nuclear fuel assembly thermal hydraulics analysis...

H. Ninokata CeSNEF - Dipartimento di Energia

2013.06.18TAA lecture

ANS-Atlanta2013.06.18

TAA Lecture ANS-Atlanta

Hisashi NINOKATAPolitecnico di MilanoDepartment of EnergyCeSNEF-Nuclear Engineering DivisionNuclear Reactors Group

Nuclear Fuel Assembly Thermal Hydraulics Analysis – Past, Present, and Future

Prof. Hisashi NINOKATAPolitecnico di Milano

Centro Studi Nucleari Enrico Fermi - CeSNEFDipartimento di Energia

via La Masa 34, 20156 MilanoItaly

E-mail: [email protected]

ISSCA‐5 TO BE ANNOUNCED

ALSO SAVE THE DATE: NUTHOS‐10 IN OKINAWA, JAPAN (DEC 14‐18, 2014) AND NURETH‐16 IN CHICAGO, USA (AUG 31 TO SEP 5, 2015)

International Seminar on Subchannel Analysis (ISSCA)

1st in Tokyo, 1992

2nd in Palo Alto, 1993

3rd in Stockholm, 1995

4th in Tokyo, 1997

5th under consideration in Milan, Italy, 2014

covers subchannel analysis and CFD/CMFD rod bundle thermal hydraulics.

Note: International seminar on subchannel analysis, CFD modeling and verification, as well as CHF experiment and benchmarking (ISACC) is going to

be held in Xi’an, China, August 3‐4, 2013

3

NOTICE



ANS-AtlantaIntroduction: CFD vs Subchannel Analysis

DNS

LES

RANS•RSM, ASM

•K-e•Two-fluid model for 2- flow

Subchannel analysis

1D system analysis

Multi-C multi- flow

Subassembly disintegration process

Fuel relocation and DHR

Post Acc. HR

Boiling flow

W-I-SVoid drift

BWR BT/post BT

3rd field (D)

1 flow

Inter-SC exchanges

Divergence X-flow

Turbulent mixing

Global Flow Pulsation

’60s~COBRA IIIC, D.S. Rowe

’70~ COBRA IV-I’80~ COBRA-TF’90~ NASCA

`70 TRAC

MP HEC availableBlugene, Earth-Simulator, …

’70 IBM 360, CDC, FACOM, NEC, etc

’80~ Vector machine (VP50, VP100,..)‘90~ Para comp.

Current and Future

W. Heisenberg at his death bed in 1976: “When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first.”[comment] “turbulence” should be changed to “two phase turbulence”



ANS-AtlantaCFD vs Subchannel Analysis

DNS

LES

RANS•RSM, ASM

•K-•Two-fluid model for 2- flow

Subchannel analysis

1D system analysis

Wire spacer TH by LES on-going (Merzari, ANL)Grid spacer TH by LES

Why not by CFD, instead of subchannel analysis?

Model experiment37-rod Bundles Air flow inside the

bundle

P/D=1.06Re=38,750

~ 20 m/s

CFD

Wire-spacer model required



ANS-AtlantaSubchannel analysis (SCA)

RANS is self-closed and not in a position to provide information to SCA

What SCA can do and CFD cannot

Based on the presmise that we could

Predict accurately the flow and temperature conditions in different portion of the whole rod bundle;

Predict − Intra-subassembly as well as inter-subassemblies transfer phenomena

− Partial and total blockage accident phenomena

− Space-dependent boiling flow dynamics behaviors

Link and correlate local flow conditions to a local CHF criterion --- use the tube CHF data or LUT; or

Directly calculate the film dryout (BT) and rewetting; with an appropriate additional droplet field



ANS-Atlanta

Velocity vector

x [cm]210-1-2

z [c

m]

500

480

460

440

420

400

380

360

340

320

300

280

260

240

220

200

180

160

140

120

100

80

60

40

20

Forced to Mixed Convection Intra S/A Redistribution bySubchannel Analysis

100% power & flow (Re=16200)

Velocity vector

x [cm]210-1-2-3

z [c

m]

500

480

460

440

420

400

380

360

340

320

300

280

260

240

220

200

180

160

140

120

100

80

60

40

20

0

Flow recirculation

5 % power & flow (Re=810)

Power skew: qmax/qmin=3.0

Heat loss from the hexcan wall: 10%

Flow and temperature re-distributions

Onset of laminarization, flow reversals and recirculation

1D Modeling



ANS-Atlanta

MIXING

Single-phase flow subassembly TH characteristics



ANS-Atlanta

Local Instantaneous Transport Equations

Integral balances

Definitions of the average:

u =- J ( )St

Volumeintegration

z

TransverseMomentumCV

Basic subchannelCV

Cross flowcomponent

1Volume integration

1 1 1Surface integration

1 1 (fluid-fluid); ] (fluid-solid)

f

ff fs ff fs

ff fs

Vf

A A A Af f f

A Af f

dVV

dA dA dAV V V

dA dAV V

≮ ≯ [

Subchannel formulation

Vol Integral of div and grad terms to surface integral: Gauss



ANS-Atlanta

Time- and CV-Averaging N-S Eqs results in DRM and Turbulent Mixing = Constitutive equations

Momentum transfer at the fluid-fluid interface of the subchannel boundary

1[ ]

ffAf

M n dAV

≮ ≯ =

J p

-≮ ≯ ≮ ≯ ≮ ≯= ≮ ≯

Mixing:

ｆｌｕｉｄ－ｆｌｕｉｄ



ANS-Atlanta

Time- and CV-Averaging N-S Eqs results in DRM and Turbulent Mixing

Local instantaneous velocity; Time- and area-averaged velocity

Mass, Momentum and Energy

Example: Turbulent shear stress tensor

For example;

must be evaluated on the CV surface and

expressed by

Calculation results from CFD/CMFD would be useful to evaluate all the tensor elements

'

'

'

u u u

u v v v

w w w

u

u v

w

≮ ≯

≮ ≯ ≮ ≯

≮ ≯

t t txx xy xz

t t t tyx yy yzt t tzx zy zz

' ', ' ', ..., .t txz yzu w v w etc

and u

≮ ≯ ≮ ≯



ANS-Atlanta

Area averaging of time-averaged velocities: Remarks

Local instantaneous velocity; Time- and area-averaged velocity

The velocity components in subchannel analysis (SCA), i.e., axial and cross-flow components (u, w), always refer to the CV area-averaged and time-averaged velocity components.

