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Preliminary study on double-blind calculation with design initial/boundary condition

Hyoung Tae Kim Joo Hwan Park, Jin Ho Song

Severe Accident and PHWR Safety Research Division, KAERI

1st Workshop for IAEA ICSP on

“HWR Moderator Subcooling Requirements to Demonstrate Backup Heat Sink Capabilities of Moderator during Accidents”

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Outlines

Introduction

Methodology and work plan

Preliminary calculation results

Summary and conclusion

Suggestions on the ICSP activities

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1. Introduction Important design features present in CANDU reactors

The subcooled heavy water moderator surrounding all horizontal fuel channels

The pressure tube in the fuel channel is normally separated from the surrounding calandria tube by a CO2-filled gap

Annulus Gas Fuel

Heavy Water Moderator

Channel Coolant Annulus Spacer

Calandria Tube Pressure Tube

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During normal operating CO2 circulates in the annulus gap between PT and CT, and

thermally isolates PT from CT During some postulated accidents (e.g. large break LOCA)

PT may strain radially and contact to CT; the moderator acts as a heat sink

Fuel channel integrity CANDU industry had widely accepted that fuel channel

integrity could be ensured if the moderator available subcooling at the onset of a large LOCA is greater than the subcooling requirements

The premise of this approach is based on a series of contact boiling experiments They derived the subcooling requirements to preclude a sustained

calandria tube dryout by the minimum available moderator subcooling and the pressure tube/calandria tube contact temperature

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Contact boiling experiment Heated and Pressurized PT section deformed through a CO2

gas gap into contact with its CT in an open tank of heated stirred water

Fig. 1 Test apparatus for contact boiling experiment

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Moderator subcooling limits Fuel channel integrity is ensured by avoiding dryout conditions

on the surface of calandria tube Contact boiling curve

generated from data collected in contact boiling experiments performed in 1980s

related moderator subcooling and pressure-tube contact temperature to the occurrence of immediate quench, patchy film boiling or extensive film boiling

Fig. 2 Moderator Subcooling Requirement Using Smooth CTs

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Contact boiling tests using glass-peened CT

Improvement in the extent of dryout observed (less severe extent of film boiling) when a glass-peened calandria tubes is tested at the same test conditions as a smooth calandria tube

The same extent of dryout may be achieved at a lower subcooling when a glass-peened calandria tube is used

The new boiling curve is applied to safety analysis of refurbished Wolsong unit-1 (Korea)

Fig. 3 Moderator Subcooling Requirement using glass-peened CTs

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2. Methodology and work plan Objective and relevant analysis models

Radiation heat transfer to the pressure tube Surface to surface radiation heat transfer through transparent medium

Pressure tube deformation or failure Thermal expansion and Young’s modulus upon the pressure difference

Pressure tube to Calandria tube heat transfer Gap conductance of CO2 and radiation heat transfer between PT and CT

Calandria tube to moderator heat transfer Convective heat transfer to surrounding water

Calandria tube deformation or failure Thermal stress model

Simulation code COMSOLTM Multiphysics ver. 4.3

User friendly for numerical modeling of physical concept Technical support by Prof. S.M. Chang (School of Mechanical and Automotive Eng.,

Kunsan National Univ.)

Peripheral use of CATHENA code Implementation of the CATHENA PT deformation model if necessary Code validation for basic heat transfer calculation

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COMSOLTM Multiphysics Governing equations

The thermal stress model in structural dynamics and the energy equation in heat transfer are simultaneously solved in each numerical time step

Structural equation:

Energy equation:

Fvσ−∇⋅ =

( )pTC u T k T Qt

ρ ∂ + ⋅∇ = ∇⋅ ∇ + ∂

Thermal Expansion

1pp RT C Tγρ ρ

γ−

= =

Deformation

)( TE ∆−= αεσ

Pressure load

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Work plan Present work for 1st workshop

COMSOL simulation setup for 2D problem Benchmark test for radiation heat transfer PT deformation simulation using the basic thermal stress model of COMSOL

