Simulation of scaled vessel failure experiments and investigation of a possible vessel support against failure

Scaled coupled melt pool convection and vessel creep failure experiments are being performed in the FOREVER program at the Royal Institute of Technology, Stockholm. These experiments are simulating the lower head of a pressurized reactor vessel under the thermal load of a melt pool with internal heat sources and a specified internal pressure. Due to the multi-axial creep deformation of the three-dimensional vessel with a prototypic non-uniform temperature field these experiments offer an excellent opportunity to validate numerical creep models. A Finite Element Model is developed and using the Computational Fluid Dynamic module, the melt pool convection is simulated and the temperature field within the vessel wall is evaluated. The transient structural mechanical calculations are then performed applying a new creep modeling procedure. Additionally, the material damage is evaluated considering the creep deformation as well as the prompt plastic deformation.After post-test calculations for the FOREVER-C2 experiment, pre-test calculations for the forthcoming experiments are performed. Taking into account both—experimental and numerical results—gives a good opportunity to improve the simulation and understanding of real accident scenarios. After analyzing the results of the calculations, it seems to be advantageous to provide a vessel support, which can unburden the vessel from a part of the mechanical load and, therefore, avoid the vessel failure or at least prolong the time to failure. This can be a possible accident mitigation strategy. Additionally, it may be advantageous to install a passive automatic control device to initiate the flooding of the reactor pit to ensure external vessel cooling in the event of a core melt down.     

基于耦合CFD-FEM方法的严重事故下RPV蠕变失效风险评估

核电站严重事故发生后，反应堆压力容器（RPV）的剩余固壁在高温差、内压、熔池重量等的作用下可能发生蠕变失效。本文以CPR1000 RPV为研究对象，基于FLUENT软件二次开发求解反应堆压力容器下封头烧蚀温度场，然后基于ANSYS Workbench开展耦合CFD-FEM力学分析，求解严重事故下RPV烧蚀温度场稳定后72 h内的等效应力、等效塑性应变和等效蠕变应变，并评估了RPV的蠕变失效风险。结果表明：当堆坑注水等措施投运后，RPV剩余固壁在72 h内不会发生蠕变失效和塑性变形失效，有效卸压可明显提升RPV结构完整性的安全裕度。     

Risk Assessment of Creep Failure for RPV under Severe Accident Condition Based on Coupled CFD-FEM Method

After a reactor core melt accident, creep failure may occur in the residual solid wall of the reactor pressure vessel (RPV) under the influence of high temperature difference, internal pressure and the weight of the molten pool. In this work, the CPR1000 RPV was used as a research object. The ablation temperature field of the lower head of RPV was solved through the secondary development of the FLUENT software. And then, a CFD-FEM coupling analysis was carried out based on ANSYS Workbench software. The equivalent stress, the equivalent plastic strain and the equivalent creep strain of the RPV within 72 h under severe accident after the wall ablation and temperature field distribution formed stably were calculated. The risk of creep failure of the RPV was evaluated. The results show that when the reactor pit water injection measure puts into operation, the residual solid wall of the RPV will not experience creep failure and plastic deformation failure within 72 h, and besides, the pressure relief can significantly increase the safety margin of the structural integrity of the RPV.     

熔融物堆内滞留条件下压力容器变形

熔融物堆内滞留(In-Vessel Retention,IVR)已经成为第三代反应堆一项关键的严重事故缓解策略,而压力容器外部冷却(External Reactor Vessel Cooling,ERVC)技术则是保证IVR得以成功实施的关键。当发生堆芯熔化时,高温熔融物对压力容器(Reactor Pressure Vessel,RPV)下封头的热冲击会导致RPV壁面和由其构成的外部冷却通道的形状发生变化,使局部传热恶化,进而造成IVR的失效。因此,有必要对IVR条件下RPV壁面的变形进行研究。本文利用有限元软件ANSYS对RPV进行了几何建模、温度场分析和力学场分析。结果表明,在RPV外部实现冷却、内部实现泄压的前提下,壁面变形为13.85-18.75 mm。在1 MPa内压的作用下,高温蠕变会使壁面变形随时间增大,但其增量有限。热膨胀是造成壁面变形的主要因素。     

