The study of the structure of stratified flow in a horizontal channel is of great significance for assessing the possibility of condensation induced water hammers. The diameter of the vertical inlet section through which the water is supplied to a horizontal channel, has a significant impact on this flow structure. Therefore, determining the effect of this parameter is crucial for predicting condensation induced water hammers. The aim of the study was to determine the effect of the internal diameter of the vertical inlet section through which the water is supplied to a horizontal channel, on the hydrodynamics in a horizontal channel. The research methodology is based on the application of the VOF numerical method for modeling twophase flows. Typical parameter values from relevant experiments were considered: the inner diameter of the horizontal pipe was 38.1 mm and its length was 2 m. The water mass flow rate at the inlet was 0.191 kg/s, which ensured stratified flow in the horizontal channel. As a result of the study, the following primary conclusions were made. 1) For large values of the inlet diameter, the flow in the horizontal channel was subcritical and the Froude number was always less than one. 2) By decreasing the diameter of the inlet section, a hydraulic jump was established in the channel, dividing the flow into supercritical and subcritical, which significantly affects the growth of hydrodynamic instability of the water surface and the occurrence of condensation-induced water hummers.

The present study utilizes the 3D thermalhydraulic STEG code to investigate the complex two-phase flow dynamics within a PGV-1500 horizontal steam generator. The results demonstrate a significant correlation between the configuration of steam outlet branch pipes and the nonuniformity of steam distribution in the upper vessel. Specifically, it is shown that increasing the number of outlet pipes from two to ten markedly enhances flow uniformity, addressing the inherent imbalances found in standard designs. Also, the research evaluates the effectiveness of twelve distinct distribution perforation sheet (DPS) schemes based on two criteria: the average deviation of steam velocity at the DPS elevation and the proportion of total flow exceeding a threshold velocity of $0.7 \mathrm{m} / \mathrm{s}$. Through detailed simulations in the STEG software, the specific perforation configurations that mitigate non-uniform steam loading were identified, providing a technical basis for optimizing steam flow distribution in such systems.

Numerical study of water jet impact on a pool of high-temperature metallic melt is carried out. Experimental studies in this field encounter difficulties in visualizing the flow and performing measurements in hot and opaque medium, while theoretical studies by multifluid models have severe limitations in describing the flow structure and interphase processes. VOF method allows one to alleviate many limitations, as well as reproduce the flow details that are hardly amenable to direct experimental measurements. The work is focused on the validation of VOF predictions against small-scale experimental data on water jet interaction with molten lead-bismuth eutectic alloy; also, features of the vapor-water cavity formation and evolution in the pool are analyzed. Simulations are performed by a solver developed in OpenFOAM software. Results are presented for three-dimensional simulations of subcooled water jet interaction with LBE melt in a vessel, which has a 10-mm thick slice configuration with semi-circular bottom. Validation is performed against two tests by Sibamoto et al, for a water jet impacting the melt at the velocity of 4.7 and 6.2 m/s. Cross-verification with two multi-fluid codes is performed. Reasonable agreement with respect to cavity geometry and evolution stages is demonstrated, further research directions are discussed. Results obtained are relevant to nuclear safety problems for advanced lead-cooled fast reactors.

To study the hydrodynamics of a two-phase flow over a submerged perforated sheet (SPS) and the entrainment of water droplets from the water-air interface, a “Bubbler” installation was built. The main observation tool was video recording of the process followed by data analysis. An SPS with two holes was used. Three experiments were performed with different air flow rates. A general picture of air flow was established: the rise of bubbles in the water volume under the SPS, the formation of an air blanket, air bubbling in the layer of water above the SPS, the formation and jump of water drops upward. For each air flow rate, the size of the bubbles in the two-phase layer and the size of the resulting droplets were determined. It was found that with increasing air flow, these parameters increase.

The regularities of the wave of the thermal interaction of water drops in high-temperature molten lead, i.e., a thermal-detonation wave, are studied. Due to the boiling of water on the surface of molten lead, both liquids (phases) are separated by a vapor film. A one-dimensional model of interacting and interpenetrating continua is used, which describes the dynamics of each fluid by introducing a special field characterized by its own velocity, temperature, and volume fraction. The wave velocity is set by the equality of phase velocities and temperatures in the Chapman–Jouguet plane. The parameters at the pressure peak are calculated from the conditions at the discontinuity which are the boundary conditions for integrating the conservation equations in the area of interaction between water droplets and the melt. The resulting structure of the thermal-detonation wave is characterized by the maximum pressure being located at some distance from the shock wave.

