IMPROVEMENT OF MOLTEN JET … OF MOLTEN JET FRAGMENTATION MODELING IN MAAP ERMSAR 2017, Warsaw, Poland May 16-18, 2017 A. Le Belguet, E. Beuzet, M. Torkhani PERICLES, Nuclear Safety

IMPROVEMENT OF MOLTEN JET FRAGMENTATION

MODELING IN MAAP

ERMSAR 2017, Warsaw, PolandMay 16-18, 2017

A. Le Belguet, E. Beuzet, M. Torkhani

PERICLES, Nuclear Safety and Fuel Cycle

Contact: [email protected]

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INTRODUCTION

Context

Many experimental and theoretical studies performed on corium jet fragmentation in water…

But still some uncertainties and lack of knowledge

MAAP(version 5.02-EDF) (Modular Accident Analysis Program)

Integral code developed by Fauske & Associates, LLC to simulate of an overall SA sequence

Adapted to French PWRs and co-developed by EDF

Jet fragmentation mechanism taken into account in MAAP

Improvement of molten jet fragmentation modeling in MAAP | 16/05/2017

Hypothetical severe accident

in a PWR

Core degradationand meltformation

Fuel-CoolantInteraction

(in or ex-vessel)

Corium jet break-up and droplet

formation

MFCI consequences ?

Goal of the present work

Improve jet fragmentation modeling to reduce MAAP conservatism regarding pressurization and melt fragmentation

Provide some developments in the code using MAAP5.02a version

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OUTLINE


1. INTRODUCTION

2. TWO-PHASE FLOW AND PARTICLE SEDIMENTATION

TWO-PHASE FLOW: AMBIENT PROPERTIES

PARTICLE SEDIMENTATION: A NEW EVALUATION OF THE DRAG COEFFICIENT

3. EVALUATION OF VAPOR PRODUCTION RATE

HEAT TRANSFER IN FILM BOILING REGIME

HEAT PARTITION AND VAPOR PRODUCTION

VAPOR CONDENSATION

4. A NEW EVALUATION OF THE SIZE OF CORIUM PARTICLES RESULTING FROM JET FRAGMENTATION

5. FARO TESTS SIMULATION

6. CONCLUSIONS AND PERSPECTIVES

TWO-PHASE FLOW AND PARTICLE SEDIMENTATION

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TWO-PHASE FLOW: AMBIENT PROPERTIES

Physical properties (density, viscosity) : involved in the evaluation of jet fragmentation, as well as the size and the sedimentation of corium debris


MFCI

Water heat-up

Vaporproduction

Intense if ΔTsub small

Increase of local αV

Physical properties : density and viscosity

Two-phase mixture MAAP

ρa = αVρV(Tsat) + (1-αV)ρL(TL)

μa = αVμV (Tsat) + (1-αV)μL(TL)

ρa = ρL(TL)

μa = μL(TL)

Ambient properties accounting for αV

implemented in MAAP

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PARTICLE SEDIMENTATION: A NEW EVALUATION OF THE DRAG

COEFFICIENT (1/2) Drag force FD: impact on debris sedimentation and cooling

The drag coefficient CD depends on:

the shape and size of the element: here a sphere

the fluid in which this element falls: here liquid water and/or steam

the flow regime (laminar or turbulent) Reynolds number Re

the boiling regime Tp > or < TMFB


Dp

2

paD CAUρ2

1F

In MAAP:CD = 1.0

C.T. Crowe, Multiphase Flow Handbook, CRC Press, September 2005 I.U. Vakarelski et al, Leidenfrost vapour layer moderation of the drag crisis and trajectories of superhydrophobic and hydrophilic spheres falling in water, The Royal

Society of Chemistry, Soft Matter, 10, 5662-5668, 2014

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PARTICLE SEDIMENTATION: A NEW EVALUATION OF THE DRAG

COEFFICIENT (2/2) New evaluation of CD proposed and implemented in MAAP

MAAP reproduces correctly experimental results, either in the film boiling regime or not, as long as Re is lower than 106. Beyond that value, no data enable to predict CD.


0,0

0,2

0,4

0,6

0,8

1,0

1,2

1E+01 1E+02 1E+03 1E+04 1E+05 1E+06 1E+07

Dra

g co

effi

cien

t, C

D

Reynolds number, ReMAAP - No vapor film MAAP - With a vapor film

[6] No vapor film (exp.) [6] With a vapor film (extrapolation)

[6] Hydrophilic spheres-No vapor film [6] Superhydrophobic spheres-With a vapor film

[8] Exp. Results-No vapor film

EVALUATION OF VAPOR PRODUCTION RATE

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CONTEXT

During MFCI, vapor production rate around particles evaluated according to :

heat lost by corium debris: Qc

heat transferred from liquid-vapor interface to coolant: Qcl

In MAAP: modeling of heat transfer and steam generation based on a simplified (but conservative) approach

Improvements suggested for a more physically consistent modeling.


