In engineering systems operating under high Schmidt (Sc) or Prandtl (Pr) number flow conditions, the demand for near-wall mesh refinement increases significantly, underscoring the need for cost-effective modeling approaches that avoid additional computational overhead. Existing models, which are predominantly designed for low-Sc flows, overlook temporal filtering effects, resulting in inaccuracies in theoretical description and mass transfer predictions. This paper addresses the impact of high Sc or Pr by refining the single-layer scalar diffusivity model. It introduces a switch between scalar filtering and eddy viscosity-dominated regions, leveraging two parameters: κ Sc, accounting for temporal filtering effects, and κ Re, addressing variations in Reynolds number. In addition, we adopted a complementary outer layer term to model the upwarding trend in low frictional Reynolds number condition. Using the two-layer model with unity Sc and/or Pr, a close agreement with the von-Kármán constant in the velocity boundary layer was observed. The modified model demonstrated strong agreement with scalar profiles across a broad range of Sc and friction Reynolds numbers (Reτ) in direct numerical simulation and large eddy simulation data, demonstrating its accuracy at low Reτ and predictive performance at high Reτ. The two-layer model improves the prediction of turbulent mass transfer, providing better alignment with high Sc engineering correlations than existing wall model approach. This study provides valuable insight for modeling the mass and heat transfer processes under high Sc or Pr conditions.

Steam injection through spargers into a Pressure Suppression Pool (PSP) is used to prevent containment overpressure during primary system depressurization in normal operation and accident conditions. Direct Contact Condensation (DCC) of steam induces mass, momentum, and heat sources and thermal stratification can develop in the pool if the momentum source is not sufficient to overcome the buoyancy created by the heat source. The thermal stratification reduces the heat storage capacity of the pool, increasing the pool surface temperature and thus containment pressure compared to mixed pool configuration. In this work we analyze the results of the large scale pool experiments in PANDA and PPOOLEX facilities to develop better understanding of the phenomena and regimes that govern the multi-scale system. Specifically, we compare the results of the tests performed with the steam injection through the sparger head (horizontal injection) and the load reduction ring (downwards injection). We demonstrate that the response of the pool in terms of stable position of the thermocline and velocity of the thermocline motion can be described with proper selection of the non-dimensional scaling parameters for both facilities and directions of the steam injection. We also summarize and interpret other observations from the tests that are important for understanding of the pool thermohydraulic phenomena and development of respective predictive capabilities.

This article presents the experimental results and the phenomenological analyses of the H2P4 tests performed in the PANDA facility, within the OECD/NEA HYMERES project. H2P4 series is characterized by two phases: (i) the steam injection in the water pool with development of thermally stratified layer and pressurization of the system, and (ii) water spray injection above the pool to depressurize the gas space. This article analyzes two tests that are characterized by different sparger submergence levels. The results indicate that the sparger submergence affects the pool's thermal behavior, and the pressurization history. A decrease in submergence height leads to a faster pressurization of the vessel. An analysis of the experimental data is carried out using mass and energy balances for the liquid and gas volumes. This analysis contributes to the understanding of the pool phenomena and suggests that mass and energy are lost through vaporization at the liquid–gas interface and a significant amount of steam is condensed at the walls.

Nordic Boiling Water Reactors employ filtered containment venting and ex-vessel debris coolability in the deep pool located under the reactor pressure vessel as cornerstones of their severe accident management strategy. This paper focuses on the uncertainty analysis of the source term in accident sequences that result in filtered containment venting to the environment using the MELCOR code. The impact of uncertain MELCOR modeling parameters and modeling options on the timing and magnitude of the source term released to the environment has been evaluated in accident sequences initiated by a large break LOCA and SBO. The performed simulations illustrate the effect of MELCOR modeling parameters and options on the code's predictions of severe accident progression, event timing, and the magnitude of the source term released to the environment in different accident scenarios. Furthermore, the results highlight the importance of various retention mechanisms that limit the release of fission products into the environment.