The STEG code is a three-dimensional two-fluid code designed for modeling thermal-hydraulic processes. To study thermal-hydraulic processes in the horizontal steam generator PGV-1500, OKB Gidropress considered a special experimental facility, which is a fragment of the steam generator along the inner surface of a baffle placed in a durable cylindrical vessel. Several experiments were carried out on this facility. One of these experiments is the calculation of the pressure drop and void fraction in the regime with and without heat release from the tube bundle. In this paper, 2 different flow regimes are simulated using STEG code. A new correlation for calculating the drag coefficient is proposed and its results are compared with the Simovic model and the TRACE code model. The results obtained showed that the new correlation works well in all spatial regions of the model.

A numerical analysis of the experiments addressed to studies of hydrodynamic processes in a horizontal steam generator has been performed using the STEG (STEam Generator) code. The main components of the experimental model include a staggered tube bundle, a submerged perforated sheet (SPS) with baffles, and a downcomer. An air–water mixture was used as a two-phase fluid. The working fluid flow in the model was driven by natural circulation induced by air supply to the lower, middle, and upper sections of the tube bundle. The gas void fraction was measured by the γ-radiography method. In addition, pressure drops along the height of the tube bundle and water levels in the model and above SPS were also measured. Each experiment was performed at a prescribed air load on the evaporation surface and water level in the model. The STEG code was developed at the Department of Nuclear Power Plants of NRU MPEI to model thermohydraulic processes in a horizontal steam generator. The mathematical model is based on a two-fluid approach to the description of a two-phase flow using balance mass, momentum, and energy conservation equations and semiempirical closing correlations for interfacial interactions and interactions with various surrounding structures (tube bundle, walls, etc.). The STEG code was used to perform calculations for nine experimental regimes differing in the perforation ratio of the submerged perforated sheet and the supplied air flowrate. The qualitative regularities of the two-phase air–water mixture circulation in the model of a horizontal steam generator and the effect of experimental values of the main parameters on the circulation have been established. Quantitative results of comparison of the predictions with the experiment demonstrate their good agreement since the relative errors in the predicted air void fractions and pressure drops do not exceed 10

The aim of the study is to numerically simulate the flow of steam/steam-water mixture through one periodic cell of a submerged perforated sheet, which is an important element of the separation scheme of a horizontal steam generator. The OpenFOAM code is used as a calculation tool. First, the flow of single-phase steam was considered. A comparison of the values of pressure drops on the perforated sheet obtained using the OpenFOAM code for two turbulence models with pressure drops determined by other CFD code FlowVision, various approximate formulas and experimental data shows that the variation of all values does not exceed 10%. The influence of a liquid film on the flow of steam through the hole and the resulting pressure drop is investigated. It is shown that the water film reduces the pressure drop on the perforated sheet by about 6% compared with the flow of single-phase steam.

The hydrodynamic and thermal interaction of water with the high-temperature melt of a heavy metal was studied via the Volume-of-Fluid (VOF) method formulated for three immiscible phases (liquid melt, water, and water vapor), with account for phase changes. The VOF method relies on a first-principle description of phase interactions, including drag, heat transfer, and water evaporation, in contrast to multifluid models relying on empirical correlations. The verification of the VOF model implemented in OpenFOAM software was performed by solving one- and two-dimensional reference problems. Water jet penetration into a melt pool was first calculated in two-dimensional problem formulation, and the results were compared with analytical models and empirical correlations available, with emphasis on the effects of jet velocity and diameter. Three-dimensional simulations were performed in geometry, corresponding to known experiments performed in a narrow planar vessel with a semi-circular bottom. The VOF results obtained for water jet impact on molten heavy metal (lead–bismuth eutectic alloy at the temperature 820 K) are here presented for a water temperature of 298 K, jet diameter 6 mm, and jet velocity 6.2 m/s. Development of a cavity filled with a three-phase melt–water–vapor mixture is revealed, including its propagation down to the vessel bottom, with lateral displacement of melt, and subsequent detachment from the bottom due to gravitational settling of melt. The best agreement of predicted cavity depth, velocity, and aspect ratio with experiments (within 10%) was achieved at the stage of downward cavity propagation; at the later stages, the differences increased to about 30%. Adequacy of the numerical mesh containing about 5.6 million cells was demonstrated by comparing the penetration dynamics obtained on a sequence of meshes with the cell size ranging from 180 to 350 µm.

