Sever accident mitigation strategy adopted in Nordic Boiling Water Reactors (BWRs) employs a deep water pool below the reactor vessel in order to fragment and quench core melt and provide long term cooling of the debris. One of the risk factors associated with this accident management strategy is early failure of the containment due to steam explosion. Assessment of the risk is subject to significant epistemic and aleatory uncertainties in (i) modelling of steam explosion and (ii) scenarios of melt release from the vessel and water pool conditions. High computational efficiency of the models is required for such assessment. A surrogate model (SM) approach has been previously developed using artificial neural network and the database of Texas-V code solutions for steam explosion loads in the Nordic type BWRs. In this paper we extend our surrogate model to allow analysis of steam explosion in relatively shallow water pools (>2 m), address effects of melt emissivity and resolve more accurately variation of pressure in the drywell. We provide detailed comparison of metallic vs oxidic melt release scenarios, incorporate uncertainty of the SM into modelling and analyze the sensitivity of our results to SM uncertainty. We estimate risks of containment failure with non-reinforced and reinforced hatch door and demonstrate the effect of the surrogate model uncertainty on the results. We analyze the results and develop a simplified approach for decision making considering predicted failure probabilities, expected costs and scenario frequencies. 

The goal of this work is to assess effectiveness of severe accident management strategy in Nordic type boiling water reactors (BWRs). Corium melt released into a deep pool of water below reactor vessel is expected to be fragmented to form a porous debris bed coolable by natural circulation of coolant. However, there is a risk that energetic steam explosion or non-coolable debris can threaten containment integrity. Both stochastic accident scenario (aleatory) and modeling (epistemic) uncertainties contribute to the risk assessment. Namely, the effects of melt release characteristics (jet diameter, melt composition, superheat), water pool conditions (i.e. depth and subcooling) at the time of the release, and modeling assumptions have to be quantified in a consistent manner. In order to address the uncertainty, we develop a Risk Oriented Accident Analysis framework (ROAAM+) where all stages of the accident progression are simulated using a set of models coupled through initial and boundary conditions. The analysis starts from plant damage states determined in PSA Level-1 and follows time dependent accident scenarios of core degradation, vessel failure, melt release, steam explosion and debris bed formation and coolability. In order to achieve computational efficiency sufficient for extensive sensitivity, uncertainty, and risk analysis the surrogate modeling approach is used. In the development of simplified but computationally efficient surrogate models (SM), we employ databases of solutions obtained by detailed but computationally expensive full models (FM). The process includes iterative refining of the framework, full and surrogate models in order to achieve completeness, consistency, and transparency in the review of the analysis results. In the paper we present results of the analysis aimed at quantification of uncertainty in the conditional containment failure probability. Specifically, we carry out sensitivity analysis using standalone and coupled models in order to identify the most influential scenario and modeling parameters for each sub-model. We assess the impact of the parameters on the prediction of the “load”, “capacity” and also failure probability. Then we quantify the effect of the most influential parameters on the failure probability. The results are presented using the failure domain approach and second order probability analysis, considering the uncertainty in distributions of the input parameters.

Severe accident mitigation strategy adopted in Nordic type Boiling Water Reactors (BWRs) employs ex vessel core melt cooling in a deep pool of water below reactor vessel. Energetic fuel coolant interaction (steam explosion) can occur during molten core release into water. Dynamic loads can threaten containment integrity increasing the risk of fission products release to the environment. Comprehensive uncertainty analysis is necessary in order to assess the risks. Computational costs of the existing fuel coolant interaction (FCI) codes is often prohibitive for addressing the uncertainties, including the effect of stochastic triggering time. This paper discusses development of a computationally efficient surrogate model (SM) for prediction of statistical characteristics of steam explosion impulses in Nordic BWRs. The TEXAS-V code was used as the Full Model (FM) for the calculation of explosion impulses. The surrogate model was developed using artificial neural networks' (ANNs) and the database of FM solutions. Statistical analysis was employed in order to treat chaotic response of steam explosion impulse to variations in the triggering time. Details of the FM and SM implementation and their verification are discussed in the paper.