示范快堆堆芯熔融物收集装置的安全分析

针对示范快堆堆芯熔融物收集装置的高温结构完整性问题，采用堆芯熔融物滞留在反应堆压力容器策略有效性评估方法（IVR-DOE10460），建立了316H本构模型、多轴修正以及具体的分析评价方法。通过搜集与分析ASME规范和R66材料数据手册中316H钢相关的材料数据，确定了输入数据。在此基础上，利用有限元分析软件ABAQUS开展堆芯熔融物堆积形态下堆芯熔融物收集装置的应力应变分析，并基于时间分数法与延性耗竭法（应变分数法）对堆芯熔融物收集装置进行蠕变强度校核。有限元分析结果表明：堆芯熔融物收集装置在设计时间内可满足时间分数和应变分数小于1的蠕变强度考核要求，且满足竖直位移小于设计指标的功能性要求。堆芯熔融物收集装置在堆芯熔化严重事故后能保持结构的完整性。     

Sensitivity study of melt behavior of Fukushima Daiichi unit 1 type accident with MELCOR code and MPS method

Sensitivity calculation on melt behavior and lower head response at Fukushima Daiichi unit 1 reactor was performed with methods for estimation of leakages and consequences of releases (MELCOR) 2.1 and moving particle semi-implicit (MPS) method. Four sensitivity cases were calculated, considering safety relief valve (SRV) seizure, penetrations and debris porosity. The results indicated that the lower head failed due to creep rupture, not considering penetrations; otherwise it would have failed due to penetration tube rupture and ejection at an earlier time, resulting in part of debris dropping into the cavity of the drywell. The temperature of residual debris in pressure vessel kept low, and the vessel wall did not suffer creep failure up to 15 hours after reactor scram from which moment the water injection became available. Another aspect was that reactor pressure vessel (RPV) depressurization postponed the lower head creep failure time, and the low debris porosity brought forward the penetration rupture time. Either lower head creep failure or penetration rupture and ejection occurred in the central part of the pressure vessel. In MPS calculation, a slice of debris bed together with lower head, including an instrument guide tube, was chosen as the computational domain. Detailed temperature profiles in debris bed, penetration and vessel wall were obtained. The penetration rupture time calculated by MPS was earlier than the MELCOR result, while the vessel wall creep failure time was later.     

严重事故IVR下反应堆压力容器耦合传热数值模拟分析

堆芯熔化严重事故下保证反应堆压力容器（RPV）完整性非常重要,高温蠕变失效是堆芯熔化严重事故下反应堆压力容器的主要失效模式。在进行严重事故堆芯熔化物堆内包容（IVR）下RPV结构完整性分析中,RPV内外壁和沿高度方向的温度分布以及剩余壁厚是结构分析的重要输入。本文采用CFD分析方法对RPV堆内熔融物、RPV壁以及外部气液两相流动换热进行热-固-流耦合分析,获得耦合情况下的温度场、流场、各相份额分布以及RPV的剩余壁厚,为RPV在严重事故IVR下的结构完整性分析提供依据。     

Bottom nozzle failure mechanism of water reactor pressure vessel under severe accident conditions

Most of past studies devoted to the creep rupture of a nuclear reactor pressure vessel (RPV) lower head under severe accident conditions, have focused on global deformation and rupture modes. Limited efforts were made on local failure modes associated with penetration nozzles as a part of TMI-2 vessel investigation project (TMI-2 VIP) in 1990s. However, it was based on an excessively simplified shear deformation model. In the present study, the mode of nozzle failure has been investigated using data and nozzle materials from Sandia National Laboratory's lower head failure experiment (SNL-LHF). Crack-like separations were revealed at the nozzle weld metal to RPV interfaces indicating the importance of normal stress component rather than the shear stress in the creep rupture. Creep rupture tests were conducted for nozzle and weld metal materials, respectively, at various temperature and stress levels. Stress distribution in the nozzle region is calculated using elastic–viscoplastic finite element analysis (FEA) using the measured properties. Calculation results are compared with earlier results based on the pure shear model of TMI-2 VIP. It is concluded from both LHF-4 nozzle examination and FEA that normal stress at the nozzle/lower head interface is the dominant driving force for the local failure. From the FEA for the nozzle weld attached in RPV, it is shown that nozzle welds failure occur by displacement controlled fracture of nozzle hole not by load controlled fracture of internal pressure. Considering these characteristics of nozzle weld failure, new concept of nozzle failure time prediction is proposed.     