It means that u and w appearing in SCA are implicitly understood as:

i.e., with over-bar and the area averaging being omitted.

In the case of square rod array configuration, the velocity components are (u, v, w), with u and v transverse components defined on the four CV surfaces at the rod-to-rod gap. For triangular arrays, the transverse component u of the velocity is defined on the three CV surfaces at the rod-to-rod gap.

Difference from the porous media formulation: All these transverse-flow components (i.e., cross-flow) are fixed in their flow direction perpendicular to the CV fluid-fluid surface at each gap. This is the major difference from the porous media formulation in 3-D space.

'

'

'

u u u

u v v v

w w w

u

u v

w

≮ ≯

≮ ≯ ≮ ≯

≮ ≯

u w≮ ≯and ≮ ≯..≮ ≯



ANS-Atlanta

Turbulent Mixing – Boussinesq Eddy Diffusivity

;

(Boussinesq's Eddy Viscosity)

t txz

udw

vdx

w

u

≮ ≯

' ' ( )

( )

( )

t txz

M

M M

dwu w

dxdw

dxdw

dx

wj+wj’

uk+ uk’

wi+wi’

Wj: time- and space-averaged axial velocity of the subchannel jWj’: its fluctuation

uk: time- and space-averaged x-flow velocity betw subchannel j and Iuk’ : its fluctuation

(u,v,w)t : independent variables in SCA (lumped, not distributed)



ANS-Atlanta

Diffusion Terms (cont’d)

when the heat conduction can be neglected relative to turbulent diffusion (Water);This is not true for low Pr liquid metals

ｆｌｕｉｄ－ｆｌｕｉｄ

Time- and CV-Averaging Energy Eq results in wall heat transfer and Turbulent Mixing

" )

1

ff

tM

H H

Af

Q q k k T

h h ndAV

≮ ≯ ≮( ≯

≮ ≯



ANS-AtlantaTurbulent Energy Mixing including Conduction

* '

1 1 1

P r

H Hij ij ijL

P ij

H

ij L Tij ij

kW s W

c x

sx x

Definition ofMixing Coefficients(MIT Mixing Project)

j i j ik ij ijL L

j jfi ij fi P ij

T T h hk kQ s s

A x A c x

'

*

1( )

1( )

Hk M ij ij j iL

jfi P ij

Hij j i

jfi

kQ Q s W h h

A c x

W h hA

Heat Conduction

Total



ANS-Atlanta

ff

j iMM A K

kf f k

w w1 1M ndA A

V V x

M ba Re , a 0.0084 and b 0.875

j iHM K

kf f k

e e1 1Q q" ndA A

V V x

H M 0.45 0.2 0.4 0.20.14 Re Pr 1 exp 71.8Re pr

k: Gap numberj: adjacent subchannel number to the gap kAk: Gap k area; xk: Turbulence characteristic length between two subchannels

Turbulence Mixing by COBRA-IIIc

Momentumdiffusionat the fluid-fluidinterface

Energy diffusionat the fluid-fluidinterface

'Hij ij ij kW s G



ANS-AtlantaTurbulence Mixing by COBRA-IIIc

Introduction of dimensionless Stanton number M

and

Mixing parameter

'Hij

ijij i

WM

s G

0.1250.001Re (2 / )ij ij ijs l

'Hij ij ij kW s G

'Hij

ijij k

W

s G

Re / ;

2k h

h ij

G D

D s

Rowe and Angle 1967Rogers and Rosehart 1972Rogers and Tahir 1975Gonzalez-Santalo and Griffith 1972Rudzinski et al. 1972Kuldip and Pierre 1973Beus 1970



ANS-AtlantaTurbulence Mixing by COBRA-IIIc (Energy)

'

1 1" j iH

fi M K Tj ij

j iHij T

k ij

h hA Q q ndA A

z z x

h hW

x

COBRA-IIIc

'Hij ij ij kW s G

So far, mechanistic modeling; Single-phase mixing parameter correlation is appropriate in the range =0.0045-0.005.

However, is often adjusted to get the best fit to experiment.



ANS-AtlantaA gap to close

Classical turbulent mixing has not been satisfactory in predicting temperature distributions

It has been pointed out some other mixing mechanisms are responsible for the gap between subchannel analysis and the experiment

Global Flow Pulsation (GFP) is proposed to close the gap



ANS-AtlantaOscillations

We want to define a characteristic frequency and a characteristic length

When Reynolds averaged Secondary Flows

Oscillations appear early in the laminar-turbulent transition (Reynolds threshold) a particular mechanism of instability plays a role ?

