View
22
Download
0
Category
Preview:
DESCRIPTION
ARIES Project Meeting on Liquid Wall Chamber Dynamics May 5-6, 2003, Livermore, CA. Numerical Simulation of Hydrodynamic Processes in High Power Liquid Mercury Targets Roman Samulyak Center for Data Intensive Computing Brookhaven National Laboratory U.S. Department of Energy rosamu@bnl.gov. - PowerPoint PPT Presentation
Citation preview
Brookhaven Science AssociatesU.S. Department of Energy
ARIES Project Meeting on Liquid Wall Chamber DynamicsMay 5-6, 2003, Livermore, CA
Numerical Simulation of Hydrodynamic Processes in High
Power Liquid Mercury Targets
Roman SamulyakCenter for Data Intensive Computing
Brookhaven National LaboratoryU.S. Department of Energy
rosamu@bnl.gov
Brookhaven Science AssociatesU.S. Department of Energy
Talk outline
Theoretical and numerical ideas implemented in the FronTier-MHD code. Numerical example: the 3D Rayleigh-Taylor instability problem.
Numerical simulation of hydro and MHD processes in the Muon Collider Target.
Cavitation modeling and numerical simulation of CERN neutrino factory target experiments. Further development of cavitation models and the simulation of hydrodynamic processes in the SNS target.
Brookhaven Science AssociatesU.S. Department of Energy
The system of equations of compressible magnetohydrodynamics:
an example of a coupled hyperbolic – parabolic/elliptic subsystems
2
2
1
1
40
t
Pt c
U Pt
ct
u
u u X J B
u u J
B u B B
B
Brookhaven Science AssociatesU.S. Department of Energy
Constant in time magnetic field approximation
The distribution of currents can be found by solving Poisson’s equation:
1
1 ,
1with ( )
c
c
c
J u B
u B
u B nn
Brookhaven Science AssociatesU.S. Department of Energy
Numerical methods for the hyperbolic subsystem. The FronTier Code
The FronTier code is based on front tracking. Conservative scheme.
Front tracking features include the absence of the numerical diffusion across interfaces. It is ideal for problems with strong discontinuities.
Away from interfaces, FronTier uses high resolution (shock capturing) methods
FronTier uses realistic EOS models: - SESAME - Phase transition (cavitation) support
Brookhaven Science AssociatesU.S. Department of Energy
Resolving interface tangling by using the grid based method
3D: We reconstruct the interface using micro-topology within each rectangular grid cell. There are 256 possible configurations for the crossings of the cell edge by the interface. Through elementary operations of rotation, reflection and separation these can be reduced to the 16 cases shown on the left.
Brookhaven Science AssociatesU.S. Department of Energy
Methods for the parabolic/elliptic subsystem
Triangulated tracked surface and tetrahedralized hexahedra conforming to the surface. For clarity, only a limited number of hexahedra have been displayed.
• Finite elements based on vector (Whitney) elements.
• Dynamic finite element grid conforming to the moving interface. Point shifting method with rectangular index structure.
Brookhaven Science AssociatesU.S. Department of Energy
Whitney elements
Let be a barycentric function of the node i with the coordinates xi
i
Whitney elements of degree 0 or “nodal elements”:
inijw
Whitney elements of degree 1 or “edge elements”:
ijjieijw
Whitney elements of degree 2 or “facet elements”:
jikikjkjifijkw 2
Brookhaven Science AssociatesU.S. Department of Energy
Elliptic/Parabolic Solvers
• 3D version of the Chavent -Jaffre mixed-hybrid finite element formulation.
• Instead of solving the Poission equation,
we solve for better accuracy.
1 , c
u B E
E
BE )u(1c
• The parallel solver is based on the domain decomposition. Linear systems in subdomains are solved using direct methods and the global wire basket problem is solved iteratively.
Brookhaven Science AssociatesU.S. Department of Energy
FronTier simulation of a 3D Rayleigh-Taylor mixing layer
Brookhaven Science AssociatesU.S. Department of Energy
Applications: Muon Collider Target
Numerical simulation of the interaction of a free mercury jet with high energy proton pulses in a 20 T magnetic field
Brookhaven Science AssociatesU.S. Department of Energy
Simulation of the Muon Collider target. The evolution of the mercury jet due to the proton energy deposition is shown.
