Elastic and viscoplastic pellets fragmentation modeling using an axisymmetrical 1D finite element code

During first rise to power in Power Water Reactor, fuel pellets crack because of thermal expansion. The phenomena of pellet cracking and fragments relocation have a major influence on rod behaviour and especially on the cladding behaviour in the case of pellet–cladding interaction.This article presents the modeling used to take into account the fragmented state of the pellet in the EDF fuel rod thermo-mechanical code, CYRANO3^®. The aim is to simulate more realistic stress and strain fields in the pellet.The investigated method consists in adding parameters in the 1D finite elements calculations in order to integrate the multi-dimensional fragmentation effects in the axisymmetrical 1D code CYRANO3^®. These parameters modify the material behaviour by describing the fuel as an anisotropic damaged material. The modeling accounts for the opening and closing of radial pellet cracks. It has been implemented in the code for elastic and viscoplastic fuel behaviours.     

Determination of stress within ZIRCALOY cladding due to pellet-cladding interaction

A precise calculation of the stress distribution within the Zircaloy cladding of a water-cooled reactor fuel rod subjected to a power increase is a complex problem which, in general, requires a computer code to integrate the behaviour of both the fuel and cladding. This paper develops a simplified model which decouples the clad and fuel pellet analyses, by considering two extremes of fuel pellet mechanical behaviour, which lead to two widely different boundary conditions at the pellet-clad interface. An axisymmetric fuel rod code can be used to give the mean cladding hoop strain imposed by the thermal expansion of the pellet, and when the interfacial friction coefficient is 0.5, this information along with the frictional boundary condition can be used to determine the stress distribution within the cladding near a fuel pellet crack. Results from this simplified approach, which does not involve an integrated code, are used to study the growth of stress corrosion cracks within the cladding.     

UO2-不锈钢燃料棒的光纤激光切割研究

为验证光纤激光用于燃料组件解体和燃料棒切割的可行性,研究光纤激光用于热物性差别很大的UO2芯块 不锈钢包壳管复合结构的切割和铀芯块的切割质量,本文采用光纤激光切割UO2芯块 316Ti包壳管元件棒,并通过扫描电子显微镜、能谱和X射线衍射对UO2芯块的切断面进行微观表征分析,研究激光切割过程对铀芯块切断的表面微观形貌、元素组成及物相的影响。研究结果表明,光纤激光可用于切割UO2芯块 316Ti包壳管元件棒,激光切割过程虽会造成铀芯块切断面出现大量微孔和碎渣,但不会造成UO2的相变。以上结果表明,光纤激光可用于UO2芯块 316Ti包壳管元件棒的切割,通过后续对激光切割系统的抗辐射屏蔽防护,可应用于乏燃料组件解体和乏燃料棒切割。     

MIPAC, a computer code for fuel performance analysis by the finite element method

An axisymmetric finite element computer code named MIPAC has been developed for analysis of the mechanical interaction behaviour between a fuel pellet and cladding. This computer code can deal with elastoplasticity of the pellet and cladding materials, creep effects for the both materials, pellet-cladding and pellet-pellet contact problems, hot pressing effect of the fuel pellet, fuel pellet cracking, and the cracked pellet's stiffness. A cyclical boundary condition is introduced to deal with one pellet length instead of the full-size fuel rod. The contact problems are solved without a fictitious contact element. In the fuel pellet cracking model the crack opening and closing behaviour under arbitrary power changes can be treated by introducing five kinds of crack modes. Mismatch of irregular crack surfaces is taken into account in the evaluation of the cracked pellet's stiffness. Finally, calculated results are compared with experimental data to show validity of the computer code.     