The ex-vessel severe accident (SA) mitigation strategy in Nordic Boiling Water Reactors (BWRs) relies on drywell flooding. In the event of the reactor lower head failure corium is released into the water pool in the drywell. The corium jet is expected to fragment, quench, and form a coolable debris bed, ultimately preventing containment failure and release of radioactive products into the environment. During corium fragmentation in water, a vapor film is formed around the melt preventing direct melt-water contact and limiting the heat transfer between the two liquids. In case of vapor film collapse an explosive conversion of thermal energy of the melt into the mechanical energy of the evaporating volatile coolant may be triggered. These phenomena are often called steam explosion (SE). The resulting pressure wave may propagate through the water-corium mixture, escalate and form a shock wave with the potential to challenge containment integrity. There are significant phenomenological and scenario uncertainties associated with steam explosion. The problem of the uncertainty quantification in the risk analysis is exacerbated further by (i) the chaotic nature of the steam explosion phenomena and (ii) the lack of steam explosion modelling codes based on the modern numerical methods with increased stability and accuracy. The goal of this work is to develop a numerical code SEMRA (Steam Explosion Modelling and Risk Analysis) for modelling of melt-coolant interactions and assessment of the risk of containment failure due to steam explosion. In this paper, we focus on the development of the deterministic part of the code that utilizes improved numerical methods to assess the propagation of steam explosions. The objective is to verify the implemented numerical schemes for pressure propagation and to establish a reference solution for the next stage of code development which incorporates more comprehensive thermodynamic modelling and transport phenomena relevant to steam explosion. Specifically, we address the phenomena shock wave triggering and propagation. We implement a numerically stable code using AUSM+ -up, Godunov and HLLC schemes to model multiphase flow. We evaluate the performance of SEMRA code against several known verification and validation problems. Then we use SEMRA code to simulate triggering tests carried out in KROTOS facility and compare the results against the experiment and TEXAS-V code calculations. We analyze the effect of the flux reconstruction method, the vanishing phase treatment and the spatial discretization on the results. We discuss the results and their contribution to the enhancement of triggering and propagation modelling in a SE code.

Boiling Water Reactor (BWR) employs the Pressure Suppression Pool (PSP) as a heat sink to prevent overpressure of the reactor vessel and containment. Steam can be injected into the PSP through spargers in normal and accident conditions and through blowdown pipes in case of a loss of coolant accident (LOCA). There is a safety limit on the maximum PSP temperature at which such steam injection might cause dynamic loads on the containment structures. The performance of the pool can be affected if thermal stratification is developed when temperature of the hot layer grows rapidly while cold layer remains inactive. Simulation of pool behavior during realistic accident scenarios requires validated models that can sufficiently address the interaction between phenomena, safety systems and operational procedures. Direct modeling of steam injection into a water pool in long-term transients is computationally expensive due to the need to resolve simultaneously the smallest space and time scales of individual steam bubbles and the scales of the whole PSP. To enable PSP analysis for practical purposes, Effective Heat source and Effective Momentum source (EHS/EMS) models have been proposed that avoid the need to resolve steam-water interface. This paper aims to implement mechanistic approaches previously developed by authors for the simulation of transient thermal stratification and mixing phenomena induced by steam injection through spargers in a Nordic BWR PSP. The latest version of the EHS/EMS models using the 'Unit cell' approach has been validated against integral effect pool tests and applied to plant simulations. Several scenarios with boundary conditions corresponding to postulated accident sequences were simulated to investigate the possibility of stratification development and the effects of activation of different systems (e.g., blowdown pipes, high momentum nozzle) on the pool behavior.

