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.     

三维燃料棒精细化模拟软件FUPAC3D与FUPAC的对比验证研究

为验证基于三维有限元分析平台建立的三维燃料棒精细化模拟软件FUPAC3D在分析评价压水堆燃料棒辐照-热-力耦合行为方面的能力和精度,本文给出了三维FUPAC3D软件采用的热学模型、燃料棒力学模型、裂变气体释放模型以及腐蚀模型,以华龙一号典型燃料棒参数和运行工况作为输入参数,分别使用三维FUPAC3D软件和已工程化应用的1.5维FUPAC软件进行建模分析,并针对2种软件在芯块和包壳温度、包壳应力与应变、芯块与包壳间间隙宽度的计算结果进行对比研究。研究结果表明,FUPAC3D软件与FUPAC软件具有相当的精度,FUPAC3D软件具备压水堆燃料棒辐照-热-力耦合行为的精细化模拟能力。      

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.     

Thermal-hydraulics analysis during fuel element failure in an operating PWR

The fuel element failure in an operating pressurized water reactor (PWR), including fuel element breaks, has an effect on the operation safety of PWR. In this paper, the RELAP5 model of the fuel element failure is established for the safety analysis. The RELAP5 time step sensitivity analyses for the element pre-break steady and post-break transient simulation are carried out. And the variations of main thermal-hydraulics parameters related to the fuel element break are quantitatively studied, which include the internal gap pressure and the maximum fuel pellet temperature as well as the releasement of noncondensables in the gap. It is found that (1) the results by the RELAP5 code is very sensitive to the time step in a volume system with the noncondensables, and the time step sensitivity analysis is necessary if the effective time step range is unknown, (2) the larger the break area is, the more quickly the gap pressure increases and the maximum pellet temperature reaches to the stable value, (3) when the gap pressure increases and reaches to the coolant pressure, at the break the liquid inflow from coolant to gap will be turned to the vapor outflow from gap to coolant, (4) during the failure transient, the gap thermal conductivity experiences a sharp decrease in the break instant, which results in the decrease of heat transferred to cladding and the sharp decrease of cladding temperature as well as the sharp increase of minimum departure from nucleate boiling ratio (MDNBR). These conclusions can provide the basic for the operation safety analysis of PWR during the fuel element failure.     

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.     

U-10Mo/Zr单片式燃料元件堆内稳态热-力学性能研究

本文建立了U-10Mo/Zr单片式燃料元件的辐照性能模型以及热-力学本构关系,采用有限元方法进行非均匀辐照场中燃料元件稳态热-力学性能的数值模拟,获得并分析了U-10Mo/Zr单片式燃料元件温度、形变和应力的分布特点及变化规律。研究结果表明,燃料芯体厚度增量在芯体和包壳结合面附近达到最大,主要受到燃料辐照蠕变的影响;在较低燃耗条件下,燃料芯体高温辐照肿胀模拟结果与低温辐照肿胀试验结果相当;燃料芯体边角区域和包壳端面外侧区域存在应力集中。      

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.     

Thermodynamic analysis of a solid nuclear fuel element surrounded by flow of coolant through a concentric annular channel

A continuous quest for efficient utilization of energy resources has motivated the researchers to search for optimal design and operating conditions during various energy conversion techniques. These conditions for such systems are often proposed by minimizing the destroyed exergy potential in course of the process. In the present paper a second law analysis is done for a nuclear fuel element inside a concentric annular coolant passage. The entropy generation analysis has been carried out through a conjugate approach, with steady state temperature profiles within the fuel element and a thermodynamic approach within fluid. The effect of solid core heat generation and the temperature gradients inside solid core, fuel-clad gap and cladding are considered as well along with the irreversibilities arising out of fluid flow under turbulent condition. The effect of Reynolds number, duty parameter, diameter ratio, Biot number, dimensionless heat flux and thermal conductivity ratios on overall entropy generation characteristics have been investigated and interpreted physically. The validation of the present calculations was confirmed by best-estimate thermal-hydraulic code RELAP. The new thermodynamic design methodology presented in this paper adheres to the safety limits in temperature. The present analysis can be extended for complex fuel pellet arrangements in subchannel structures by an “equivalent annulus model”.     

