Cavitation Models

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Cavitation Models
Roman Samulyak, Yarema Prykarpatskyy
Center for Data Intensive Computing Brookhaven
National Laboratory U.S. Department of
Energy rosamu_at_bnl.gov, yarpry_at_bnl.gov
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Talk outline

• Modeling of the equation of state for two-phase
  fluid systems
• Numerical simulation of the interaction of
  mercury with a proton pulse in a thimble (BNL
  AGS and CERN ISOLDE experiments)
• Conclusions
• Future research

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The system of equations of compressible
hydrodynamics

• The system is solved using the front tracking
  technique for free surfaces

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Isentropic two phase EOS model for cavitating
liquid

• Approach connect thermodynamically consistently
  different models for different phases
• Pure liquid is described by the stiffened
  polytropic EOS model (SPEOS)
• Pure vapor is described by the polytropic EOS
  model (PEOS)
• An analytic model is used for the mixed phase
• SPEOS and PEOS reduced to an isentrope and
  connected by the model for liquid-vapor mixture
• All thermodynamic functions depend only on
  density

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• The EOS
• does not take into account drag forces, viscous
  and surface tension forces
• does not have full thermodynamics
• Current work on improved models will be
  discussed in section Future Research

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Simulation of the Mercury SplashSchematic of
the experiment
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Mercury splash (thimble) experimental data
Mercury splash at t 0.88, 1.25 and 7 ms after
proton impact of 3.7 e12 protons
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Mercury splash (thimble) numerical simulation
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Mercury splash (thimble) numerical simulation
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Increasing the spot size of the proton beam
results in a decrease of the splash velocities
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The splash velocity of mercury depends linearly
on the proton intensity
Numerical simulations
Approximation from experimental data
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Conclusions

• Numerical simulations show a very good agreement
  with experimental data at early time.

• The lack of full thermodynamics in the EOS leads
  to some disagreements with experiments for the
  time evolution of the velocity. Can be corrected
  by the energy deposition.

Experimental data on the evolution of the
explosion velocity (from Adrian Fabichs thesis)

• Equation of states needs additional physics
  (better mechanism of mass transfer, surface
  tension, viscosity etc.)

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Future Research

• Further work on the EOS modeling for cavitating
  and bubbly flows.
• a) Direct method study a liquid-vapor gas
  mixture as a system of one phase domains
  separated by free surfaces using FronTiers code
  interface tracking capability

a)

b)
c) Direct numerical simulation of
the pressure wave propagation in a bubbly liquid
a) initial density red mercury, blue gas
bubbles, b) initial pressure the pressure is
500 bar at the top and 1 bar at the bottom, c)
pressure distribution at time 100 microseconds
pressure is 6 bar at the bottom.
Future problem develop a nonlocal Riemann solver
for the propagation of free interfaces which
takes into account the mass transfer due to phase
transitions

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• b) Homogeneous method use a continuous
  description of the liquid-vapor gas mixture by
  means of homogeneous equation of state models and
  the Rayleigh-Plesset equation for the average gas
  bubble size evolution

Future problem include terms describing the
mass transfer due to phase transitions
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• Further studies of the muon collider target
  issues. Studies of the cavitation phenomena in a
  magnetic field.
• Studies of hydrodynamic aspects of the
  cavitation induced erosion in the SNS target.