1 / 51

Ocean Acoustics: Intense Sounds & Non-Linear Phenomena

This lecture explores the behavior of intense sounds in ocean acoustics, including non-linear phenomena such as shock waves, cavitation, and parametric sources. It also examines the equation of state and wave growth in relation to sound intensity.

gillj
Download Presentation

Ocean Acoustics: Intense Sounds & Non-Linear Phenomena

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ORE 654Applications of Ocean AcousticsLecture 5Intense sounds: non-linear phenomena Bruce Howe Ocean and Resources Engineering School of Ocean and Earth Science and Technology University of Hawai’i at Manoa Fall Semester 2011 ORE 654 L5

  2. Summary • All previous discussion assumed infinitesimal amplitude • Extraordinary behavior when pressures large • Steepening of wave slopes to produce shocks • Streaming • “parametric” sources – two high frequencies beat to produce high intensity pencil beam ORE 654 L5

  3. Intense sounds: non-linear phenomena • Harmonic distortion and shock waves • Cavitation • Parametric, difference frequency, sources • Acoustic radiation pressure • Acoustic streaming • Explosives as sound sources • Any non-linear system – with high/finite amplitude – harmonics and subharmonics; sum and difference frequencies, from basic physics or less-than-ideal systems • Perturbations in, say density, no longer small, need to include higher order terms ORE 654 L5

  4. Speed of sound pressure • Sound speed is function of ambient pressure • Hooke’s Law - linear Stress (pressure change) and strain (density change) - slope determines c • Bulk modulus of elasticity E • Slope - sound speed - is a function of ρA • Slope and speed increase with ρA density ORE 654 L5

  5. Equation of state • To calculate c, need analytic relation for equation of state • This form of equation (adiabatic – no heat exchange) is well known for gases; Γ is the ratio of specific heat at constant pressure to specific heat at constant volume; K depends on units and atomic mass of gas • For water, p includes not only external pressure, but an internal cohesive pressure of ~ 3000 atm. Γ and K not ratio of specific heats but must be determined empirically ORE 654 L5

  6. Include higher order term • Differentiate to get sound speed at ambient density, and therefore c • Expand density in Taylor series and substitute • Approximate by first two terms of binomial expansion • Thus c reduces to cA if density changes very small ORE 654 L5

  7. Alternative form for equation of state • Latter is empirical, can try a different curve fit – power series (Beyer, 1975) • Equate with previous (equivalent), slightly different interpretation • B/A – “parameter of nonlinearity” used in high intensity studies • Water B/A = 5.0 at 20°C and 4.6 at 10°C • Air Γ = 1.4, B/A = 0.40 ORE 654 L5

  8. Steepening of waves • Expression for u from earlier (acoustic Mach number definition et al.) • Signal speed u + c • Faster where pressure is locally high and vice versa ORE 654 L5

  9. Harmonic distortion and shock waves • Signal speed u+c • Faster than cA where pressure is locally high and vice versa • Different signal speeds at different parts of wave • Advance of crests relative to troughs • Sawtooth / repeated shock • Loss of energy from fundamental to harmonics • Then high frequencies dissipate due to absorption Distance from source increasing ORE 654 L5

  10. Wave growth • On axis particle travels • Δx1 =cA Δt • Peak of wave travels Δx2 in same time interval • ΔX crest advance relative to axis • Assume distorted wave is fundamental + 2nd harmonic • The peak has zero slope • For small kx (i.e., kΔX), sin(kΔX) ≈ kΔX and cos(kΔX) ≈ 1 • Relative strength of 2nd harmonic P in terms of fundamental P ORE 654 L5

  11. Wave growth2nd harmonic pressure • Use basic definition of c2 = (Δp/Δρ) and say P1 ~ Δp • For plane waves 2nd harmonic growth ~ • square of fundamental P1 and • number of wavelengths progressed by fundamental kX • This for unattenuating plane wave • Spherical waves diverge, will require greater initial amplitudes to achieve same degree of distortion ORE 654 L5

