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Multiparameter and Multiscale Problems with “Sharpening" in Cavitation

Multiparameter and Multiscale Problems with “Sharpening" in Cavitation. Robert I. Nigmatulin RUSSIAN ACADEMY OF SCIENCES P.P. Shirshov Institute of Oceanology nigmar@ocean.ru. The 5-th International Conference SOLITONS, COLLAPSES and TURBULENCE:

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Multiparameter and Multiscale Problems with “Sharpening" in Cavitation

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  1. Multiparameter and Multiscale Problems with “Sharpening" in Cavitation Robert I.Nigmatulin RUSSIAN ACADEMY OF SCIENCES P.P. Shirshov Institute of Oceanology nigmar@ocean.ru The 5-th International Conference SOLITONS, COLLAPSES and TURBULENCE: Achievments, Developments and Perspectives2- 7 August, 2009

  2. Shock Tube High pressure chamber Diaphragm Low pressure chamber Pressure Transducers

  3. pG Classic Equation of State Local Deformational Inertia of Bubbly Liquids

  4. Free volume oscillations of the spherical air bubble in water

  5. Thermophysical parameters in bubbly liquid a - radius of the bubbles (monodispersed mixture) n - number concentration of the bubbles - volume concentration of the bubbles (G < 0,1) - density of the liquid - densityof the gas - density of two phase mixture i- thermal conductivity of the liquid (i= L) and gas (i= G) сi- heat capacity of the liquid (i= L) and gas (i= G) Сi-sound speed in the liquid (i= L) and gas (i= G) G –adiabatic exponent of the gas L– viscosity of the liquid  -surface tension

  6. After Transformations for potential flow:

  7. No bubbles With bubbles 0 = 1% AMPLIFICATION OF SHOCKWAVES WHEN REFLECTINGFROM BUBBLY SHIELDS

  8. HPC p0 DIAPHRAGM 2m 5m 7m AMPLIFICATION OF SHOCK WAVES IN CLAY SUSPENSIONS(with bubbles) WATER+MONTMORILLONITE (6%, a~10-1mm) WATER+KAOLINITE (25%, a~1+10-1mm) 200 REFLECTION FROM WALL WATER+MONTMORILLONITE (15%, a~10-1mm)

  9. Multibubble & Single Bublle SONOLUMINESCENCE SBSL MBSL

  10. 20 m 0 0.0 65 13.3 95 19.4 150 30.6 180 36.7 Frame Time: s 20 m 185 37.7 190 38.7 199 40.6 204 41.6 209 42.6 Frame Time: s 20 m Frame Time: s 45 9.2 180 36.6 120 24.5 155 31.6 160 32.6 165 33.6 190 38.7 245 49.9 195 39.8 210 42.8 220 44.8 230 46.9 Frame Time: s Images of oscillating bubbles with SONOLUMINESCENCE Nonspherical shapes and NO SONOLUMINESCENCE

  11. dtC ~ 10-8s tw50s t w~ 30s 6 days dtC ~ 30 ns 7 min dtF ~ 50 ps 0,7 s SPECIFIC FEATURES OF SINGLE BUBBLE SONOLUMINESCENCE • Two parts of the period: • SLOW expansion and initial stage of compression • EXTREMELY FAST collapse with the «sharpening» • Equilibrium bubble size • a0 ~ 3 – 5 mm • Adiabatic temperature of the compressed gas Tmax ~ 5000 K (?!) • Noble gas effect a tw Radius of the bubble • Cold water effect a0 amin t Tmax ~ 5000 K (adiabatic compression • EXTREMELY SHORT light flashes !!! tF ~ 50 ps = (5 - 10) 10-11s Light emission →t   30 s→4 years →tFusion  0.2 ps→ 0.7 s dtF ~ 10-11- 10-10 s t

  12. SPHERICAL SHOCK WAVE CONVERGENCE AND CUMULATIONCollapsed Bubble as Micro-Hydrogen Bomb Initiation of a Spherical Shock Waveby the Convergent Interface • Selfsimilar Cumulation • of the Spherical Shock Wave from the Infinity • Guderley, 1942; • Nigmatulin, 1967 Micro-Hydrogen Thermonuclear Bomb with Deutorated Vapor Micro-Bubble? Focusing of the Spherical Shock Waveat the Center of the Bubble The Spherical Shock Waveafter the Reflectionfrom the Center of the Bubble

