H. Ninokata - Nuclear Reactors Group 2013.02.05 FR13, Paris 2013.03.05 FR13, Paris Hisashi NINOKATA Politecnico di Milano Department of Energy CeSNEF-Nuclear Engineering Division Nuclear Reactors Group Modeling of Multi-Physics Phenomena in Fast Reactors Design/Safety and Experimental Validation International Conference on Fast Reactors and Related Fuel Cycles (FR13) 4-7 March 2013, Paris, France Hisashi Ninokata, Hideki Kamide, Marco Pellegrini Marco Ricotti
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H. Ninokata - Nuclear Reactors Group
2013.02.05 FR13, Paris
2013.03.05 FR13, Paris
Hisashi NINOKATA
Politecnico di Milano
Department of Energy
CeSNEF-Nuclear Engineering Division
Nuclear Reactors Group
Modeling of Multi-Physics Phenomena in Fast Reactors
Design/Safety and Experimental Validation
International Conference on Fast Reactors
and Related Fuel Cycles (FR13)
4-7 March 2013, Paris, France
Hisashi Ninokata,
Hideki Kamide,
Marco Pellegrini
Marco Ricotti
H. Ninokata - Nuclear Reactors Group
2013.02.05 FR13, Paris
Multi-physics phenomena of concern
Characterized by time-space scales − Microscopic
− Mesoscopic
− Macroscopic
− Global scales
Described by mass fields (components), flow fields, temperature fields − Homogeneous mixture model
− Multi-fluid model or multi-fluid multi-field model
Coupled with chemical reactions, structural mechanics, material sciences − Chemical reactions … Na burning, Na-H2O,
Taking place when fast reactors are under − S.S. full power operations: cavitation, erosion, corrosion, FP deposition, crud
sedimentation, thermal striping/stratification,
− DHR conditions
− Transient conditions
− Accident conditions: fuel S/A degradation, core meltdown and relocation
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
Bovisa
MULTI-PHYSICS PHENOMENA MODELING
(NOTES ARE FROM OR BASED ON THE INFORMATION FROM JAEA)
Examples:
1. High cycle thermal fatigue in JSFR: Coupling of CFD and FEM
2. Sodium water reaction
3. Fuel S/A degradation and CDAs
Topics 1
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
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High Cycle Thermal Fatigue at TOP Core Instrumentation Plate
Thermal Fatigue caused by Thermal Mixing between
- Hot Sodium from Fuel Subassemblies and
- Cold sodium from Control Rod Channels and Blanket Fuel Subassemblies
Backup Control Rod
(BCR)Primary Control Rod
(PCR)
Fuel Subassembly (FS)
Electromagnet
for SASSC/R
Driving
Rod
1st Baffle Plate
Core Instruments
Plate (CIP)
Upper
Guide
Tube
Flow-hole
Hot
Sodium
FS
Hot
Sodium
Cold Sodium
from C/R(UIS)
Target Areas
Concerning about
Thermal Fatigue
(Top view image
around a control
rod channel)
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
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Japan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy Agency
②Local analysis Local analysis around
PCR of JSFR
①Whole upper plenum analysis
③Thermal stress analysis
(for CRs) (for BFs)
Temperature information in structure
Boundary conditions for local analysis
③Estimation of structural integrity
by thermal stress analysis (FINAS)
①Thermal-hydraulics in upper plenum
by RANS - UIS external flow for blanket fuels
- UIS internal flow for control rods
② Fluid-structure thermal interaction
LES and heat conduction in structure
simulation by MUGTHES in local areas
around - Control rod (CR) channels
- Blanket fuel (BF) subassemblies
Numerical Estimation Method for Thermal Fatigue on CIP
Japan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy Agency
Numerical Simulations of Thermal Mixing
in WATLON T-Pipe as Validation
262,632 cells Main pipe Branch pipe
Inner Diameter: 0.15 m(=Dm) 0.05 m(=Db)
Inlet Temperature: 48℃ (=Tm) 33℃ (=Tb)
Mean Velocity:
(Impinging jet case) 0.26 m/s(=Wm) 1.0m/s(=Vb)
(Wall jet case) 1.46 m/s(=Wm) 1.0m/s(=Vb)
Main pipe flow
Branch pipe flow
mb
Db
Dm
Db
W
U
mm
mb
mm
噴流の向き
Mm
Mb
Mb
Mm
0.001
0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100
Mb (kg.m/s2)
Mm (
kg
.m/s
2)
Mr < 0.35 (◆:Impinging jet)
0.35<Mr<1.35
(●:Deflecting jet)
Mr > 1.35 (■:Wall jet)Mr = Mm/Mb
(Low Main Flow: Impinging Jet)
(High Main Flow: Wall Jet)
○4,000 data at 1kHz sampling during last 4 seconds