Melt fragmentation, quenching and long term coolability in a deep pool of water under the reactor vessel are employed as a severe accident mitigation strategy in several designs of light water reactors. The success of such strategy is contingent upon the natural circulation effectiveness in removing the decay heat generated in the porous debris bed. The maximum height of the bed is one of the important factors which affect the debris coolability. The two-phase flow within the bed generates mechanical energy which can change the geometry of the debris bed by the "self-leveling" phenomenon. In this work.we developed an approach to modeling of the self-leveling phenomenon. Sensitivity analysis was carried out to rank the importance of the model uncertainties and uncertain input parameters i.e. the conditions of the accident scenario and the debris bed properties. The results provided some useful insights for further improvement of the model and reduction of the output uncertainties through separate-effect experimental studies. Finally, we assessed the self-leveling effectiveness, quantified its uncertainties in prototypic severe accident conditions and demonstrated that the effect of self-leveling phenomenon is robust with respect to the considered input uncertainties.

Efficient removal of decay heat from the nuclear reactor core debris is paramount for termination of severe accident progression. One of the strategies is based on melt fragmentation, quenching and cooling in a deep pool of water under the reactor vessel. Geometrical configuration of the debris bed is among the important factors which determine possibility of removing the decay heat from the debris bed by natural circulation of the coolant. For instance, a tall mound-shape debris bed can be non-coolable, while the same debris can be coolable if spread uniformly. Decay heat generates a significant amount of thermal energy which goes to production of steam inside the debris bed. Two-phase flow escaping through the top layer of the bed becomes a source of mechanical energy which can move the particulate debris along the slope of the bed. The motion of the debris will lead to flattening of the bed. Such process is often called "self-leveling" phenomenon. Spreading of the debris bed by the self-leveling process can take significant time, depending on the initial debris bed configuration and other parameters. There is a competition between the time scales for reaching (i) a coolable configuration of the bed, and (ii) onset of dryout and re-melting of the debris. In the previous work we have demonstrated that the rate of particulate debris spreading is determined by local gas velocity and local slope angle of the bed. In this work we develop a scaling approach and a closure for prediction of debris spreading rate based on generalization of available experimental data. We demonstrate that introduced scaling criteria are universal for particles of different shapes and size distributions.

Termination of severe accident progression by core debris cooling in a deep pool of water under reactor vessel is considered in several designs of light water reactors. However, success of this accident mitigation strategy is contingent upon the effectiveness of heat removal by natural circulation from the debris bed. It is assumed that a porous bed will be formed in the pool in the process of core melt fragmentation and quenching. Debris bed coolability depends on its properties and system conditions. The properties of the bed, including its geometry are the outcomes of the debris bed formation process. Spreading of the debris particles in the pool by two-phase turbulent flows induced by the heat generated in the bed can affect the shape of the bed and thus influence its coolability. The goal of this work is to provide experimental data on spreading of solid particles in the pool by large-scale two-phase flow. The aim is to provide data necessary for understanding of separate effects and for development and validation of models and codes. Validated codes can be then used for prediction of debris bed formation under prototypic severe accident conditions. In PDS-P (Particulate Debris Spreading in the Pool) experiments, air injection at the bottom of the test section is employed as a means to create large-scale flow in the pool in isothermal conditions. The test section is a rectangular tank with a 2D slice geometry, it has fixed width (72 mm), adjustable length (up to 1.5 m) and allows water filling to the depth of up to 1 m. Variable pool length and depth allows studying two-phase circulating flows of different characteristic sizes and patterns. The average void fraction in the pool is determined by video recording and subsequent image processing. Particles are supplied from the top of the facility above the water surface. Results of several series of PDS-P experiments are reported in this paper. The influence of the gas flow rate, pool dimensions, particle density and size on spreading of the particles is addressed. A preliminary scaling approach is proposed and shown to provide good agreement with the experimental findings.