  13. SUPERCOMPRESSION BY CONVERGENT SPHERICAL SHOCK WAVE • W. Moss et al (Livermore National Laboratory, 1994) • Gasdynamic code for air bubble in water for single bubble sonoluminescence • (There are some principle errors in the code) • Radius of supercompressed and superhot plasma core:109 m = 1 – 3 nm • Density: 10 g/cm3 • Temperature: 106 K • Duration:  1011 s = 10 ps • FOR BUBBLE WITHDEUTERIUM (D2)or • FOR BUBBLE WITHDEUTORATED WATER VAPOR(D2O) • in heavy (deutorated liquid waterD2O) • MAXIMUM TEMPERATUREis afew time less • (They say that they don’t know how to take into account the phase transitions) No Thermonuclear Fusion

  14. HOW TO AMPLIFY THE SUPERCOMPRESSION? • AMPLIFING THE ACOUSTIC WAVE (pI  15-20 bar) • GAS IN THE BUBBLE:CONDENSING VAPOR (VAPOR CAVITATION) • - Minimizing Effect of Gas Cushioning • - Higher Kinetic Energy of Convergent Liquid • COLD LIQUID • – More Intensive Condensation • LARGE MOLECULES (ORGANIC) LIQUID • -Low Sound Speed in Vapor ( ), where MG ismolecular weight) • - High Condensation (Accommodation) Coefficient (  1, for water  0. 04) • - High Cavitation Strength • CLUSTER of the Bubbles: Two “sharpening”: • - in bubbly cluster • - in central bubbles

  15. Tritium and Fast Neutron Production R. Taleyarkhan, C. West, R. Lahey, R. Nigmatulin, R. Block, 2002- 2008. 14 12 Standart Deviation 10 8 T ~7105 s-1 6 4 Change in count, min-1 T ~ 4105 s-1 2 0 Background -2 -4 NPNG ~ 106 s-1, Nzone~ 10 сs-1 Е = 14 MеV fPNG = 200 sс-1 -6 0 2 4 6 8 10 12 14 Time (hours)

  16. CLUSTER of Microbubbles: Formation and Evolution Spherical Cluster d 1 cm 1 cm Loosing of Spherical Shape andLast Neutron emissions Acetone, T0 = 4C, p0 = 16.7 kPa p = 17 bars, Comet like streamers Duration  50 ms No strong Shocks on the Glass Wall Y. Xu & A. Butt,Confirmatory experiments for nuclear emissions during acoustic cavitation, Nuclear Engineering and Design, 2005

  17. The first approximations for the bubbles in the cluster r - Lagrangian radial macro-coordinate for two-phase continua in the cluster r – Eulerian radial micro-coordinate for the testing bubble x(r, t) – Eulerian radial coordinate for two phase r r  = L0(1 - G), 1  4.5 G R R. Nigmatulin, “Dynamics of Multiphase Flow”, Hemisphere, 1991 R. Nigmatulin, et al. TheTheory of Supercompression of Vapor Bubbles and Nano-Scale Thermonuclear Fusion, Physics of Fluids, Vol. 17, 107106, 1-31, 2005.

  18. Amplification of the Compression Wave in Cluster Объемное содержание пузырьков Number of bubbles N=50 Maximum microbubble radius Radius of the cluster a, m R 0.05 a = a = 400 mм 0max R = 4 мм 0 r = 0 r = 2mm r = 4mm t,s m p, bar p,bar t = 32 s m m t, s r,mm Nigmatulin, et al. TheTheory of Supercompres-sion of Vapor Bubbles and Nano-Scale Thermonuclear Fusion, Physics of Fluids, Vol. 17, 107106, 1-31, 2005. R. Nigmatulin“Dynamics of Multiphase Flow”, Hemisphere, 1991

  19. Low Mach Number Stage (microseconds) 0.12 a, m a, m/s a 6 800 7 5 600 0 8 4 400 9 1 0 200 40 1 1 3 2 1 1 2 1 4 0 80 t, s 0 1 0 2 0 3 0 4 0 G , kg/m3 310 0.3 TG , K 0.2 290 ° T G . 20 8 0 0.08 6 0 a r pG, bar a 4 0 b , I p 3 0.04 2 0 pG 1 p I 0 15-26 t° t° -20 0 0 1 0 2 0 3 0 4 0 t, s 330 mG, ng 200  ° m G 100 G 270 0.1 0 t, s t, s 0 1 0 2 0 3 0 4 0 0 1 0 2 0 3 0 4 0