Computational Approach

DNS LES URANS

Simpler eccentric annular channels bundle subchannels



ANS-Atlanta

37-rod Bundles Air flow inside the

bundle

Large scale oscillations when P/D < 1.1Experiments of Krauss and Meyer

Data from: Krauss, T. and Meyer, L., Nuc. Eng. And Design (1998)

Experimental facts

P/D=1.06Re=38,750

~ 20 m/s

Power spectra of the cross velocity



ANS-Atlanta

URANS for Global Pulsation in Pin Subassemblies

URANS test calc.Presented at NURETH-12 by E. Merzari + H. Ninokata

Cyclic B.C.s

600mm ~ 4



ANS-AtlantaGlobal Flow Pulsation

Below is the single-phase flow phenomena; while Two-phase flow structure is in chaos and never as clean as that of single phase turbulent

flows. Void drift: Driving force? Probably due to anisotropic structure of two-phase flow between

subchannels – analogy from the single-phase secondary flow motion to Global Flow Pulsation

Section



ANS-Atlanta

24 Take into account the oscillation:

− Frequency, amplitude and wave length of the cross flow oscillation; and

− Traveling speed

both to be obtained by DNS/LES/URANS

Example for comparison:

Enhanced Mixing by Flow Pulsation

0

0

:

( ) sin 2 ( )

25

0.0125 (80 )

5% ax

The cross flow velocity is assumed to follow

z tu z u

Tcm

T s Hz

u w

Turbulence and Conduction only

Outlet temp. SC i and j are 438C and 462 C

Time average



ANS-AtlantaAssumptions to Make CV Formulation and Analysis Tractable

Assumptions Liquid is treated incompressible; Transport due to turbulence is dealt with by effective eddy diffusivity

approach; Energy dissipation is neglected; and

Spatial fluctuations on the subchannel control volume surface areaare not accounted for.

Area average + spatial non-uniformity

Always we assume uniform distribution on the CV surfaces: this is not aunique problem in SCA

Three 1/6 rods share one subchannel

, ) ( , )x y x y ≮ ≯

+ Cross correlation termsu u ≮ ≯ ≮ ≯≮ ≯≮ ≯

u ≮ ≯ ?



ANS-Atlanta

Flow distribution is never uniform on the SC CV surfaces

u ≮ ≯ ?

Cannot be neglected in many cases

Cross-flows

Axial-flows



ANS-AtlantaSubchannel sub-division idea

A B

C

To represent better fuel cladding temperature distributionsHowever, this is no longer SCA …

Three 1/6 rods share one subchannel



ANS-AtlantaConstitutive Equations

State Variables: a set of subchannel equations are solved for:

and fuel temperature distributions

Constitutive eqs must be expressed in terms of averaged state variables!

, ,

in case of the two-fluid modelk k k k k ku v w and e or T

k L and G

≮ ≯ ≮ ≯, ≮ ≯



ANS-Atlanta

Physical models (constitutive models) for pressure drop ---- experimental correlation basis

P for 1D System and Subchannel Analysis code

P modeling state of the arts SOK* Responses

1D SystemAnalysis

Bundle P for Axial Flow (Re high) good

Bundle P for Axial Flow (Nat Conv) fair

Sub-channel Analysis

Subchannel P for Axial Flow (Re high) good

Subchannel P for Cross-Flow (Low Re) fair CFD

Subchannel P for Buoyancy Dominated Flows

Large Uncertainties

CFD

* State of knowledge



ANS-AtlantaInter-Subchannel Exchange Mechanisms

Subchannel exchanges are a result of cross-flow convection as well as molecular and turbulent diffusion mechanisms. Convection includes those due to divergence cross flow, global flow pulsation and void drift.

There are several mechanisms of exchange phenomena that are known even in the absence of pressure gradient in the cross-flow direction such as GFP and VD.

Void drift phenomena of two-phase flows may be calculated by a diffusion model on the long-time-average basis but are not a diffusion phenomenon but a result of cross-flow convection to the equilibrium void redistribution

Single-phase flow Two-phase flow

1. Divergence Cross Flowpressure drop correlation

Two-phase multiplier applied

2. Turbulent Diffusioneddy diffusivity model (turbulent mixing)

Two-phase multiplier applied

3. Global flow pulsation phenomena

Void drift phenomena0

dp

dx

0dp

dx



ANS-Atlanta

Heat Transfer Coefficient

In general, Nu=f(Re, Pr): Dittus-Boetler equation and its variants

Sodium flows in rod bundles: FFTF-CRBRP

Non-metallic flows in rod bundles

5.0 3.8 0.864.0 0.16 / 0.33 / ( /100)

/ , Re Pr

Nu P D P D Pe

where

Nu hD k Pe



ANS-Atlanta

WIRE-WRAPPED FUEL ROD BUNDLE

Bundle vs subchannel pressure drop model

Forcing function model and Distributed Resistance Model



ANS-AtlantaPressure Drop Correlations

Subchannel p/z for wire-wrapped fuel subassemblies: Novendstern

Chen-Todreas Model

S/A inlet outlet form losses

1 smoothf Mf

0.8856.94 0.086

10.124 2.239

29.7( / ) Re1.034

( / )/

P DM

H DP D

Note: these integral bundle-based models do not account for the distributed resistance, in subchannel-wise



ANS-Atlanta

wj

Wire Forcing Function model and DRM

Wire forced flow assumption --- no consideration for momentum conservation; in the classic COBRA-IIIC

===================================

Was replaced by DRM

Built in subchannel analysis code ASFRE at PNC (JAEA)

DRM: Ninokata Efthimiadis and Todreas(Nucl Eng Des 104 (1987) 93-102

COBRA-IIIC: A digital computer program for steady state and transient thermal-hydraulic analysis of rod bundle nuclear fuel elements, D.S. Rowe, BNWL-1695, 1973tan ,

: wire wrap angle; : wire wrap pitch

ij j

Du w

PP



ANS-Atlanta

Time- and CV-Averaging N-S Eqs results in DRM and Turbulent Mixing (Once again)

Distributed Resistance at the Fluid-Solid Interface

1[ ] [ ]

fs

DRAf

F p pn n dAV



ANS-AtlantaDistributed Resistance Model for Wire Spacers 1

Ninokata et al., NED, 1987.v

w

u

Conventional flow resistance models: Employ average characteristics of SCs

Complete separation of axial and lateral components

Distributed resistance models: Employ local characteristics of each SC

Proper decomposition of flow resistance forces

Solve N-S eq with these forces; As a result of force balance:, the velocity is obtained



ANS-AtlantaDistributed Resistance Model for Wire Spacers 2

Modified Blasius type friction model by Rehme, …, etc

For predominantly lateral flows, Gunther-Shaw models, taking account the wire position (Fig), etc.