堆芯熔化严重事故下反应堆压力容器下封头高温蠕变分析

核电厂在发生堆芯熔化严重事故时，采用堆内熔融物滞留（IVR）策略将熔融物包容在反应堆压力容器（RPV）内是一项重要缓解措施。在IVR策略期间，RPV下封头在熔融物的极高温度载荷和力学载荷的共同作用下很有可能因过度蠕变变形而失效。因此，有必要对熔融物滞留条件下RPV下封头进行蠕变变形分析，以保证RPV结构完整性。该文在假定IVR条件下，采用有限元方法对RPV下封头进行热-结构耦合分析，通过计算得到容器壁的温度场和应力场，以及下封头的塑性和蠕变变形，并结合塑性和蠕变断裂判据对下封头进行失效分析。结果表明，考虑蠕变影响后，结构的变形将大大增加；严重事故下采取熔融物滞留策略期间，RPV下封头的主要失效模式为蠕变失效而非塑性失效；内压对蠕变变形量和蠕变失效时间有较大影响。该文为严重事故下RPV下封头的蠕变和失效研究提供了分析方法。      

Assessment of reactor vessel integrity (ARVI)

The assessment of reactor vessel integrity (ARVI) project involved a total of nine organizations from Europe and USA. The work consisted of experiments and analysis development. The modeling activities in the area of structural analyses were focused on the support of EC-FOREVER experiments as well as on the exploitation of the data obtained from those experiments for modeling of creep deformation and the validation of the industry structural codes. Work was also performed for extension of melt natural convection analyses to consideration of stratification, and mixing (in the CFD codes). Other modeling activities were for (1) gap cooling CHF and (2) developing simple models for system code. Finally, the methodology and data was applied for the design of IVMR severe accident management scheme for VVER-440/213 plants.The work was broken up into five packages. They were divided into tasks, which were performed by different partners. The major experimental project continued was EC-FOREVER in which data was obtained on in-vessel melt pool coolability. In previous EC-FOREVER experiments data was obtained on melt pool natural convection and lower head creep failure and rupture. Those results obtained were related to the following issues: (1) multiaxial creep laws for different vessel steels, (2) effects of penetrations, and (3) mode and location of lower head failure. The two EC-FOREVER tests reported here are related to (a) the effectiveness of gap cooling and (b) water ingression for in vessel melt coolability. Two other experimental projects were also conducted. One was the COPO experiments, which was concerned with the effects of stratification and metal layer on the thermal loads on the lower head wall during melt pool convection. The second experimental project was conducted at ULPU facility, which provided data and correlations of CHF due to the external cooling of the lower head.     

严重事故下反应堆压力容器材料高温蠕变研究进展

介绍了近年来在假想堆芯熔化严重事故下国内外反应堆压力容器材料高温蠕变行为的研究进展及现状,着重阐述了在材料高温蠕变试验、缩比模型试验和数值模拟等方面取得的成果,并提出了目前存在的问题及未来的发展方向。     

Overview of NRC sponsored LWR lower head failure research program

The US Nuclear Regulatory Commission (US NRC) has sponsored a research program to investigate the mode and timing of vessel lower head failure. Major objectives of the program were to identify plausible failure mechanisms and to develop a method for determining which failure mode would occur first for different light water reactor designs and accident conditions. Failure mechanisms, such as tube ejection, tube rupture, global vessel failure, and localized vessel creep rupture, were studied. Newly developed models and existing models were applied to predict which failure mechanism would occur first in various severe accident scenarios. So that a broader range of conditions could be considered simultaneously, the calculations relied heavily on models with closed-form or simplified numerical solution techniques. Finite element techniques were employed for analytical model verification and examination of more detailed phenomena. High-temperature creep and tensile data were obtained for predicting the vessel and penetration structural response. This paper summarizes major accomplishments and conclusions from research performed in the NRC sponsored lower head failure project.     

