DEVELOPMENT OF COMPUTATIONAL MULTIFLUID DYNAMICS … · DEVELOPMENT OF COMPUTATIONAL MULTIFLUID DYNAMICS MODELS FOR NUCLEAR REACTOR APPLICATIONS Henryk Anglart Royal Institute of

DEVELOPMENT OF COMPUTATIONALMULTIFLUID DYNAMICS MODELS FORNUCLEAR REACTOR APPLICATIONS

Henryk AnglartRoyal Institute of Technology, Department of Physics

Division of Nuclear Reactor TechnologyStockholm, Sweden

SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006

2

Outline of the Presentation

• Introduction

• Prospective applications of CMFD innuclear field– focus on fuel assemblies

• Model description

• Example predictions

• Conclusions


3

Introduction

• CMFD is used for thermal-hydraulic analyses ofvarious parts of nuclear power plants:– Reactor cores and fuel assemblies

– Primary systems

– Containment systems

• Analysis of fuel assemblies has large potentialdue to:– Economical reasons (increased power)

– Safety reason (better estimation of thermal margins)


4

Typical LWR Fuel Assemblies


Top tie plate

Fuel rod

BoxWater cross

Spacer grid

Bottom tie plate

PWR fuelassembly

BWR fuelassembly

5

Typical Spacer Grid


Spacer grid is made of platewith 0.2-0.3 mm thickness.Grid height is ~30 mm, andside length ~65 mm

There are usually 7-8 spacergrids along assembly fulllength (~3.7 m)

6

Thermal Hydraulic Performanceof Fuel Assemblies

• Predictions of thermal-hydraulicperformance of fuel assemblies withspacers– Pressure drop

– Void fraction distributions

– Thermal margins, that is conditions whencritical heat flux occurs


7

Design of Fuel Assemblies

• For design purposes, it is interesting toknow the influence of geometry featureson the thermal performance:– Rod lattice pattern (pitch/diameter ratio, etc)

– Shape of sub-channels

– Spacer grid details (shape, mixing vanes, tabs,etc)


8

Four-Fluid Model – GoverningEquations

• Mass

• Momentum

• Energy


( ) ( ) ( )∑≠=

Γ−Γ=⋅∇+∂

∂ pN

kjjjkkjkkk

kkt ,1

Uραρα

( ) ( ) ( )( )[ ]

( ) ∑∑≠=≠=

+Γ−Γ

++∇−∇+∇⋅∇=⋅∇+∂

∂

pp N

kjjkj

N

kjjkjkjkj

kkkkT

kkekkkkkk

kkk pUUt

,1,1

MUU

gUUU

ρααµαραρα

( ) ( ) ( ) ∑∑≠=≠=

+Γ−Γ+=∇−⋅∇+∂

∂ pp N

kjjkj

N

kjjkjkjkjkk

ekkkkkk

kkk EHHQTHt

H

,1,1

λαραρα

U

9

Turbulence Model


∑≠=

++=pN

kjj

tkj

tkk

ek

,1

µµµµ lbbblbtlb dC UU −= αρµ µ

k

kk

tk

KC

ερµ µ

2=

Effective viscosity

laminar eddy

Interface-induced

( ) ( ) ( ) ( )kj

N

kjj

Kkj

N

kjjkjkjkj

Kkkk

ekkkkkk

kkk KKcKKSKKt

K pp

−+Γ−Γ+=∇−⋅∇+∂

∂∑∑

≠=≠= ,1,1

αµαραρα

U

( ) ( ) ( ) ( )kj

N

kjjkj

N

kjjkjkjkjkkk

ekkkkkk

kkkpp

cSt

εεεεαεµαεραερα εε −+Γ−Γ+=∇−⋅∇+

∂

∂∑∑

≠=≠= ,1,1

U

K-_ model

10

Interfacial Transfer Terms

• Mass– Homogeneous condensation

– Heterogeneous evaporation

• Momentum– Drag force

– Lift force

– Wall lubrication force

– Turbulent dispersion force

– Virtual mass


11

Subcooled Boiling Model


Γlb' ' =

hlb Tsat − Tl( )hfg

Γbl

bwg

w

fg

df N subcooled

q

hsaturated

''

