Constraints from the implosion
Pascal Vernin, CEA/DSM/IRFU/SPP Saclay
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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CONSTRAINTS FROM THE IMPLOSION
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Risk of sympathetic implosion (SuperK…)
Only very little data on deep sea implosions of 17” empty glass spheres from
the literature:
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S.O. Raymond (Benthos Cie.) 1975
M. Orr et al 1976  2600 to 3600m, yield=21%
P.W. Gorham et al (DUMAND) 1992  4140 to 4470m, yield=45%
P. Duformentelle, IFREMER internal note (ANTARES) 2000 1200m, yield=9.5%
Yield=(sound total energy) / (potential energy of the implosion)
Potential energy of the implosion= P x V
-P= ambiant hydrostatic water pressure
-V=empty volume inside the glass sphere
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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CONSTRAINTS FROM THE IMPLOSION
• Calculation of the sound wave total energy from
the measured time profile of the pressure signal:
-time-integrate the square of the pressure energy
surface density on the surface of the wave
-assume it is isotropic (need the distance),
-neglect the viscous attenuation of the sound (just
p~1/r)
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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CONSTRAINTS FROM THE IMPLOSION
• P.W. Gorham et al. conclusion:
“A simple qualitative analysis of the development of
the shock wave also indicates that the shock
conditions, requiring supersonic collision of the
infalling material, are strongly satisfied in such an
implosion event.”
Was the infall velocity supersonic in the DUMAND
conditions?
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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A SIMPLIFIED MOFEL FOR THE IMPLOSION
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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RESULT OF THE GEOMETRICAL MODEL
c=1500 m/s ct=0.75m for t=0.5 ms
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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THE INFALL VELOCITY IS INFINITE AT THE END OF THE FILLING
A finite flaw inside a pipe which cross section tends to zero has a
velocity which tends to infinity
stop the filling when the water reaches the volume occupied by
the residual materials
take into account the inertia of the water
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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IMPROVED IMPLOSION MODEL
If we adopt the spherical symmetry, it becomes a
simple one-dimensional shock wave problem
-divide the radius in mm size steps (meshs)
-divide the time in us steps
-apply to the mesh of water the equations of the
mechanics (F=mg) during a step of time
-use a way to stabilize the integration (trick!)
-17” empty sphere: R from 216mm133mm
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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TEST THE VALIDITY OF THE INTEGRATION
The conservation of the mass is built inside the code (moving mesh)
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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ANOTHER DEPTH
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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RESULTING INFALL VELOCITY AT THE END OF THE FILLING
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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CONCLUSION
There is no sound wall at the bottom of the
sea!
(An internal note is coming soon)
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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CONSTRAINTS FROM THE IMPLOSION
Pascal Vernin CEA DSM Irfu Saclay KM3net WP meeting Paris 23/02/2009
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