Title: Mitigation of Cavitation Damage Erosion in Liquid Metal Spallation Targets Nov. 30
1Mitigation 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
2Talk 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
3Main 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
4Resolving 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
5Main 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
6- Modeling of Bubbly and Cavitating Flows using the
Method of Front Tracking
7Two models for cavitating and bubbly fluids
8Features 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).
9Theory on Bubbly Flows
Mass and Momentum Conservation
The Keller Equation
10Theory 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
11 Linear Wave Propagation
Dispersion Relation
Phase Velocity
Attenuation Rate
V (cm/ms)
a (dB/cm)
12Shock 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.
13Shock 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
14Dynamic 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
15- Riemann Problem for the Phase Boundary
16Governing Equations and Boundary Conditions
Phase Boundary Conditions (Generalized
Rankine-Hugoniot Conditions)
17Interfacial Thermal Conditions
2. Two cases a) Contact with thermal
conduction b) Phase boundary
Contact with thermal conduction
18Phase Boundary Conditions
A deviation from Clausius-Clapeyron on vapor side
is allowed. Similar to Matsumoto etal. (94)
19Two Characteristic Equations
20Phase 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.
21Validation Phase Boundary Solutions
22- Applications
- Liquid jet breakup and atomization
- Neutrino Factory / Muon Collider target
- Cavitation mitigation in SNS target
23Liquid 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
24Simulation setup and processes influencing
atomization
- Inlet pressure fluctuation
- Cavitation in the nozzle and free surface jet
- Boundary rearrangement effect
25Simulation Results
- Density Plot of Jet Simulation Using Discrete
Vapor Bubble Model
- Density Plot of Jet Simulation Using Homogenized
EOS Model
26Animation of Simulation Using Discrete Bubble
Model
27Neutrino Factory / Muon Collider Target
28Numerical 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)
29Cavitation in the mercury jet interacting with
the proton pulse
Initial density
Density at 20 microseconds
Initial pressure is 16 Kbar
400 microseconds
30MHD effects in the Mercury Target
Distortion of the mercury jet by a magnetic field
Stabilizing effect of the magnetic field
31SNS and Cavitation Mitigation
Courtesy of Oak Ridge National Laboratory
32Step 1 DNS of pressure wave propagation in the
container pure mercury
Pure Mercury
33Step 2 DNS of pressure wave propagation in the
container mercury containing gas bubbles
Bubbly Mercury ( R1.0mm, b2.5 )
34Step 3 Collapse pressure of cavitation bubbles
The Keller Equation
Empirical formula for P lt 10Kbar and T lt 1ms
35Step 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
36Conclusions 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