  20. Interface (nanosecond stage) a , m La , kg/m3 14 18-26 15 4 0 16 17 2 0 a, km/s a 0 0 - 2 0 0 2 0 1 0 1 0 1 n s t - 2 TLa, K 1 0 2000 5 1 0 1000 4 1 0 t - t° = - 0.78 ns 3 0 1 0 2 0 - 0 0 1 0 2 0 - 0 0 0 , n t - t 2000 a Shock wave 1000 1 0 - 1 - - o , t 6 pLa, bar t - 1 - 1 1 o , n s s t - t o

  21. Shock jump and critical point (submicrosecond stage) 4 14 13 Critical point 11 3 1 0 1 0 14 Critical point 3 1 3 1 0 12 2 1 0 12 3 2 1 0 m r / a g b k , , 1 p 1 0 r 1 1 0 11 0 1 0 - 1 0 1 0 1 0 r, m 0 4 0 8 0 1 2 0 1 6 0 2 0 0 0 4 0 8 0 1 2 0 1 6 0 Shock jump r, m t11 =t- 0.25 s, t12 =t- 0.07 s, t13 =t- 0.04 s, t14 =t- 0.015 s, t 41.9932 s - minimum bubble radius - interface 0 4 0 8 0 1 2 0 1 6 0 2 0 0 0 . 0 1 6 0 0 1 4 - 0 . 4 11 1 2 0 0 12 - 0 . 8 w, km/s K 1 3 13 8 0 0 , Critical point 1 2 T - 1 . 2 14 11 4 0 0 - 1 . 6 - 2 . 0 0 r, m 0 4 0 8 0 1 2 0 1 6 0

  22. , kg/m3 BLOW UP“Sharpening” - 20 - 10 - 40 0 t - t*, 106 ps max 104 103 (4) Sh Sh 102 ad 101 100 - 30 0 - 0.5 0.5 t - t*, ps 0 min p, bar pmax 109 Sh 106 Evolution of density, pressure and temperature for r = r*, where maximum neutron production takes place 103 100 - 20 - 10 - 40 - 30 0 t - t*, 106 ps 10-1 pmin T , K Tmax 108 Sh 106 104 - 20 - 10 - 40 - 30 t - t*, 106 ps 0 -1 -0.5 0 0.5 t - t*, ps

  23. THERMO-NUCLEAR CORE 0.12 1010 Tmax T, K 108 TSh 0.08 Nr, nm-1 106 max ,kg/m3 0.04 104 . (4) Sh r * 102 ad min 0 20 40 60 80 r* 0 100 r, nm 1 1000 100 10 r, nm r* = 27 nm – Radius of the maximum neutron production rF≈ 60 nm – Radius of the Fusion Core Convolution: (×0)

  24. RESULTS OF ANALYSIS Sonoluminescence (Livermore) Bubble Fusion (Ufa Branch of RAS +ORNL+RPI) Density: 10-20 g/cm3 Temperature: 108 K = 10 KeV Pressure: 1011 bar = 102Gbar Velocity: 1000 km/s Density:10 g/cm3 Temperature:106K Pressure:3108 bar Velocity:10 km/s t 50 s→ 1 year t(M 1)  300 ns → 2 days t(Dis, Ion)  2 ns → 20 min tFusion0.2 ps→ 0.1 s Duration: 1013 – 10-12 s = 101 – 1 ps Radius of the Thermonuclear Core: 100 nm Number of Ions in the Thermonuclear Core: 2  109 Duration:10 ps Radius of theТ = 106 Кcore:1-3 nm Number of Ions in the Core: 2  105 Production of the Fast Neutrons and Tritium nucleus 105 - 106 s-1

  25. DISTURBANCES OF SPHERICALSHAPE DURING INTENSIVE COLLAPSE of VAPOR BUBBLE - - amplitude of disturbance (Legedre polynomial power i) 5 i = 2 3 4 Absolute instability 104  103 Disturbances 102 10 3 40 i 2 10 102103 104 Relative amplitude growth depending on i • LIQUID VISCOSITY (acetone) during collapse: • does not influence for growth of long wave disturbances for ; • kills short wave disturbances(, i> 40); • helps to save almost spherical shape of the bubble.

  26. The PARADOXES are MILESTONES in the space of SCIENCE PARADOX is a real phenomenon that contradicts ordinary insights, intuition and prejudices Bubbly Liquids are the most Paradoxical Fluids

  27. LONG LIVE VLADIMIR ZAKHAROV

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