For predominantly axial flows, modified G-S correlation by drag coefficient for the free stream flow over a cylinder

A TR WF and F components

L NR WF and F components

Need to provide local flow resistance models to



ANS-Atlanta

Other Modeling of Wire-Wrap Effects – Momentum Source Model (Rui Hu, ANL)

38

φ

θ

npn

nn

nt

perpendicular to the paper plane

x

z

nt

nn

pin surface

Fill the gap between the traditional CFD method and the sub-channel method

Reduce the geometric mesh complexity

Directly derived from N-S Equations, and dependent on local velocity

Mesh flexible for implementation

The MSM blocks the flow in the wire normal directions:

fn

Cvn (vn vt cos vpn )

dw

(nn

) fpn

Cvpn (vn vt cos vpn )

dw

(npn

)

ft

f frvt

2

2dw

(nt

)

Introduce additional friction in the wire tangential direction:



ANS-Atlanta

Number of Calculation FEM Meshes: 2.8 Million

Turbulence Model: k-/k-e Model for momentum/energy

Convection Term: SUPG (Brooks & Hughes)

Wall Boundary: Wall Function

(Reichardt Eq./Kader Eq.)

Calculation Mesh (Horizontal Section)

Simulation by the FEM code SPIRAL (JAEA)(Courtesy of Dr. Hideki Kamide, JAEA)

39



ANS-Atlanta

40

Axial Velocity

Lateral Velocity Streamline

Measured Temperature

Predicted Temperature

4.5mm below Top of Heated Region

Simulation by the FEM code SPIRAL (JAEA)(Courtesy of Dr. Hideki Kamide, JAEA)



ANS-Atlanta

ハンドリングヘッド

上部スペーサパッド

中間部スペーサパッド

下部スペーサパッド

エントランスノズル

ワイヤースペーサ

炉心燃料棒

ラッパー管

＜水平断面図＞

＜全体図＞

Wire-SpacerFuel Pin

Wrapper Tube

Entrance Nozzle <Cross Section>

Fuel Assembly

Difficulties in Mockup Experiments Complicated Geometry, High Cost Numerical

Approach

Detailed Temperature Distributions

Structural Integrity of Fuel Pin

- Normal Operation

(Full Power ~ N.C. Decay Heat Removal)

- Transient / Accident Conditions (Local Fault, Boiling)

- Deformed Geometry Condition (Swelling, Creep)

Clarification of Thermal-Hydraulic

Phenomena in Fuel Assembly

High Performance Core of Sodium Cooled Fast Reactor (High Burn-up, High Power Density)

Experimental Approach

Subassembly Thermal Hydraulics Engineering (JAEA)(Courtesy of Dr. Hideki Kamide, JAEA)

41



ANS-Atlanta

Fuel Pin Deformation Distribution by BAMBOO

図 3.2-8 169 本燃料ピンバンドル水平断面内冷却材温度分布変化

＜変形前＞＜変形後＞

Coolant temperature distribution by a subchannel analysis ASFRE

<Horizontal Cross Section> <Axial Cross Section>

< Before Deformation > < After Deformation >

SCA Applications to Fluid-Structure Interactions (Courtesy of Dr. Hideki Kamide, JAEA)



ANS-Atlanta

TWO-FLUID MODEL SUBCHANNEL ANALYSIS

Formulation

Constitutive equations



ANS-AtlantaTwo-phase flow patterns in a boiling channel

Flow pattern diagram must be provided

BWR BT/Post-BT

SFR low pressure sodium boiling --- low Pr, high to low q’’

L/G ~ 103



ANS-AtlantaTwo-Phase Flow Models

HEM 2-fluid 2-field model: F+G 2-fluid 3-field model: F+G+D Multi-component 2-fluid 2- (3-) field model

Judgment of CHF is made based on experimental correlations Film dryout CHF can be well predicted

A number of constitutive equations (closure relations or physical models) required

Inter-phase transfer phenomena Interface area concentration Well-posed vs. ill-posed (pure mathematical)

q”

F G

D



ANS-AtlantaTwo-fluid model (RANS)

PDE DNS

• Local instantaneous PDE• N-S eqs• Energy eq

• Local instantaneous PDE• N-S eqs• Energy eq

Time average

• (LES to RANS)• Time-smoothed-out conservation eqs with interface tracking • (LES to RANS)• Time-smoothed-out conservation eqs with interface tracking

Leibnitz rule & local CV

average

• Local volume average with Leibnitz rule applied to moving boundary surface at the phase interface (L-G)

• Two-fluid model equation system with void fraction (RANS level)

• Local volume average with Leibnitz rule applied to moving boundary surface at the phase interface (L-G)

• Two-fluid model equation system with void fraction (RANS level)

Large SC CV average with Gauss

• 2-fluid 2-field 10 equations for 3-D representation• Physical models (closure equations)• 2-fluid 2-field 10 equations for 3-D representation• Physical models (closure equations)



ANS-AtlantaNeglected local effects

Higher order tensor terms appear as a result of the space averaging in terms of the cross-products of deviations from the area averaged state variables.

