Comprehensive nuclear materials 3 19 oxide fuel performance modeling and simulations

Comprehensive nuclear materials 3 19 oxide fuel performance modeling and simulations Comprehensive nuclear materials 3 19 oxide fuel performance modeling and simulations Comprehensive nuclear materials 3 19 oxide fuel performance modeling and simulations Comprehensive nuclear materials 3 19 oxide fuel performance modeling and simulations Comprehensive nuclear materials 3 19 oxide fuel performance modeling and simulations

3.19 Oxide Fuel Performance Modeling and Simulations P Van Uffelen European Commission, Joint Research Centre, Institute for Transuranium Elements, Eggenstein-Leopoldshafen, Germany M Suzuki Japan Atomic Energy Agency, Tokai-mura, Ibaraki, Japan ß 2012 Elsevier Ltd All rights reserved 3.19.1 3.19.1.1 3.19.1.2 3.19.1.3 3.19.2 3.19.2.1 3.19.2.1.1 3.19.2.1.2 3.19.2.1.3 3.19.2.1.4 3.19.2.1.5 3.19.2.2 3.19.2.2.1 3.19.2.2.2 3.19.2.2.3 3.19.2.2.4 3.19.2.3 3.19.2.3.1 3.19.2.3.2 3.19.3 3.19.3.1 3.19.3.1.1 3.19.3.1.2 3.19.3.2 3.19.3.2.1 3.19.3.2.2 3.19.4 3.19.4.1 3.19.4.2 3.19.4.3 3.19.4.4 3.19.5 References Introduction Importance of Fuel Performance Modeling Geometrical Idealization and Size of the Problem Uncertainties and Limitations Basic Equations and State of the Art Heat Transfer Axial heat transfer in the coolant Heat transport through the cladding Heat transport from cladding to the fuel pellet Heat transport in fuel pellets The structure of the thermal analysis Mechanical Analysis Main assumptions and equations Calculation of strains Boundary conditions Pellet–cladding interaction Fission Gas Behavior Basic mechanisms Modeling the fission gas behavior Design Basis Accident Modeling Loss-of-Coolant Accident Specific LOCA features Specific LOCA modeling requirements Reactivity-Initiated Accidents Specific RIA features Specific RIA modeling requirements Advanced Issues and Future Needs Deterministic Versus Probabilistic Analyses The High Burnup Structure Mixed Oxide Fuels Multiscale Modeling Summary and Conclusions Abbreviations bcc BOL BWR CANDU (C)SED CSR Body-centered cubic Beginning of life Boiling water reactor CANada Deuterium Uranium (Critical) strain energy density Volatile fission product release CZP DFT DNB ECCS ECR EOL EPMA fcc 536 536 536 537 538 538 538 539 539 540 541 541 541 542 546 547 551 551 554 557 557 557 558 561 561 562 564 564 566 568 570 572 574 Cold zero power Density functional theory Departure from nucleate boiling Emergency core cooling systems Equivalent cladding reacted End of life Electron microprobe analysis Face-centered cubic 535 536 Oxide Fuel Performance Modeling and Simulations FDM FEM FGR HBS HCP HM HZP IAEA IFA LEFM LHR LOCA LWR MC MD MIMAS MOX NEA O/M OECD PAS PCI PCMI PWR RIA S/V SANS SCC SM TAD TEM Finite difference method Finite element method Fission gas release High-burnup structure Hexagonal closed packed Heavy Metals Hot zero power International Atomic Energy Agency Instrumented fuel assembly Linear elastic fracture mechanics Linear heating rate Loss-of-coolant accident Light water reactor Monte Carlo Molecular dynamics Micronized master blend Mixed oxide Nuclear Energy Agency Oxygen-to-metal ratio Organisation for Economic Cooperation and Development Positron annihilation spectroscopy Pellet–cladding interaction Pellet–cladding mechanical interaction Pressurized water reactor Reactivity-initiated accident Surface-to-volume ratio Small-angle neutron scattering Stress corrosion cracking Shell model Temperature-accelerated dynamics Transmission electron microscopy 3.19.1 Introduction 3.19.1.1 Importance of Fuel Performance Modeling In order to ensure the safe and economical operation of fuel rods, it is necessary to be able to predict their behavior and lifetime The accurate description of the fuel rod’s behavior, however, involves various disciplines ranging from the chemistry, nuclear and solid-state physics, metallurgy, ceramics, and applied mechanics The strong interrelationship between these disciplines, as well as the nonlinearity of many processes involved, calls for the development of computer