modeling of multi-physics phenomena in fast reactors...

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


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,

− Fluid-structure interactions … chemical, mechanical, thermal

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


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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


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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)


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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

~ Fluid-Structure Thermal Interaction Simulation ~


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6


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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7


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


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(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


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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


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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


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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.


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(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


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Computational model

SAS/SIMMER code system for CDAs since 1970’s

KAMUI – for fuel S/A degradation by subchannel analysis

Multi-component multi-phase flow Multi-component multi-field formulation

In case of fuel S/A degradation: 3 components, 3-phases and 2- or 3-velocity fields (mixture velocity fields):

[ex] Liquid-phase and solid-phase assigned to one field and gas-phase to the other;

Mixture fields required mixture material properties (viscosity, heat capacity, conductivity, .. etc.)

Phase interfaces --- topology

Lumped modeling of heat, momentum and mass transfers at the phase interfaces among all components; all from experiment

Component Solid-phase Liquid-phase Vapor-phase

Fuel X X X

Steel X X X

Sodium X X

(2velocity fields) Mixture velocity field Gas-phase v


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In-Pile Experiment

CABRI

SCARABEE

TREAT

EBR-II

…

IGR-EAGLE (Experimental Acquisition of Generalized Logic to

Eliminate criticalities)

16


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Bovisa CDA Evaluation Methods & Mitigation Measures

- IGR (Impulse Graphite Reactor) in EAGLE Project -

CEC

Reactor core

Cooling water cavity

Control rod

channel

Cross-section of IGR core

(NNC in Kazakhstan)

17

PERFORMANCE

Max. thermal neutron flux density:

Max. thermal neutron fluence:

Min. half-width of pulse:

Max. energy release:

Central Experimental Channel (CEC):

7×1016 n/cm2s

3.7×1016 n/cm2

0.12 s

5.2 GJ

φ228mm×L3825mm


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Bovisa CDA Evaluation Methods & Mitigation Measures

- Upward Discharge Experiment in EAGLE Project -

Insertion of test section into IGR core

Test section for

upward discharge

Inner duct

SA can wall

Cross

section

Core

Discharge path

Closed end

FAIDUS option

(reference for JSFR)

IGR core

Fuel pins to be molten

Simulated core part

Discharge path

Simulated upper plenum Sodium

18


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Validation of subassembly degradation and core

meltdown_relocation models

CABRI hodo-scope data

SCARABEE TIB

temperature flow data

TREAT/SLSF

ACRR

1

2

3

4 5

Flow blockage at the start of transient

Coolant

Wall

Fuel pin

6 5 4 3

1 2

14 13 12 11 10 9 8 7

19 18 17 16 15

Fissile length 60cm


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-4

-2

0

2

4

6

0 2 4 6 8 10 12 14 16 18 20 22 24

tim e (sec)

flow rate (m3/h)

BE+2 outflow

800

1000

1200

1400

0 2 4 6 8 10 12 14 16 18 20 22 24

tim e (sec)

temperature (C)

tcool(4,9)tcool(4,10)tcool(4,11)

800

1000

1200

1400

0 2 4 6 8 10 12 14 16 18 20 22 24

tim e(sec)

temp

erat

ure

(C)

tclad(1,9)tclad(1,10)tclad(1,11)

Time (sec)

Time (sec)

Time (sec)

Flo

w r

ate (

m /h)

3

Tem

pera

ture

(

)

℃

Tem

pera

ture

(

)

℃

Computation

Coolant T (S/A

peripheral)

Exit flow

Multi-component multi-field model validation for

SCARABEE-BE+2 Experiments -2 (TIB)

Cladding T (S/A

center)


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B

E

+

2

at

7

s

Fuel

Vapor

Liquid

Sodium

Clad Clad Fuel

Vapor

Liquid

Sodium

Liquid

Steel

Steel

Blockage

５ｓ７ｓ

Good agreement for the onset timings of sodium boiling

and cladding melting-relocation



S/A Centerline

S/A wall


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１５ｓ

Fuel Clad

Vapor

Liquid

Sodium

Liquid

Steel

Steel

Blockage

Fuel Particle

S/A center fuel melting_relocation.

S/A peripheral fuels no melting →

agreement with the experiment




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SCARABEE-BE+2 Experiments -5

Subchannel analysis results

KAMUI BE+2

KAMUI APL

Kasahara BE2.mpg

Kasahara apl1title.mpg

Agreement? Excellent, good, fair, poor?

Trend agreement is important but meaningless if the users

don’t try to catch physics

To minimize subjective judgment on modeling multi-

physics, we need:

Identification and estimation of uncertainties

Only visual comparisons are not sufficient


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Oct

ober

4,

200

7

H. Ninokata and E.

Merzari 25

How do you catch physics?

I. In case of DNS or LES

So much information from DNS or LES

Many new phenomena, detailed turbulent structure through visualization …

Done by visualization thanks to rapid progresses in CG technology …. Fancy -- but it’s a subjective approach

Objective education techniques, to avoid possible controversy and to identify nature and significance of the structure

Ex. Proper Orthogonal Decomposition Technique


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Oct

ober

4,

200

7

H. Ninokata and E.

Merzari 26

To identify the motions which contain the most energy.

Lumley (1967) Berkooz, Holmes & Lumley (1993), Holmes et al, (1996)

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


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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


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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


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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, ..


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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


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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


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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!


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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


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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,

sodium/molten fuel, molten fuel/molten steel, etc)

Between liquid and vapor-gas (Interfacial heat transfer and

heat transfer with interfacial mass transfer)

Radiation heat transfer

…

modeling of multi-physics phenomena in fast reactors...

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