Analysis of mechanical load on cladding induced by fuel swelling during power ramp in high burn-up rod by fuel performance code FEMAXI-6

Mechanical load on cladding induced by fuel swelling in a high burn-up BWR type rod was analyzed by a fuel performance code FEMAXI-6. The code was developed for the analysis of LWR fuel rod behaviors in normal operation and transient conditions using finite element method (FEM).During a power ramp for the high burn-up rod, instantaneous pellet swelling can significantly exceed the level that is predicted by a “steady-rate” swelling model, causing a large circumferential strain in cladding. This phenomenon was simulated by a new swelling model to take into account the fission gas bubble growth. As a result it was found that the new model can give reasonable predictions on cladding diameter expansion in comparison with PIE data. The bubble growth model assumes that the equilibrium state equation holds for a bubble under external pressure, and simultaneous solution is obtained with both bubble size determination equation and diffusion equation of fission gas atoms. In addition, a pellet-clad bonding model which has been incorporated in the code to assume solid mechanical coupling between pellet outer surface and cladding inner surface predicted the generation of bi-axial stress state in the cladding during ramp.     

Calculational procedure for determining creep collapse of LWR fuel rods

Observed collapses in pressurized water reactor fuel rods have been attributed to the radiation enhanced creep of Zircaloy cladding into regions where separations in the fuel pellet stack have occurred. A computer code, COLAPX, has been written to determine the growth of ovality and the ultimate collapse of fuel rod cladding under reactor operating conditions. This paper describes the theoretical bases of this code, the finite element formulation used, the constitutive relations between the displacement fields and the element forces, and the radiation, temperature and stress dependent material model for creep of Zircaloy tubing. Comparisons of the creep rate predictions and of the ovality predictions with data from irradiated tubes and fuel cladding are presented.     

A model for predicting pellet-cladding interaction-induced fuel rod failure

A model for predicting pellet-cladding mechanical-interaction-induced fuel rod failure is presented. Cladding failure is predicted by explicitly modelling the formation and propagation of radial cladding cracks by the use of non-linear fracture mechanics concepts in a finite element computational framework. The failure model is intended for implementation in finite element fuel performance codes in which local pellet-clad interaction is modelled. Crack initiation is supposed to take place at pre-existing cladding flaws, the size of which is estimated by simple probabilistic concepts, and the subsequent crack propagation is assumed to be due to either iodine-induced stress corrosion cracking or ductile fracture. The novelty of the outlined approach is that the development of cladding cracks which may ultimately lead to fuel rod failure can be treated as a dynamic and time-dependent process. The influence of complex or cyclic loading, ramp rates and material creep on the failure mechanism can thereby be investigated. The presented failure model has been incorporated in the ABB Atom transient fuel performance code. Numerical results from some applications of the code are used to illustrate the usefulness of the model.     

Theoretical evaluation of rifled cladding for LWR fuel: A study based on the computer codes INTERPIN and FREY-01

Rifled Cladding deviates from regular fuel designs mainly by the inner surface of the cladding tube being prismatic, with a large number of faces. The design has been tested in the R2 test reactor at Studsvik, and is scheduled for testing in a Swedish BWR. Its observed technical merit is to reduce the fission gas release and increase the failure threshold during overpowers. The present study aims to find an explanation of the observed increase in failure threshold, i.e., the heat rating at which cladding failure occurs. Failure is strongly related to the maximum mechanical stress. The INTERPIN code was used to calculate the starting conditions for an overpower event, and the FREY-01 code was used for finite element calculations of cladding stress distributions during the overpower. FREY-01 accounts for the kinetics of fuel pellet cracking and its impact on cladding stresses. The study focuses on the conditions that produce the highest cladding stress. It was found that the worst case is associated with cracks opening close to the fuel-cladding contact loci, i.e., the midface positions of the prismatic surface, with no additional cracks at non-contact positions. This situation is similar to what holds for regular fuel. If, however, cracks also open at corner positions, then the calculated maximum stresses are considerably less. This latter situation is, in fact, observed in hot cell examinations of ramped rifled cladding rods. Therefore, the improved failure resistance of rifled cladding rods can be explained in terms of a reduction of the strong azimuthal mechanical interaction between fuel and cladding that may occur in fuel rods of regular design.     