codes describing the general fuel behavior Fuel designers and safety authorities rely heavily on these types of codes since they involve minimal costs in comparison with the costs of an experiment or an unexpected fuel rod failure The codes are being used for R&D purposes, for the design of fuel rods, new products, or modified fuel cycles, and for supporting loading of fuel into a power reactor, that is, to verify compliance with safety criteria in safety case submissions A list of commonly used fuel performance codes is provided in Table 3.19.1.2 Geometrical Idealization and Size of the Problem In principle, our spatial problem is three-dimensional (3D) However, the geometry of a cylindrical fuel rod (a very long, very thin rod) suggests that any section of a fuel rod may be considered as part of an infinite body: that is, neglecting axial variations By further assuming axially symmetric conditions because of the cylindrical geometry, the original 3D problem is reduced to a 1D one Analyzing the fuel rod at several axial sections with a (radially) 1D description is sometimes referred to as quasi-2D or-11=2D Most fuel rod performance codes fall into this category Real 2D codes such as, for instance, the FALCON code,1 offer the possibility to analyze r–z problems (no azimuthal variation) and r–’ problems (no variation in axial direction) An example of a 3D code is TOUTATIS2 and DRACCAR3 and is dealt with in Chapter 3.22, Modeling of Pellet–Cladding Interaction DRACCAR is addressed later in Section 3.19.3.1.2 Generally, 2D or 3D codes are used for the analysis of local effects, whereas the other codes have the capability to analyze the whole fuel rod during a complicated, long power history In order to estimate the ‘size’ of the problem at hand, the number of time steps must also be specified For a normal irradiation under base load operation, that is, under no-load follow operation, $100–500 time steps are sufficient However, for an irradiation in a research reactor, such as the heavy-water boiling water reactor (BWR) of the Organisation for Economic Cooperation and Development (OECD), Halden, many more variations of the linear rating with time are recorded In such a situation, one must either simplify the complicated power history or increase the number of time steps to the order of several thousands The simplest geometrical idealization needs $20 radial and 20 axial nodes; a 2D representation of a single pellet would approximately need several hundred nodes Therefore, local models, which are in almost all cases nonlinear, must be very carefully constructed, since even for the simplest geometrical idealization the number of calls may easily reach the order of millions: 15 radial  15 axial nodes  5000 time steps  iterations ¼ 3:4  106 calls Oxide Fuel Performance Modeling and Simulations Table 537 List of fuel performance codes COMETHE COPERNICa ENIGMA FALCON, FREY FEMAXI FRAPCON METEORa PIN-micro START TRANSURANUS Hoppe, N.; Billaux, M.; van Vliet, J.; Shihab, S COMETHE version 4D release 021 (4.4-021), Vol 1, general description; Belgonucleaire Report, BN-9409844/220 A; Apr 1995 Bonnaud, E.; Bernard, C.; Van Schel, E Trans Am Nucl Soc 1997, 77 Kilgour, W J.; Turnbull, J A.; White, R J.; Bull, A J.; Jackson, P A.; Palmer, I D Capabilities and validation of the ENIGMA fuel performance code In Proceedings of the ENS Meeting on LWR Fuel Performance, Avignon, France, 1992 Rashid, J.; Montgomery, R.; Yagnik, S.; Yang, R Behavioral modeling of LWR fuel as represented in the FALCON code In Proceedings of the Workshop on Materials Modelling and Simulations for Nuclear Fuel, New Orleans, LA, Nov 2003 Suzuki, M.; Saitou, H Light Water Reactor Fuel Analysis Code FEMAXI-6 (Ver 1); JAEA-Data/Code 2005-003, Feb 2006 Berna, G A; Beyer, C E.; Davis, K L.; Lanning, D D FRAPCON-3: A computer code for the calculation of steady-state, thermal-mechanical behaviour of oxide fuel rods for high burnup; NUREG/CR-6534, PNNL-11513; Dec 1997 Struzik, C.; Moyen, M.; Piron, J High burnup modelling of UO2 and MOX fuel with METEOR/ TRANSURANUS Version 1.5 In Proceedings of