Three-dimensional FE analysis of the thermal–mechanical behaviors in the nuclear fuel rods

In order to implement numerical simulation of the thermal–mechanical behaviors in the nuclear fuel rods, a three-dimensional finite element model is established. The thermal–mechanical behaviors at the initial stage of burnup in both the pellet and the cladding are obtained. Comparison of the obtained numerical results with those from experiments validates the developed finite element model. The effects of the constraint conditions, several operation and structural parameters on the thermal–mechanical performances of the fuel rod are investigated. The research results indicate that: (1) with increasing the heat generation rates from 0.15 to 0.6 W/mm³, the maximum temperature within the pellet increases by 99.3% and the maximum radial displacement at the outer surface of the pellet increases by 94.3%. And the maximum Mises stresses in the cladding all increase; while the maximum values of the first principal stresses within the pellet decrease as a whole; (2) with increasing the heat transfer coefficients between the cladding and the coolant, the internal temperatures reduce and the temperature gradient remains similar; when the heat transfer coefficient is lower than a critical value, the temperature change is sensitive to the heat transfer coefficient. The maximum temperature increases only 7.13% when h changes from 0.5 W/mm² K to 0.01 W/mm² K, while increases up to 54.7% when h decreases from 0.01 W/mm² K to 0.005 W/mm² K; (3) the initial gap sizes between the pellet and the cladding significantly affect the thermal–mechanical behaviors in the fuel rod; when the gap size varies from 0.03 mm to 0.1 mm, the highest temperature in the pellet increases by 19.7%, and the maximum first principal stress at the outer pellet surface decreases by 17.4%; it is critical to optimize the gap size in order to reduce the pellet–cladding mechanical interaction and avoid their contact at early stage. This study lays a foundation for the further research on the irradiation-induced mechanical behaviors in the fuel rods.     

高燃耗下UN-FeCrAl燃料元件稳态及瞬态热力学性能分析

UN-FeCrAl燃料元件作为耐事故燃料高燃耗应用的主要方案之一,需要评价其在高燃耗下的热力学性能。本研究基于FUPAC软件对UN-FeCrAl燃料元件在燃耗68000 MW·d·t^-1(U)下的稳态和瞬态热力学性能进行了预测。分析结果表明,稳态工况下UN-FeCrAl燃料元件热力学性能表现良好;瞬态下UN燃料的芯块中心温度最高仅为862℃,可满足芯块温度设计要求,但FeCrAl包壳的瞬态应力最大将达到459 MPa,且瞬态应变量相比于稳态应变量最大增加了0.23%,这可能会使FeCrAl包壳面临瞬态应力和瞬态应变准则超限的风险。因此后续研究应重点关注FeCrAl包壳的瞬态应力和瞬态应变性能。     

Parametric analyses of partial sub-assembly blockages of the 50 MWth gas cooled experimental technology and demonstrator reactor (ETDR)

This paper presents a parametric study of thermal hydraulic and structural mechanic analyses of accidental blockages of the hottest sub-assembly of the 50 MWth gas-cooled fast reactor, ETDR. The blockage ratios were 60% and 100% of the sub-assembly flow cross-section located at the first row of grid spacers. Temperature profiles in the fuel and cladding were calculated as a function of time using computational fluid dynamics. The results were incorporated into finite elements analyses to evaluate thermal and mechanical stresses and strains in the cladding and fuel. 2D simulations with generalized plane strains were used in the structural analyses applying the maximum power density in the pellet as calculated by CFD. The thermal analyses showed that a 60% partial blockage increases the maximum cladding temperature by 130 °C within a time period of 50 s, whereas a full blockage will lead to clad melting (1320 °C) in about 8 s after accident initiation. In the finite element analyses several, mainly conservative, assumptions have been made to incorporate the phenomena occurring in the pellet-cladding interaction. The results of the finite element analyses represent a first study of the pellet-cladding mechanical interface under given transients, exploring the development of a methodology to be used for future analyses. The model has been verified to predict realistic contact stresses in line with analytical solutions during partial or full blockages. However, more elaborate 2D and 3D contact models, with creep and irradiation creep material models for both fuel and clad, together with parametric studies on friction coefficients and number of fuel fragments are foreseen for future work on failure criteria.     