This article examines the effect of wind load on the safety of spent fuel storage in a naturally ventilated building. To assess the influence of wind influences characteristic of the Akkuyu NPP site on the temperature of fuel rod cladding, a CFD model of the spent fuel storage building was developed. Reynolds-averaged governing equations of motion (RANS model) with a k-ε turbulence model were used. Computational grid included about 17 million cells. The CFD model allowed us to study different directions and intensities of wind loads, estimate the temperature around the containers and identify stagnant zones. Based on the modeling results, the dependences of the influence of wind load on the thermal fields in the building were obtained. These dependencies allowed for design decisions to be made that guaranteed safety and ensured the continuation of construction of the building.

The analysis of uncertainties was performed for the significant parameters for conditions with loss of the spent fuel pool cooling using best estimate code SOCRAT-B1/B2. Based on the analysis results, the parameters which have the largest impact on significant results of the calculation are determined. It is also shown that simultaneous deviation of the initial parameters first to the conservative side (for getting maximal cladding temperature at the end of calculation higher so to obtain the worst results in terms of safety) and then to the optimistic side (to obtain the most favorable results in terms of safety) leads to interval of the results larger than the range of uncertainties under consideration. The results of the performed analysis show that this approach can be used for NPP safety justification in accident conditions with loss of spent fuel pool cooling in addition to the methods recommended in regulatory documents.

A review of experimental and computational-theoretical works devoted to the study of the interaction of high-temperature melts with liquids, which can lead to the release of mechanical energy (steam explosions), being a potential hazard for industrial facilities, primarily for nuclear power plants, is carried out. Both large-scale steam explosions involving tens of kilograms of melts and small-scale interactions of individual melt drops with liquid coolants are considered. The importance of the regime of unstable film boiling for determining the conditions for the initiation of a steam explosion is noted. Studies of the influence of the solidification of the melt surface on the thermal interaction of the melt with the coolant are analyzed. The role of melt-oxidation processes in the development of a steam explosion is shown.

This paper presents a mathematical model of a stationary wave of thermal detonation in the “liquid lead - water” system, which can occur after the rupture of a steam generator tube of the reactor BREST-OD-300. The model is based on the mechanics of multiphase fluid flows. The system under study includes a continuous phase of liquid lead, in which drops of water surrounded by a steam film are dispersed. Heat exchange between high-temperature molten lead and water drops is carried out in the film boiling mode. A shock wave propagating in this multiphase system causes all phases in motion. Due to the significant difference in density between liquid lead and water, a difference in velocities arises between dispersed water drops and liquid lead, which cause the fragmentation of water droplets. The shock wave velocity and amplitude are determined by constructing the shock adiabat and the Hugoniot adiabat for the parameters of the studied multiphase mixture. To describe the fragmentation of water droplets, heat transfer between phases, and interfacial friction, the empirical correlations of the thermal detonation theory are used. The obtained numerical solutions describe the distributions of parameters in the zone of melt – water interaction.

The article considers the existing models and correlations for describing heat transfer during film boiling. Film boiling is an important thermophysical process that determines the course of interaction of the melt of reactor core materials with the coolant, which can potentially occur during a severe accident at a nuclear power plant with a pressurized water-cooled reactor (VVER/PWR). The values of the Nusselt number predicted by these models are compared. A fairly significant dispersion of calculated parameters has been established, making it difficult to unambiguously choose one or another correlation. However, in the range of parameters typical for the interaction of a high-temperature melt of reactor core materials with a coolant, several correlations give quite close values, which allows them to be recommended for use in calculation codes for modeling thermal-hydraulic processes during a severe accident at a nuclear power plant with VVER/PWR type.

The model of interaction of a water jet with a melt was validated using experimental data from experiments in which a water jet was injected into a vessel filled with a melt of a eutectic alloy of lead and bismuth. The model is based on the VOF method for immiscible liquids. In the experiments, the experimental data of which were used to validate the model, high-speed X-ray photography was carried out to trace the evolution of the shape of a water jet after its injection into a vessel with a melt. The configurations of the water jet that disintegrates in the melt volume obtained in the calculations were compared with photographs taken during the experiment. Good qualitative agreement between calculations and experiment was obtained. A quantitative comparison of the jet propagation in the melt showed that the jet propagation speed in the calculations is overestimated relative to the experiments at a high water injection rate. This is due to the fact that the model does not take into account the boiling of water on the surface of a hot melt, which is planned to be done in future activity.