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HEAT TRANSFER IN FILM BOILING REGIME

Heat transfer between corium and the surroundings: mainly in film boiling, particularly for low subcooling and high superheat

Evaluation of forced convection in film boiling regime Qconv and radiative heat transfer Qrad:

Qc = Qconv + J Qrad with J = 7/8

In MAAP: Qc based on corium enthalpy change from the jet temperature Tj to the final particle temperature Tp

Evaluation of Qconv: based on Epstein-Hauser correlation (used in MC3D)

Evaluation of Qrad assuming that:

Heated surface and the L-V interface = two plane-parallel plate at respectively Tpm and Tsat

Corium: opaque and gray body, steam: transparent, water: black body

Liquid and vapor properties:

In MAAP: evaluated at TL and Tsat

Use of mean temperatures: TLm = (TL + Tsat)/2 and TVm = (TL + Tj)/2

Expected to have a significant impact on convective heat transfer but steam tables in MAAP do not allow to reach such temperatures


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HEAT PARTITION AND VAPOR PRODUCTION

Heat partition during MFCI

Evaluation of Qcl proposed in MAAP

Whitaker’s correlation: forced convection correlation around a solid sphere at the temperature Tsat

Considering that 90% of the radiative heat transfer from corium particles are devoted to heat up water, while the remaining 10% are absorbed at the liquid-vapor interface to produce vapor


Heat lost by corium particles

Water heat-up Qcl

Vaporproduction

Qcv

c

cl

c

cvcv

Q

Q1

Q

QF

Heat partition Fcv

Qc = Qcv + Qcl

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VAPOR CONDENSATION

Vapor produced around corium particle:

Flows upward in water

Condensates in the surroundings, depending on water subcooling, vapor superheat and flow rate

In MAAP: vapor condensation considered through the use of the Jakob number Ja:

Accounts for the temperature variation of entrained water, with no phase change

Not consistent with vapor condensation through convective heat transfer between possibly superheated vapor and water

Void fraction: user-defined parameter involved in Fcv calculation

New evaluation of vapor bubble condensation

Evaluation of Qcond using Whitaker’s correlation (forced convection heat transfer around a solid sphere)

Evaluation of Fcv considering vapor condensation in water:


Ja1FF cv

*

cv

fgg

wsatw,pw

hρ

TTcρJa

c

condcl

c

condcvcv

Q

QQ1

Q

QQF

A NEW EVALUATION OF THE SIZE OF CORIUM PARTICLES RESULTING FROM JET FRAGMENTATION

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SIZE OF CORIUM PARTICLES RESULTING FROM JET FRAGMENTATION

In MAAP: the particle diameter Dp assumed to be at least:

the capillary length in case of gravity pour

the stable particle diameter defined as a function of the critical Weber number in case of a hydrodynamic fragmentation

A new correlation of Dp in MAAP: Namiech’s correlation

Corium particles stripped from the jet as it penetrates water

Namiech’s model: focus on the erosion process (particles part of the counter-current vapor flow surrounding the jet)

Particle diameter only accounts for primary fragmentation, without considering secondary fragmentation

Particle diameter evaluated from the derived correlation


FARO TESTS SIMULATION

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FARO EXPERIMENT

Large-scale experimental program dedicated to MFCI analysis and quenching behavior under both in- and ex-vessel severe accident conditions

Prototypical corium poured by gravity into a pool of saturated or subcooled water

Water mass: 330 kg - 719 kg

Corium mass: 39 kg - 177 kg

Initial jet diameter: 50 mm - 100 mm

Water subcooling: 0 K - 122 K

Consistent information on jet fragmentation and premixing (12 tests)

L-28 and L-31 tests selected: saturated vs. subcooled conditions


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FARO L-28 TEST SIMULATION

FARO L-28 calculation without modification, compared to experimental data

Pressure: 17% higher

Overestimation of gas temperature (~ 75 K) and of water temperature (to a lesser extent)

Final particle size: good agreement with the mean diameter of collected debris


5,0E+05

8,0E+05

1,1E+06

1,4E+06

1,7E+06

2,0E+06

0 1 2 3 4 5 6 7 8

Pre

ssu

re (

Pa)

Time (s)

Exp. data

Reference

400

425

450

475

500

0 1 2 3 4 5 6 7 8W

ate

r te

mp

era

ture

(K

)Time (s)

Pressure (Pa) Water temperature (K)

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When considering developments (at TV = Tsat):

Pressure: largely underestimated (~ 44%), as well as

Water temperature: also underestimated (~ 32 K)

