Convection within shallow pools of liquid metals heated from below is of significant interest for the In-Vessel Retention (IVR) strategy for Pressurised Water Reactors (PWR) as focusing of the lateral heat flux at the reactor wall presents a risk to the thermomechanical integrity of the reactor vessel. Under an IAEA Coordinated Research Project on corium melt retention, various international research institutions have performed CFD simulations to predict the thermal–hydraulic behaviour of a prototypic light metal layer of low Prandtl number (Pr=0.02) and high external Rayleigh number (RaΦ∼1012) dissipating heat from the free surface and at the lateral reactor wall. Various computational approaches including LES-WALE, LES-Smagorinsky and spectral-DNS were validated under the conditions of two BALI-Metal experiments in water (Pr=6.9), revealing promising agreement in the predicted repartition of the heat flux at the vertical and lateral boundaries. Simulations in a prototypic light metal layer indicated 30–34 % of heat dissipation due to thermal radiation at the free surface. Average thermal losses at the lateral wall corresponded to a focusing effect of 3.3–3.7 times the imposed heat flux. A spike in lateral heat flux close to the free surface equated to a local focusing effect 6-times the imposed heat flux from below. The fluid dynamics, driven largely by thermal losses at the reactor wall, were characterised by downwards acceleration adjacent to the lateral wall and ejection of a cold jet parallel to the lower boundary, forming a large convection cell comparable in size to the radius of the reactor.

Supervised machine learning (SML) techniques have been developed since the 1960s. Most of their applications were oriented towards developing models capable of predicting numerical values or categorical output based on a set of input variables (input features). Recently, SML models' interpretability and explainability were extensively studied to have confidence in the models' decisions. In this work, we propose a new deployment method named Decision Tree Insights Analytics (DTIA) that shifts the purpose of using decision tree classification from having a model capable of differentiating the different categorical outputs based on the input features to systematically finding the associations between inputs and outputs. DTIA can reveal interesting areas in the feature space, leading to the development of research questions and the discovery of new associations that might have been overlooked earlier. We applied the method to three case studies: (1) nuclear reactor accident propagation, (2) single-cell RNA sequencing of Niemann-Pick disease type C1 in mice, and (3) bulk RNA sequencing for breast cancer staging in humans. The developed method provided insights into the first two. On the other hand, it showed some of the method's limitations in the third case study. Finally, we presented how the DTIA's insights are more agreeable with the abstract information gain calculations and provide more in-depth information that can help derive more profound physical meaning compared to the random forest's feature importance attribute and K-means clustering for feature ranking.

Internally heated (IH) natural convection can be found in nature, industrial processes, or during a severe accident in a light water reactor. In this accident scenario, the nuclear reactor core and some internal structures can melt down and relocate to the lower head of the reactor pressure vessel (RPV) and interact with the remaining coolant. Subsequent re-heating and re-melting under decay and oxidation heat creates a transition from a debris bed to a molten pool. The molten pool, which can involve more than hundred tons of dangerously superheated oxidic and metallic liquids, imposes thermo-mechanical loads on the vessel wall that can lead to a thermal and/or structural failure of the vessel and subsequent release of radioactive materials to the reactor pit, and can possibly make its way to the environment. This study uses Direct Numerical Simulation (DNS) to investigate homogeneous IH molten pool convection in a hemispherical domain using Nek5000, an open-source spectral element code. With a Rayleigh number of 1.6 × 1011, the highest reached through DNS in this confined hemispherical geometry, and a Prandtl number of 0.5, which corresponds to a prototypic corium, the study provides detailed information on the thermo-fluid behavior. The results show a turbulent flow with three distinct regions, consistent with the general flow observations from the BALI experiments. The study also presents detailed information on turbulence, such as turbulent kinetic energy (TKE), turbulent heat flux (THF), and temperature variance. Additionally, the study provides 3D heat flux distributions along the boundaries. The heat fluxes along the top boundary fluctuate due to the turbulent eddies in the vicinity, while along the curved boundary the heat fluxes increase nonlinearly from the bottom to the top.