In the present work, the effect of a noncondensable gas on the collapse of a hot bubble in cold water was studied. It is assumed that the bubble consists of a gas mixture of steam, which can condense on cold water, and a noncondensable gas. The dynamics of the bubble was modeled by the integral equations of mass and energy supplemented by the steam diffusion equation. The steam condensation rate was determined by heat fluxes on the interfacial surface from the steam and water sides. It was used a one-dimensional spherically symmetric approach. The water surrounding the bubble was considered as an incompressible fluid, the flow of which was described by the Rayleigh-Plesset. Heat transfer in water is described by a one-dimensional heat equation, which takes into account conductive and convective mechanisms of heat transfer. Calculations performed using this model showed that the presence of a noncondensable gas in a bubble does not significantly affect its collapse in cold water. This means that the noncondensable gas cannot significantly weaken the impact of water on the melt, which occurs when a bubble collapses near the interface, which leads to a stratified steam explosion.

The patterns of the wave of thermal interaction of water drops in a high-temperature molten lead, are studied. Due to the boiling of water on the surface of molten lead, both liquids (phases) are separated by a vapor film. A one-dimensional model of interacting and interpenetrating continuums is used, which describes the dynamics of each fluid by introducing a special field characterized by its own velocity, temperature, and volume fraction. Wave velocity is determined by the equality of phase velocities and temperatures in the Chapman-Jouguet plane. The parameters at the pressure peak are calculated from the conditions at the discontinuity which are the boundary conditions for integrating the conservation equations in the zone of interaction of water droplets with the melt. The resulting structure of the thermal detonation wave is characterized by the fact that the maximum pressure is at some distance from the shock wave.

To evaluate the consequences of an accidental rupture of a steam generator heat exchange tube in a reactor with a heavy liquid metal coolant, a mathematical model of the interaction of a steam-water cavity with molten metal near a solid wall was developed. The melt flow is considered as a potential flow of an incompressible fluid. The heat exchange between the melt and the steam-water mixture is not taken into account. The steam-water mixture is modeled by an equilibrium two-phase model. It is believed that the evolution of the steam-water cavity is an isentropic process. The numerical implementation of the mathematical model was performed using the boundary element method. Verification of the developed model using a numerical solution of a spherically symmetric problem of the interaction of a spherical steam-water cavity with a melt in infinite space, obtained using the Rayleigh-Plesset equation, showed good agreement between the solutions obtained by different methods. Using the developed model, a test calculation of the interaction of a steam-water cavity with the surrounding molten metal near a solid wall was performed. Analysis of the calculation revealed several stages of this interaction

One of the possible consequences of a severe accident at a nuclear power plant with a pressurized water reactor is a steam explosion that occurs as a result of the interaction of a high-temperature melt of core materials with water and can lead to the failure of the containment. The paper considers the initial stage of the steam explosion (premixing of the melt with water) under the stratified geometry. The key phenomenon leading to premixing is the dynamic effect of a collapsing vapor bubble in a liquid on the melt surface. The influence of a vapor film located near a melt surface on the dynamics of a vapor bubble is considered. The Kelvin impulse is used as the main criterion characterizing the dynamic effect of a collapsing bubble on the liquid-vapor interface and on the melt surface. The influence of all the main parameters on the Kelvin impulse was numerically studied. Based on the calculations carried out on the plane of the parameters “film thickness - vapor density”, the region of the dynamic impact of the collapsing bubble on the surface is determined. The greatest impacts are observed for thin films of vapor having a high density.

The penetration of a liquid jet into a space filled with another liquid for the case of large difference in density between these liquids is examined as applied to the fragmentation and mixing of jets during various accident scenarios at nuclear power plants (discharge of corium melt into water or water into a volume filled with liquid lead). The hydrodynamic equations for several immiscible liquids with sharp interfaces were solved using the Volume of Fluid (VOF) method. Mathematical models of multiphase flows, implemented numerically in the OpenFOAM open source package, are presented. A series of verification and research calculations was performed in a two-dimensional (plane) approximation, and the obtained results were compared with the published data. The results of calculation of the penetration of a Wood’s metal melt jet into a deep water-filled vessel, performed using this approach, revealed successive stages in the evolution of a fragmenting jet. A good qualitative and quantitative agreement of the predictions with the published results of the calculation of this process by the ANSYS Fluent code were attained. The regularities of mixing of a water jet discharged into a volume filled with initially stagnant liquid (molten) lead are studied. It has been demonstrated that the fragmentation of the water jet occurs almost immediately after it enters the liquid lead in this case. The effect of the grid cell size on the characteristics of phase mixing was examined. The predicted characteristic sizes of the formed fragments, their dispersed composition, and the interfacial surface area during mixing are presented. Nomograms of the size distribution for the fragments formed during the jet breakup were plotted for both studied problems. It is shown that the melt fragments formed in this process are much smaller than the minimum limit size of melt droplets freely falling in water.