Cross products terms are those with deviations of void fraction distribution, cross-flow and three axial-flow components of each phase and their time variations. Normally these terms are ignored.

, ) ( , )k k kx y x y ≮ ≯

+ Cross correlation termsk k k k k ku u ≮ ≯ ≮ ≯≮ ≯≮ ≯

k ku ≮ ≯ ?



ANS-AtlantaNeglected local effects

Result in a loss of local information in the subchannel formulation. The information of these deviations should be obtained by experiment for the moment. Otherwise by CMFD.

These higher order tensor terms are to be expressed in terms of main subchannel state variables (surface averaged velocity components, pressure, density of each phase.) This step is undone yet.

k ku ≮ ≯ ?



ANS-Atlanta

Numerical Solution Scheme: Needs implicit coupling for low pressure boiling

Mass, Momentum, Energy of each phase

Successive substitution-type iteration scheme

− Easy coordination among separate subprogram developments;

− User feedbacks easily implemented

should, nonetheless, be avoided.

All information should be concentrated in the Poisson eqmatrix

− Almost prohibits collaborations among code subprogram development teams

Mass

MomentumEnergy EOS

Mass

Momen-tumEnergy



ANS-AtlantaSolution by Modified ICE (TRAC)

All equations are dicretized (averaged per computing cell, mesh, FE or CV)

Key 1. Need to implicit coupling of mass, momentum and energy

Key 2. Linearized convective terms

Key 3. ICE: Implicit Continuous Eulerian

Linearization of all the momentum equations

Obtain these linearized (new) velocity-pressure gradient equations and

substitute into both mass & energy equations

Eliminate energy terms from both equations and

construct a Poisson equation for the

pressure distribution

Solve the Poisson equation

Obtain new velocity as well as temperature

distributions [end of one time step]



ANS-AtlantaPhysical models

Experimental correlations for pipes of various diameter

Most physical models of subchannel analysis are based on modified version

Major Physical models SOK

Wall-fluid momentum exchange (W-F), (W-G) … P models good

Wall-fluid energy exchanges …. hWF and hWG (Dittus-Boelter) good

Interfacial momentum exchanges … Fanning friction factor concept at the interface; Wallis 1D model for annular flows; Chawla-Ishii for slug-bubbly

Large uncertainties

Interfacial mass exchanges --- kinetic theory of gases; … evaporation-condensation process is always under non-equilibrium condition

Relativelygood

Interfacial heat transfer: q”GI and q”FI, interface htc Fair

Interfacial area and Flow regime identification in two-fluid model representation

Large uncertainties

q”

F G

D



ANS-AtlantaVoid distribution in a channel two-phase flow

Simply described by

and S (= wG/wF) with quality x

and S are dictated by what?

Inter-phase Shear I

wG/wF

SAs I

At z0S and

Vapor concentration

z0




Simply described by



As I

relative to W

Inter-phase Shear I

wG/wF

SWall

shear W

f

z0




Simply described by



Inter-phase Shear I

wG/wF

SWall

shear W

f

As W or f

with the other fixed

z0

z0



ANS-Atlanta

Inter-relationship among void fraction, wall friction and interphase friction

The void concentration distribution is very sensitive (low pressure boiling, in paticular):

Steady-state One-dimensional annular flow(In the following, the subscripts G and F are denoted by g and f)

q”

F G

D

(Triangular relationship)



ANS-Atlanta

Two-phase flow multiplier, interfacial friction, void fraction and slip ratio

(I) For constant (Cf)I=0.07 (II) For constant f=16;S and are very sensitive to small changes in f and (Cf)I, respectively

(III) As (Cf)I increases; or(IV) As liquid wall shear or f increases, at the location tends to increase or decrease, respectively

Eq. (c)

Eq. (b)

H. Ninokata and A. Deguchi, Assessment of the physical models in a two-fluid model code and interpretation of experiments, Nucl. Energy, 1989, 28, No. 3, 161-170



ANS-Atlanta

References to two-fluid model boiling flow subchannel analysis

H. Ninokata and A. Deguchi, Assessment of the physical models in a two-fluid model code and interpretation of experiments, Nucl. Energy, 1989, 28, No. 3, 161-170

Ninokata, H., Okano. T., SABENA: Subassembly boiling evolution numerical analysis, Nucl. Eng. Des. 120, 349-367, 1990.

Development of the NASCA code for predicting transient BT phenomena in BWR rod bundles, H. Ninokata, M. Aritomi, T. Anegawa, et al., Proc. OECD-CSNI Workshop on Advanced Thermal-Hydraulic and Neutronic Codes: Current and Future Applications, Barcelona, April 10-11, 2000.



