This work is motivated by the problem of restraining temperature escalation inside a porous heat-releasing media submerged in a pool of liquid coolant. When coolant temperature reaches saturation, boiling begins in the bulk of the porous bed, with void generation rate determined by the heating power. Amount of void determines hydrostatic pressure difference that drives natural circulation of two-phase flow through the porous material. At a certain critical value of the heat release rate, the driving head cannot overcome drag of the two phase porous media flow, which results in complete evaporation of coolant in some zone. Temperature of material in the dry zone increases significantly due to deterioration of heat exchange with single phase vapor flow in comparison with boiling flow heat transfer. The paper considers the problem of determining the critical conditions for onset of dryout in a heat-releasing porous bed of an arbitrary shape. The well-known one-dimensional problem for a flat top-flooded bed is revisited, and the functional form of the dryout boundary (expressed as the dryout heat flux, DHF) is derived using non-dimensional parameters. Asymptotic behavior of the solution is analyzed, and, by the method of asymptotic interpolation, a surrogate model is proposed consisting of three single-argument, non-dimensional functions. It is shown that such a model provides acceptable accuracy even in the cases where complete similarity of solutions is not achieved. The results obtained provide important insights into the physics of the problem, reduce the number of free parameters, and enable fast evaluation of dryout conditions without the need of numerical solution of algebraic equations involved in the exact formulation. The ultimate goal of the surrogate model development, i.e. its application to multidimensional configurations, is discussed.

Computational Fluid Dynamics (CFD) provides means for high-fidelity 3D thermal-hydraulics analysis of Generation IV pool-type nuclear reactors. However, to be used in the decision making process a proof of code adequacy for intended application is required. This paper describes the Verification, Validation and Uncertainty Quantification (VVUQ) of a commercial CFD code Star-CCM + for forced, natural and mixed convection regimes in lead-bismuth eutectic (LBE) coolant pool flows. Code qualification is carried out according to an iterative VVUQ process aiming to reduce user effects. Validation data is produced in TALL-3D experimental facility - a 7 m high LBE loop featuring a 3D pool-type test section. Accurate prediction of mutual interaction between thermal stratification and mixing in the pool and the loop dynamics requires 3D analysis, especially during natural circulation. Solution verification is used to reduce the numerical uncertainty during code validation activities. Sensitivity Analysis (SA) is used to identify the effect of the most influential uncertain input parameters (UIPs) on numerical results. Two new visualization methods are proposed to enhance interpretation of the SA results. Dedicated experiments are performed according to the SA results to reduce the uncertainties in the most important UIPs. Automated calibration method for large CFD models is tested and demonstrated in combination with manual calibration using detailed temperature profile measurements in the pool. Calibration reveals the deficiencies in the modeling of heat losses owing to the presence of thermal bridges and other local effects in thermal insulation that are not explicitly modeled. It is demonstrated that Star-CCM + is able to predict thermal stratification and mixing phenomena in the pool type geometries. The results are supported by an Uncertainty Analysis (UA).

Spargers are multi-hole injection pipes used in Boiling Water Reactors (BWR) and Advanced Pressurized (AP) reactors to condense steam in large water pools. A steam injection induces heat, momentum and mass sources that depend on the steam injection conditions and can result in thermal stratification or mixing of the pool. Thermal stratification reduces the steam condensation capacity of the pool, increases the pool surface temperature and thus the containment pressure. Development of models with predictive capabilities requires the understanding of basic phenomena that govern the behavior of the complex multi-scale system. The goals of this work are (i) to analyze and interpret the experiments on steam injection into a pool through spargers performed in the large-scale facilities of PPOOLEX and PANDA, and (ii) to discuss possible modelling approaches for the observed phenomena. A scaling approach was developed to address the most important physical phenomena and regimes relevant to prototypic plant conditions. The focus of the tests was on the low steam mass flux and oscillatory bubble condensation regimes, which are expected during a long-term steam injection transient, e.g. in the case of a Station Black Out (SBO). Exploratory tests were also done for chugging and stable jet conditions. The results showed a similar behavior in PPOOLEX and PANDA in terms of jet induced by steam condensation, pool stratification, and development of hot layer and erosion of the cold one. A correlation using the Richardson number is proposed to model the erosion rate of the cold layer as a function of the pool dimensions and steam injection conditions.