in 10 seconds transient calculation
Flow-pattern map
Jet direction
Main pipe flow:
Branch pipe flow:
2
mbmmm WDDM
224 bbbb VDM
Wm
Vb
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2013.01.25 9:30-1030
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7
Japan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy Agency
Typical Numerical Results of Fluid Temperature Distributions
at Impinging Jet and Wall Jet Cases in WATLON
Impinging jet case
Wall jet case
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
(T -T b )/dT , T' /dT
y/D
m
Experiment, (T-Tb)/dT
LES(Cs=0.14),
Experiment, T'/dT
LES(Cs=0.14),
(T -T b )/dT
(T -T b )/dT
T' /dT
T' /dT
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
(T -T b )/dT , T' /dT
y/D
m
Experiment, (T-Tb)/dT
LES(Cs=0.14), (T-Tb)/dT
Experiment, T'/dT
LES(Cs=0.14), T'/dT
(T -T b )/dT
(T -T b )/dT
T' /dT
T' /dT
temperature large-scale eddy structure
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
Bovisa
MULTI-PHYSICS PHENOMENA MODELING
(NOTES ARE FROM OR BASED ON THE INFORMATION FROM JAEA)
Examples:
1. High cycle thermal fatigue in JSFR
2. Sodium water reaction: wastage, failure propagation
3. Fuel S/A degradation and CDAs
Topics 2
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Sodium-Water Reaction (SWR) Accident
9
Water side: about 15 MPa
Shell side: 0.2 MPa
Safety assessment of steam generator (SG) in sodium-cooled fast reactor
SG (evaporator)
in Monju
Reacting jet Na
Failed tube Adjacent tube
Sodium-water reaction
Water,
vapor
Erosion
FAC
Combination
Strength
degradation
Wastage
Over-heating rupture
Secondary failure (failure propagation)
Multi-physics nature: thermal hydraulics, multiphase flow, chemical reaction,
structure, material complex
Progression of damage
Evaluation of possibility of propagation
most important issue
H. Ninokata - Nuclear Reactors Group
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Evaluation of Failure Propagation
Final goal is to evaluate
wastage environment
wastage rate
possibility of failure propagation
Evaluation for SG in prototype FR A large number of mock-up tests
Evaluation for SG in commercial FR Numerical analysis and minimal
mock-up test
Analytical evaluation system
10
(1) SERAPHIM
Analysis of compressive
multicomponent multiphase
flow with SWR
(2) TACT
Analysis of target tube heat
transfer and stress, evaluation of
wastage rate and failure
propagation
(3) RELAP5
Analysis of boiling two-phase flow
B.C.
B.C.
Wastage
environment
H. Ninokata - Nuclear Reactors Group
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Numerical Methods in SERAPHIM
Finite difference method
3D Cartesian coordinate (x, y, z), 2D cylindrical coordinate (r, z)
Multi-fluid model (water, liquid sodium and multi-component gas)
HSMAC method (modified for compressible multiphase flow)
Phase change model
EOS: Modified Benedict-Webb-Rubin equation
Surface reaction model (gas-liquid reaction)
Gas-phase reaction model (gas-gas reaction)
Basis
Compressible multiphase flow model
Sodium-water chemical reaction model
11
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Surface Reaction Model
Surface reaction = Chemical reaction at interface between water vapor and liquid sodium
Model assumptions
Na(l) + H2O(g) NaOH(l) + 1/2H2(g)
Infinite reaction rate (progress of chemical reaction is limited
by mass flow rate of reactant gas toward interface)
Reaction products move to gas phase
Reaction heat is added to gas phase
Na(liquid)
NaOH
H2O
H2
Interface
Multicomponent gas:
H2O, Na(gas), NaOH(aerosol),
NaOH(gas), H2
Mass flow rate
12
aYl
DSh jg
mjsf
j aYC
HLe j
pg
glbsf
j
1
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
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Numerical results for the SWAT-1R test
[oC]
1400
400
Experiment Calculation
(weight averaged) (measured) Cylindrical vessel
filled with liquid
sodium
Diameter: 0.4 m
Height: 1.8 m
43 tubes
Water vapor
leaks from the
lowest tube and
goes upward
Conditions of
water vapor:
17.0 MPa,
352 oC
Conditions of
sodium:
0.2 MPa,
470 oC
Void fraction Computational Domain
Gas phase goes upward
Temperature Field
High temperature region
expands to upper left both in
the experimental result and the
numerical result.