ANS-Atlanta

TWO-FLUID REPRESENTATION WITH AN ADDITIONAL DROPLET FIELD

BWR new fuel bundle design – axially heterogeneous, with burnable poison (Gd) distributed concentration,

New spacer design

BT and post BT phenomena

Need to predict droplet motion and their influences



ANS-AtlantaDroplets

Lagrangean treatment not appropriate

Another field added for a group of droplets

Size distribution



ANS-Atlanta

60

Liquid Film Model

Entrainment due to boilingin a film

Entrainmentdue to wavedisturbances

Deposition

Dryout

NASCA



ANS-AtlantaInfluences of Spacers

61NASCA

Three major depositionenhancement effects due to

◆ turbulence generatedbehind spacers

◆ run-off of droplets collected on spacers

Enhanceddeposition

Turbulence Runoff

Enhanceddeposition

◆ change in flow directions due to spacer

Spacer



ANS-Atlanta

Convection Diffusion Sources

Mass( )K K Ku F-G

D-GF-D

Ev.Cord

Entr & Deposit

MomentumF-GD-GF-D

F-GD-GF-D

( )K K K Ku u

( )K K K Ku e Energy

Distributed ResistanceTurbulent Mixing

Distributed heat transfer

Turbulent mixing

Two-fluid three-field formulation -1



ANS-AtlantaExamples

NASCA

H. Ninokata, T. Anegawa, M. Aritomi, T. Hara, H. Kamo, S. Kusuno, K. Mishima, S. Morooka, K. Nishida, M. Sadatomi,

A. Sou, Y. Yabushita, and Y.Yamamoto

DEVELOPMENT OF THE NASCA CODE FOR PREDICTING TRANSIENT BT

PHENOMENA IN BWR ROD BUNDLES

NASCA

OECD/CSNI Workshop on Advanced Thermal-Hydraulicsand Neutronic Codes: Current and Future ApplicationsBarcelona, Spain, April 10-13, 2000

Introduction

• NASCA (Nuclear Reactor Advanced Sub-Channel Analysis)

• is aimed at simulating thermal-hydraulics phenomena in BWR rod bundles during transients, in particular BT and post BT

• is useful to understand the BT and post BT phenomena; and

• is going to be used as a standard code in Japanese utilities and BWR vendors.

65NASCA

NASCA Code Development• On the basis of available and well established concepts;• Two-fluid three-field subchannel formulation;• Basic version completed 1996 [ISSCA-4]• Major efforts (1997- ) centered on modeling:

- two-phase turbulent mixing and void drift;- spacer effects; - BT and post BT phenomena; and- validation for separate effects experiments as well as for bundle integral experiments.

66NASCA

Two-phase flow turbulent mixing

• : 1, w, h; k : G or L

• TM : Two-phase multiplier for turbulent mixing, due to Beus / Kelly and Kazimi

• Model verification for equilibrium two-phase flows in the inter-connected two-subchannel test sections (Kumamoto University)

67

jkkikkkgapTMTP

kij

,

,

NASCA

,

kTM

TP TM SP

Void drift• Void re-distribution to equilibrium distribution• Mechanisms not clearly identified• Modeling based on the inter-connected two-subchannel experimental data

(Kumamoto University)

68

EQjkkkikkkjkkkikkkVD

VDTPkij

,

)(

k

VDSPVDTP ,

iA

jA

jkkkikkkiAjAjGiG

jGiG

aKEQjkkkikkk )()(

)/(

(Lahey’s Model)

NASCA

Two-phase multipliers

• For Mixing TM < 5 (Beus / Kelly-Kazimi)

• For VD VD = 15 for churn-turbulent flow regime (0.5 < < 0.7)

69NASCA

Results for GE3x3 bundle experiments

70

18.7mm58.8mm

Heater rod（φ14.5mm）

Channel BoxCorner

Side

Center

Fig. 1 GE 3x3 rod bundle cross section

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500

Experiment (kg/m2s)

Bundle average mass flux： 651-2672 kg/m2s

CornerSideCenter

Cal

cula

tion

(k

g/m

2s) Inlet subcooling

1174kJ/kg

Fig. 2 Comparison of subchannel mass fluxbetween calculation and experiment

NASCA

71

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5

Quality [Experiment] (-)

Qual

ity

[Cal

cula

tion]

(-)

CornerSide

Center

+0.024

-0.024

Results for GE3x3 bundle experiments

NASCA

BT and Post BTDryout Phenomena

• Vaporization of liquid film in the forced convection mode

• Droplet entrainment and deposition models• Validation for single tube experiments including

Bennet’s cold patch experiments• Check consistency with the CISE correlation• Need to improve a dependency of the critical power

on the heated length (upstream effects)• Entrainment due to boiling in the liquid film (Ueda’s

model); tuning against the Bennet cold patch tests

72NASCA

BT and Post BTRewetting phenomena

• In general very complicated• Hydrodynamic-limited regime in annular-mist flows

73

For simplicity, in NASCA, Rewetting = Liquid film flow recovery

NASCA

BT and Post BTSpacer model tuning

• For BT/post BT tests in an annular channel with simulated spacers (Yokobori, et al)

• Tuning of the weighting factors for the three major independent deposition models with respect to BT timing, location, BT duration and rewetting

• Finally for 4x4, 8x8 bundle experiments

74NASCA

Results of Bundle Calculations

75NASCA

0.9 0.9 0.9 0.9

0.9 1.3 1.3 0.9

0.9 1.3 1.3 0.9

0.9 0.9 0.9 0.9

T/C

3.7m

Spacer

0.0 0.5 1.0 1.5Relative power

Axi

al p

ositi

on

76

Comparisons of steady-state critical power

0

1

2

3

0 500 1000 1500

質量流束[kg/m2/s]

限界

出力

[MW

]

測定データ

NASCA ・Good agreement between cal. and exp.

