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.     

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.     

Development of a 2D conduction code for a finned fuel element analysis

The fuel element of KMRR (Korea Multi-purpose Research Reactor) has 8 longitudinal, rectangular fins to enhance the heat transfer performance. The existence of these fins makes it difficult to analyze the heat transfer phenomena within the fuel element using the conventional one-dimensional heat conduction model. As the uncertainty in the computation of the maximum sheath temperature significantly affects the core thermal margin, a computer code, called, TEMP2D, which is based on a two-dimensional heat conduction model has been developed to deal with the finned element and validated. This computer code TEMP2D has a fully implicit numerical scheme and can solve both the steady state and transient problems such as the changes in coolant thermal-hydraulic conditions and fuel pin power. The code accuracy, which proved to be an excellent one, was verified by comparing its results with those from two widely accepted computer codes, MARC and ADINA. The result of this code calculation has been used to compute the KMRR core thermal margin and to develop a correlation for the equivalent 1D heated diameter which can reproduce the maximum cladding temperature (or heat flux) at various steady states when used in the 1D heat conduction model.     

BACO (Barra Combustible), a computer code for simulating a reactor fuel rod performance

The basic philosophy and mathematical structure of the fuel performance simulation code BACO is described. This code is based on a central finite-difference quasi-bidimensional approximation. Within that approximation, the thermoelastic-plastic behaviour of a in-service fuel rod is calculated by a set of equations which are linearized and solved for each time step by a sparse matrix inversion subroutine. The numerical method is shown to be stable and to converge rapidly to physically sound results for the stresses and strains. Changes in the fuel shape due to cracking and restructuring are included in the calculation within a self-consistent mathematical frame. Code convergence and accuracy are discussed by comparing some predictions against thermoelastic and plastic analytic solutions. An example of the code predictions for the rod state during a reactor shutdown is presented and discussed.     

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.     

Sensitivity analysis of fuel pin failure performance under slow-ramp type transient overpower condition by using a fuel performance analysis code FEMAXI-FBR

The FEMAXI-FBR is a fuel performance analysis code and has been developed as one module of core disruptive evaluation system, the ASTERIA-FBR. The FEMAXI-FBR has reproduced the failure pin behavior during slow transient overpower. The axial location of pin failure affects the power and reactivity behavior during core disruptive accident, and failure model of which pin failure occurs at upper part of pin is used by reflecting the results of the CABRI-2 test. By using the FEMAXI-FBR, sensitivity analysis of uncertainty of design parameters such as irradiation conditions and fuel fabrication tolerances was performed to clarify the effect on axial location of pin failure during slow transient overpower. The sensitivity analysis showed that the uncertainty of design parameters does not affect the failure location. It suggests that the failure model with which locations of failure occur at upper part of pin can be adopted for core disruptive calculation by taking into consideration of design uncertainties.     

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.     

FEMAXI-IV: A computer code for the analysis of fuel rod behavior under transient conditions

A fuel rod behavior code FEMAXI-IV, presently under development, is an improved version of the FEMAXI-III code for the analysis of fuel rod behavior under transient conditions. To apply the FEMAXI-III code to transient conditions, the following additional models have been incorporated into the FEMAXI-III code: transient heat transfer model: axial gas mixing model; diffusion-type fission gas release model. This paper summarizes the above additional models, and the comparison of the FEMAXI-IV calculations with the experimental data.     

Irradiation swelling, creep and thermal-stress analysis of LWR fuel elements, computer code isune-2

The irradiation swelling, creep, and thermal-stress analysis of light-water reactor (LWR) oxide (UO₂) fuel elements is analysed. The analysis is based on the basic physical and mathematical assumptions and the experimental data of the fuel and cladding (or canning) materials. In the analysis, the nuclear, physical, metallurgical, and thermo-mechanical properties of the fuel and cladding materials under irradiation environment are examined carefully. The objectives of the paper are mainly (1) to formulate and carry out the irradiation swelling, irradiation creep, and thermal-stress analysis of fuel elements for LWR power reactors, and (2) to develop a computer code which will facilitate the computations for fuel element design, safety analysis, and economic optimization of the power reactors. In a general procedure of the analysis, the irradiation swelling, irradiation creep, temperature distribution, etc. in the fuel and cladding of the oxide fuel elements during the reactor in operation are studied. Some theoretical models and empirical relations (on the basis of accepted experimental data) for irradiation swelling and creep in the fuel and irradiation creep in cladding materials are postulated and developed. Some analytical and empirical relations (based on test results) for heat generation and temperature distribution in the fuel during fuel restructuring are derived. The fuel restructure is, in general, divided into the central void, columnar grain, equiaxed grain, and unaffected grain zones (or regions) after a sufficiently long period for the fuel elements to be irradiated (or operated). From these relations derived for irradiation swelling, irradiation creep, and temperature distribution in the fuel and cladding, together with the well-known strain-stress, incompressibility, compatibility, and stress equilibrium equations, the irradiation swelling, creep, and thermal-stress analysis for the LWR fuel elements can be carried out.From the analytical results obtained, a computer code, ISUNE-2 (which is in the sequence of computer code ISUNE-1 and -1A developed and used previously for liquid-metal fast breeder reactor fuel element design and safety and economic analysis), can be developed. With some reliable experimental data (measured during fuel elements in operation) as input, the computer code may predict various cases of LWR (oxide or carbide) fuel elements in operation. The general scope and resulting contribution of this paper is to provide a realistic analysis and a reliable operating LWR fuel element code for use by nuclear power utilities to predict the fuel element behavior in power reactors. The fuel element design, safety analysis, and economic optimization depend largely on the fuel element behavior in the power reactors.     