  12. Wave growth - numbers • For water B/A = 5, β = 3.5 • For air B/A = 0.4 and β = 1.2 • Strongest factor is denominator – factor 16,000 larger for water • Net effect – for same fundamental pressure, 2nd harmonic grows grows to same magnitude in a distance 1/5000 as far in air as in water, or conversely, 5000 times as far in water ORE 654 L5

  13. Wave growth – how far to formation of shock wave? • Say shock wave formed when 2nd harmonic is half the fundamental • Distance for this case? • Sawtooth wave real situation; with diverging spherical wave happens at larger range • Distance ~ 1/Mach, 1/non-linearity, ~ wavelength • Must take into account absorption (not here) • Saturation limits sound energy that can be input • More energy – more harmonics – more loss • Higher intensity axial beam attenuated more, beam broadens ORE 654 L5

  14. Wave growth - saturation • Saturation limits sound energy that can be input • If linear, lines/curves 45° • Lines at right asymptotic limits • For 10 m case, actual level is about 6 dB less than linear at ~550 kPa (~235 dB re 1 μPa) ORE 654 L5

  15. Donald Ross Cavitation • In rarefaction/tension phase, pressure can go “negative” and the medium ruptures • Small bubbles always present near sea surface are the nuclei for rupture initiation • From Bernoulli effects/propeller blades (mixture of dipole and monopole) • Life processes (snapping shrimp) • Increases chemical activity • Erode metals, plastics, stones (kidney), … • Light production – sonoluminescence • Very high pressure, 30,000 K • Picosecond light pulses ORE 654 L5 Brian Pollack

  16. Cavitation - 2 • As sound levels rise, bubble resonance, harmonics generated • Bubbles generate subharmonics if driven near 2 x resonance • 5% harmonic distortion for signals > 0.1 atm • If peak p > 1 atm (105 Pa = 220 dB re 1 μPa) • Negative pressure is trigger for sharp increase in distortion and broadband noise, if CW f < 10 Hz • Function of f, duration, repetition, nuclei • If drive too hard, generate bubbles that decrease far-field sound propagation • Gaseous cavitation - streaming bubble clouds jet away from generation site (relative amounts of gas and water vapor ~ constant) • Vaporous cavitation – collapse of single bubbles - radiates shock waves of broadband noise ORE 654 L5

  17. Cavitation - 3 • Nuclei often bubbles trapped in cracks/crevices of solid particles • Grow by “rectified” diffusion • Start with small bubbles < 1 μm • More gas diffuses into the bubble during expansion than out during contraction when surface area smaller (more time is spent large than small) • At a critical radius, will grow explosively • Threshold definition – distortion/harmonics and/or broad band noise • Above 10 kHz, steep increase in amount of CW pressure amplitude to produce cavitation • Large differences for “pure” water and tap or seawater ORE 654 L5

  18. Cavitation - 4 • Ocean-going transducer – regions on face that exceed cavitation pressure limits, combined with near surface bubbles • “hot spots” – p > nominal • Can have greater source levels at depth, high ambient pressure effectively inhibits cavitation • Fewer cavitaiton nuclei • Smaller nuclei • Streaming moves bubbles to new locations ORE 654 L5

  19. Cavitationpulse duration and duty cycle • Pulse duration < 100 ms, average acoustic intensity required for 10 % distortion is >> than CW • At low duty cycle can drive harder cavitation 10%  Duty cycle ORE 654 L5

  20. Parametric, difference frequency, sonars • If two distinct intense sound beams are co-axial at different frequencies, non-linearity creates sum and difference frequencies • Each beam modulates the other • E.g., 500 and 600 kHz produce 100 kHz and 1100 kHz • “parametric” or virtual sources distributed along intense portion of interacting beams ORE 654 L5

  21. Parametric, difference frequency, sonars - 2 • Difference frequency – lower frequency (less absorption) • very narrow beam, ~same width as for the primaries (but with smaller transducer) • Acts as if a highly directional end-fire array (“virtual end-fire array”) • Bandwidth of difference frequency very large ORE 654 L5

  22. Parametric, difference frequency, sonars - 3 • Two signals (ignore x or observing location kx = nπ) • Instead of amplitude at a point being simple sum, amplitude of p1 will be modulated by p2 • Last term – non-linear interaction, strength m(P1,P2) • Non-linear interaction has produced sum and difference frequencies ORE 654 L5

