基于MOOSE框架的五方程两相流分析程序开发

基于多物理场耦合框架MOOSE,采用五方程两相流模型开发了模块化程序ZEBRA,实现了高阶时间、空间离散格式两相流动传热问题的求解。采用Bartolomei开展的垂直圆管过冷沸腾实验对ZEBRA进行验证,在不同热流密度、质量流密度、压力工况下,将程序计算值与实验值进行了数值验证和计算分析。结果表明：ZEBRA中五方程模型预测值与实验值符合良好,沸腾起始点和空泡份额的预测合理,表明ZEBRA初步具备了处理两相流问题的能力。     

A three-dimensional study of nuclear fuel rod behavior during startup

A three-dimensional finite element study is made of the behavior of cylindrical uranium dioxide fuel pellets during startup. The finite element code uses an eight-noded box element of arbitrary shape to build up the stiffness and stress characteristics by Gaussian integration. Each box has 33 degrees of freedom: 24 corresponding to the three motions at each of the eight nodes; and nine internally eliminated to minimize strain energy. The nine internal degrees of freedom are highly effective in eliminating shear error, and thus permitting far fewer elements than are required when tetrahedron elements are used. The element uses an isoparametric approach, so that the box can have eight arbitrarily positioned nodes. So long as the thermal expansions of the fuel rod can be described by a linear variation in the element, the code takes highly accurate account of it. Plasticity is accounted for by the secant modulus approach. Friction between the pellet and the cladding can be introduced by springs between the relevant finite elements in each area. A feature of the analysis allows cracks to appear in the uranium dioxide fuel as it is heated and the growth of the cracks can be traced as a function of linear power generated in the rod. The code can predict such things as pellet deformations and the stress and strain distributions within the pellets and the cladding. The three-dimensionality of the analysis allows a detailed view of these stresses and strains, and the interaction between the axial and plane stress distributions.     

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.     

Model of fracture for the Zry cladding of nuclear fuel rods included in the code DIONISIO 1.0

The DIONISIO code describes most of the main phenomena occurring in a fuel rod during normal operation of a nuclear power reactor. Starting from the irradiation history, the code predicts the temperature distribution, elastic and plastic stress and strain, creep, swelling and densification, release of fission gases, caesium and iodine to the internal rod volume, gas mixing, pressure increase, irradiation growth of the cladding, development of an oxide layer on its surface and hydrogen uptake, restructuring and grain growth in the pellet.This work presents the model of Zircaloy fracture included in the code DIONISIO 1.0. The model of pellet-cladding mechanical interaction (PCMI) provides the forces caused by the solid-solid contact which add to the changing internal pressure and to the constant external pressure. Besides, the program evaluates the effects of a corrosive atmosphere (stress corrosion cracking, SCC) internal or external. With these data, the code calculates the J integral around the tip of an initiated crack, and proceeds to analyze, according to the quantity of corrosive substance dissolved and the cladding stress field, if the crack remains unchanged, if it grows due to the I-SCC mechanism, or if propagation is ductile, following the R curve of the material.Results corresponding to different PHWR and PWR reactors are presented and compared with code results. In particular, good agreement is obtained in the simulation of MOX experiments, where the cladding failed due to propagation of cracks originated in SCC.     

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.     

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.     

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.     

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.     

超临界水堆燃料棒流致振动简化模型

在超临界水堆中,当超临界水流过带有绕丝的燃料棒时可能诱发其发生振动,使得燃料包壳发生疲劳现象。带有的接触的非线性有限元模型使得计算量大大增加,而且其计算精度仍有待实验验证。本文针对超临界水堆流致振动实验,将绕丝的影响简化为弹簧,建立燃料棒流致振动的简化模型,并通过有限元模型对燃料棒的固有特性进行分析,验证了模型的正确性。最后,以功率谱对模型加载,求得了超临界水堆燃料棒的位移响应和1δ解。     