Double-blind calculation COMSOL simulation setup for 3D problem Investigation of mechanical properties of Zircaloy Sensitivity study on the mechanical properties of Zircaloy Implementation of the CATHENA PT deformation model to COMSOL, if necessary Define the CT dryout conditions and modeling of heat transfer from CT to surrounding

water Define the PT/CT failure criteria and modeling

Blind calculation Identification of the modeling limit of COMSOL and production of a

compromizing model Simulation test using real initial/boundary conditions

Open calculation Comparison of the blind calculation results with test data Identification of the model effect on the improvement of code prediction New simulation for better prediction

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3. Preliminary calculation results Definition of problem

The main geometrical conditions are identified from the ICSP information document

The dominant mode of heat transfer is thermal radiation The conduction heat transfer occurs in the solid wall and CO2 medium.

However the gap conduction heat transfer is ignored in the preliminary simulation for modeling simplicity

Initial conditions Solid temperature: 20℃ Rapid heat up from zero heater power

Graphite heater (Diameter: 38 mm)

Heated length: 900 mm

PT

CT

PT ID: 103.6 mm

CT ID: 129 mm

PT thickness: 4.4 mm CT thickness: 1.42 mm

Computational domain Concentric configuration is assumed for of heater, PT, and CT

2-D View

CO2 gas ~ 1 atm

Pressure Tube: Zircaloy

Calandria Tube: Zircaloy

Pressure: 3.5 MPa Heat Power: 150 kW

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Boundary condition

Surface-to-Surface Radiation

Pressure: 3.5 MPa

Ambient Water:

Subcooling: 30 oC T_inf = 70 oC

( ) ( )( )

4

40

ˆ

1

n k T G T

G J T

ε σ

ε εσ

⋅ ∇ = −

− = −

0.8ε =

0.34ε =

Fixed

Prescribed

0 0( )ru T T rEσα = − +

Pressure: 0.1 MPa

Heat Power: 150 kW

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Physical properties for Zircaloy Zircaloy thermodynamic

properties In CANDU-6 reactor PT and CT consist of

Zr-2.5 Nb and Zircaloy-2, respectively. However, the material properties of

Zircaloy are assumed to be the same both for PT and CT

Reference:

Temperature (K)

Thermal Conductivity k (W/m-K)

Thermal Capacity Cp (J/kg-K)

300

400

640

1090

1093

1113

1133

1153

1173

1193

1213

1233

1248

1300

1500

1700

1900

2100

12.68

14.04

16.96

23.00

23.05

23.38

23.73

24.09

24.45

24.83

25.22

25.61

25.92

27.03

32.12

38.82

47.48

58.49

281

302

331

375

502

590

615

719

816

770

619

469

356

356

356

356

356

356

Table 1 Zircaloy thermodynamic properties

T.G. Beuthe, and B.N. Hanna (editors), “CATHENA MOD-3.5c/Rev 0 Theoretical Manual”, CANDU Owners Group Report, COG-99-007, 1999.

MATPRO-Version 11 (Revision 1) a handbook of material properties for use in the analysis of light water reactor fuel rod behavior, 1980, NUREG/CR-0497, TREE-1280.

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Zircaloy thermodynamic properties - cont’d

T(K)

k(W

/mK

)

T(K)

Cp(J

/kgK

)

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Mechanical properties of Zircaloy

Reference

11 7

11 7

10 7

1.24 10 6.22 10 [1/ ], 1,090[ ] 1.52 10 8.79 10 [1/ ], 1,090 1255

9.21 10 4.05 10 [1/ ], 1, 255

T K T KE Pa T K K T K

T K K T

× − × ≤= × − × < < × − × ≤

0.4ν =

311 7

6595 0.1477 [1/ ], 1,083[ / ]