No magnetic field.
t = 0
t = 80
Brookhaven Science AssociatesU.S. Department of Energy
Brookhaven Science AssociatesU.S. Department of Energy
MHD simulations: stabilizing effect of the magnetic field.
a) B = 0b) B = 2Tc) B = 4Td) B = 6Te) B = 10T
Brookhaven Science AssociatesU.S. Department of Energy
Velocity of jet surface instabilities in the magnetic field
Brookhaven Science AssociatesU.S. Department of Energy
Evolution of a liquid metal jet in 20 T solenoid
Brookhaven Science AssociatesU.S. Department of Energy
Equation of state: the problem of cavitation
Material properties strongly influence the wave dynamics. The wave dynamics is significantly different in the case of cavitating flows.
The one-phase stiffened polytropic EOS for liquid led to much shorter time scale dynamics and did not reproduce experimental results at low energies.
An important part of our research is EOS modeling for cavitating and bubbly flows.
Brookhaven Science AssociatesU.S. Department of Energy
Thermodynamic properties of mercury (ANEOS data)
Thermodynamic properties of mercury were obtained using the ANEOS data. Isotherms of the specific internal energy, pressure and entropy as functions of density are shown in a large density – temperature – pressure domain which includes liquid, vapor and mixed phases.
Brookhaven Science AssociatesU.S. Department of Energy
Analytical model: Isentropic EOS with phase transitions
• A homogeneous EOS model
• Gas (vapor) phase is described by the polytropic EOS reduced to an isentrope.
0
00
( 1) ,
,
(log log ) .1
P EPTR
RS P
1 1, , ,1( 1)where exp
S const
P E TR
SR
Brookhaven Science AssociatesU.S. Department of Energy
The mixed phase
• Mixed phase is described as follows:
.
,
,
,
2222
22
2
222
2
lv
l
llvv
lvllvvvl
llvvvvl
lvlvvvl
satl
aaaaP
dPE
aaaaPPP
satv
:fraction void the isand
where
log
Brookhaven Science AssociatesU.S. Department of Energy
The liquid phase
• The liquid phase is described by the stiffened polytropic EOS:
.1
log)(log
,
,)()1(
00
RPPS
RPP
T
PEEP
1 1
,
, ,1
( 1)where exp
S const
P PPE E T
RSR
Brookhaven Science AssociatesU.S. Department of Energy
CERN neutrino factory target experiments
Schematic of the experimental setup
Brookhaven Science AssociatesU.S. Department of Energy
Mercury splash (thimble): experimental data
CERN neutrino factory target experiments
0.88 1.25 7t ms t ms t ms
Energy deposition:
5 J/g
30 J/g
Brookhaven Science AssociatesU.S. Department of Energy
Mercury splash (thimble): numerical simulation
250 530 730 1t s t s t s t ms Energy deposition = 15 J/g
Brookhaven Science AssociatesU.S. Department of Energy
Hydrodynamic processes in the SNS target
The mercury target for SNS will consist of a sealed stainless steel chamber filled with mercury interacting with 20 kJ proton pulses at frequency 60 Hz. The desired target lifetime implies that the target should withstand ~1.e+8 proton pulses. The pitting of walls was observed experimentally after 200-1000 pulses.Future targets will require much higher beam intensities.
An effective approach capable of reducing the strength of rarefaction and shock waves is to use bubbly layers near flanges and bubbles in the bulk mercury.
Direct (tracked bubbles) and continuum (new eos model) simulations.
Brookhaven Science AssociatesU.S. Department of Energy
Further development of continuum homogeneous equation of state models for bubbly flows
The (modified) Rayleigh-Plesset equation gives a dynamic closure for the fluid dynamics equation:
2
3 3
3 1 2 1 1 11 0,2 2
where is the effective dumping coefficient is the Weber number
is the cavitation number is the pressure term
tt t D t p
D
p
RR R R CR We R R R
We
C
Brookhaven Science AssociatesU.S. Department of Energy
Direct simulation approach: a system of tracked bubbles
Mean particle radius = 2mm One phase mercury EOS for the liquid, the ideal gas EOS for the bubble gas Uniform in x and gaussian in y initial energy deposition with the center at the container top resulting in the maximum pressure 500 bar.
Initial density Initial pressure
Brookhaven Science AssociatesU.S. Department of Energy
Direct simulation: the pressure evolution
106 , 4t s p bar 106 , 2t s p bar
80 bubbles 130 bubbles
Max pressure at the bottom, t = 37
Total max pressure at the
bottom1 phase fluid 322 32280 bubbles 3.8 ~10130 bubbles 2.1 ~7
Brookhaven Science AssociatesU.S. Department of Energy
Future research
Futher work on the EOS modeling for cavitating and bubbly flows.
Futher studies of the muon collider target issues. Studies of the cavitation phenomena in a magnetic field.
Studies of hydrodynamic issues of the cavitation induced erosion in the SNS target.
Studies of the MHD processes in liquid lithium jets in magnetic fields related to the APEX experiments.
Recommended