A methodology for the evaluation of fuel rod failures under accident conditions

Abstract

Recent studies on the long-term behaviour of high-burnup spent fuel have shown that, under normal conditions of storage, challenges to cladding integrity from various postulated damage mechanisms, such as delayed hydride cracking, stress-corrosion cracking and long-term creep, would not lead to any significant safety concerns during dry storage, and regulatory rules have subsequently been established to ensure that a compatible level of safety is maintained. However, similar regulatory rules have not yet been developed to address failures of fuel rod cladding that could potentially lead to reconfigured fuel geometry under hypothetical transport accidents. At issue is the effect on cladding ductility of potential changes in zirconium hydride morphology during dry storage. Recent studies have shown that above a certain level of cladding hoop stress, the decaying temperature history during dry storage can cause the hydrogen in solid solution to precipitate in the form of radial hydrides, which, depending on their relative concentration, can induce brittle failures in the cladding. From a US regulatory perspective such cladding failures, if they were to cause fuel reconfiguration, could invalidate the cask's criticality and shielding licensing analyses, which are based on coherent geometry. This paper describes a methodology for high-burnup spent fuel to determine the frequency of cladding failure and failure modes under drop accidents, considering end-of-storage spent fuel conditions. The degree to which spent fuel reconfiguration could occur during handling or transport accidents would depend to a large extent on the number of fuel rod failures and the type and geometry of the failure modes. Such information can only be developed analytically, as there are no direct experimental data that can provide guidance on the level of damage that can be expected. To this end, this paper focuses on the development of a methodology for modelling and analysis that deals with this general problem on a generic basis. First, consideration is given to defining accident loading that is equivalent to the bounding hypothetical transport accident of a 9 m drop onto an essentially unyielding surface. Second, an analytically robust material constitutive model, an essential element in a successful structural analysis, is required. A model of material behaviour, with embedded failure criteria, for cladding containing various concentrations of circumferentially and radially oriented hydrides has been developed and implemented in a finite-element code. The hydride precipitation model, which describes the hydride structure of the cladding at the end of dry storage, and the hydride-dependent properties of high-burnup fuel cladding form the main input to the constitutive model. The third element in the overall process is to utilise this material model and its host finite-element code in the structural analysis of a transport cask subjected to bounding accident loading to calculate fuel rod failures and failure mode configurations. This requires detailed modelling of the transport cask and its internal structure, which includes the canister, basket, fuel assembly grids and fuel rods. The overall methodology is described.     

WTRLGD—A computer program for the transient analysis of waterlogged fuel rods under the RIA condition

A computer code WTRLGD has been developed to describe the transient internal pressure of a waterlogged fuel rod during power burst and also to predict the possibility of the rod failure in the mode of cladding rupture. The code predicts transient thermal behavior of the fuel rod on the basis of an assumption of axisymmetry, and thermal-hydraulic transients of the internal water on the basis of a homogeneous volume-junction model modified so as to involve the cladding deformation. Calculated transients of the rod pressure are in fairly good agreement with those measured in the NSRR experiments, simulating the fuel rod behavior under an RIA condition. The comparison between calculation and experiment verifies that the code is an effective tool for the prediction of the failure of a waterlogged fuel rod.     

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.     

Oxide thickness-dependent transient cladding hoop stress

A few thrice-burned Zry-4 fuel assemblies which were loaded in one of the PWRs operating in Korea were found to be failed due to PCI during a power ramp following a rector trip, while thrice-burned Zr–Nb fuel assemblies and twice-burned Zry-4 ones were intact. To investigate the effect of fuel rod oxide thickness on power ramp-induced cladding hoop stress, three intact fuel rods were selected, which include an intact twice-burned Zry-4 fuel rod, an intact thrice-burned Zr-4 fuel rod and an intact thrice-burned Zr–Nb fuel rod. With the use of a fuel performance analysis code, burnup-dependent steady-state cladding stress and ramp power-dependent cladding stresses at the power-ramped burnup were predicted for the three intact fuel rods. It was found that the cladding oxide thickness has a considerable effect on the ramp power-dependent cladding hoop stresses. In addition, the cladding maximum stress of the thrice-burned Zry-4 fuel rod with 125 μm oxide thickness exceeded an ultimate cladding tensile strength of the Zry-4 cladding when the pellet–clad friction coefficient-dependent cladding stress concentration ratio was considered. However, the thrice-burned Zr–Nb fuel rod with 50 μm oxide thickness was evaluated to have a considerable margin against the power ramp-induced PCI failure.     

Evaluation of LWR fuel rod behavior under operational transient conditions

To evaluate the effects of fission gas flow and diffusion in the fuel-cladding gap on fuel rod thermal and mechanical behaviors in light water reactor (LWR) fuel rods under operational transient conditions, computer sub-programs which can calculate the gas flow and diffusion have been developed and integrated into the LWR fuel rod performance code BEAF. This integrated code also calculates transient temperature distribution in the fuel-pellet and cladding.The integrated code was applied to an analysis of Inter Ramp Project data, which showed that by taking into account the gas flow and diffusion effects, the calculated cladding damage indices predicted for the failed rods in the ramp test were consistent with iodine-SCC (Stress Corrosion Cracking) failure conditions which were obtained from out-of-reactor pressurized tube experiments with irradiated Zircaloy claddings. This consistency was not seen if the gas flow and diffusion effects were neglected. Evaluation were also made for the BWR 8 × 8 RJ fuel rod temperatures under power ramp conditions.     

