Mathematical description of WAFER-1, a three-dimensional code for LWR fuel performance analysis

This article describes in detail the mathematical formulation used in the WAFER-1 code, which is presently used for three-dimensional analysis of LWR fuel pin performance. The code aims at a prediction of the local stress-strain history in the cladding, especially with regard to the ridging phenomenon. To achieve this, a clad model based on shell theory has been developed. This model interacts with a detailed finite difference pellet model which treats radial and transversal cracking in the pellet in a deterministic way, based on certain assumptions with respect to the cracking pattern. Pellet and clad creep are taken into account. The inner core of the pellet, bounded by a specified isotherm, may be treated as a viscous material. Axial force exchange between pellet and clad is also included. The axial loading is distributed on the pellet end face with due regard to any pellet dishing. An arbitrary power history may be used as input to the model.     

Modeling of fission gas swelling in LWR UO2 fuel under irradiation

An understanding of the behavior of fission gas in uranium dioxide (UO₂) fuel is necessary for the prediction of the performance of fuel rods under irradiation. A mechanistic model for matrix swelling by the fission gas in LWR UO₂ fuel is presented. The model takes into account intragranular and intergranular fission gas bubbles behavior as a function of irradiation time, temperature, fission rate and burn-up. The intragranular bubbles are assumed to be nucleated along the track of fission fragments, which play the dual role of creator and destroyer of intragranular bubbles. The intergranular bubble nuclei is produced until such time that a gas atom is more likely to be captured by an existing nucleus than to meet another gas atom and form a new nucleus. The capability of this model was validated by a comparison with the measured data of fission gas behavior such as intragranular bubble size, bubble density and total fuel swelling. It was found that the calculated intragranular bubble size and density are in reasonable agreement with the measured results in a broad range of average fuel burn-ups 6–83 GW d/tU. Especially, the model correctly predicts the fuel swelling up to a burn-up of about 70 GW d/tU.     

FEMAXI-III,a computer code for fuel rod performance analysis

This paper presents a method of fuel rod thermal-mechanical performance analysis used in the FEMAXI-III code. The code incorporates the models describing thermal-mechanical processes such as pellet-cladding thermal expansion, pellet irradiation swelling, densification, relocation and fission gas release as they affect pellet-cladding gap thermal conductance. The code performs the thermal behavior analysis of a full-length fuel rod within the framework of one-dimensional multi-zone modeling. The mechanical effects including ridge deformation is rigorously analyzed by applying the axisymmetric finite element method. The finite element geometrical model is confined to a half-pellet-height region with the assumption that pellet-pellet interaction is symmetrical. The 8-node quadratic isoparametric ring elements are adopted for obtaining accurate finite element solutions. The Newton-Raphson iteration with an implicit algorithm is applied to perform the analysis of non-linear material behaviors accurately and stably. The pellet-cladding interaction mechanism is exactly treated using the nodal continuity conditions. The code is applicable to the thermal-mechanical analysis of water reactor fuel rods experiencing variable power histories.     

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.     

Radiation and creep analysis for tubular fuel elements at unsteady state

A radiation and creep analysis for strain rates, strains and stresses induced by thermal cycling, radiation and creep in long, tubular fuel elements at unsteady state is presented. The primary effects of thermal-cycling growth, irradiation growth, swelling and creep of the fuel materials for nuclear power reactors are considered.The thermal, radiation and time effects on the components of strain rate, strain and stress produced in the fuel elements are shown from equations and the calculated results of a numerical example.     

Irradiation creep and interrelation with swelling in austenitic stainless steels

The available experimental data on irradiation-induced creep in austenitic stainless steels are summarized and the existing theories reviewed. Attention is paid to the influence of material composition and pretreatments on irradiation creep. In particular the stress, flux, fluence and temperature dependencies are reported and possible correlations of irradiation creep with the microstructural evolution, the swelling behaviour and the precipitation kinetics of the materials are outlined. The consequences of stress effects connected with swelling for the irradiation-creep behaviour, especially the stress-dependence, are discussed.     

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.     

Coupled thermal structural analysis of LWR vessel creep failure experiments

Considering the hypothetical core melt down scenario for a light water reactor (LWR) the failure mode of the reactor pressure vessel (RPV) has to be investigated to determine the loadings on the containment. The failure of reactor vessel retention (FOREVER)-experiments, currently underway, are simulating the thermal and pressure loadings on the lower head for a melt pool with internal heat sources. Due to the multi-axial creep deformation of the vessel with a non-uniform temperature field these experiments are an excellent source of data for validation of numerical creep models. Therefore, a finite element (FE) model has been developed based on a commercial multi-purpose code. Using the computational fluid dynamics (CFD) module the temperature field within the vessel wall is evaluated. The transient structural mechanical calculations are performed using a new numerical approach, which avoids the use of a single creep law employing constants derived from the data for a limited stress and temperature range. Instead of this a three-dimensional array is developed where the creep strain rate is evaluated according to the values of the actual total strain, temperature and equivalent stress. Care has to be exercised performing post-test calculations particularly in the comparisons of the measured data and the numerical results. Considering the experiment FOREVER-C2, for example, the recorded creep process appears to be tertiary, if a constant temperature field is assumed. But, small temperature increase during the creep deformation stage could also explain the observed creep behavior. Such considerations provide insight and better predictive capability for the vessel creep behavior during prototypic severe accident scenarios.     