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
Bovisa
MULTI-PHYSICS PHENOMENA MODELING
(NOTES ARE FROM OR BASED ON THE INFORMATION FROM JAEA;
AND TOKYO INSTITUTE OF TECHNOLOGY R&D RESULTS)
Examples:
1. High cycle thermal fatigue in JSFR
2. Sodium water reaction
3. Fuel S/A degradation and CDAs: calculation quality depends on the physical models
Topics 3
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
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Computational model
SAS/SIMMER code system for CDAs since 1970’s
KAMUI – for fuel S/A degradation by subchannel analysis
Based on the Karhunen-Loeve expansion, a basic tool in pattern recognition;
DNS (or LES) data: <U(x)>+u(x,t); Energy: u2
Principle:
− Expand u(x,t) by the orthogonal functions; u(x,t) ~ San(t)jn(x)
− Maximize u2 : Orthogonal functions as a weighting function;
− The process reduced to an Eigen-value problem (l1>l2>l3, …>lN>...);
− Higher order terms can be curtailed: a partial sum is sufficient
Therefore the maximization problem automatically selects the decomposition that contains the highest amount of energy in the first few modes. It allows us to truncate the expansion at low values of N
POD: Proper Orthogonal Decomposition
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
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Oct
ober
4,
200
7
H. Ninokata and E.
Merzari 27
How do you catch physics?
II. In case of multi-physics simulation
As more multi-physics involved, more complex calculation system with so many physical models representing the interactions
Physical models are based on known knowledge and a result of assumptions, approximations, compromises
With the CV sizes larger, more uncertainties
Comparisons must be done with experiment (and theory if any), Done by visualization – Not sufficient
Needs to identify modeling uncertainties, to avoid possible controversy and to identify nature and significance of the structure
An attempt to quantify uncertainty
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
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Uncertainty identification in physical modeling -1
Erroneous example: stratification in sodium flow
turbulence heat flux model should take into account the gravity
We would like to know how erroneous the predictions are when the turbulent heat
flux is modeled w/ or w/o gravity effects
We follow the Bayesian rule P(B|A)={P(A|B)*P(B)}/P(A)
Prior probability P(B) [calculation] can be updated to P(B|A) with P(A), probability of
A by experimentation, where P(A|B) a likelihood function;
Noted that the likelihood P(A|B) is given a’priori but subjective; should be improved
by optimal estimation-control theories
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
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Uncertainty identification in physical modeling -2
Assume a degree of being subjective for a certain model, P(B),
P(B) could be updated based on a direct comparison of the model prediction with
experiment, to P(B|A)
By carrying out as many as calculations as possible with different model parameter
values, we obtain P(B|A)
P(B|A) accounts also for the uncertainty in the experimental results P(A) and
provides statistical information on the mean value, standard deviation, tolerance
limits, ..
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
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Uncertainty identification in physical modeling -3
A Simple Example:
Suppose the model for the turbulent heat flux in a CFD code is expressed in terms of velocity gradient (C1) and the gravity effect (C3)
Run as many cases for C1 and C3 as possible (Monte Carlo or economical Latin Hypercube Sampling) to construct a response surface
Mean value of C1 and C3 represent optimal values while the standard deviation could be interpreted as a subjective degree of belief in C1 and C3 model parameters.
C1 trustable; C3 questionable …….. Note: this is just an example
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
Bovisa Final Comments
• Focused on the current practices of numerical modeling and simulations
of thermal hydraulic phenomena in sodium-cooled fast reactor systems
• All these multi-physics simulation models have been subject to on-going
validation programs
• In practice, validation of engineering multi-physics phenomena is likely to
be made on rather qualitative basis, often relying on many subjective
judgments in comparison with the results from large-scale integral tests or
mock-up experiments
• In validation processes, although an eventual subjective judgment cannot
be ruled out but should be made minimal. To make it more quantitative
and rational, a proposal has been made of the identification of errors
and/or uncertainties inherent in computations based on the Bayesian rule
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
Bovisa 2013.01.25 9:30-1030
Bovisa
Hisashi NINOKATA
Politecnico di Milano
Department of Energy
CeSNEF-Nuclear Engineering Division
Nuclear Reactors Group
END
Thank you!
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
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Modeling wall friction; Interfacial friction
21
1/2 2, , 1/2
4
2
nn f
WL Z f fi l Wh L
GCF
D
( ) ,Re
f W m
f
bC a
fhff DG /Re
Fluid mixture wall friction factor
: two phase flow pressure drop multiplier
f: mixture viscosity
wwwwCnL
nG
nL
nG
n
Gfn
zI11112/1
,2
1 1/2 1/2
, , ,, 1/2
n nIL z I z I zi l
F A
1/2 1/2
, , ,, 1/2
n nIG z I z I zi l
F A
A I,z:Interfacial area concentration; ρG:vapor density; Cf:Interfacial friction factor
(Wallis) ; w: axial velocity
A I,z : α > 0.6 annular flow model
0.6 > α > 0.4 Ishii & Chawla for slug flows
0.4 > α Ishii & Chawla for bubbly flow model
H. Ninokata - Nuclear Reactors Group
2013.01.25 9:30-1030
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Heat transfers
Between solid wall and liquid (sodium, liquid phase of steel,
MOX fuels)
− HT correlations for liquid metals
Between solid wall and vapor-gas
− Dittus-Boelter etc.
Between fluid and different fluid (sodium/molten steel,