Mitigation of Cavitation Damage Erosion in Liquid Metal Spallation Targets Nov. 30

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Mitigation of Cavitation Damage Erosion in Liquid
Metal Spallation TargetsNov. 30 Dec. 1, 2005,
ORNL
Direct Numerical Simulation of Bubbly and
Cavitating Flows and Applications to Cavitation
Mitigation
Roman Samulyak, Tianshi Lu In collaboration
with James Glimm, Zhiliang Xu
Computational Science Center Brookhaven National
Lab Upton, NY 11973
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Talk outline

• Main ideas of front tracking and the FronTier
  code
• Direct numerical simulation of cavitating and
  bubbly flows
• Discrete vapor bubble model
• Dynamic bubble insertion algorithms
• Riemann solution for the phase boundary
• Validation of models
• Simulation of multiphase flows in the following
  applications
• Atomization of a high speed jet
• Neutrino Factory/Muon Collider target
• Cavitation mitigation in the SNS target
• Conclusions and Future Plans

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Main ideas of front tracking
Front Tracking A hybrid of Eulerian and Lagrange
methods Major components 1) Front propagation,
2) Wave (smooth region) solution

• Two separate grids to describe the solution
• A volume filling rectangular mesh
• A unstructured (N-1) dimensional Lagrangian mesh
  to represent interface

• Advantages of explicit interface tracking
• Real physics models for interface propagation
• Different physics / numerical approximations in
  domains separated by interfaces
• No interfacial diffusion

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Resolving interface tangling by using the grid
based method
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
• Phase transition models
• Exact and approximate Riemann solvers, realistic
  EOS models
• Adaptive mesh refinement

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Main FronTier applications

• Rayleigh Taylor and Richtmyer-Meshkov fluid
  instabilities

Targets for future accelerators
Tokamak refueling through the ablation of frozen
deuterium pellets
Liquid jet breakup and atomization
Supernova explosion
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• Modeling of Bubbly and Cavitating Flows using the
  Method of Front Tracking

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Two models for cavitating and bubbly fluids
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Features of the discrete vapor bubble model

• First principles simulation.
• Accurate description of multiphase systems
  limited only by numerical errors.
• Resolves small spatial scales of the multiphase
  system.
• Accurate treatment of drag, surface tension,
  viscous, and thermal effects.
• Mass transfer due to phase transition (Riemann
  problem for the phase boundary).

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Theory on Bubbly Flows
Mass and Momentum Conservation
The Keller Equation
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Theory on Bubbly Flows
Dispersion Relation
c low frequency sound speed cf sound speed in
pure fluid wB resonant frequency d damping
coefficient
Steady State Shock Speed
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Linear Wave Propagation
Dispersion Relation
Phase Velocity
Attenuation Rate
V (cm/ms)
a (dB/cm)
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Shock Wave Propagation
Shock speeds measured from the simulations are
within 10 deviation from the steady state
values.
Shock Profile

• The oscillation amplitude is smaller for gas with
  larger g.
• The oscillation period is longer for larger
  bubble volume fraction.

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Shock Wave Propagation
Shock profile of SF6 gas bubbles
Experiment
Simulation
The oscillation period is shorter than the
experimental value by 28.
courtesy of Beylich Gülhan
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Dynamic Bubble Insertion Algorithm for Direct
Numerical Simulation

• A cavitation bubble is dynamically inserted in
  the center of a rarefaction wave of critical
  strength
• A bubbles is dynamically destroyed when the
  radius becomes smaller than critical. In
  simulations, critical radius is determined by the
  numerical resolution. With AMR, it is of the same
  order of magnitude as physical critical radius.
• There is no data on the distribution of
  nucleation centers for mercury at the given
  conditions. Some estimates within the homogeneous
  nucleation theory

critical radius
nucleation rate
1/2
Critical pressure necessary to create a bubble in
volume V during time dt
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• Riemann Problem for the Phase Boundary

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Governing Equations and Boundary Conditions
Phase Boundary Conditions (Generalized
Rankine-Hugoniot Conditions)
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Interfacial Thermal Conditions
2. Two cases a) Contact with thermal
conduction b) Phase boundary
Contact with thermal conduction
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Phase Boundary Conditions
A deviation from Clausius-Clapeyron on vapor side
is allowed. Similar to Matsumoto etal. (94)
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Two Characteristic Equations
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Phase Boundary Propagation
An Iteration Algorithm. 1. Solve for mass flux
and interfacial temperature by
2. Solve the characteristic equations with the
jump conditions
3. Compare the newly obtained and
with the previous iteration to determine the
convergence of the iteration.
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Validation Phase Boundary Solutions
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• Applications
• Liquid jet breakup and atomization
• Neutrino Factory / Muon Collider target
• Cavitation mitigation in SNS target

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Liquid Jet breakup and Spray Formation

• Breakup Regimes
• 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. 1998.
30 65-105
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Simulation setup and processes influencing
atomization

• Inlet pressure fluctuation

• Cavitation in the nozzle and free surface jet

• Boundary rearrangement effect

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Simulation Results

• Density Plot of Jet Simulation Using Discrete
  Vapor Bubble Model

• Density Plot of Jet Simulation Using Homogenized
  EOS Model

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Animation of Simulation Using Discrete Bubble
Model
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Neutrino Factory / Muon Collider Target

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Numerical simulations of the mercury jet target

• Simulation of the mercury jet target interacting
  with a proton pulse in a magnetic field
• Studies of surface instabilities, jet breakup,
  and cavitation
• MHD forces reduce both jet expansion,
  instabilities, and cavitation

Richtmyer-Meshkov instability of the mercury
target surface. Single fluid EOS (no cavitation)
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Cavitation in the mercury jet interacting with
the proton pulse
Initial density
Density at 20 microseconds
Initial pressure is 16 Kbar
400 microseconds
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MHD effects in the Mercury Target
Distortion of the mercury jet by a magnetic field
Stabilizing effect of the magnetic field
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SNS and Cavitation Mitigation
Courtesy of Oak Ridge National Laboratory
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Step 1 DNS of pressure wave propagation in the
container pure mercury
Pure Mercury
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Step 2 DNS of pressure wave propagation in the
container mercury containing gas bubbles
Bubbly Mercury ( R1.0mm, b2.5 )
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Step 3 Collapse pressure of cavitation bubbles
The Keller Equation
Empirical formula for P lt 10Kbar and T lt 1ms
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Step 4 Estimation of efficiency of the
cavitation damage mitigation

• Statistical averages of collapsing bubbles
  pressure peaks

R0 1.0 mm pg0 0.01 bar
E(b,R) is independent of R0 and pg0.
E 40 at R 0.5 mm and 0.5 void fraction
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Conclusions and Future Plans

• Developed components enabling the direct
  numerical simulation of cavitating and bubbly
  flows
• Discrete vapor bubble model
• Dynamic bubble insertion algorithms
• Riemann solution for the phase boundary
• Studied multiphase flows in the following
  applications
• Atomization of a high speed jet
• Neutrino Factory/Muon Collider target
• Cavitation mitigation in the SNS target
• Future work
• Investigate the influence of the init. bubble
  size on the simulation.
• Improve the bubble insertion algorithm -
  implement a conservative insertion.
• Studies of accelerator targets and liquid jets