Nordic-type boiling water reactors employ melt fragmentation, quenching, and long term cooling of the debris bed in a deep pool of water under the reactor vessel as a severe accident (SA) mitigation strategy. The height and shape of the bed are among the most important factors that determine if decay heat can be removed from the porous debris bed by natural circulation of water. The debris bed geometry depends on its formation process (melt release, fragmentation, sedimentation and settlement on the containment basemat), but it also changes with time afterwards, due to particle redistribution promoted by coolant flow (self-leveling). The ultimate goal of this work is to develop an approach to the assessment of the probability that debris in such a variable-shape bed can reach re-melting (which means failure of SA mitigation strategy), i.e. the time necessary for the slumping debris bed to reach a coolable configuration is larger than the time necessary for the debris to reach the re-melting temperature. For this purpose, previously developed models for particulate debris spreading by self-leveling and debris bed dryout are combined to assess the time necessary to reach a coolable state and evaluate its uncertainty. Sensitivity analysis was performed to screen out less important input parameters, after which Monte Carlo simulation was carried out in order to collect statistical characteristics of the coolability time. The obtained results suggest that, given the parameters ranges typical of Nordic BWR5, only a small fraction of debris beds configurations exhibits the occurrence of dryout. Of the initially non-coolable configurations, a significant portion becomes coolable due to debris bed self-leveling.

Validation simulations by DECOSIM code are performed against recent PDS-P experiments on particle spreading in a planar vertical water pool with bottom air injection. The model implemented in the code considers two-fluid formulation (water, air), turbulence effects in liquid phase are taken into account by k-epsilon model with additional generation terms accounting for two-phase effects. Particles are described by Lagrangian model, with turbulent dispersion modeled by random-walk model. Simulations are performed in conditions corresponding to experimental setup, the test section was a plane rectangular tank of variable length (0.9 and 1.5 m) and pool depth (0.5, 0.7, and 0.9 m), the superficial gas injection velocity ranged between 0.12 and 0.69 m/s. Sedimentation of spherical stainless steel (1.5 and 3 mm) and glass (3 mm) particles was calculated and compared with experiments with respect to the mean spreading distance and lateral distributions of mass fraction of particles. Reasonable agreement between the results obtained and experimental measurements is achieved for all pool geometries, gas injection rates, and particle types, confirming adequacy of the modeling approach and suitability of DECOSIM code for severe accident analysis related to debris bed formation. Possible ways to further reduction of uncertainty in model validation are discussed.

Severe accident mitigation strategies in Nordic boiling water reactors (BWRs) employ core melt cooling in a deep pool of water under the reactor pressure vessel. Corium melt released from the vessel is expected to fragment, solidify and form a porous debris bed coolable by natural circulation. However, steam explosion can occur upon melt release threatening containment integrity and potentially leading to large early release of radioactive products to the environment. Significant aleatory and epistemic uncertainties exist in accident scenarios, melt release conditions, and modeling of steam explosion phenomena. Assessment of the risk of ex-vessel steam explosion requires application of the Integrated Deterministic Probabilistic Safety Analysis (IDPSA). IDPSA is a computationally demanding task which makes unfeasible direct application of Fuel-Coolant Interaction codes. The goal of the current work is to develop a Surrogate Model (SM) of the Texas-V code and demonstrate its application to the analysis of explosion impact in the Nordic BWR. The SM should be computationally affordable for IDPSA analysis. We focus on prediction of the steam explosion loads in a reference Nordic BWR design assuming a scenario of coherent corium jet release into a deep water pool. We start with the review of the Texas-V sub-models in order to identify a list of parameters to be considered in implementation of the SM. We demonstrate that Texas-V exhibits chaotic response in terms of the explosion impulse as a function of the triggering time and introduce a statistical representation of the explosion impulse for given melt release conditions and arbitrary triggering time. We demonstrate that characteristics of the distribution are well-posed. We then separate out the essential portion of modelling uncertainty by identification of the most influential uncertain parameters using sensitivity analysis. Both aleatory uncertainty in characteristics of melt release scenarios and water pool conditions, and epistemic uncertainty in FCI modeling are considered. Ranges of the uncertain parameters are selected based on the available information about prototypic severe accident conditions in a Nordic BWR. A database of Texas-V solutions is generated and used for the development of the SM. Performance, predictive capability and application of the SM to risk analysis are discussed in detail.

Debris bed formation and coolability are studied by DECOSIM code. Main physical mechanisms affecting dispersed particle spreading in the course of melt-water interaction are considered, and their relevance to the formation of porous debris bed in various melt ejection modes is discussed. Numerical simulations of gradually growing and instantly formed debris beds are performed by DECOSIM code. Also, coupled simulations are carried out in which all mechanisms are taken into account simultaneously. It is shown that particle spreading limits the height of debris bed. Also, it is obtained that in some parameter ranges even if local dryout occurs, further particle spreading can render the debris bed coolable, resulting in its reflooding and quenching of the material.