Particle size (Namiech’s correlation): correct order of magnitude (20% higher)

Secondary fragmentation, not accounted for in Namiech’s correlation


5,0E+05

8,0E+05

1,1E+06

1,4E+06

1,7E+06

2,0E+06

0 1 2 3 4 5 6 7 8

Pre

ssu

re (

Pa)

Time (s)

Exp. data

Reference

Modified

400

425

450

475

500

0 1 2 3 4 5 6 7 8W

ate

r te

mp

era

ture

(K

)

Time (s)


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Vapor properties involved in heat transfer calculation evaluated at Tsat

≠ Vapor film temperature around corium particles: much higher, at TVm

Significant impact on convective heat transfer

New calculation considering TVm: extrapolation of steam tables in MAAP: hV, ρV + λV, cp,V

Improvement of pressure and water temperature prediction

Importance of having steam tables valid for a wider temperature range in MAAP


5,0E+05

8,0E+05

1,1E+06

1,4E+06

1,7E+06

2,0E+06

0 1 2 3 4 5 6 7 8

Pre

ssu

re (

Pa)

Time (s)

Exp. data

Reference

Modified

Modified+VaporProperties

400

425

450

475

500

0 1 2 3 4 5 6 7 8W

ate

r te

mp

era

ture

(K

)

Time (s)


CONCLUSIONS AND PERSPECTIVES

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CONCLUSIONS AND PERSPECTIVES

Developments carried out in MAAP5.02-EDF to improve jet fragmentation modeling:

Sedimentation of corium debris in two-phase flow: ambient properties, drag coefficient depending on turbulence and on water boiling regime

Heat transfer between melt and the surroundings: film boiling heat transfer, vapor production, steam condensation

Debris size: implementation of Namiech’s correlation for primary jet fragmentation with no adjustment parameter nor arbitrary critical Weber number

More physical consistency in MAAP modeling, avoiding the use of user-defined parameters

FARO L-28 and L-31 simulations with MAAP5.02-EDF

With the developments: computed pressure and water temperature underestimated

BUT improvement when considering steam properties at a more physical temperature, i.e. the vapor film temperature, instead of saturation conditions

Need for steam tables in MAAP to be valid for a wider temperature range

Further improvements identified such as:

Extending steam tables validity in MAAP

Improving debris size and corium oxydation modeling


ANNEX

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FARO EXPERIMENT

Large-scale experimental program dedicated to MFCI analysis and quenching behavior under both in- and ex-vessel severe accident conditions

Prototypical corium poured by gravity into a pool of saturated or subcooled water

Water mass: 330 kg - 719 kg

Corium mass: 39 kg - 177 kg

Initial jet diameter: 50 mm - 100 mm

Water subcooling: 0 K - 122 K

Consistent information on jet fragmentation and premixing (12 tests)

L-28 and L-31 tests selected: saturated vs. subcooled conditions


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5,0E+05

8,0E+05

1,1E+06

1,4E+06

1,7E+06

2,0E+06

0 1 2 3 4 5 6 7 8

Pre

ssu

re (

Pa)

Time (s)

Exp. data

Reference

Modified

Modified+VaporProperties

400

425

450

475

500

0 1 2 3 4 5 6 7 8

Wat

er

tem

pe

ratu

re (

K)

Time (s)


400

450

500

550

600

0 1 2 3 4 5 6 7 8

Gas

te

mp

era

ture

(K

)

Time (s)

0,0E+00

1,0E-03

2,0E-03

3,0E-03

4,0E-03

5,0E-03

0 1 2 3 4 5 6 7 8

Par

ticl

e d

iam

ete

r (m

)

Time (s)

Particle diameter (m) Gas temperature (K)

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Particle diameter (m) Gas temperature (K)

1,8E+05

2,0E+05

2,2E+05

2,4E+05

2,6E+05

2,8E+05

0 1 2 3 4 5 6

Pre

ssu

re (

Pa)

Time (s)

Exp. Data

Reference

Modified

280

320

360

400

440

480

0 1 2 3 4 5 6

Gas

te

mp

era

ture

(K

)

Time (s)

280

300

320

340

360

380

0 1 2 3 4 5 6

Wat

er

tem

pe

ratu

re (

K)

Time (s)

0,0E+00

1,0E-03

2,0E-03

3,0E-03

4,0E-03

5,0E-03

0 1 2 3 4 5 6

Par

ticl

e d

iam

ete

r (m

)

Time (s)

Documents

IMPROVEMENT OF MOLTEN JET … OF MOLTEN JET FRAGMENTATION MODELING IN MAAP ERMSAR 2017, Warsaw, Poland May 16-18, 2017 A. Le Belguet, E. Beuzet, M. Torkhani PERICLES, Nuclear Safety