Large strain, viscoelastic and elasto-viscoplastic numerical analysis by means of the finite element method

Finite element procedures and illustrative numerical examples for linear and nonlinear viscoelastic and elasto-viscoplastic bodies are discussed. According to the well-known theory in rheology, the constitutive equation of viscoelastic bodies can be described by the first-order simultaneous differential equation system. Using this result, the finite element equation leads to an equation similar to the Hookean elastic body except for the inclusion of the time increment. The procedure is applicable to certain forms of nonlinear viscoelastic and elasto-viscoplastic bodies. To solve the nonlinear simultaneous equation system, it is convenient to employ the incremental displacement method for the nonlinear problems such as large deformation loading, unloading and cyclic loading behavior.     

Structural analysis of a three-dimensional perforated plate by the finite element method with test correlation

An application of the finite element method to a three-dimensional perforated plate structure is presented using a nested modeling technique. Stresses calculated by a general three-dimensional finite element computer program were compared with those obtained from a model test. The structure considered in this analysis is a plenum cover of a pressurized water reactor internal which is a circular perforated plate stiffened with welded cross ribs. This type of structure is common in reactor internals. The nested model analyses consist of two finite element models; one is for the overall structure model and the other for an isolated portion of the structure with refined grid system for more accurate stress calculation. The first model was analyzed to obtain the nodal displacements under the applied loads. Then the second model was run using the displacement boundary conditions obtained from the first model analysis. A fully instrumented Plexiglas model test was conducted to verify this method. Comparison between the test results and the calculated stresses from the second model analysis showed good agreement.     

Feasiblity study of a direct second order finite element method for structures analysis

The classical modelizations used in structures analysis fail for singular situations which give high gradients. All numerical methods lead then to inaccurate or instable results, due to the geometrical and/or loading singularities.High gradients zones (even very localized) are precisely damaging areas, especially responsible for fatigue collapses. Therefore, it seems of particularly interest to introduce a better modelization in order to eliminate the mentioned difficulties, ensuring at the same way a complete compatibility in complex structures analysis.     

Development of a thermal-hydraulic analysis code for annular fuel assemblies

A thermal-hydraulic analysis code which is capable of modeling both internally and externally cooled annular fuel pins was developed. The coolant flow distribution in the annular fuel-based assemblies is adjusted by a pressure drop model allowing for conditions such as non-equal velocity and non-saturated phases. The heat transfer fraction is determined by the ratio of cross-sectional areas distinguished by the radius at which the first derivative of the temperature within the annular fuel equals zero. The code predictions have been compared with calculations from Korea Atomic Energy Research Institute (KAERI) and MIT. The heat transfer fraction difference between the code and RELAP was about 3.9%, and the Departure from Nucleate Boiling Ratio (DNBR) prediction of the code agreed well with the MIT’s result in the region below 3 m. For the application of the code, thermal-hydraulics of thorium-based fuel assemblies loaded with annular seed pins were compared with those of the existing thorium-based assemblies. The pressure drop in the assembly generally increased in the case of annular fuel due to the larger wetted perimeter. In the inner subchannels of the seed pins, mass fluxes were high due to the grid form losses in the outer subchannels. About 43% of the heat generated from the seed pin flowed into the inner subchannel and the rest into the outer subchannel. The minimum DNBRs (MDNBRs) of the annular fuel-based assemblies were higher than those of the existing ones. Because interchannel mixing cannot occur in the inner subchannels, temperatures and enthalpies were higher in the inner subchannels.     

A fluid-structure finite element method for the analysis of reactor safety problems

A method is presented for the safety analysis of reactor containment structures by means of finite elements. The finite element equations of both fluid and structural elements for arbitrarily large, non-linear response are developed and the way in which they are combined is indicated. Both explicit and implicit integration of the equations in time is considered. Three examples of the application of these methods to the analyses of reactor safety problems are described.     

Plastef: A code for the numerical simulation of thermoelastoplastic behaviour of materials using the finite element method

A general code for solving two-dimensional thermo-elastoplastic problems in geometries of arbitrary shape using the finite element method, is presented. The initial stress incremental procedure was adopted, for given histories of load and temperature. Some classical applications are included.     

A parametric analysis of creep buckling of a shallow spherical shell by the finite element method

This paper presents a parametric analysis of the creep buckling of a shallow spherical shell subjected to uniform external pressure using the finite-element incremental method. Axisymmetric creep deformation analysis is first performed to obtain pre-buckling behavior by the time incremental method. The buckling modes considered are both bifurcation and axisymmetric snap-through types. Fourier expansion technique is conveniently employed to construct the stiffness matrices corresponding to asymmetric bifurcation as well as axisymmetric snap-through modes of deformation. The critical time for creep buckling is defined by the time at which either stiffness matrices corresponding to the axisymmetric or asymmetric modes lose their positive definiteness. The critical times and the buckling modes are obtained over a fairly wide range of the geometric parameters pertaining to shallow spherical shell subjected to uniform external pressure.