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.     

Analysis of MOX fuel behavior in reduced-moderation water reactor by fuel performance code FEMAXI-RM

To assess the feasibility of the 31% Pu-MOX fuel rod design of reduced-moderation water reactor (RMWR) in terms of thermal and mechanical behaviors, a single rod assumed to be irradiated in the core of RMWR up to 106 GWd/tHM has been analyzed by a fuel performance code FEMAXI-RM which is an extended version of FEMAXI-6 code. In the analysis, design specifications of fuel rod and irradiation conditions have been input, and available models of both MOX fuel and UO₂ fuel have been used as appropriate. The results are: fission gas release is several tens of percent, rod internal pressure does not exceed the coolant pressure, and the highest fuel center temperature is 2400 K, while cladding diameter increase caused by pellet swelling is within 1% strain. These predictions suggest that the MOX fuel rod integrity will be held during irradiation in RMWR, though actual behavior of MOX pellet swelling and cladding oxidation require to be investigated in detail.     

Heat transfer in LMFBR fuel elements Part I: Effects of fuel pellet displacement

Random displacement of mixed oxide fuel pellet axes from the central axis of their overall liquid metal fast breeder reactor fuel element occurs when the pellcts are randomly loaded within the fuel element cladding sheath. Assuming azimuthally symmetric heat transfer from the outer cladding surface to the bulk coolant, the influence of this random displacement upon the temperature distribution throughout the fuel element is examined when the granular or porous detailed fuel structure and cracks in the fuel (discussed in Part II) are ignored. It is shown that for a typical example, in which the maximum displacement is only 0.0075 cm and the fuel pellet radius is 0.2465 cm, the variance of the maximum fuel temperature is in the vicinity of 115° C, so that this random displacement effect can be quite important especially for those fuel pellets with an expected maximum temperature near the melting point of the fuel.     

Multidimensional gap conductance model for thermo-mechanical simulation of LWR fuel behavior using a virtual link element

In light water reactor (LWR) fuel, the modeling of the heat transfer across the gap between the fuel pellets and the protective cladding is essential to understanding the fuel behavior. Based on the Ross and Stoute model, the gap conductance that specifies the temperature gradient within the gap depends on the gap thickness, which is related to the mechanical behavior. A multidimensional gap conductance problem can be challenging in terms of convergence and nonlinearity. In this work, a virtual link gap (VLG) element has been proposed to resolve the convergence issue and nonlinear characteristic of multidimensional gap conductance. The elements that link the node of a pellet surface with the node of the cladding surface are virtually generated so as to transfer heat as a function of gap thickness at every iteration step. To evaluate the proposed methodology for the simulation of the gap conductance, a thermo-mechanical model has been established using ANSYS Parametric Design Language (APDL) for a preliminary study, and a 3D thermo-mechanical module using FORTRAN77 has been implemented. In terms of calculation accuracy and convergence efficiency, the proposed VLG model has been evaluated. As a result, the convergence criterion of the thermo-mechanical calculation considering the iteration characteristics of the VLG element has been proposed. To demonstrate the effect of the VLG model in a 3D simulation with the implemented thermo-mechanical module, the simulation results of a missing pellet surface (MPS) have been compared.     

兆瓦级空间气冷堆系统启停堆瞬态分析

本文针对兆瓦级高温气冷堆布雷顿循环系统,采用Fortran语言开发系统分析程序TASS,包括堆芯、透平-发电机-压气机、回热器、冷却器和热管式辐射散热器等模型。通过设计值与程序计算值对比对TASS进行验证,并利用TASS对系统启动、停堆瞬态工况进行数值模拟。结果显示,通过分两阶段、阶梯式引入正反应性和提高涡轮机械的转轴速度,堆芯流量和功率匹配良好,系统可在3.5 h内完成启动过程,达到反应堆功率3 406 kW、流量14.2 kg/s的稳态运行。系统停堆过程中,反应堆可依靠自身的非能动余热排出能力,确保芯块和包壳温度与熔点间存在较大安全裕量,实现安全停堆。     