Irradiation devices for the study of creep and swelling in ceramic fuels

In fuel element design for advanced nuclear reactors perfect knowledge of fuel behaviour under irradiation plays a decisive role, above all for long service lives and high burnups. Therefore, the development of fast breeder fuel elements within the framework of the Karlsruhe Fast Breeder Project included various irradiation rigs which allow continuous measurement during irradiation of fuel specimen creep and swelling. A survey is presented of some of these irradiation rigs.     

Radiation growth and swelling analysis for strains and stresses in short cylindrical fuel elements

Based on the present, accepted experimental results of radiation growth and swelling in nuclear fuels, a theoretical analysis for strain and stress distributions in short solid-cylindrical fuel elements is presented. The exact solutions of the modified Bessel functions for neutron flux distribution and temperature distribution in the fuel elements are respectively obtained from the simple diffusion equations and Poisson's heat conduction equation.The strain and stress equations for the fuel elements are derived. From the calculated results of a numerical example, the components of strain and stress produced in the fuel elements are shown by the curves. For purposes of comparison, the strain and stress distributions developed in the long, solid-cylindrical fuel elements are also given. From the results of comparison it appears that short fuel rods or slugs offer definite advantages over long fuel elements when the stability of fuel element and burn-up level are concerned.     

Enhancing the ABAQUS thermomechanics code to simulate multipellet steady and transient LWR fuel rod behavior

A powerful multidimensional fuels performance analysis capability, applicable to both steady and transient fuel behavior, is developed based on enhancements to the commercially available ABAQUS general-purpose thermomechanics code. Enhanced capabilities are described, including: UO₂ temperature and burnup dependent thermal properties, solid and gaseous fission product swelling, fuel densification, fission gas release, cladding thermal and irradiation creep, cladding irradiation growth, gap heat transfer, and gap/plenum gas behavior during irradiation. This new capability is demonstrated using a 2D axisymmetric analysis of the upper section of a simplified multipellet fuel rod, during both steady and transient operation. Comparisons are made between discrete and smeared-pellet simulations. Computational results demonstrate the importance of a multidimensional, multipellet, fully-coupled thermomechanical approach. Interestingly, many of the inherent deficiencies in existing fuel performance codes (e.g., 1D thermomechanics, loose thermomechanical coupling, separate steady and transient analysis, cumbersome pre- and post-processing) are, in fact, ABAQUS strengths.     

FRAP-T6: A computer code for the transient analysis of oxide fuel rods

The FRAP-T6 computer code was developed to model the transient performance of light water reactor fuel rods during reactor transients ranging from mild operational transients to large break loss-of-coolant accidents. The code models all of the thermal, structural, and chemical phenomena needed for the complete evaluation of light water reactor fuel rod performance. The code was developed using rigorous quality assurance procedures and a large assessment data base. The results of assessment show that the code accurately models the response of light water reactor fuel rods.     

高温气冷堆包覆燃料颗粒破损机制及失效模型

高温气冷堆的燃料元件的基本构成单元是全陶瓷型的包覆燃料颗粒,其性能决定了高温气冷堆的安全性。除了传统的辐照实验检测外,建立理论模型对其研究具有重要的意义。本文主要介绍了TRI-SO型包覆燃料颗粒的结构及破损机制,以及国外现有的几个主要模型的基本假设,计算原理和特点,通过对比几个模型的优缺点,提出今后研究的方向。     

SAMURA—A fast computer code for reactor fuel pin performance modelling and analysis

A very fast integral numerical computer code for the modelling of transient and steady-state thermal and mechanical behaviour of Zircaloy-clad UO₂ fuel pins in water reactors has been developed. The computational technique which determines the stress and deformation state of the fuel pin is based upon an extremely efficient finite difference scheme, i.e. the non-linear terms in the constitutive equations which produce a non-linear system of equations have been linearised using a Taylor expansion technique coupled with a very sophisticated error minimization algorithm and then solved with great accuracy. An improved numerical method has also been developed for the fast and efficient solution of the transient heat conduction equation. In this way a very stable and economical one-dimensional code (with appropriate provisions made for its conversion to a quasi two-dimensional code) has been obtained. The physical processes included are thermo-elastic deformation, thermal and irradiation creep, plasticity, fission gas swelling and release, formation of cracks in the fuel, hot pressing, densification, pore migration and dish or central void filling. Here the mathematical basis of SAMURA is presented along with some preliminary calculations and benchmarkings. It is concluded that SAMURA is quite fast indeed, converges to accurate results and within the margins of the error criterion chosen has very reasonable computer demands. It is also stable under all conditions tested.