A numerical model to simulate molten metal relocation with phase change is proposed, coupling the level-set method to track the metal-gas interface and an enthalpy-porosity model to handle phase changes between solid and liquid metal. This coupling simultaneously solves the evolution of the metal-gas interface and liquid-solid metal. The numerical model is validated by a melting experiment involving a Sn–Bi eutectic alloy on a copper substrate, wherein the alloy's transient morphology and spreading diameter are measured. The numerical simulation effectively replicates the observed melting and spreading behaviors of the metal on the solid surface. Further validations, including a melt infiltration simulation and experiment, are consistent with findings from previous research. These simulations affirm the model's capability and efficiency in accurately representing the dynamics of melt relocation across various geometries, even within complex porous structures.

In the framework of the IAEA Coordinated Research Project on In-Vessel Melt Retention, a benchmark of CFD simulations, devoted to thermal-hydraulic behavior of the light metal layer involves several research organizations: KTH of Sweden, SSTC NRS of Ukraine, ÚJV Řež of Czech Republic and CEA of France. This work aims at better simulating the focusing effect phenomenon leading to a heat flux peak along the height of the light metal layer, which is formed above the oxide layer in a stratified corium pool configuration during a PWR severe accident. This is a known safety issue compromising the reactor vessel integrity. The first benchmark step provides a solid foundation to the CFD schemes (physical models, meshes) by comparing the results of CFD simulations with thermal-hydraulic experimental data obtained using water as simulating fluid in a representative and quite laminar configuration. Then a similar but highly turbulent case, of higher height, is considered for more complex validation of the numerical simulation approach. Results with different turbulent models are compared against experimental data. On the strength of this encouraging work, a simulation of the same height configuration but considering steel fluid under severe accident conditions is foreseen at the final stage of this benchmark.

The severe accident scenario propagation studies of nuclear power plants (NPPs) have been one of the most critical factors in deploying nuclear power for decades. During an NPP accident, the accident scenario can change during its propagation from the initiating event to a series of accident sub-scenarios. Hence, having time-wise updated information about the current type of accident sub-scenario can help plant operators mitigate the accident propagation and underlying consequences. In this work, we demonstrate the capability of machine learning (Decision Tree) to help researchers and design engineers in finding distinctive physical insights between four different types of accident scenarios based on the pressure vessel's maximum external surface temperature at a particular time. Although the four accidents we included in this study are considered some of the most extensively studied NPPs accident scenarios for decades, our findings shows that decision tree classification could define remarkable distinct differences between them with reliable statistical confidence.

The present study is intended to investigate the dryout and remelting phenomena of a debris bed during the late phase of an in-vessel severe accident progression. The SIMECO-2 facility at KTH is adapted to conduct the experimental investigation. For selection of an appropriate debris bed in the facility, pre-test simulations are performed by using the COCOMO code to determine: (i) simulant materials of debris particles; (ii) debris bed particle diameters; (iii) configuration and geometry of the debris bed (e.g., shape, layers, dimensions). Candidate particulate beds packed with different mixtures of particles are identified and simulated to obtain their thermal hydraulics in the hemispherical slice test section with radius of 500 mm and width of 120 mm. Based on the simulation results, a particulate bed is chosen and loaded in the SIMECO-2 facility for a scoping investigation. FBG probes with multiple measurement points of each probe are employed to acquire the temperature field of the particulate bed inductively heated. A video recording is applied to detect the dryout and remelting phenomena. In the scoping test, the dryout phenomenon occur first at the elevation of 5 cm from the bed surface under the induction heating power of 14.8 kW, which are comparable with the data predicted by the COCOMO code (6 cm from the bed surface under the heating power of 13.8 kW) in the pre-test simulations.

