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Abstract: Research into gas–liquid countercurrent two-phase flow in a model of pressurized water reactor (PWR) hot leg has been carried out over the last several decades. An extensive experimental data base has been accumulated from these studies, leading to the development of phenomenological correlations and scaling parameters of the countercurrent flow limitation (CCFL). However, most of the proposed correlations apply under a relatively narrow range of conditions, generally limited to the test section conditions and/or geometry. Moreover the development of mechanistic models based on the underlying physical processes has been limited. In contrast to this mechanistic form of modelling, the implementation of computational fluid dynamics (CFD) techniques has also been pursued, but the considerable robust three-dimensional (3D) closure relations for this application remain an unachieved goal due to lack of detailed phenomenological knowledge and consequent application of empirical one-dimensional experimental correlations to the multidimensional problem. This paper presents a comprehensive review of research work on countercurrent gas–liquid two-phase flow in a PWR hot leg and provides direction regarding future research on this topic. In the introductory section, the problems facing current research are described. In the following sections, recent experimental as well as theoretical research achievements are overviewed. In the last section, the problems that remain unsolved are discussed, along with some concluding remarks. It was found that only limited theoretical developments exist in the literature, however highly reliable experimental data are needed to support this effort. Additional work, both analytical and experimental, needs to be carried out on the effects of mass transfer on countercurrent flow limitation to improve the existing correlations and analytical models. [Copyright &y& Elsevier]

Abstract: In order to improve the understanding of counter-current two-phase flow and to validate new physical models, CFD simulations of a 1/3rd scale model of the hot leg of a German Konvoi pressurized water reactor (PWR) with rectangular cross section were performed. Selected counter-current flow limitation (CCFL) experiments conducted at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) were calculated with ANSYS CFX using the multi-fluid Euler–Euler modelling approach. The transient calculations were carried out using a gas/liquid inhomogeneous multiphase flow model coupled with a shear stress transport (SST) turbulence model. In the simulation, the drag law was approached by a newly developed correlation of the drag coefficient () in the Algebraic Interfacial Area Density (AIAD) model. The model can distinguish the bubbles, droplets and the free surface using the local liquid phase volume fraction value. A comparison with the high-speed video observations shows a good qualitative agreement. The results indicate also a quantitative agreement between calculations and experimental data for the CCFL characteristics and the water level inside the hot leg channel. [Copyright &y& Elsevier]

Abstract: This paper replaces the paper published in the journal by . Because of an error in the implementation of the air flow meter some of the data given by are wrong. They are corrected within the present paper. The general results and conclusions remain unchanged. An experimental investigation on the air/water counter-current two-phase flow in a horizontal rectangular channel connected to an inclined riser has been conducted. This test-section representing a model of the hot leg of a pressurized water reactor is mounted between two separators in a pressurized experimental vessel. The cross-section and length of the horizontal part of the test-section are (0.25m×0.05m) and 2.59m, respectively, whereas the inclination angle of the riser is 50°. The flow was captured by a high speed camera in the bended region of the hot leg, delivering a detailed view of the stratified interface as well as of dispersed structures like bubbles and droplets. Counter-current flow limitation (CCFL), or the onset of flooding, was found by analyzing the water levels measured in the separators. The counter-current flow limitation is defined as the maximum air mass flow rate at which the discharged water mass flow rate is equal to the inlet water mass flow rate. From the high-speed observations it was found that the initiation of flooding coincides with the formation of slug flow. Furthermore, a slight hysteresis was noticed between flooding and deflooding. The CCFL data was compared with similar experiments and empirical correlations available in the literature. Therefore, the Wallis-parameter was calculated for the rectangular cross-sections by using the channel height as length, instead of the diameter. The agreement of the CCFL curve is good, but the zero liquid penetration was found at lower values of the Wallis parameter than in most of the previous work. This deviation can be attributed to the special rectangular geometry of the hot leg model of HZDR, since the other investigations were done for pipes. [Copyright &y& Elsevier]

