Improvements on FRAPCON3 and FRAPTRAN Mechanical Modelling

1
Improvements on FRAPCON3 and FRAPTRAN Mechanical
Modelling

• Arttu Knuutila, Seppo Kelppe
• SAFIR-PUOLIVÄLISEMINAARI 20.-21.1.2005

2
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

3
Basic construction of a fuel rod

• TYPICALLY
• Cladding material various zirconium alloys
• Diameter 9mm
• Length 2500-3500 mm
• Fill gas Helium to 0.6-1.5 MPa

4
Geometry of a Cracked Fuel Pellet
5
Pellet-Cladding Mechanical Interaction (PCMI)
6
Modes of Axial PCMI
7
Pellet-Ciad Interaction (PCI) Failure
8
Deformed pellet schematically1-D vs.2-D
Desrciptions
9
Generic Example of FEM Applied to Rod Structural
Analysis
10
Sequence of events in a LOCA
11
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 (?)

12
Reactivity Transient (RIA)(1)
13
Reactivity Transient (RIA)(2)
14
Different Clad Performance Scenaria in a RIA
Transient
Failure model Ballooning
model Dispersed Fuel to Water
Interaction
15
Clad Failure Modes in a RIA

• Competing Mechanisms
• Early PCMI Failure
• DNB - High Temperature - Ballooning and Burst -
  Oxidation and Embrittlement

16
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

17
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

18
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)

19
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

20
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

21
LARGE STRAIN MODELLING

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

22
Pellet cladding contact with Coulomb friction

• Coulomb friction
• t lt ?p ? solid contact
• t ?p ? sliding with friction
• Where t is tangential traction, p is contact
  pressure, and ? is friction coefficient

23
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

24
FRAPCON3 validation case IFA-525
25
(No Transcript)
26
FRAPCON3 validation case IFA-585
27
(No Transcript)
28
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