1. Improvements on FRAPCON3 and FRAPTRAN Mechanical Modelling Arttu Knuutila, Seppo Kelppe SAFIR-PUOLIVÄLISEMINAARI 20.-21.1.2005

2. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 2 VTT PROCESSES Introduction and Contents t Description of elaborations on fuel mechanical modelling made under a one-year attachment to PNNL Laboratory in the US t Contents – Introduction to requirements of modelling the mechanical behaviour in a fuel rod – Summary description of the refined FEM approach – Examples of verification

3. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 3 VTT PROCESSES Basic construction of a fuel rod t TYPICALLY: t Cladding material: various zirconium alloys t Diameter ~ 9mm t Length 2500-3500 mm t Fill gas: Helium to 0.6-1.5 MPa

4. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 4 VTT PROCESSES Geometry of a Cracked Fuel Pellet

5. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 5 VTT PROCESSES Pellet-Cladding Mechanical Interaction (PCMI)

6. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 6 VTT PROCESSES Modes of Axial PCMI

7. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 7 VTT PROCESSES Pellet-Ciad Interaction (PCI) Failure

8. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 8 VTT PROCESSES Deformed pellet schematically 1-D vs.2-D Desrciptions

9. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 9 VTT PROCESSES Generic Example of FEM Applied to Rod Structural Analysis

10. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 10 VTT PROCESSES Sequence of events in a LOCA

11. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 11 VTT PROCESSES Large Clad Deformations in a LOCA test t a) Säteilytetty sauva – polttoainemuruja pullistumassa t b) Tuore suojakuoriputki – säteilytetystä poikkeava halkeaman muoto t Muodonmuutokset samankaltaiset - säteilyvauriot pääosin hehkuttuneet pois (?)

12. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 12 VTT PROCESSES Reactivity Transient (RIA)(1)

13. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 13 VTT PROCESSES Reactivity Transient (RIA)(2)

14. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 14 VTT PROCESSES Different Clad Performance Scenaria in a RIA Transient Failure model Ballooning model Dispersed Fuel to Water Interaction

15. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 15 VTT PROCESSES Clad Failure Modes in a RIA t Competing Mechanisms t Early PCMI Failure t DNB - High Temperature - Ballooning and Burst - Oxidation and Embrittlement

16. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 16 VTT PROCESSES USNRC steady-state and transient codes FRAPCON3 t Steady-state fuel performance code t Capable of modelling fuel thermal- mechanical behaviour of and fission gas release in a LWR fuel rod during normal operations t Validated up to 65 MWd/kgU burnup FRAPTRAN t Transient fuel performance code t Capable of analysing thermal mechanical behaviour of a LWR fuel rod in reactivity accidents, loss-of-coolant accidents, or anticipated transients without scram t Validated up to 65 MWd/kgU burnup

17. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 17 VTT PROCESSES FRAPCON3/FRAPTRAN mechanical modelling t 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 t 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 t 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 t FRACAS I does not include stress-strain analysis for the fuel pellet stack

18. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 18 VTT PROCESSES New mechanical modelling t a stress-strain analysis option with finite element model has been implemented in FRAPCON3/FRAPTRAN codes t 1½D, 2D, and 3D analysis capability t capability of modelling large strains and displacements, e.g. localized deformations can be modelled t Modelled deformation mechanisms – Elasticity with nonlinear hyperelastic model – Large strain plasticity with J 2 flow theory (von Mises) and isotropic hardening – Creep, a time dependent extension to the J 2 flow theory – Thermal dilation and irradiation growth – Dilation of ideal gas t 1½D and 2D contact with friction (Coulomb friction model)

19. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 19 VTT PROCESSES 1½D, 2D, and 3D elements t 1½D axisymmetric linear, 2D axisymmetric bilinear, and 3D trilinear solid elements with mean dilation formulation t 1½D and 2D contact interface with Coulomb friction with penalty method t 1½D axisymmetric, 2D axisymmetric, and 3D gas cavities with ideal gas

20. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 20 VTT PROCESSES Efficient sparse matrix solver t Efficient sparse matrix solution by using matrix reordering to reduce the matrix profile and direct solution methods, LU and LDL T factorisations t An example of a stiffness matrix where the memory space needed for the matrix factorisation is reduced by 70% by reordering

21. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 21 VTT PROCESSES LARGE STRAIN MODELLING t Capability to model localized deformations. For example ballooning of the cladding during loss-of-coolant accident

22. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 22 VTT PROCESSES Pellet cladding contact with Coulomb friction t Coulomb friction t <  p  solid contact t =  p  sliding with friction Where t is tangential traction, p is contact pressure, and  is friction coefficient

23. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 23 VTT PROCESSES Verification of FE modelling t Patch tests to verify the element performance and correctness even in badly distorted element mesh t Extensive verification for large strain elasto-plasticity with verification cases that have an analytical solution or reference solution in the literature t An example of large strain verification case, a compressed billet

24. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 24 VTT PROCESSES FRAPCON3 validation case: IFA-525

25. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 25 VTT PROCESSES

26. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 26 VTT PROCESSES FRAPCON3 validation case: IFA-585

27. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 27 VTT PROCESSES

28. VTT TECHNICAL RESEARCH CENTRE OF FINLAND 28 VTT PROCESSES Conclusion t 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 t Modularity and flexibility were among the goals - Results will be readily applicable in other analytical environments t Verification of formulation confirms robust numerical performance and improved representativity to real-life behaviour t Validation and applications now (early 2005) in progress