Simulation of the fracture behavior of Zircaloy-4 cladding under reactivity-initiated accident conditions with a damage mechanics model combined with fuel performance codes FEMAXI-7 and RANNS

A continuum damage mechanics model using FEM calculations was proposed to be applied to an analysis of the fuel failure due to pellet cladding mechanical interaction (PCMI) under reactivity-initiated accident conditions. The model expressed ductile fracture via two processes: damage nucleation related to void nucleation and damage evolution related to void growth and linkage. The boundary conditions for the simulations were input from the fuel performance codes FEMAXI-7 and RANNS. The simulation made reasonable predictions for the cladding hoop strain at failure and reproduced the typical fracture behavior of the fuel cladding under the PCMI loading, characterized by a ductile shear zone in the inner region of the cladding wall. It was shown that occurrence of a through-wall crack is determined at an early stage of crack propagation, and the rest of the through-wall penetration process is achieved with a negligible increment in strain. The effect of a local temperature rise in the cladding inner region on the failure strain was found to be less than 5% for the conditions investigated. Failure strains predicted under a plane strain loading were smaller by 20%–30% than those predicted under equibiaxial tensions between the hoop and the axial directions.     

Unbiasedness Evaluation of Statistical Error in Staged Monte Carlo Calculation

Fuel rod failure behavior has been studied under a reactivity initiated accident condition in Nuclear Safety Research Reactor (NSRR), JAERI. In the studies, inetallurgical observations showed that the incipient fuel rod failure mode was oxygen-induced embrittlement of the cladding independent of the test conditions such as fuel designs and cooling environments except for pressurized and waterlogged fuels. Development of the oxidation layers and embrittlement of β-Zry were quantitatively evaluated through the metallurgical examinations. A diffusion equation of oxygen was solved under a finite system with moving boundary conditions to obtain the oxygen concentration and evaluate the cladding embrittlement. The calculation showed that the wall thinning due to the cladding melt is needed for the complete embrittlement because the wall thinning enhances the oxygen concentration in the β-Zry, which well explain the experimental results. Therefore the failure threshold energy is determined by the cladding melting temperature. The failure threshold derived from this study is expected to be applicable to predicting the fuel rod failure behavior in computer analyses and also useful to evaluate the failure threshold energy for the new types of fuel rod.     

Analysis of the degradation of a PWR control rod during a loss of coolant accident, using the ICARE2 code

Conditions leading to AIC control rod damage during a loss of coolant accident in a PWR geometry, even in absence of violation of the LOCA licensing criteria, are investigated using several versions of the ICARE2 code (IPSN). Before being applied to the reactor case, the code and the modelling procedure are validated against the out-of-pile severe fuel damage experiment CORA-5. Three particular initial configurations are considered for the subsequent control rod damage analysis: nominal control rod and guide tube geometry, zircaloy guide tube bowing with concurrent cladding thickness reduction and finally control rod cladding perforation. For each of these cases the thermal, mechanical and chemical behaviour is presented. Phenomena such as ballooning and cladding failure of fuel rods, guide tube failure, melt relocation and final fluid channel cross-section modification are described. Finally, the conclusions of numerous sensitivity studies are discussed and some suggestions are given for possible improvements of the ICARE2 code.     

Modeling of Jet Pump by RELAP4 Code in Loss-of-Coolant Accident Analysis

Waterlogged fuel rod experiments performed at the NSRR are analyzed using the computer code WTRLGD, which was devised for the analyses of thermo-dynamical behavior of a waterlogged fuel rod. The numerical results are compared with the data from the experiments in order to assess the validity of the computer code. Parameters in the analyses are volumetric fraction of water, reactor period, gap width, a pin hole and the end peaks. Thus the analyses cover almost all the waterlogged fuel rod experiments at the NSRR.

The comparison shows good agreement between the experimental results and numerical ones on the transient thermo-dynamical behaviors of fuel, such as, rod internal pressure, cladding surface temperature and cladding strain. The numerical results also quantitatively agree with the experimental data concerning the effects of the above parameters on failure threshold energy. From the above findings, the computer code is assessed to be valid enough for the analyses of the failure behavior of the waterlogged fuel rod under a reactivity initiated accident condition.     

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.