燃料棒破损热力学模块开发及在严重事故分析程序中的应用

包壳肿胀和破损是严重事故早期阶段的重要现象。包壳形变不仅会造成局部流动堵塞,同时,水蒸气会从破裂处进入包壳气隙,增加包壳被蒸汽氧化的表面积。广泛使用的一体化严重事故分析程序不能分析早期事故过程中燃料棒的热力学行为,判断包壳破裂也只是基于简单的参数模型。本文开发了分析燃料棒热力学行为的FRTMB模块,并集成在严重事故分析程序ISAA中。使用开发的耦合系统ISAA FRTMB分析了CAP1400反应堆直接注射（DVI）管线小破口事故过程中燃料棒的热力学行为,并预计了包壳破裂时间及相应的失效温度。计算结果整体验证了ISAA FRTMB分析瞬态事故过程中燃料棒热力学行为以及判断包壳破裂的适用性和可靠性。     

轻水堆含钆燃料棒稳态辐照行为分析

国内外的压水堆燃料组件最新设计中,广泛采用钆燃料（UO₂-Gd₂O₃）作为可燃毒物来控制初始反应性和展平堆芯功率分布。钆燃料棒的性能与普通燃料棒存在较大差异,本文利用燃料元件性能分析程序FRAPCON-3.5对BR3堆内含钆燃料棒性能进行计算,并与实验测量值进行比较。结果表明：FRAPCON-3.5对含钆燃料棒的计算结果与实验测量值符合较好;含钆燃料棒在辐照初期强化了燃料棒自屏效应,对燃料的径向功率分布影响显著;在平均功率密度相同的情况下,燃料中加入钆会导致热导率降低,芯块温度升高;钆含量不同,裂变气体释放及燃料和包壳的变形略有差异。     

Development and benchmarking of a mechanical model for GFR plate-type fuel

The reference fuel design currently being considered within the Generation-IV Gas-cooled Fast Reactor (GFR) project is a ceramic plate matrix with a honeycomb inner structure containing small fuel cylinders. The fuel is mixed plutonium–uranium carbide, while the matrix material is silicon carbide. The present paper describes the mechanical part of a thermal–mechanical model being developed for studying the transient behavior of this highly heterogeneous fuel type. Benchmarking has been carried out against detailed finite-elements modeling (FEM).The resultant thermal–mechanical model can provide reliable fuel and cladding (matrix) stress/strain conditions to evaluate temperatures and neutronic feedbacks. As such, it has been integrated into PSI’s coupled code system “FAST”, which aims at the comprehensive safety analysis of advanced fast reactor systems.The detailed FEM analysis of the GFR fuel has been useful not only for benchmarking the new model, but also for obtaining an in-depth understanding of fuel stress/strain characteristics, which cannot be reproduced with simplified models. Thereby, the range of applicability of the new model has clearly been defined. In particular, the 3D FEM analysis has revealed a concentration of stresses at the pellet corners during pellet/matrix contact, which could lead to fuel element failure. This effect is found to be mitigated considerably, if the fuel pellets are shaped in a manner which enhances the contact area.     

Effect of Fuel Pellet Eccentricity with Cladding on Fuel Rod Thermal Behavior under Reactivity Initiated Accident Condition

Fuel rod behavior under Reactivity Initiated Accident (RIA) conditions has been studied in the Nuclear Safety Research Reactor (NSRR), JAERI. In the experiments, cladding thermal behavior was observed to be influenced by the fuel pellet eccentricity to produce large azimuthal temperature variation in the cladding. The maximum azimuthal cladding temperature difference was measured to be as large as 150°C by thermocouples attached to opposite sides of the cladding around the circumference, though the thermocouples did not always detect the maximum temperature difference around the circumference. The actual temperature differences in the fuel rods subjected to less than 290 cal/g?UO₂ were estimated to be 350°C at maximum based on metallographies. A simple calculation considering gap conductance variations also showed that the maximum temperature difference became 350°C under fully eccentrical condition in the fuel rod subjected to 260 cal/g?UO₂. Moreover, as the rod damage such as cladding deformation, melting and failure occurs unevenly around the circumference due to the fuel pellet eccentricity in general, the fuel pellet eccentricity should influence the fuel rod failure under RIA conditions.