Severe accident management strategy in Nordic boiling water reactors (BWRs) employs ex-vessel corium debris coolability. In-vessel core degradation and relocation provide initial conditions for further accident progression. Characteristics of debris bed in the reactor vessel lower plenum affect corium interactions with the vessel structures, vessel failure and melt ejection mode. Melt release from the vessel determines conditions for ex-vessel accident progression and potential threats to containment integrity, i.e. steam explosion, debris bed formation and coolability. Outcomes of core relocation depend on the interplay between (i) accident scenarios, e.g. timing and characteristics of failure and recovery of safety systems and (ii) accident phenomena. Uncertainty analysis is necessary for comprehensive risk assessment. However, computational efficiency of system analysis codes such as MELCOR is one of the big obstacles. Another problem is that code predictions can be quite sensitive to small variations of the input parameters and numerical discretization, due to the highly non-linear feedbacks and discrete thresholds employed in the code models.

The goal of this work is to develop a computationally efficient surrogate model (SM) for prediction of main characteristics of corium debris in the vessel lower plenum of a Nordic BWR. Station black out scenario with a delayed power recovery is considered. The SM has been developed using artificial neural networks (ANNs). The networks were trained with a database of MELCOR solutions. The effect of the noisy data in the full model (FM) database was addressed by introducing scenario classification (grouping) according to the ranges of the output parameters. SMs using different number of scenario groups with/without weighting between predictions of different ANNs were compared. The obtained SM can be used for failure domain and failure probability analysis in the risk assessment framework for Nordic BWRs.

Coolant solidification is a phenomenon of potential safety importance for Liquid Metal Cooled Fast Reactors (LMFRs). Coolant solidification can affect local flow, heat transfer and lead to partial or complete blockage of the coolant flow paths jeopardizing decay heat removal function. It is also possible that reduced flow circulation may increase coolant temperature, counteract solidification and prevent complete blockage of the flow. Complex interactions between local physical phenomena of solidification and system scale natural circulation make modelling of solidification uncertain. Development and validation of adequate models requires validation grade experimental data. In this work we discuss results of analysis carried out in support of experiment development, specifically, design of a solidification test section and a test matrix for TALL-3D experimental facility (lead-bismuth eutectic (LBE) thermal-hydraulic loop). The aim of the analysis is experimental design that satisfies requirements stemming from the process of model qualification. We focus on two aspects: (i) design of solidification test section (STS) for investigation of solidification phenomena in lead-bismuth eutectic (LBE), and (ii) effect of the STS pool on the system scale behavior of the TALL-3D facility. Selection of the STS characteristics and experimental test matrix is supported using computational fluid dynamic (CFD) and system thermal-hydraulic (STH) codes. 

Severe accident management (SAM) in Nordic Boiling Water Reactors (BWR) employs ex-vessel core debris coolability. The melt released from the vessel is poured into a deep pool of water and is expected to fragment, quench, and form a coolable debris bed. Success of the strategy is contingent upon the melt release mode from the vessel, which determine conditions for (i) the debris bed coolability, (ii) steam explosion that present credible threats to containment integrity. Melt release conditions are recognized as the major source of uncertainty in quantification of the risk of containment failure in Nordic BWRs. The characteristics of melt release are determined by the in-vessel accident scenarios and phenomena, subject to aleatory and epistemic uncertainties respectively. Specifically, properties of the debris relocated into the lower head determine conditions for the corium interactions with the vessel structures (such as instrumentation guide tubes IGTs, control rod guide tubes CRGTs), vessel failure and melt release. This work is focused on the evaluation of uncertainty in core degradation progression and its effect on the resultant properties of relocated debris in lower plenum of Nordic BWR. We use MELCOR code for prediction of the accident progression. The main goal of this paper is to characterize the range of possible debris properties in lower plenum and its sensitivity towards different modelling parameters, which is of paramount importance for the analysis of in-vessel debris coolability and vessel failure mode in the risk assessment framework.