Transcript Cavitation Models Roman Samulyak, Yarema Prykarpatskyy

Cavitation Models
Roman Samulyak, Yarema Prykarpatskyy
Center for Data Intensive Computing
Brookhaven National Laboratory
U.S. Department of Energy
[email protected], [email protected]
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
The system of equations of compressible
hydrodynamics

   0
t
 v
    v  v  P  0
t
1
 v( v 2  e)
1
2
   (  v( v 2  e)  Pv)  0
t
2
P  P (  , e)
• The system is solved using the front tracking technique
for free surfaces
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
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
Simulation of the Mercury Splash
Schematic of the experiment
Mercury splash (thimble): experimental data
Mercury splash at t = 0.88, 1.25 and 7 ms after proton impact of 3.7
e12 protons
Mercury splash (thimble): numerical
simulation
I  3.7 x1012 protons / pulse
t  240  s
t  480  s
t  609  s
t  1.014 ms
Mercury splash (thimble): numerical
simulation
t  200 s
I  17 x1012 protons / pulse
t  515  s
t  810  s
t  1.2 ms
Increasing the spot size of the proton beam results in
a decrease of the splash velocities
I  17 x1012 protons/pulse
t  2 microseconds
The splash velocity of mercury depends linearly on the proton intensity
t  2 microseconds
Numerical simulations
Approximation
from experimental
data
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 Fabich’s thesis)
• Equation of states needs additional physics (better mechanism of mass transfer,
surface tension, viscosity etc.)
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 FronTier’s 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
b) Homogeneous method: use a continuous description of the liquidvapor gas mixture by means of homogeneous equation of state
models and the Rayleigh-Plesset equation for the average gas
bubble size evolution
RRtt 
3
1
2 1
1
2
R


R


 t D t
2
R
We  R R 3
 
  2
1

1

 R 3

  C p  0,
where
 D is the effective damping coefficient
We is the Weber number
 is the cavitation number
C p is the pressure term
Future problem: include terms describing the mass transfer due to
phase transitions
• 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.