・Dependency on massflow rate

Measurement

Mass flux

Crit

ical

pow

er

NASCA

77

Too long BT duration by cal.Conservative pred. for low mass fluxes NASCA

500

600

700

800

900

10 15 20 25 30時間[s]

燃料

棒表

面温

度[K

]

NASCA

測定第７スペーサ上流位置

0

0.2

0.4

0.6

0.8

1

1.2

10 15 20 25 30時間[s]

流動

パラ

メー

タ相

対値

流量出力

圧力

入口冷却材温度

500

600

700

800

900

10 15 20 25 30時間[s]

燃料

棒表

面温

度[K

]

NASCA

測定

第６スペーサ上流位置

500

600

700

800

900

10 15 20 25 30時間[s]

燃料

棒表

面温

度[K

]

NASCA

測定

第５スペーサ上流位置

500

600

700

800

900

10 15 20 25 30時間[s]

燃料

棒表

面温

度[K

]

NASCA

測定第４スペーサ上流位置

Comparisons for Flow Transient

Time (s)Time (s)

Rod

sur

face

tem

pera

ture

[K]

Rod

sur

face

tem

pera

ture

[K]

Inlet coolant temp

pressurePower

Flow

Upstream of 4th spacer




meas.

meas.

meas.

meas.

78

Good agreement for BT timing, temperature behaviors and rewetting NASCA

0

0.5

1

1.5

2

10 15 20 25 30時間 [s]

流動

パラ

メー

タ相

対値

出力

圧力

流量入口温度

500

600

700

800

900

10 15 20 25 30時間 [s]

燃料

棒表

面温

度[K

]

NASCA

測定第 7スペーサ上流位置

500

600

700

800

900

10 15 20 25 30時間 [s]

燃料

棒表

面温

度[K

]

NASCA

測定第６スペーサ上流位置

500

600

700

800

900

10 15 20 25 30時間[s]

燃料

棒表

面温

度[K

]

NASCA

測定第５スペーサ上流位置

500

600

700

800

900

10 15 20 25 30時間[s]

燃料

棒表

面温

度[K

]

NASCA

測定第４スペーサ上流位置

Comparisons forPower Transient

Power

FlowInlet coolant temp

pressure

Time (s)Time (s)

Rod

sur

face

tem

pera

ture

[K]

Rod

sur

face

tem

pera

ture

[K]





meas.

meas.

meas.

meas.

79

Changes in liquid volume fraction and fuel rod surface temperature distributions (1/6) [Power transient]

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

15 20 25 30 35 40 45 50

軸方向ノード位置

液膜

体積

割合

スペーサ位置

500

550

600

650

700

750

800

850

900

15 20 25 30 35 40 45 50


燃料

棒表

面温

度[K

]

スペーサ位置

Steady-statebefore transient

T=16 s

F

ilm

Axial Node PositionR

od S

urfa

ce T

emp

[K]

Axial Node PositionNASCA

Spacer position

Spacer position

80

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

15 20 25 30 35 40 45 50


液膜

体積

割合

スペーサ位置

500

550

600

650

700

750

800

850

900

15 20 25 30 35 40 45 50


燃料

棒表

面温

度[K

]

スペーサ位置

T=17 s

Film thinning

NASCA


Rod

Sur

face

Tem

p[K

]

F

ilm

Axial Node Position

Axial Node Position

Spacer position

Spacer position

81

NASCA


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

15 20 25 30 35 40 45 50


液膜

体積

割合

スペーサ位置

500

550

600

650

700

750

800

850

900

15 20 25 30 35 40 45 50


燃料

棒表

面温

度[K

]

スペーサ位置

T=18 s

ＢＴＢＴＢＴ

Film Film

Spacer position

Spacer position

Rod

Sur

face

Tem

p[K

]

Axial Node Position

F

ilm

Axial Node Position

82

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

15 20 25 30 35 40 45 50


液膜

体積

割合

スペーサ位置

500

550

600

650

700

750

800

850

900

15 20 25 30 35 40 45 50


燃料

棒表

面温

度[K

]

スペーサ位置

T=19 s

Film thickening

NASCA


Rod

Sur

face

Tem

p[K

]

F

ilm

Axial Node Position

Axial Node Position

Dryout

Spacer position

Spacer position

83

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

15 20 25 30 35 40 45 50


液膜

体積

割合

スペーサ位置

500

550

600

650

700

750

800

850

900

15 20 25 30 35 40 45 50


燃料

棒表

面温

度[K

]

スペーサ位置

Thick film propagation

Film thickness increase downstream of a spacer

Rewetting due to the propagation of a film down-stream of the spacer

T=20 s

NASCA


Rod

Sur

face

Tem

p[K

]

F

ilm

Axial Node Position

Axial Node Position

Spacer position

Spacer position

84

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

15 20 25 30 35 40 45 50


液膜

体積

割合

スペーサ位置

500

550

600

650

700

750

800

850

900

15 20 25 30 35 40 45 50


燃料

棒表

面温

度[K

]

スペーサ位置

Rewetting completed

T=21 s

NASCA


Rod

Sur

face

Tem

p[K

]

F

ilm

Axial Node Position

Axial Node Position

Spacer position

Spacer position

85

Summary of Bundle Calculations• Critical power prediction：flow rate dependency

• Steady-state critical power: good agreement with experiment

• Flow transient： good agreement for BT timing；late for rewetting

• Power transient： good agreement for BT timing； earlier rewet timing

• Additional subdivision of subchannels yields good results for high burnup 8×8 fuel rod bundles with unheated water rod(s) [not shown here]

• Good results obtained for NUPEC 8x8 rod bundle experiments [not shown here]

NASCA

DEVELOPMENT OF THE NASCA CODE FOR PREDICTING TRANSIENT BTPHENOMENA IN BWR ROD BUNDLES

NASCA



ANS-AtlantaRecent results

Application of NASCA to OECD/NRC NUPEC BWR Full Size Fine-Mesh Bundle Test, K. Nozaki, et al. NURETH-12 (2007)

Analytical Study on Boiling Transition under Flow-Power Oscillating Condition for Hyper ABWR, K. Nozaki, et al, 13th JSME Symposium on Power and Energy Technology, June (2008)

