Brookhaven National Laboratory / CMR-RPI Collaboration Meeting
Rensselaer Polytechnic Institute, Troy, New York
Thursday, March 29, 2007
Front Tracking Multiphase Code - FronTier
Tianshi Lu
Roman Samulyak
Computational Science Center
Brookhaven National Laboratory
Collaborators:
James Glimm, Stony Brook University / BNL, Modeling, numerical algorithms
Xiaolin Li, Stony Brook University, front tracking software development
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1
Outline
1. Numerical Techniques of FronTier
2. Main FronTier Applications
3. Proposed numerical study of LMFBR
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Main FronTier Applications
Rayleigh-Taylor
instability
Richtmyer-Meshkov
instability
Targets for future
accelerators
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Liquid jet breakup
and atomization
3
Supernova
explosion
Tokamak refueling
through the ablation
of frozen D2 pellets
Main Ideas of Front Tracking
Front Tracking: A hybrid of Eulerian and Lagrangian methods
Two separate grids to describe the solution:
1. A volume filling rectangular mesh
2. An unstructured codimension-1
Lagrangian mesh to represent interface
Major components:
1. Front propagation and redistribution
2. Wave (smooth region) solution
Advantages of explicit interface tracking:
• No numerical interfacial diffusion
• Real physics models for interface propagation
• Different physics / numerical approximations
in domains separated by interfaces
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The FronTier Code
FronTier is a parallel 3D multiphysics code based on front tracking
 Physics models include
Compressible fluid dynamics
 MHD
 Flow in porous media
 Elasto-plastic deformations

Interface untangling by
the grid based method
Realistic EOS models
 Exact and approximate Riemann solvers
 Phase transition models
 Adaptive mesh refinement

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FronTier-MHD numerical scheme
Elliptic step
Hyperbolic step
Fijn
Fijn1/ 2
Fijn1
Point Shift (top) or Embedded Boundary (bottom)
in, j 1/ 2
• Propagate interface
• Untangle interface
• Update interface
states
• Apply hyperbolic
solvers
• Update interior
hydro states
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in1/1/2,2 j
• Generate finite element grid
• Perform mixed finite element discretization
or
• Perform finite volume discretization
• Solve linear system using fast Poisson solvers
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• Calculate
electromagnetic
fields
• Update front and
interior states
Embedded Boundary Elliptic Solver
Main Ideas
• Based on the finite volume discretization
• Domain boundary is embedded in the
rectangular Cartesian grid, and the
solution is treated as a cell-centered
quantity
• Using finite difference for full cell and
linear interpolation for cut cell flux
calculation
• Advantage: robust, readily parallelizable,
compatible with FronTier grid-based
interface tracking algorithm.
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Two Models for Cavitating and Bubbly Fluids
Heterogeneous method (Discrete Bubble Model): Each individual bubble is
explicitly resolved using FronTier interface tracking technique.

Stiffened Polytropic
EOS for liquid
Polytropic EOS for
gas (vapor)
Homogeneous EOS model. The mixture of liquid and vapor is treated as a
pseudofluid (single-component flow); Suitable averaging is performed over a
length scale of several bubbles. Small spatial scales are not resolved.

