Temperature, Strain and Pressure Analysis of a fuel ROD
The TESPA-ROD code allows analysing the fuel rod behaviour under various accident conditions, normal operation as well as long-term storage condition. In particular the accident conditions refer to both loss-of-coolant accident (LOCA) and reactivity initiated accident (RIA). The analysis of the fuel rod behaviour under normal operation refers to transients with pellet-cladding (mechanical) interaction (PCI/PCMI) during load follow operation. For long-term storage, the TESPA-ROD code predicts the behaviour for a timescale in the range of 100 years.

TESPA-ROD Code Description
The TESPA-ROD code analyses the thermo-mechanical load on the fuel rod cladding for RIA-transients, LOCA-transients, PCMI-transients- and long-term storage transients.

The TESPA-ROD code represents the fuel rod behaviour in a 1½ dimensional spatial resolution. It provides the transient radial temperature distribution in a cross-sectional area of a fuel rod while the axial temperature distribution is approximated from an axial power factor. Characteristic fuel volumes like fuel rod plena or gap volume are described in distinguished volumes. Fission gas communication among these volumes is assumed.

Cladding failure can be determined from stress/strain relations who are specific to the cladding materials Duplex, E110, M5, Zirlo, Zry-2 and Zry-4. Various fuels types (UO2, MOX, and Gadolinium doped fuel) at all burn-up levels can be analysed.

Both pressure differences across the cladding and pellet/cladding contact can provoke tensile hoop stresses in the cladding. While elastic and plastic strains are considered as homogeneously distributed across the cladding circumference, the creep strain of the cladding can be determined localized depending on the pellet’s eccentricity parameter. All hoop strains result in cladding thinning according to conservation of volume.

TESPA-ROD uses a plasticisation model for prediction of plastic deformation. If the hoop stress in the strained cladding exceeds yield stress but does not outreach the burst stress, strain hardening is predicted. By exceeding the burst stress, burst of cladding is assumed. The burst stress in TESPA-ROD is determined based on the correlation developed at KfK Karlsruhe for Zircaloy-4 in the early 1980’s. Based on EDGAR tests, this burst criterion has been up-dated.

If cladding strain leads to a ballooning of the cladding (strain above 7 %), axial fuel relocation within the fuel rod is considered. This fuel relocation is associated with increase in power density in the ballooned fuel rod region.

Distinguished cladding creep models for Duplex, E110, M5, Zirlo, Zry-4, Zry-2 are available in TESPA-ROD. The high temperature creep prediction takes into account both hydrogen up-take and oxygen up-take in the cladding. It furthermore depends strongly on the metallic phase transformation of the Zirconium alloy between hexagonally close-packed crystal structures to body-centred cubic crystal structures. Phase transformation can be dynamically (time-dependent) determined. Low temperature creep of cladding materials (M5, Zirlo, Zry-2) as is relevant for PCMI transients and for long-term storage transients has been modelled in TESPA-ROD recently

For high temperature oxidation TESPA-ROD predicts the oxide layer growth, the oxide up-take and the hydrogen up-take into metallic layer of the cladding. The TESPA-ROD code provides various weight gain correlations for oxide layer growth prediction (Leistikov, Baker/Just and others).

The gap between the pellet outer surface and the cladding inner surface contains helium and depending on burn-up also fission gases. The gap conductance model in TESPA-ROD predicts the thermal resistance for the heat flow depending on the gas composition, fission gas pressure and gap size. The largest impact on the gap conductivity is given by the gap size. Separate effect tests provided by the Halden reactor project have been used for the TESPA-ROD gap conductance model validation.

TESPA-ROD utilises an empirical fission gas release model. It is based on a gas diffusion model. The transitional fission gas release model additionally depends on the local power density which accounts for the inter-granular fission gas release during RIA transients.

The gap between the pellet and the cladding is determined by dimensional changes of both the fuel and the cladding. Geometrical changes of the fuel pellet consider densification, swelling and radial relocation as a function of power and pellet burn-up. An extra model in TESPA-ROD predicts transitional pellet swelling due extreme high power densities like those occurring in RIA transients. Additionally, pellet swelling due to helium production during long-term storage has been modelled in TESPA-ROD recently.

Developmental History of TESPA-ROD code
In the early 1980’s, the code was developed for LOCA transients with the intention to identify fuel rods in a core loading which would fail during a LOCA transient. The percentage of fuel rods predicted with the code could be compared with the regulatory limit for LOCA transients, which is that not more than 10 % of all fuel rods may fail during the transient.

From the very beginning until today, the code is applied by technical inspection agencies (TÜVs) for assessing each core loading before a new reactor cycle starts.

Because the code predicts the thermo-mechanics of a fuel rod, the code’s application has been extended toward RIA transients since 2000. The RIA transient is characterised by a power pulse of rather short duration. Within milliseconds the enthalpy of the fuel raises up to more than 100 cal/g. Recent code benchmarks (2016) have shown that the TESPA-ROD code performs with similar quality as other codes like SCANAIR, which are explicitly developed for predicting such RIA transients.

Since the advent of renewables in the electric grid, load follow operation reaches significance for the fuel rod behaviour. PCI-/PCMI-transients need to be analysed in order to prevent fuel rod failure. Thus, TESPA-ROD code development focussed on the pellet/cladding interaction behaviour. Specific cladding creep models have been implemented into the code which allows predicting the stress relaxation in cladding after a stepwise power increase. The time-scale of this transient is in the range of hours and days.

In a different time-scale the thermal-mechanics of a fuel rod is very important for transients of the long-term storage. The presently envisaged extension of the long-term storage from 40 to more than 100 years requires qualified tools to determine both the dimensional changes of the fuel rod and the changes of fracture toughness due to corrosion progression.

Present code version of TESPA-ROD predicts thermal-mechanical parameters of a fuel rod under long-term storage condition including the transition from wet storage to dry storage. It is intended to implement meaningful models in TESPA-ROD which allow an assessment of hydrogen-related fracture toughness reflecting the re-orientation of hydride precipitation in the cladding during the long-term storage.

Selected TESPA-ROD predictions
The application of the TESPA-ROD code for two extreme timescales is RIA transient and long-term storage transient. For both timescales (several milliseconds, several decades) results are shown:

TESPA-ROD analysis for RIA transient:

Power and Temperature Development during RIA-Transient

TESPA-ROD analysis for Long-term storage transient:

TESPA-ROD prediction of cladding surface temperature, rod internal fission gas pressure, gap width between fuel and cladding and cladding hoop stress during dry storage (4 years) and wet storage (up to 100 years) if burnup of UO2 fuel is 80 MWd/kg