  23. Parametric, difference frequency, sonars - 4 • These sum and difference frequencies generated at all points of intense interaction along beam • Analogous to a line array of sources - end-fire ORE 654 L5

  24. Parametric, difference frequency, sonars - 5 • More detailed analysis • Re-cast wave equation for secondary or “scattered” pressure, with non-linear source term • Westervelt’s wave equation for non-linear secondary tones • Assume two primaries with attenuation (they die off quickly) • Get get 2nd (and higher) harmonics and sum and differences • Difference frequency generated whenever P1P2 large, contribution from beam near source largest • Once generated – launched, “on its own” (Huygen’s wavelets along beam) • Primary and sum frequencies die off ORE 654 L5

  25. Parametric, difference frequency, sonars – 6 • Narrow beam pattern (high directional resolution with small transducer) • Beamwidth relatively insensitive to changes in difference frequency • No side lobes in Dd (secure acoustic comms) • Inherent broad bandwidth • Projector cavitation not a problem ORE 654 L5

  26. Parametric, difference frequency, sonars - 7 • Increase in bandwidth • BW of a primary typically ±5% • f1 = 418 ± 21 kHz; f2 = 482 ± 24 kHz • fave = 450 ± 22.5 kHz • fdiff = 64 kHz ± 22.5 kHz - ±35% ORE 654 L5

  27. Parametric source example • Given 2 f’s, what is beam width? • What size piston to produce the LF? • What size piston needed? • What is the reduction in source radius for same beamwidth? ORE 654 L5

  28. Parametric source efficiency • Same power W and pressure P • Power radiated through primary beam area S0 • On-axis rms Pd (using beam width) • Average intensity ~ P2d ORE 654 L5

  29. Parametric source example • For preceding parameters, P1=100W • Efficiency = 0.7% • Increase efficiency: • Increase difference frequency • Increase power • Decrease beamwidth (lower primary frequency with constant beam area – larger transducer) • Only Power increase without sacrificing advantages – limit by saturation effects and beam broadening and cavitation • Level can be increased by non-linear oscillation of bubbles, but some loss in radiation directionality • Used for sub-bottom profiling ORE 654 L5

  30. Tritech SeaKing Parametric SBP Sub-Bottom Profiler • Primary frequency 200 kHz • Primary beamwidth 4 degrees • Low frequency 20 kHz • Low frequency beamwidth 4.5 degrees • Pulse length 100 μseconds • Range resolution of HF Dependent upon rangescale (10-100mm) • Range resolution of LF Dependent upon rangescale (60 μseconds@30m) • Power requirements 24VDC @ 410mA (Nominal for DST model) • Transducer 200 mm diameter • Weight in air 6.3kg • Weight in water 2.7kg • Maximum operational depth 4000m ORE 654 L5

  31. Acoustic streaming • Non-linear – harmonic distortion and shocks • Can also cause unidirectional flow • “quartz wind” outward jetting or drift of water in front of transducer • Strongest on axis, distances of meters • Can be >1000 acoustic velocity • Eddy/recirculate/3-D ORE 654 L5

  32. Movie -1 ORE 654 L5

  33. Movie - 2 ORE 654 L5

  34. Acoustic streaming – radiation pressure • Langevin radiation pressure = average momentum carried through unit area in unit time = time average of momentum per unit volume ρAu by particle velocity u (U = rms velocity) • This also = average energy density in beam = <ε> = average intensity / cA ORE 654 L5

  35. Acoustic streaming – momentum transfer • Spatial change in momentum – absorption / dissipation • Newton’s 2nd law – rate of change of momentum per unit area is force per unit area or change in pressure ΔPAacross slab dx • Loss of acoustic pressure in path dx creates pressure gradient causing flow • Or, loss of momentum in acoustic beam made up with gain in momentum of fluid mass – conservation of momentum • Bubbles on a transducer face – cavitation, asymmetric toroid produces destructive jet into wall, but superimposed on mean flow pattern ORE 654 L5