A continuum model for cracked UO2 fuel

This paper presents a constitutive model for uranium dioxide fuel pellets in light water reactor fuel rods. The proposed model accounts for the fuel mechanical behaviour under pellet cracking, fragment relocation and pellet-clad mechanical interaction. Moreover, the detrimental effect of cracking on the fuel thermal conductivity is considered in the model. An essential part of the model is the representation of pellet cracks, which significantly affect both the mechanical and thermal behaviour of nuclear fuel under operation. Cracking is modelled in a continuum context, where cracks are represented by nonelastic strains in the material. The continuum representation is particularly suitable for finite element computer codes, since cracking can be treated in the same manner as plasticity and creep. The model is derived in the form of a nonlinear constitutive relation for the fuel material, that may be implemented in either two- or three-dimensional finite element fuel performance computer codes. The fundamentals of the model are presented, and issues concerning its numerical implementation are discussed. The model's ability to capture important aspects of the cracked fuel behaviour is also illustrated by comparisons with in-reactor experiments.     

Comparative effects of structural and material parameters variability on Pellet–Cladding Interaction in a PWR fuel rod

In the water pressurised nuclear reactors, the fuel rod cladding is the first barrier against radioactive isotopes release. Its integrity must be demonstrated all along the fuel rod irradiation with increasing strenuous operating conditions. This paper deals with a study made with Electricité de France (EDF) in order to improve the understanding and modelling of the thermomechanical behaviour of fuel rods under these more arduous conditions. The aim of this study is to evaluate the separate influences of structural and material parameters variability on Pellet–Cladding Interaction (PCI). The following parameters have been tested by 3D simulations for a common ramping condition: axial and radial pellet cracks numbers, pellet fragment size, relative fragments displacement, non-symmetrical configuration, pellet–pellet friction and pellet–cladding friction. The second part of the article deals with the development of a model, which gives a better assessment of cladding stress concentration near radial fuel cracks. The implementation in the 1D fuel rod EDF code CYRANO3 and the validation of the model are presented.     

Analysis on split failure of cladding of high burnup BWR rods in reactivity-initiated accident conditions by RANNS code

A computer code RANNS was developed to analyze fuel rod behaviors in the reactivity-initiated accident (RIA) conditions. RANNS performs thermal and finite-element mechanical calculation for a single rod in axis-symmetric geometry, where fuel pellet consists of 36 equal-volume ring elements and cladding metallic wall consists of eight equal-thickness ring elements and one outer oxide element. The code can calculate temperature profile inside the rod, contact pressure generated by pellet–clad mechanical interaction (PCMI), stress–strain distribution and their interactions elaborately. An experimental analysis by RANNS begins with pre-test conditions of irradiated rod which are given by the fuel performance code FEMAXI-6.In the present study, analysis was performed on the simulated RIA experiments in the “nuclear safety research reactor” (NSRR), FK-10 and FK-12, with high burnup BWR rods in a cold-start up condition, and stress–strain evolution in the PCMI process was calculated extensively. In the analysis, the pellet–clad bonding was assumed both in the heat conduction and in mechanical restraint. The calculated hoop strain increase was compared with the measured strain gauge data, and satisfactory agreement was obtained. Simulation calculations with broader power pulses anticipated in RIA of commercial BWR were carried out and the resulted cladding hoop stress was compared with the failure stress estimated by comparison of analysis with experimental data.     

Simulation of pellet-cladding thermomechanical interaction and fission gas release

This paper summarizes the present status of a computer code that describes some of the main phenomena occurring in a nuclear fuel rod throughout its life. Temperature distribution, thermal expansion, elastic and plastic strains, creep, mechanical interaction between pellet and cladding, fission gas release, gas mixing, swelling, and densification are modeled. The modular structure of the code allows for the incorporation of models to simulate different phenomena and material properties. Collapsible rods can be also simulated.The code is bidimensional, assumes cylindrical symmetry for the rod and uses the finite element method to integrate the differential equations. The stress–strain and heat conduction problems are nonlinear due to plasticity and to the temperature dependence of the thermal conductivity. The fission gas inventory is calculated with a diffusion model, assuming spherical grains and using a one-dimensional finite element scheme. Pressure increase, swelling and densification are coupled with the stress field.Good results are obtained for the simulation of the irradiation tests of the first argentine prototypes of MOX fuels, where the bamboo effect is clearly observed, and of the FUMEX series for the fuel centerline temperature, the inside rod pressure and the fractional gas release.     

