise Times and High-frequency Energy . 91 7.2 Research Findings of Brittan-Powell et al. 92 Chapter 8 Conclusions 93 8.1 Summary and Conclusions ....................... 93 8.2 Suggestions for Future Work ...................... 97 Appendix A Photographs from Blast Experiments 99 A.1 Microphone Ba²e Diagram ...................... 99 A.2 Photographs ...............................100 A.3 Blast Video ...............................119 Appendix B Johnson and Hammerton Model MATLAB Code 120 B.1 Introduction ...............................120 B.2 MATLAB Code .............................121 B.2.1 JH Model Program . 121 B.2.2 ODE Subroutine . 126 Appendix C Anderson Model MATLAB Code 127 C.1 Introduction ...............................127 C.2 MATLAB Code .............................128 C.2.1 Main Propagation Code . 128 C.2.2 Absorption Subroutine . 134 C.2.3 Example Plotting Program . 136 C.2.4 Rise Time Calculation Subroutine . 139 C.2.5 LE Subroutine . 141 vii Appendix D Microphone Calibrations 145 Bibliography 147 viii List of Figures 1.1 Bat audiogram showing maximum hearing sensitivity for the Big Brown Bat in the frequency range 10 kHz to 100 kHz. 3 1.2 Blast wave signature for an uncon¯ned explosion in free air. 4 1.3 Pro¯le of a frozen step shock as a function of time for a ¯xed position and graphical de¯nition of shock rise time. .............. 7 1.4 Pro¯le of a measured blast wave shock as a function of time, includ- ing the 10% and 90% points used to calculate the rise time. 8 1.5 Additional spreading due to nonlinearity reported theoretically by Naugol'nykh et al. and empirically by Reed. 10 1.6 Waveform predicted by Polyakova et al. analytical model for a sta- tionary wave in a monorelaxing fluid. Comparison of multivalued asymptotic result and correction with weak shock theory. 17 1.7 Comparison of numerical and asymptotic solutions of Eq. 1.8 at three di®erent length scales. Parameters used are ¢1 = 0:1, ¿1 = 1, ¡5 ¢2 = 0:2, ¿2 = 0:01, and ± = 5 £ 10 . Adapted from Johnson and Hammerton. ............................... 20 2.1 Comparison of total absorption ®total, thermoviscous absorption ®tv, nitrogen relaxation absorption ®r;N, and oxygen relaxation absorp- ± tion ®r;O as a function of frequency. Atmosphere at 20 C, 40% relative humidity, and 1 atm ambient pressure. 26 2.2 Rise time of a plane wave vs. shock overpressure comparison for calculations with ®tv and ®total. .................... 27 2.3 Rise time of a spherical wave vs. range for di®erent source pressure values. Source frequency is 10 kHz, with an atmosphere at 20±C, 40% relative humidity, and 1 atm ambient pressure. 29 2.4 Characteristic frequencies as a function of range from a 10 kHz spherical source of 170 dB at 1 m. Calculated using ®tv. Atmo- sphere at 20±C, 40% relative humidity, and 1 atm ambient pressure. 30 ix 3.1 Unba²ed 3.175-mm microphone mounted on a measurement pole at 90 ±. .................................. 35 3.2 Ba²ed 3.175-mm microphone mounted on a measurement pole at 0 ±. 36 3.3 Synthesized ba²ed waveform comparison. The upper waveform (unba²ed) is doubled and summed with the middle waveform (de- layed), yielding the waveform in the lower plot. Synthesized wave- forms from both circular and square ba²ed assumptions are com- pared to a ba²ed measurement. .................... 38 3.4 Wide-band microphone and preampli¯er mounted on a measure- ment pole at 0 ±. ............................. 39 3.5 Composition C-4 plastic explosive folded in half with blasting cap inserted. ................................. 40 3.6 Experimental setup with microphones mounted on poles at 25, 50, and 100 m.
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