Multi-component multi-phase flow subchannel analysis

Relevant to Nuclear Reactor Thermal Hydraulics



ANS-Atlanta

MULTI-PHYSICS PHENOMENA MODELING

(the following notes consist of information from JAEA and R&D results at the Tokyo Institute of Technology)

Fuel S/A degradation and CDAs

Calculation quality depends on the physical models



ANS-AtlantaComputational 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 (fuel, steel, Na), 3-phases and 2-

or 3-velocity fields (mixture velocity fields):

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

Phase interfaces --- topology

Component Solid-phase Liquid-phase Vapor-phase

Fuel X X X

Steel X X X

Sodium X X

2 velocity fields Mixture velocity field Gas-phase v



ANS-AtlantaIn-Pile Experiments

International cooperation: PNC (JAEA)-DeBeNe-CEA, PNC(JAEA)-USNRC/DOE, …, etc CABRI

SCARABEE

TREAT, SLSF

EBR-II

…

IGR-EAGLE (Experimental Acquisition of Generalized Logic to Eliminate criticalities)

Phebus

NSRR, …

91



ANS-Atlanta

CEC

Reactor core

Coolingwater cavity

Control rod channel

Cross-section of IGR core(NNC in Kazakhstan)

CDA Evaluation Methods & Mitigation Measures- Upward Discharge Experiment in EAGLE Project of JAEA -

PERFORMANCEMax. thermal neutron flux density:Max. thermal neutron fluence:Min. half-width of pulse:Max. energy release:Central Experimental Channel (CEC):

7×1016 n/cm2s3.7×1016 n/cm2

0.12 s5.2 GJφ228mm×L3825mm



ANS-Atlanta

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)

IGRcore

Fuel pins to be molten

Simulated core part

Discharge path

Simulated upper plenumSodium

CDA Evaluation Methods & Mitigation Measures- Upward Discharge Experiment in EAGLE Project of JAEA -

93



ANS-Atlanta

Validation of subassembly degradation and core meltdown, relocation models by TIT

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

Fuelpin

6 5 4 3

1 2

14 13 12 11 10 9 8 7

19 18 17 16 15

Fissile length 60cm



ANS-Atlanta

Multi-component multi-field model application to SCARABEE-BE+2 and APL Experiments: VIDEO

Subchannel analysis for interpretation of SCARABEE in-pile experiments by the KAMUI code

KAMUI BE+2 : Instantaneous total inlet blockage Fuel assembly at full power What happened if the inlet nozzle were totally blocked and if

scram failed?

KAMUI APL : Unprotected loss of flow Fuel assembly at full power What happened if the pump stopped and if the scram failed?

The multi-fluid multi-phase subchannel analysis code KAMUI for subassembly accident analysis of an LMFR, Fumio Kasahara and Hisashi Ninokata, Journal of Nuclear Science and Technology, 37, No.8 (2000) 654-669.

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



ANS-Atlanta

H. Ninokata and E. Merzari 97

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

Proper Orthogonal Decomposition (POD) Technique (Elia Merzari, NED 241 (2011) 4621-4632; PhD thesis at Tokyo Inst Tech)



ANS-Atlanta

H. Ninokata and E. Merzari 98

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



ANS-Atlanta

Uncertainty identification in physical modeling -1 Marco Pellegrini, PhD thesis, TIT (2012)

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



ANS-Atlanta


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, ..



ANS-Atlanta


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 surfaceMean 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



ANS-AtlantaComments

• 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



ANS-Atlanta

103

CFD Applications to LMFRs, LWRs

Replacement of subchannel analysis by LES would be desired eventually --- Less modeling required

Computational results are substantially dependent on:

Specified mesh schemes and boundary conditions;

Numerical schemes in general, model selections which require users’ knowledge on turbulence and expertise in creating specific simulation models and interpreting the results of the simulations.

Note: there is no universal approach in CFD other than directly

solving the N-S equations (DNS)



ANS-Atlanta

Principle of physics modeling for subchannel analysis

Physical models incorporated into the subchannel analysis (as well as other computational methods) must be as simple as possible

Only small scale channel experiments are good enough Similarity is better to be established

Up to now, classical correlations have been the substantial ingredients of subchannel analysis

However, most correlations were developed when a large CPU was not available

Mechanistic modeling Need large expensive mock-ups? No Clarify mechanisms of the phenomena, identify key parameters

and express them in terms of the state variables of SCA Some regulatory authorities, project leaders or management often

don’t understand the importance and therefore the need from computations



ANS-Atlanta

Profile of Hisashi NINOKATABA in physics (1970), MS (‘72) and Dr. Eng (‘77) in NE, The University Tokyo

TEPCO (’77‐’80), PNC (’80‐’93), TITech (’93‐’12), POLIMI (’12‐ )

Rotary International Fellowship Exchange Student to MIT NE where he has started his rod bundle TH since 1972: MIT Mixing Project ; VELASCO code;

… in ’80s to ’90s,

Involved in Liquid Metal Boiling Working Group (LMBWG) organized by JRC Ispra, KfK, CEA and PNC in ’80s, IAHR Liquid Metal WG

Fast breeder TH and safety: subchannel analysis code (ASFRE and SABENA) development for Na boiling; COMMIX‐AQUA code development (ANL);

SIMMER‐AFDM development (LANL); CABRI project

… from ’90’s to present,

BWR BT and post BT analysis; SMR design (IRIS, SFR)

NRx core neutronics‐TH design, self‐controllability, Risk‐informed Design with PSA

CFD applications to turbulent flows in fuel subassemblies

Fukushima Dai‐ichi accident evaluation in AESJ, ANS, …communication with the public

ENDand

Thank you

nuclear fuel assembly thermal hydraulics analysis...

Documents