FARST — A computer code for the evaluation of FBR fuel rod behavior under steady-state/transient conditions

FARST, a computer code for the evaluation of fuel rod thermal and mechanical behavior under steady-state/transient conditions has been developed. The code characteristics are summarized as follows:

1. (i) FARST evaluates the fuel rod behavior under the transient conditions. The code analyzes thermal and mechanical phenomena within a fuel rod, taking into account the temperature change in coolant surrounding the fuel rod.

2. (ii) Permanent strains such as plastic, creep and swelling strains as well as thermoelastic deformations can be analyzed by using the strain increment method.

3. (iii) Axial force and contact pressure which act on the fuel stack and cladding are analyzed based on the stick/slip conditions.

4. (iv) FARST used a pellet swelling model which depends on the contact pressure between pellet and cladding, and an empirical pellet relocation model, designated as “jump relocation model”.

The code was successfully applied to analyses of the fuel rod irradiation data from pulse reactor for nuclear safety research in Cadarache (CABRI) and pulse reactor for nuclear safety research in Japan Atomic Energy Research Institute (NSRR).The code was further applied to stress analysis of a 1000 MW class large FBR plant fuel rod during transient conditions. The steady-state model which was used so far gave the conservative results for cladding stress during overpower transient, but underestimated the results for cladding stress during a rapid temperature decrease of coolant.     

Thermal Stress Analysis of High-Burnup LWR Fuel Pellet Pulse-Irradiated in Reactivity-Initiated Accident Conditions

For RIA-simulated experiments in the NSRR with high-burnup PWR fuel and BWR fuel, numerical analyses were performed to evaluate the temporal changes of profiles of temperature and thermal stress in pellet induced by pulse power, using the RANNS code. The pre-pulse states of rods were calculated using the fuel performance code FEMAXI-6 along the irradiation histories in commercial reactors and the results were fed to the RANNS analysis as initial conditions of the rod. One-dimensional FEM was applied to the mechanical analysis of the fuel rod, and the calculated cladding permanent strain was compared with the measured value to confirm the validity of the PCMI calculation. The calculated changes in the profiles of temperature and stress in the pellet during an early transient phase were compared with the measured data such as the internal gas pressure rise, cracks and grain structure in the post-test pellet, anddiscussed in terms of PCMI and grain separation. The analyses indicate that the pellet cracking appearances coincided with the calculated tensile stress state and that the compressive thermal stress suppresses the fission gas bubble expansion leading to grain separation.     

Pellet compliance model based on out-of-pile simulation

The thermal and mechanical behavior of fuel rods is significantly influenced by the extent of their relocation and by compliance of the cracked pellets. Movement of the cracked pellet pieces towards the cladding results in softer pellets with crack voids which accommodate some fraction of the thermoelastic pellet deformation and make the pellet more compliant under the restraint of the cladding. It is difficult to model such a pellet compliance independently of experimental observations because the cracked pellet behavior is uncertain by nature.Electrically heated simulation of pellet-cladding mechanical interaction (PCMI) facilitates much quicker and more flexible experimentation than actual in-pile tests. Testing apparatus consists of the simulated fuel rod with hollow UO₂ pellets and a tungsten rod in the center, and a diameter measuring device including three pairs of diameter sensors. Test parameters include the pellet-cladding gap and the cladding thickness. Results show that rods with a smaller gap have a larger increasing rate of cladding diameter. This suggests that a group of cracked pellet pieces induced by thermal stress has an apparent compliance which increases with pellet-cladding gap. Results also show more sensitivity to cladding thickness than those calculated assuming pellets having intrinsic stiffness. This also suggests the compliant nature of cracked pellets.Such a compliant nature can almost be described by reducing the elasticity of the pellet. A simple pellet compliance model was obtained by fitting calculations with measurements to describe a cracked pellet as a uniform axisymmetric body with apparent elasticity.     