''

''=

πρ

3

6

convection evaporation quenching

convection evaporation quenching

12

Computational Grid Used forSVEA Fuel Assembly


13

Phase Distribution in Two-PhaseBubbly Flows

Measured void fraction distribution in a 5x5 bundle: G = 1460.6 kg/m2/sp = 31.9 bar, q’’ = 543 kW/m2, inlet subcooling 6 K


14

Phase Distribution in Two-PhaseBubbly Flows

0

5

10

15

20

25

30

35

40

25 26 27 28 29 30

Subchannel Number

Voi

d fr

acti

on

MeasuredCalculated

Predicted void fraction distribution in a 5x5 bundle: G = 1460.6 kg/m2/sp = 31.9 bar, q’’ = 543 kW/m2, inlet subcooling 6 K


15

Two-Phase Annular Flow Model

• Additional mass, momentum and energyconservation equations are solved for liquid filmin annular flow

• Interfacial mass transfer includes– Evaporation– Entrainment– Deposition

• Wall shear model based on local film thickness• The modal enables prediction of dryout of the

liquid film

Workshop on Modelling and Measurements of Two-Phase Flows and Heat Transfer in NuclearFuel Assemblies, October 10-11 2006, KTH, Stockholm, Sweden

16

thinnest film measured dryout

G = 450 kg/m2/s,

p = 70.8 bar,

q = 1259 kW/m2,

inlet subcooling 15.8 K

Predicted thinnest liquid film is inneighborhood of rods which wentunder dryout

Annular Two-Phase Flows

6.344.7845.2

5.83.6633.6

6.213.9634.9

5.53.4132.3

6.163.9834.2

5.663.5533.1

6.653.8331.6

5.362.927.6

5.432.9427.8

6.043.9635.6

5.43.3432.0

5.973.3229.4

6.343.6030.6

6.623.8031.5

6.244.0635.9

5.303.2531.5

5.302.8427.2

5.773.1828.8

6.003.3630.3

5.904.0036.8

6.143.9434.0

5.433.4833.4

6.103.9435.3

5.934.0337.0

Inlet film mass flux, 10 -2 kg/ms

Outlet film mass flux, 10 -2 kg/ms

Outlet film thickness, 10 -6 m

Inlet film mass flux, 10-2 kg/ms

Outlet film mass flux, 10-2 kg/ms

Liquid film thickness, 10-6 m


17

thinnest film measured dryout

G = 1571 kg/m2/s,

p = 70.9 bar,

q = 2612 kW/m2,

inlet subcooling 10.5 K

Predicted thinnest liquid film is onthe rod which went under dryout

Annular Two-Phase Flows

42.1 30.6 30.6 29.3 29.9

29.8 26.5 26.0 26.0 32.1

29.2 25.7 25.7 26.4 31.2

28.8 25.6 24.9 25.9 32.9

29.4 31.1 30.9 32.8


18

Conclusions

• Current model can be applied for prediction ofphase distribution and heat transfer in dispersedtwo phase flows (bubbly and annular flows)

• Challenges for future development include:– Prediction of turbulence structure in fuel assembly

– Phase distributions in two-phase non-disperse flows

– Prediction of CHF (DNB and dryout) based onmechanistic principles


19

Conclusions (cont’ed)

• Future focus will be on development ofsub-models suitable for rod bundlegeometry

• Validation should be performed againstdetailed measurements in rod bundles– Validation against data obtained in pipes is

not enough


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DEVELOPMENT OF COMPUTATIONAL MULTIFLUID DYNAMICS … · DEVELOPMENT OF COMPUTATIONAL MULTIFLUID DYNAMICS MODELS FOR NUCLEAR REACTOR APPLICATIONS Henryk Anglart Royal Institute of