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Front Tracking with Phase Transitions
Kinetic Relation
Phase Boundary Conditions
[ un ]  s[  ]
[ un2  p ]  s[ un ]
[ Eun  pun  
psat (T)  pv
2πRT
α : evaporation coefficient
psat (T) : Clausius - Clapeyron equation
Mass flux : M ev  α
T
]  s[ E ]
n
Interfacial Temperature
Equilibrium
Tl  Tv  Ts
pv : vapor pressure
R
kB
; k B is Boltzmann const.; m is molecular mass
m
A deviation from Clausius-Clapeyron
on vapor side is allowed.
Similar to: Matsumoto etal. (94’)
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Two Characteristic Equations at Phase Boundary
t  t
S l S r New Position
Phase Boundary
  u  c
  u  c
t
S2
S 1 S f
un
dp
 2T
 c
 2
d
d
n
un
dp
 2T
 c
 2
d
d
n
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S 0 S 0
Sb
S1
S2
• Characteristic equations are solved
with the boundary conditions using
an iterative solver.
• A subgrid model was developed to
account for thin thermal layers next
to the phase boundary.
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x
Main FronTier Applications
Fluid Interface Instability
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Rayleigh-Taylor Instability
Multimode
Single mode, bubble and spike
The growth rate predicted by FronTier agrees
with experiments, while the prediction from
untracked (TVD) simulations was about half.
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Richtmyer-Meshkov Instability
Untracked
Tracked
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Main FronTier Applications
Bubbly/Cavitating Flows
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SNS and Cavitation Mitigation
P0 (r , z )  500e  r
2
0.1z
bar
Courtesy of Oak Ridge National Laboratory
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DNS of pressure wave propagation in the SNS target
Bubbly Mercury ( R=1.0mm, b=2.5% )
Pure Mercury
Statistical average of collapsing bubble pressure predicts the mitigation
efficiency of 32 for injected air bubbles of radius 1mm and void fraction 2.5%.
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Liquid Jet Breakup and Spray Formation
Breakup Regimes:
1.
2.
3.
4.
Rayleigh breakup
First wind-induced breakup
Second wind-induced breakup
Atomization
DROP AND SPARY FORMATION
FROM A LIQUID JET,
S.P.Lin, R,D. Reitz,
Annu. Rev. Fluid Mech.
30: 65-105 (1998)
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Diesel Jet Atomization through a Nozzle
• Micron-size vapor bubbles
created and collapsed
dynamically
• Adaptive Mesh Refinement
implemented for the
axisymmetric simulations
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• Spray mass flux, opening angle
and tip velocity agree with
experiments
• Opening angle too large if jet
were treated as gas, no opening
if treated as pure liquid
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Main FronTier Applications
Multiphase MHD
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Applications
Neutrino Factory / Muon Collider target
has been proposed as a free mercury jet
interacting with an intensive proton pulse
in a 20Tesla magnetic field
Tokamak applications
• Pellet ablation
• Striation instabilities
• Laser driven pellet acceleration
• Gyrotron driven pellet acceleration
• Plasma disruption mitigation
Laser driven pellet
acceleration
Injection of a high speed gaseous jet
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Laser ablation
plasma plume
Mercury Jet Expansion induced by Proton Pulses
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
Studies of surface
instabilities, jet breakup,
and cavitation

MHD forces reduce both jet
expansion, instabilities,
and cavitation
Pellet Ablation for Tokamak Fueling: Main Models
• Equation of state with atomic processes
• Kinetic model for the interaction of hot electrons with the ablated gas
• Surface ablation model
• Cloud charging and rotation models
• New conductivity model (ionization by electron impact)
Schematic of
processes in the
ablation cloud
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Formation of the ablation channel in the pedestal
Critical observation:
• Formation of the ablation channel strongly
depends on the pedestal properties
• Radius depends on the warm-up time (pedestal
width/pellet velocity)
• Important to use accurate n and T in the pedestal
region (from edge codes)
• Ablation rate strongly depends on the channel
radius
• In ITER, fast pellets in narrow pedestal region will
result in narrow channels and small ablation rate
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Solid line:
tw =10, ne = 1.0e14 cm-3
Dashed line: tw = 10, ne = 1.6e13 cm-3
Dotted line: tw = 5, ne = 10e14 cm-3
Proposed Numerical Study of LMFBR

Simulation of material relation in a Core
Disruptive Accident (CDA) in a liquidmetal fast breeder reactor (LMFBR).

Numerical investigation of the surface
instability and liquid entrainment in the
expansion of an CDA bubble.
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Material Relocation in a Core Disruptive Accident
TOP condition
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LOF condition
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Proposed Numerical Study of LMFBR
Simulation of material relocation in a core disruptive accident
•
•
•
•
•
•
•
•
Initiation by TOP ( transient overpower ) or LOF ( loss of coolant flow )
Fuel heat up and melting within the fuel rod
Release of fission gas in the melt volume
Axial and radial growth of melt volume
Clad failure due to melt through or over pressure
Motion of fuel and clad debris up into outlet plenum or down into core
Possibility of clad or fuel refreezing near location of clad failure
Growth pattern of the sodium vapor bubble if the coolant boils
Multiphase, multicomponent flow of fuel, steel, fission gas, and sodium
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Proposed Numerical Study of LMFBR
Simulation of the expansion
of Core Disruptive Accident
(CDA) bubbles.
 An CDA bubble is a twophase bubble containing liquid
fuel and its vapor.
 Liquid entrainment by the
bubble is associated with
Kelvin-Helmholtz instability
and Rayleigh-Taylor instability.
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BlueGene/L at BNL
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