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.     

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.     

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.     

A new mechanistic code SFPR for modeling of single fuel rod performance under various regimes of LWR operation

A new mechanistic code SFPR for modeling of single fuel rod behavior under various regimes of LWR reactor operation (normal and off-normal, including severe accidents) is under development at IBRAE. The code is designed by coupling of two stand-alone mechanistic codes MFPR (for modeling of irradiated UO₂ fuel behavior and fission product release) and SVECHA/QUENCH, or S/Q (for modeling of Zr cladding thermo-mechanical and physico-chemical behavior). Both codes were initially designed for accident conditions (and for this reason, are rather mechanistic) and later extended to various normal operation conditions. On the base of thorough validation against various out-of-pile and in-pile experiments, development of an advanced fuel performance code for best estimate code calculations for both normal and off-normal LWR operation regimes is foreseen.     

Modeling of gap conductance for LWR fuel rods applied in the BISON code

ABSTRACT

A new gap conductance model is proposed in this study as a combination of Toptan’s model and the Ross-Stoute model. A variance-based sensitivity analysis is performed to understand how simulation results depend on all input parameters of the proposed model. Additionally, new modeling options (e.g. fill gas thermal conductivity, temperature jump distance, thermal accommodation coefficient, etc.) are added into the nuclear fuel performance code, BISON. The need for further investigation of the gap heat transfer between fuel and cladding in BISON motivated this study to evaluate its impact on the code’s predictions. New gap conductance modeling is proposed. A series of integral-effects validation tests is performed: (1) to demonstrate the impact of the proposed model on the code’s fuel temperature predictions at the beginning of life and through the reactor’s life; (2) to ensure that the proposed model is capable of accurately modeling gap heat transfer characteristics in real-world problems; and (3) to investigate the impact of the estimation of fission gas release on the fuel temperature predictions with the proposed model. The results indicate that the proposed gap conductance model improves BISON’s predictions.     

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.     

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.     

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.     

Uranium dioxide properties for LWR fuel rods

Uranium dioxide pellets have become the most important nuclear fuel, and will remain so far a long time, with the fissile isotope ²³⁵U being replaced by PuO₂ additions. This does not significantly change the pellet properties.Uranium dioxide properties affect fuel rod performance more than previously anticipated, because UO₂ pellets show a distinct response to irradiation, and because of mechanical and chemical interaction with cladding. Here elastic and plastic behaviour, fracturing, irradiation densification, and dimensional behaviour under steady and power cycling conditions are mainly covered.     

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.     

How to make a fuel rod modelling code meet the requirements of design applications

The tasks of the fuel rod designer and the resulting requirements on fuel rod modelling codes are described in the first part. These requirements have increased during recent years in connection with the goal to increase the burnup. Cutting of overconservatism can contribute to this goal, but this needs good and accurately calibrated models. The second part of the paper discusses the special rules which control the use of a fuel rod modelling code in design applications. It is demonstrated how an uncontrolled piling-up of scatter bands and parameter bounds will very rapidly end in hypothetic results. Only a reasonable coordination of unfavourable input parameters leads to “realistic” conservatism from an engineer's point of view. A sound data base is the prerequisite for the respective methods. Further efforts will be necessary to qualify codes and procedures for future probabilistic methodologies.     

The performance of defected spent LWR fuel rods in inert and dry air storage atmospheres

A testing program using eight commercial PWR and BWR spent fuel rods was conducted to investigate their long-term stability under a variety of possible dry storage conditions. The objective of this project is to provide the Nuclear Regulatory Commission (NRC) with the information to confirm or establish spent-fuel, dry storage licensing positions regarding long-term, low-temperature ( <523 K) spent fuel rod behavior during dry storage, and for radioactive contamination arising from spallation of cladding crud. Until now, the testing program has included three interim nondestructive examinations and one destructive examination. This paper presents the results of the third examination conducted to determine any degradation in eight fuel rods after being subjected to 13168 h at temperature. During this examination, visual observations, diametrical measurements, and isotopic analysis of smears were used to assess the fuel rod behavior and particulate release.     

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.     

Probabilistic models for fuel rod puncturing in an LWR core during a LOCA

The number of fuel rods which puncture during an LWR loss-of-coolant accident (LOCA) must be estimated as part of the plant radioactivity release analysis. Due to the great number of fuel rods in the core and the great number of contributing parameters, many of them associated with wide uncertainty and/or truly random variability limits, probabilistic methods are well applicable. A succession of computer models developed for this purpose is described together with applications to a WWER-440 PWR. Deterministic models are shown to be seriously inadequate and even misleading under certain circumstances. A simple analytical probabilistic model appears to be suitable for many applications. Monte Carlo techniques allow the development of such sophisticated models that errors in the input data presently available for practical problems probably become dominant in the residual uncertainty of the core-wide fuel rod puncture analysis.     

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.