the International Topical Meeting on LWR Fuel Performance, Portland, OR, Mar 1997 Pazdera, F.; Strijov, P.; Valach, M.; et al User’s guides for the computer code PIN-micro; UJV 9512-T, Rez; Nov 1991 Bibilashvili, Y K.; Medvedev, A V.; Khostov, G A.; Bogatyr, S M.; Korystine, L V Development of the fission gas behaviour model in the START-3 code and its experimental support In Proceedings of the International Seminar on Fission Gas Behaviour in Water Reactor Fuels, Cadarache, France, Sept 2000 Lassmann, K The TRANSURANUS code – past, present and future; Review article, ITU Activity Report 2001 – EUR 20252, ISBN 92-894-3639-5; 2001 a Based on TRANSURANUS 3.19.1.3 Uncertainties and Limitations In general, the uncertainties to be considered may be grouped into four categories The first category deals with the prescribed or input quantities for the fuel rod performance code: fuel fabrication parameters (rod geometry, composition, etc.), which are often available with an acceptable precision and are subject to specification limits The second category covers irradiation parameters (reactor type, coolant conditions, irradiation history, etc.) Although they contain a certain level of uncertainty, they can be properly managed in actual analyses The third category of Deformed geometry Nondeformed geometry (fresh fuel) Fuel pellet One-dimensional description Cladding Even with the computer power of today, a full 3D analysis of, for instance, a simulation of a complex irradiation history in an experimental reactor is practically impossible with deterministic models In some cases, it is possible, but in a limited part of a rod, such as a certain fraction of the axial length or of the azimuth angle of a rod In addition, such an analysis is limited by the fact that the shape and positions of the fuel fragments are determined by a stochastic process Nevertheless, attempts toward 3D analysis tools exist, such as the simplified 3D model DRACCAR which is useful in predicting the assembly-wise behavior during a loss-of-coolant accident (LOCA) Two-dimensional description Figure Schematic view of a deformed fuel pellet; comparison between a one-dimensional and a two-dimensional description uncertainties is related to the material properties, such as the fuel thermal conductivity or the fission gas diffusion coefficients The fourth and last category of uncertainties is the so-called model uncertainties A good example of such an uncertainty is the plain strain assumption in the axial direction as illustrated in Figure 1, representing the interaction of the deformed and cracked fuel with the cladding Intuitively, it is clear that for a detailed analysis 538 Oxide Fuel Performance Modeling and Simulations of such problems, 2D or even 3D models are indispensable One of the most important consequences of all uncertainties is that one must implement models of ‘adequate’ complexity 3.19.2 Basic Equations and State of the Art 3.19.2.1 Heat Transfer The objective of this section is to describe how the temperature distribution in a nuclear fuel rod is calculated in a fuel rod performance code The scope is limited to a description of the important physical phenomena, along with the basic equations and the main assumptions Detailed numerical aspects as well as mathematical derivations are provided in some reference works.4–6 The temperature distribution in a fuel rod is of primary importance for several reasons First of all, the commercial oxide fuels have poor thermal conductivities, resulting in high temperatures even at modest power ratings Second, the codes are used for safety cases where one has to show that no fuel melting will occur, or that the internal pressure in the rod will remain below a certain limit Finally, many other properties and mechanisms are exponentially dependent on temperature The most important quantity is of course the local power density q 000, which is the produced energy per unit volume and time It is usually assumed that q 000 depends only on the radius and on time The linear rating is then simply given by ð rcl;o q 000 r ị2pr dr q0 ẳ rf ;i rcl;o ð