1.52 10 8.79 10 [1/ ], 1,083 1,800T K T K

kg mT K K T K

ρ − <

= × − × ≤ ≤

6 3

5 3

4.95 10 [1/ ] 1.49 10, 1,083

1.26 10 [1/ ] 3.78 10p

a

T KT K

T Kεε

− −

− −

= × − × <= × − ×

6 2

6 3

9.70 10 [1/ ] 1.04 10, 1,244

9.76 10 [1/ ] 4.40 10p

a

T KK T

T Kεε

− −

− −

= × − × <= × − ×

3[1/ ] 1,0832.77763 1.09802cos 10 ,161

1,083 1,244

p aT K

K T K

ε ε π − − = = + × ≤ ≤

K. J. Geelhood, C. E. Beyer, and WG Luscher, “PNNL Stress/Strain Correlation for Zircaloy”, Pacific Northwest National Laboratory, PNNL-17700, 2008.

W.G. Luscher and K.J. Geelhood , “Material Property Correlations: Comparisons between FRAPCON-3.4, FRAPTRAN 1.4, and MATPRO,” (NUREG/CR-7024) PNNL-19417, NRC, U. S. 2011.

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Mechanical properties of Zircaloy - cont’d

E(P

a)

Density(k

g/m

^3)

Therm

al E

xp_z

(/K

)

Therm

al E

xp_x

y(/

K)

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Benchmark test results for radiation heat transfer No strain calculation

Normal concentric configuration

Analytic solution:

( ) ( )( )

4

40

ˆ

1

n k T G T

G J T

ε σ

ε εσ

⋅ ∇ = −

− = −

1 1

2 2

A rA r

=

12 1F =

1

2

( )4 41 1 2

122 1

1 2 2

2

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r T TQ

rr

π

εε ε

−=

−+

1

2

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Benchmark test results for radiation heat transfer – cont’d Comparison of a simulation result with an analytic solution

1 0.8ε =

2 0.3ε =

1 0.3r m=

2 0.5r m=

( )2 45.67 8 /e W m Kσ = − ⋅

From Simulation,

1 1456.5T K=

2 946.5T K=

( )4 41 1 2

122 1

1 2 2

2149.1

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r T TQ kW

rr

π

εε ε

−= =

−+

0 150Q kW= (Volumetric heat source)

Error = 0.6 %

PT deformation simulation results Radial expansion of PT

80 s

20

40 s

160 s

PT deformation simulation results – cont’d Temperature

40 s

21

80 s 160 s

Time variation

PT deformation simulation results – cont’d Transient temperature variation

Heater

PT

CT

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Enhancement of Thermal Expansion in the 2D Problem 3D shape is integrated to 2D

The mean expansion should be enhanced to describe real bending effect of PT in 3D

Thermal expansion coefficient ~ 20 times enhanced on the 2D plane ~ 5×10-6 [K-1] (nearly constant region < 1083 K) →100×10-6 [K-1] The outer surface of PT is expanded to contact with the inner

surface of CT

After enhancement of α

Using reference property data α

Time variation

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4. Summary and Conclusion COMSOL Multiphysics code is used to simulate the

PT/CT radiation heat transfer and deformation Thermal stress model by COMSOL is compatible to simulate the multiple

heat transfers and stress strain in the ICSP experiment 2D problem for ICSP test conditions is set up Mechanical property data for Zircaloy has discontinuity in a certain

temperature range and more investigation is needed for the solid properties used in the experiment

Preliminary calculation results Benchmark calculation results for radiation heat transfer are in good

agreement with the analytical solutions PT deformation simulation result show that the ballooning of PT is limited

within the inner radius of CT When 3D shape is integrated to 2D the mean expansion should be enhanced to describe real bending

effect of PT in 3D Thermal stress model by COMSOL needs to be more investigated and validated by code comparison

(e.g. CATHENA)

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Assessment of the CATHEA PT deformation model Circular PT deformation model by Shewfelt and Godin

The model assumes that the tube remains circular and that only membrane stresses need be considered. The local transverse creep (strain) rate is given by

Phenomena identification and discussion on Effect of mechanical properties on PT/CT deformation Convective heat transfer from PT to surrounding water and dry out

5. Suggestions on the ICSP activities