Simple Method for Evaluating Mesh Size Effects in Control Rod Worth Analysis

It has been pointed out that the reactor coolant system piping could fail prior to the meltthrough of the reactor pressure vessel in a high pressure sequence of pressurized water reactor severe accidents. In order to apply to the evaluation of the piping failure which influences the subsequent accident progression, models for the strength of piping materials at high temperatures were examined. It was found that 0.2% proof stress and ultimate tensile strength above 1,073 K obtained from tensile tests was reproduced by a quadratic equation of the reciprocal absolute temperature. Short-term creep rupture time and minimum creep rate at high temperatures were well correlated by the modified Norton's Law as a function of stress and temperature, which implicitly expressed the effect of the precipitation and the resolution of precipitates on the creep strength. The modified Norton's Law gave better results than the conventional Larson-Miller method. Relating applied stress vs. minimum creep rate and tensile properties vs. applied strain rate obtained from the creep and tensile tests, a temperature range where the dynamic recrystallization significantly occurred was evaluated.     

Recursively coupled thermal and mechanical FEM-analysis of lower plenum creep failure experiments

Postulating an unlikely core melt down accident for a light water reactor (LWR), the possible failure mode of the reactor pressure vessel (RPV) and its failure time have to be investigated for a determination of the load conditions for subsequent containment analyses. Worldwide several experiments have been performed in this field accompanied with material properties evaluation, theoretical, and numerical work.     

Semi-analytical modeling of a PWR lower head failure under severe accident conditions using an axisymetrical shell theory

The USNRC/SNL OLHF program was carried out within the framework of an OECD project. This program consisted of four one-fifth scale experiments of a reactor pressure vessel (RPV) lower head failure (LHF) under well controlled internal pressure and large throughwall temperature differentials; the objectives were to characterize the mode, timing and size of a possible PWR lower head failure in the event of a core meltdown accident. These experiments should also lead to a better understanding of the mechanical behavior of the reactor vessel lower head, which is of importance both in severe accident assessment and the definition of accident mitigation strategies. A well-characterized failure of the lower head is of prime importance for the evaluation of the quantity of core material that can escape into the containment, since this defines the initial conditions for all ex-vessel events. A large quantity of escaping corium may lead to direct heating of the containment or ex-vessel steam explosion. These are important issues due to their potential to cause early containment failure. The experiments also provide data for model development and validation. For our part, as one of the program partners, a 2D semi-analytical model has been developed and used to simulate these experiments. The aim of this effort is to develop a simplified but well predicting code that can be then implemented in European integral severe accident computer codes (ASTEC, ICARE/CATHARE). This paper presents the detailed mathematical formulation of this simplified method which is used to interpret the experimental results. The axi-symmetric shell theory under internal pressure proposed by Timoshenko has been utilised. The solution to the equilibrium equations is presented, with particular attention to the Rabotnov analytical formula. The radius and the polar angle of the deformed structure have been written as analytical expressions in order to take the large displacements and large strains into account using our mathematical formulation. The Norton type creep law and the Kachanov damage law have been used. Several failure criteria were used in the calculations and their effect on the numerical results is discussed. This 2D semi-analytical model gives very satisfactory results when compared, with the experimental and numerical results that were presented recently in the Benchmark calculations based on the first test of the OLHF program. The performance of this model is also illustrated by its capacity to accurately simulate the deformation of the lower head, including the variation of wall thickness.     

