Improvements on FRAPCON3 and FRAPTRAN Mechanical Modelling

Improvements on FRAPCON3 and FRAPTRAN Mechanical Modelling

Arttu Knuutila, Seppo Kelppe

SAFIR-PUOLIVÄLISEMINAARI 20.-21.1.2005

VTT TECHNICAL RESEARCH CENTRE OF FINLAND

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Introduction and Contents

Description of elaborations on fuel mechanical modelling made under a one-year attachment to PNNL Laboratory in the US

Contents– Introduction to requirements of modelling the mechanical behaviour in

a fuel rod– Summary description of the refined FEM approach– Examples of verification


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Basic construction of a fuel rod

TYPICALLY:Cladding material: various zirconium alloys Diameter ~ 9mmLength 2500-3500 mmFill gas: Helium to 0.6-1.5 MPa


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Geometry of a Cracked Fuel Pellet


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Pellet-Cladding Mechanical Interaction (PCMI)


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Modes of Axial PCMI


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Pellet-Ciad Interaction (PCI) Failure


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Deformed pellet schematically1-D vs.2-D Desrciptions


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Generic Example of FEM Applied to Rod Structural Analysis


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Sequence of events in a LOCA


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Large Clad Deformations in a LOCA test

a) Säteilytetty sauva– polttoainemuruja pullistumassa

b) Tuore suojakuoriputki– säteilytetystä poikkeava

halkeaman muoto Muodonmuutokset samankaltaiset - säteilyvauriot pääosin hehkuttuneet pois (?)


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Reactivity Transient (RIA)(1)

0

10

20

30

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60

70

80

90

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

0

500

1000

1500

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2500

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3500

4000

4500

Enthalpy (cal/g)

TIME-LAW

H (cal/g)

t(s)

Pcore (MW)


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Reactivity Transient (RIA)(2)

0

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

2 5 0 0

0.2 0.3 0.4 0.5Time, s

0

0 .0 0 2

0 .0 0 4

0 .0 0 6

0 .0 0 8

0 .0 1

0 .0 1 2

0 .0 1 4

PowerFuel Centerline TemperatureFuel Surface TemperatureTotal Hoop Strain


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Different Clad Performance Scenaria in a RIA Transient

Failure model Ballooning model Dispersed Fuel to Water Interaction


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Clad Failure Modes in a RIA

Competing Mechanisms

Early PCMI FailureDNB - High Temperature - Ballooning and Burst - Oxidation and Embrittlement


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USNRC steady-state and transient codes

FRAPCON3 Steady-state fuel performance

code Capable of modelling fuel thermal-

mechanical behaviour of and fission gas release in a LWR fuel rod during normal operations

Validated up to 65 MWd/kgU burnup

FRAPTRAN Transient fuel performance code Capable of analysing thermal

mechanical behaviour of a LWR fuel rod in reactivity accidents, loss-of-coolant accidents, or anticipated transients without scram

Validated up to 65 MWd/kgU burnup


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FRAPCON3/FRAPTRAN mechanical modelling

Both codes employ a rather simple stress-strain modelling for the cladding called FRACAS I that originates from the development work done in the 70s

FRACAS I uses a 1D thin shell model for the cladding stress-strain analysys, where the fuel rod is divided into axial slices and each slice has its own separate 1D mechanical solution

FRACAS I can model pressure loaded cladding (open gap) or PCMI loaded cladding (closed gap) with solid contact, i.e. it does not allow slippage between the fuel pellet stack and the cladding if the gap is closed

FRACAS I does not include stress-strain analysis for the fuel pellet stack


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New mechanical modelling

a stress-strain analysis option with finite element model has been implemented in FRAPCON3/FRAPTRAN codes

1½D, 2D, and 3D analysis capability capability of modelling large strains and displacements, e.g.

localized deformations can be modelled Modelled deformation mechanisms

– Elasticity with nonlinear hyperelastic model– Large strain plasticity with J2 flow theory (von Mises) and isotropic

hardening– Creep, a time dependent extension to the J2 flow theory

– Thermal dilation and irradiation growth– Dilation of ideal gas

1½D and 2D contact with friction (Coulomb friction model)


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1½D, 2D, and 3D elements

1½D axisymmetric linear, 2D axisymmetric bilinear, and 3D trilinear solid elements with mean dilation formulation

1½D and 2D contact interface with Coulomb friction with penalty method

1½D axisymmetric, 2D axisymmetric, and 3D gas cavities with ideal gas


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Efficient sparse matrix solver Efficient sparse matrix solution by using matrix reordering to

reduce the matrix profile and direct solution methods, LU and LDLT factorisations

An example of a stiffness matrix where the memory space needed for the matrix factorisation is reduced by 70% by reordering


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LARGE STRAIN MODELLING

Capability to model localized deformations. For example ballooning of the cladding during loss-of-coolant accident


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Pellet cladding contact with Coulomb friction

Coulomb frictiont < p solid contact

t = p sliding with friction

Where t is tangential traction, p is contact pressure, and is friction coefficient


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Verification of FE modelling Patch tests to verify the element performance and correctness

even in badly distorted element mesh Extensive verification for large strain elasto-plasticity with

verification cases that have an analytical solution or reference solution in the literature

An example of large strain verification case, a compressed billet


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FRAPCON3 validation case: IFA-525


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FRAPCON3 validation case: IFA-585


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Conclusion

Modelling elaborations to the USNRC fuel performance codes FRAPCON and FRAPTRAN that significantly improve provisions of more detailed analyses of rod mechanical behaviour were introduced and taken into use

– 2-D and 3-D descriptions were made available through advanced FEM formulation

– Bases for covering crucial detail as frictional pellet-to-clad contact, pellet and clad creep-plastic deformation, and large-deformation ballooning were laid

Modularity and flexibility were among the goals - Results will be readily applicable in other analytical environments

Verification of formulation confirms robust numerical performance and improved representativity to real-life behaviour

Validation and applications now (early 2005) in progress

Improvements on FRAPCON3 and FRAPTRAN Mechanical Modelling

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