Principle of rationalizing the criteria for abnormal transients of the Super LWR with fuel rod analyses

A detailed fuel rod design is carried out for the first time in the development of Supercritical-pressure Light Water Reactor (Super LWR). The fuel rod design is similar to that of LWR, consisting of UO₂ pellets, a gas plenum and a Stainless Steel Cladding. The principle of rationalizing the criteria for abnormal transients of the Super LWR is developed. The fuel rod integrities can be assured by preventing plastic strains on the cladding, preventing the cladding buckling collapse, and keeping the pellet centerline temperature below its melting point. The FEMAXI-6 fuel analysis code is used to evaluate the fuel rod integrities in abnormal transient conditions. Detailed analyses have shown that allowable limits to the maximum fuel rod power and maximum cladding temperature can be determined to assure the fuel integrities. These limits may be useful in the plant safety analyses to confirm the fuel integrities during abnormal transients.     

Heat transfer in LMFBR fuel elements Part I: Effects of fuel pellet displacement

Random displacement of mixed oxide fuel pellet axes from the central axis of their overall liquid metal fast breeder reactor fuel element occurs when the pellcts are randomly loaded within the fuel element cladding sheath. Assuming azimuthally symmetric heat transfer from the outer cladding surface to the bulk coolant, the influence of this random displacement upon the temperature distribution throughout the fuel element is examined when the granular or porous detailed fuel structure and cracks in the fuel (discussed in Part II) are ignored. It is shown that for a typical example, in which the maximum displacement is only 0.0075 cm and the fuel pellet radius is 0.2465 cm, the variance of the maximum fuel temperature is in the vicinity of 115° C, so that this random displacement effect can be quite important especially for those fuel pellets with an expected maximum temperature near the melting point of the fuel.     

回收铀燃料元件UO2芯块辐照后显微组织研究

为评价回收铀燃料元件中UO₂芯块的辐照稳定性,采用热室金相显微镜对辐照后高放射性UO₂芯块沿轴向及径向的辐照肿胀、裂纹分布、晶粒尺寸及分布和晶粒长大行为进行了观察和分析。结果表明:燃料元件芯块中均存在大量的裂纹,回收铀燃料元件UO₂芯块裂纹呈明显的环形分布特征,天然铀燃料元件UO₂芯块呈放射性发散分布特征。两者的燃料芯体晶粒呈等轴状,均出现从边缘区域向芯块中心区域晶粒逐渐长大现象,辐照后晶界变粗化。两者晶粒尺寸、形貌及分布特征并无明显差别。此外,在相同的堆内运行工况条件下,回收铀燃料元件UO₂芯块辐照肿胀不明显,芯块破碎程度及晶粒长大过程与天然铀并无明显差别。      

An empirical model of the effects of pellet cracking on the thermal conductivity of UO2 light water reactor fuel

Light water reactor fuel pellet cracking and pellet fragment relocation into the pellet-to-cladding gap during normal operation alters both the fuel thermal conductivity and the thermal resistance of the gap. Uranium dioxide fuel pellet thermal conductivity data from a series of tests being conducted in the Power Burst Facility to evaluate the thermal performance of LWR design fuel are presented. These data indicate that the effective thermal conductivity of a cracked and relocated light water reactor fuel pellet is strongly influenced by the closing or opening of the cracks as the rod power is increased or decreased and is dependent on the initial pellet and cladding dimensions. An empirical correlation is introduced which provides a means for calculating the effective thermal conductivity of cracked and relocated fuel within helium bonded fuel rods. The method also provides a means for estimating the relocated hot pellet-to-cladding gap width as a function of rod power.     

三维燃料棒精细化模拟软件FUPAC3D与FUPAC的对比验证研究

为验证基于三维有限元分析平台建立的三维燃料棒精细化模拟软件FUPAC3D在分析评价压水堆燃料棒辐照-热-力耦合行为方面的能力和精度,本文给出了三维FUPAC3D软件采用的热学模型、燃料棒力学模型、裂变气体释放模型以及腐蚀模型,以华龙一号典型燃料棒参数和运行工况作为输入参数,分别使用三维FUPAC3D软件和已工程化应用的1.5维FUPAC软件进行建模分析,并针对2种软件在芯块和包壳温度、包壳应力与应变、芯块与包壳间间隙宽度的计算结果进行对比研究。研究结果表明,FUPAC3D软件与FUPAC软件具有相当的精度,FUPAC3D软件具备压水堆燃料棒辐照-热-力耦合行为的精细化模拟能力。