承压热冲击下DVI接管动态应力特性研究

压力容器直接注入（DVI）接管在热冲击下的动态应力特性对于反应堆压力容器（RPV）结构完整性评估具有重要意义。建立了含DVI接管的RPV压力壳热流固耦合数值计算模型,并进行了验证分析;然后研究了蓄压安注箱（ACC）和堆芯补水箱（CMT）安注时RPV筒体和DVI接管热工水力特性;最后分析了热冲击下RPV筒体和DVI接管连接高应力区的温度分布、等效应力和等效塑性应变分布特性。研究结果表明,ACC安注阶段RPV筒体和DVI接管连接区存在较大的温度梯度和等效应力,且发生了局部塑性变形。若发生承压热冲击事件,应控制好DVI接管连接区温差,确保反应堆压力容器的结构完整性。本文开发的热冲击下热流固耦合数值计算模型和计算方法可用于核岛内DVI接管与RPV筒体的安全性评价,也可用于类似承压结构在热冲击下的动态应力特性分析。      

Characterization of heat transfer processes in a melt pool convection and vessel-creep experiment

The results of an integral experiment on melt pool convection and vessel-creep deformation are presented and analyzed. The experiment is performed on a test facility, named Failure Of REactor VEssel Retention (FOREVER). The facility employs a 1/10-scaled 15Mo3-(German)-steel vessel of 400-mm diameter, 15-mm wall thickness and 750-mm height. A high-temperature (1300 °C) oxide melt is prepared in a SiC-crucible placed in a 50 kW induction furnace and is, then, poured into the 1/10th scale vessel. A MoSi₂ 50 kW electric heater is employed in the melt pool to heat and maintain its temperature at 1200 °C. The vessel is pressurized with argon at the desired pressure. In the FOREVER/C1 experiment, the vessel wall, maintained at about 900 °C and pressurized to 26 bars, was subjected to creep deformation in a 24-h non-stop test. The FOREVER/C1 test is the first integral experiment, in which a decay-heated oxidic naturally-convecting melt pool was maintained in long-term contact with the hemispherical lower head of a pressurized, creeping, steel vessel. A sizeable database was obtained on melt pool temperatures, melt pool energy split, heat transfer rates, heat flux distribution on the melt (crust)–vessel contact surface, vessel temperatures and, in particular the vessel wall creep rate as a function of time. The paper provides information on the FOREVER/C1 measured thermal characteristics and analysis of the observed thermal behavior. The coupled nature of thermal and mechanical processes, as well as the effect of other system conditions (such as depressurization) on the melt pool and vessel temperature responses are analyzed.     

Fracture mechanical evaluation of an in-vessel melt retention scenario

This paper presents methods to compute J-integral values for cracks in two- and three-dimensional thermo-mechanical loaded structures using the finite element code ANSYS. The developed methods are used to evaluate the behavior of a crack on the outside of an emergency cooled reactor pressure vessel (RPV) during a severe core melt down accident. It will be shown, that water cooling of the outer surface of a RPV during a core melt down accident can prevent vessel failure due to creep and ductile rupture. Further on, we present J-integral values for an assumed crack at the outside of the lower plenum of the RPV, at its most stressed location for an emergency cooling (thermal shock) scenario.     

Finite element analysis for creep failure of coolant pipe in light water reactor due to local heating under severe accident condition

During severe accident of a light water reactor (LWR), the piping of the reactor cooling system would be damaged when the piping is subjected to high internal pressure and very high temperature, resulted from high temperature gas generated in a reactor core and decay heat released from the deposit of fission products. It is considered that, under such a condition, short-term creep at high temperatures would cause the piping failure. For the evaluation of piping integrity under a severe accident, a method to predict such high temperature short-term creep deformation should be developed, using a creep constitutive equation considering tertiary creep. In this paper, the creep constitutive equation including tertiary creep was applied to nuclear-grade cold-drawn pipe of 316 stainless steel (SUS316), based on the isotropic damage mechanics proposed by Kachanov and Ravotnov. Tensile creep test data for the material of a SUS316 cold-drawn pipe were used to determine the coefficients of the creep constitutive equation. Using the constitutive equation taking account of creep damage, finite element analyses were performed for the local creep deformation of the coolant piping under two types of conditions; uniform temperature (isothermal condition) and temperature gradient of circumferential direction (non-isothermal condition). The analytical results show that the damage variable integrated into the creep constitutive equation can predict the pipe failure in the test performed by Japan Atomic Energy Research Institute, in which failure occurred from the outside of the pipe wall.