rf ;o 000 q 000 ¼ qf f ðr ị2pr dr ỵ cl 2pr dr rf ;i rcl;i ẵ1 where rf ;i /rcl;i is the inner fuel/cladding radius, rf ;o /rcl;o is the outer fuel/cladding radius, q000 f and q000 are the average power density in the fuel and cl cladding, respectively, and f ðr Þ is a radial distribution (form) function (see below) Generally, the linear rating is a prescribed quantity and is a function of the axial coordinate z and the time t For some phenomena (e.g., cladding creep), the fast neutron flux is also needed It can be prescribed as well but may also be calculated from the local power density q 000 3.19.2.1.1 Axial heat transfer in the coolant In general, three regimes must be covered in a light water reactor (LWR): The subcooled regime, where only surface boiling occurs This regime is typical for pressurized water reactors (PWRs) under normal operating conditions The saturated, two-phase regime This regime is typical for BWRs under normal operating conditions The saturated or overheated regime This regime may be reached in all off-normal situations A typical example is a LOCA The fuel rod performance codes use 1D (axial) fluid dynamic equations that can only cope with the first two regimes For simulating the third type of regime, the whole reactor coolant system needs to be analyzed by means of thermohydraulic system codes such as RELAP, TRACE, or ATHLET in order to provide adequate boundary conditions to the fuel rod performance code The temperature calculation in the coolant serves two purposes First of all, the axial coolant temperature in the basic (fictional) channel provides the (Dirichlet) boundary condition for the radial temperature distribution in the fuel rod It results from the combined solution of the mass, momentum, and energy balance equations The simplified equation used in fuel performance codes reads cr @T @T 00 2prcl;o ỵ qc000 ỵ crw ẳ qcl;c A @t @z ẵ2 where c represents the heat capacity, r the density, 00 the heat w the velocity, T the temperature, qcl;c flux from the cladding to the coolant, A the channel cross-sectional area, rcl,o the cladding outer radius, and qc000 the power density in the coolant In general, 00 the heat flux from cladding to coolant qcl;c should be computed by means of a thermohydraulic code Mathematically, the boundary condition is of the convective type:  @T r ; t ị 00 ẳ l ẳ afT r ẳ rcl;o ịTc g qcl;c @r rcl;o where a is the heat transfer coefficient between the cladding and the coolant and Tc ¼ Tc ðz; t Þ is the (bulk) coolant temperature Only for a steady-state condition crw dT q ẳ ỵ qc000 A dz ½3Š Oxide Fuel Performance Modeling and Simulations the heat flux from the cladding to the coolant is known and is given by 00 ¼ qcl;c q0 2prcl;o Under normal operational conditions, the mass flow rate m_ ¼ Arw, and the coolant inlet temperature and pressure are prescribed In an off-normal or accidental situation, the normal operational condition is the initial condition, but the boundary conditions must be provided by the thermohydraulic system codes The second objective of the heat flow calculation in the coolant is the derivation of the radial temperature drop between the coolant and the cladding Tcl À Tc, resulting from convection: q00 ¼ afilm ðTcl À Tc Þ ¼ qc000 2prcl;o The heat transfer coefficient in the film depends on the type of convection (forced or natural) and the type of coolant (gas, liquid, liquid metal) In the subcooled regime of a PWR, the Dittus–Boelter correlation is largely applied, whereas in the saturated regime of a BWR, the Jens–Lottes correlation is applied (see separate lecture on thermohydraulics) 3.19.2.1.2 Heat transport through the cladding The heat transport through the cladding occurs through conduction:   1@ @T r lc ỵ qcl000 ẳ r @r @r where lc is the cladding conductivity ($20 W mKÀ1 for Zircaloy), and the heat generation in the cladding is generally neglected (the g-heating as well as the exothermic clad oxidation process are generally disregarded) In order to account for the presence of an outside oxide layer with a thermal conductivity on the order of W mKÀ1 for ZrO2 (thickness