For Light Water Reactor (LWR) safety, spray cooling during severe accidents is one of the promising approaches to achieve In-Vessel Retention of corium by External Reactor Vessel Cooling (IVR-ERVC). To study the efficiency of multi-nozzle spray cooling (nozzles of 2×3 matrix) on a downward-facing FeCrAl heated surface, a lab-scale experimental facility was built. It should be emphasized, however, that a direct measurement of Heat Transfer Coefficient (HTC) on the sprayed side is challenging due to the strong interference of water flow and intrusiveness of standard instrumentation methods. In this paper, a 3D numerical model has been established with the same geometric and material parameters as the foil sample in a multi-nozzle upward spray cooling. Given the experimental temperature profiles on the sample's dry side measured by an IR camera, the complementary numerical simulations have revealed the HTCs and corresponding temperature profiles on the sprayed side, which enabled the prediction of the maximum heat fluxes (MHFs). The maximum heat fluxes for the given spray cooling conditions can reach up to 3.25 MWm2, which is more than adequate for what is required for a successful IVR-ERVC for high-power reactors. At the same time, the maximum temperature on the dry side at the highest input power is still much lower than the expected failure temperature of the sample material.

In this paper, a Direct Numerical Simulation (DNS) of an internally heated (IH) natural convection in a 3D semicircular slice molten pool is conducted using Nek5000, a CFD solver with spatial discretization based on the spectral element method. The mesh requirements in the bulk and boundary layers are both fulfilled using known correlations. A calculation of a simplified internally heated box is first established with an excellent agreement to existing data. Next, simulation of the 3D semi-circular is performed showing qualitative agreement with the general flow observations from the BALI experiments. The velocity field shows that the flow domain is divided into three regions, i.e., intensive turbulent eddies in the upper domain, weak flow motion in the lower domain, and the descending flow along the curved boundary. Correspondingly, the temperature field in the upper domain is relatively homogenous, while that in the lower domain is characterized by stratified layers. Further, the heat flux distribution along the boundaries shows that the heat fluxes fluctuate along the top wall due to turbulent eddies, and the heat fluxes at the curved wall increase nonlinearly from the bottom to the top. Finally, the influence of Prandtl number indicates that smaller Prandtl number will lead to more turbulence eddies, deeper descending flow, and more even redistribution of heat thereby lowering the maximum heat flux to the curved walls.

Fluid infiltration, solidification, and remelting in a particle bed are complex phenomena that can occur in the lower head of a reactor pressure vessel (an in-vessel phenomenon) or in the reactor cavity below the vessel (an ex-vessel phenomenon) during a severe accident in a nuclear power plant. When the non-homogeneous corium, consisting of metal and oxide components, reheats, the lower-melting metals will melt first and move downward to the bottom of the reactor pressure vessel. This will change the global debris bed configuration and its physical and chemical properties, and thereby actively influence the accident progression, specifically the mode and timing of possible vessel failure and the melt characteristics upon release. Similar ex-vessel debris can form on the cavity floor below the vessel, which can threaten containment integrity if stable cooling is not established. In this paper, we present an experimental program employing recently constructed MRSPOD (multicomponent remelting, relocation, and solidification in porous debris) facility that mainly investigates melt infiltration, solidification, remelting, and relocation in a particulate debris bed. The facility uses a 12 x 130 cm(2) (OD x Length) quartz tube in a cylindrical furnace and allows a debris bed to be configured, heated, and/or pressurized prior to fluid infiltration through the bed. The MRSPOD experiments were instrumented with thermocouples (TCs), fiber Bragg grating (FBG) sensors, laser sensor, video, and infrared cameras, which are essential in describing the overall melt infiltration and solidification behavior. Here, a eutectic Sn-Bi melt with superheat temperature between 50 and 70 & DEG;C is poured into a preheated particle bed consisting of 1.5-mm spherical particles made of either copper (Cu), Sn-coated Cu, stainless steel (SS), Sn-coated SS, and/or glass beads to study the effect of thermal properties and wettability on the melt infiltration. Moreover, melt infiltration into a single-layer, multi-layer, and two-columnar particle beds is performed. Measurements from TCs, FBGs, and observations from video cameras have revealed a non-linear kinetics of melt infiltration. Moreover, the extracted ingots after the experiments have shown the complex infiltration process under similar test conditions.