Advanced Pressurized Water Reactors (APWRs) and Boiling Water Reactors (BWRs) employ a suppression pool as a heat sink to prevent containment overpressure. Steam can be discharged into the pool through multi-hole spargers or blowdown pipes in both normal and accident conditions. Direct Contact Condensation (DCC) creates sources of momentum and heat. The competition between these two sources determines the development of thermal stratification or mixing of the pool. Thermal stratification is of safety concern as it reduces the cooling capability compared to a completely mixed pool condition. In this work we develop a scaling approach to prediction of the thermal stratification in a water pool induced by steam injection through spargers. Experimental data obtained from large-scale pool tests conducted in the PPOOLEX and PANDA facilities, as well as simulation results obtained using validated codes are used to develop the scaling. Two injection orientations, namely radial injection through multi-hole Sparger Head (SH) and vertical injection through Load Reduction Ring (LRR), are considered. We show that the erosion rate of the cold layer can be estimated using the Richardson number. In this work, scaling laws are proposed to estimate both the (i) transient erosion velocity and (ii) the stable position of the thermocline. These scaling laws are then implemented into a 1D model to simulate the thermal behavior of the pool during steam injection through the sparger.

This study investigates near-wall diffusive flux modeling for passive scalar transport in turbulent flows with high Schmidt (Sc) or Prandtl (Pr) numbers. Under these conditions, the diffusion boundary layer becomes significantly thinner than the velocity boundary layer. Capturing the concentration boundary layer presents challenges due to additional scaling in the viscous-diffusive regime. For DNS, mesh resolution requirements to capture passive scalar behavior near the wall are more stringent than those for Kolmogorov scales in pure hydrodynamics investigations. Consequently, wall-resolved approaches in both RANS and WMLES demand excessive wall refinement, limiting their practicality for high Reynolds numbers and industrial applications. In this work, we focus on turbulent flow without an adverse pressure gradient. Existing wall models fail to provide accurate estimates of wall diffusive flux for passive scalar transport at high Sc. This failure arises from the breakdown of the assumption of eddy diffusivity asymptotic behavior. Using such models for simulating surface processes (e.g., flow-accelerated corrosion) in RANS and WMLES can lead to non-negligible errors. Our study introduces a two-layer scalar diffusivity model to enhance wall modeling capabilities in passive scalar transport at high Sc or Pr numbers.

In this article we present the results of six experiments identified as HP5 series, performed in the large-scale PANDA (Passive Nachzerfallswärmeabfuhr und Druck-Abbau Testanlage) thermal-hydraulics facility within the OECD/NEA HYMERES (Hydrogen Mitigation Experiments for Reactor Safety) project. These experiments focus on thermal stratification and mixing induced by steam injection in a water pool through a vertical sparger with horizontal holes. The pool stratification was created at low steam flow rate and mixing was achieved by either: steam injection at higher flow rate or a combined effect of injection low steam flow rate and horizontal water jet. The phenomena investigated are relevant for the safety of light water reactor, normal operation and accident scenarios during which steam is directly vented and condensed in a large water pool. We find that the initial pool temperature plays an important role in the thermocline formation. Higher initial pool temperature leads to the formation of a thermocline at lower elevations farther away from the sparger and with a larger density difference across the thermocline. The flow field in the pool is affected by initial pool temperature as indicated by Particle Image Velocimetry (PIV). Higher steam flow rate during the second phase showed the effect of steam momentum on mixing. It was found that for the range of parameters considered in the experiments with water injection the density difference between the pool water and the water injected by the nozzle has a greater influence on the mixing time compared with the momentum of the water jet.

Measurement of the velocity field in thermal-hydraulic experiments is of great importance for phenomena interpretation and code validation. Direct measurement by means of Particle Image Velocimetry (PIV) is challenging in some multiphase's tests where the measurement system would be strongly affected by the phase interaction. A typical example can refer to the test with steam injection into a water pool where the rapid collapse of bubbles and significant temperature gradient makes it impossible to obtain main flow information in a relatively large steam flux. The goal of this work is to investigate the capability of the use of machine learning for the flow reconstruction of the jet induced by steam condensation from sparse temperature measurement with ThermoCouples (TCs). Two frameworks of (i) 'FDD' using pure data-driven modeling and (ii) 'FPINN' combining data-driven and Physics-Informed Neural Networks (PINN) are proposed and investigated. The frameworks are applied to a single-phase turbulent planar jet with data generated by CFD simulations.