  36. Acoustic streaming velocity u2 • Non-linear – magnitude proportional to intensity – Eckart, 1948 • For ideal beam in a tube P(r) = P for r<a and P(r) = 0 for a0≥r≥a • a = radius of non-divergent sound beam • a0 (larger) radius of tube • Measurements -> calculate bulk viscosity μ’ from intensity and streaming velocity • Liebermann (1949) helped resolve difference between theoretical and experimental values of attenuation • For fluids in general ORE 654 L5

  37. Explosives as sound sources • TNT etc ~ 4,400 J/g = 1050 cal/g • Rapid reaction/detonation – 3000 °C, p ~ 50,000 atm • Detonation velocity 5,000 - 10,000 m/s • Gunpowder – burning – 0.3 m/s, slowly growing • Two sources of sound • The shock wave ~ half the energy, propagates at > cA • Large oscillating gas bubble / gas globe ORE 654 L5

  38. Explosives as sound sources ORE 654 L5

  39. Shock wave • Instantaneous rise in pressure Pm • Then exp decay, time constant τs s • Both scale by (w1/3/R) – w weight of explosive kg, R range m • Common SUS 0.82 kg • No attenuation exponents 1 and 0 • Absorption and non-linearity ORE 654 L5

  40. Shock front propagation; the Rankine-Hugoniot equations • Earlier wave equation – infintesimal waves • Conservation of mass • Conservation of momentum • Water only slightly compressible so density ratio ~ 1 • Shock speed U depends on average slope dp/dρ in p(ρ) • Speed of sound of peak cm depends on local incremental slope ORE 654 L5

  41. Shock front velocity • Need equation of state and conservation of momentum • Speed of shock u + c can be > c ORE 654 L5

  42. Gas globe • Contains chemical gas products and water vapor • Contains half total energy of explosion • Initial acceleration, expands, decelerates, continues past radius where internal p equals external, reaches maximum radius with internal p less than external, bubble contracts, oscillates, produces bubble pulses • Period of oscillation f(energy after shock, ambient pressure and density) • Assume spherical, need partition of non-shock energy, Y ORE 654 L5

  43. Gas globe - frequency • Assume spherical, need partition of non-shock energy, Y (Joules) • At maximum radius am, KE is zero, internal energy << PE • Assume all non-shock energy (~1/2 explosion energy) Y is PE • Period of spherical bubble in ambient (future derivation) • Substitute • Period T ~ depth and yield • Real – • not spherical (large ambient p difference) • often splits in two because of dimpling • Non-sinusoidal oscillation • Frequency changes as bubble rises ORE 654 L5

  44. Interaction with ocean surface • Reflections off surface, phase reversed • “noise” after reflection – under tension/negative pressure – cavitation, microbubbles radiate, causes reflected shock to loose energy ORE 654 L5

  45. Perth-Bermuda - 1960 • 300 lb TNT (4400 J/g) • 1000 m deep • w = 136 kg • R = 1 m • Pm = 318 MPa • τ = 0.0002 s • PA = 107 Pa (1000 m) • Y = 3x108 J • am = 1.9 m • T = 0.06 s ORE 654 L5

  46. Explosion test facility • Brett et al., An experimental facility for imaging of medium scale underwater explosions, DSTO-TR-1432, 2003 • Defense Science and Technology Organization, Australia • Near Melbourne ORE 654 L5

  47. Video • 0.5 kg • 1 ms resolution • Frame 4 – shock wave causes cavitation on camera window at 4 ms • Initial phase spherical and smooth (note sunlight) • During contraction – asymmetric, flattened base – pA(z) • Bubble rises about 0.4 m ORE 654 L5

  48. P(t) • Rapid expansion and collapse near minimum radius • Slow at maximum radius • Rmax – 1.14 m, rmin – 0.27 m in 97 ms • 6.1 m3 in 0.09 s – 6 tons • 68 m3/s • Vmax = 3.6 m/s • Hydrophone 4.5 m range • Shock wave, bubble pulse at min radius • Surface reflect at 4.5 ms, walls/floor 13-19 ms ORE 654 L5

  49. ORE 654 L5

  50. ORE 654 L5

More Related