Abstract: An experimental investigation on the air/water counter-current two-phase flow in a horizontal rectangular channel connected to an inclined riser has been conducted. This test-section representing a model of the hot leg of a pressurized water reactor is mounted between two separators in a pressurized experimental vessel. The cross-section and length of the horizontal part of the test-section are (0.25m×0.05m) and 2.59m, respectively, whereas the inclination angle of the riser is 50°. The flow was captured by a high-speed camera in the bended region of the hot leg, delivering a detailed view of the stratified interface as well as of dispersed structures like bubbles and droplets. Countercurrent flow limitation (CCFL), or the onset of flooding, was found by analyzing the water levels measured in the separators. The counter-current flow limitation is defined as the maximum air mass flow rate at which the discharged water mass flow rate is equal to the inlet water mass flow rate. From the high-speed observations it was found that the initiation of flooding coincides with the formation of slug flow. Furthermore, a hysteresis was noticed between flooding and deflooding. The CCFL data was compared with similar experiments and empirical correlations available in the literature. Therefore, the Wallis-parameter was calculated for the rectangular cross-sections by using the channel height as length, instead of the diameter. The agreement of the CCFL curve is good, but the zero liquid penetration was found at lower values of the Wallis parameter than in most of the previous work. This deviation can be attributed to the special rectangular geometry of the hot leg model of FZD, since the other investigations were done for pipes. [Copyright &y& Elsevier]

The study on the interfacial phenomena of flooding during the counter-current flow of gas-liquid in a complex pipe was carried-out experimentally. It consists of a combination of the horizontal pipe, elbow and inclined pipes to simulate the hot leg pipe in a PWR. The inner diameter was 25.4 mm as scale down of real hot leg pipe of German Konvoi type reactor. The visual observations were performed using high-speed video cameras. The measured parameters were the liquid film thickness and the pressure difference between reactor pressure vessel (RPV) simulator and steam generator (SG) simulator. The film thickness inside the test pipe was determined by using the processed image of visual data. As a result, three different mechanisms at the onset of flooding in counter-current were clarified, and are strongly affected by liquid superficial velocity. At low liquid superficial velocity (J L ), the flooding mechanism is triggered by the presence of wavy interface along the horizontal pipes in the form of a liquid blockage on the elbow. At the medium J L , the slug was detected along the horizontal pipe. However, the slug collapses immediately since the water is insufficient to maintain the blockage. At high J L , the slug occurs and travels along the horizontal pipe until the elbow. Moreover, the effect of the length of horizontal pipe on the interfacial behavior of air water counter current flow also can be explained. As the length of the horizontal pipe decreases, the onset of flooding occurs at a higher gas liquid mass flow rate. [ABSTRACT FROM AUTHOR]

• The liquid hold-up fluctuations of gas-liquid counter-current flow in PWR hot leg was analyzed statistically. • The data were analyzed using non-linier statistics, discrete wavelet transforms, and the Kolmogorov entropy. • There were no significant differences between the flooding mechanisms for both air/water and steam/water flows. • The higher the system pressure, the higher the frequency occurrence of slugging during flooding. • Kolmogorov entropy enables to correlate the stabilizing effect due to the fluid resistance during flooding. This study addresses a statistical characterization of the interfacial behaviors during gas/liquid counter-current flow in a large scale of pressurized water reactor's hot leg typical geometry on the basis of both time and frequency domain analyses. Here, the visualizations were captured by high-speed cameras. Furthermore, the image processing algorithm on the basis of pixel identification was developed to identify the time-series interfacial dynamics of the liquid holdup fluctuations, comprising the wave growth and its movement. The obtained data were further analyzed by using various advanced statistical tools comprising the probability density function, power spectral density function, and also discrete wavelet transform. Additionally, chaotic levels of the flow were obtained through the Kolmogorov-entropy analysis. Particular results reveal that a typical mechanism of flooding begins with the appearance of a wavy interface which further develops into either a roll or large wave, and later blocks the entire cross-sectional area of the conduit around the bend region. This later stage indicates the inception of flooding which is characterized by the increase of the water level close to the bend region. Next, the higher the pressure of system, the higher the frequency occurrence of slugging, while the injected gas flow rate obtained a different trend. However, the Kolmogorov entropy enables to correlate the stabilizing effect due to the fluid resistance which corresponds to either the pressure of the system or the physical properties of the fluid. In addition, there were no significant differences between the flooding mechanisms for both the air/water and steam/water flows. [ABSTRACT FROM AUTHOR]

[Display omitted] • The effect of liquid properties on counter-current flow limitation in 1/30 downscale PWR hot leg was investigated. • Five water-based solutions with different physical properties were utilized as the tested liquids. • The CCFL characteristics were examined by various existing correlations and models. • An empirical correlation was proposed to predict the flooding superficial velocity. To promote the safety of the nuclear reactors, numerous authors have carried out investigations of gas/liquid counter-current two-phase flow in order to understand the characteristics during the inception of flooding or CCFL. The present work covers an experimental and analytical study on the effect of liquid properties on CCFL characteristics in a complex geometry representing 1/30 scaled-down version of a German-Konvoi PWR hot leg. The obtained results reveal that the gas velocity to initiate the flooding monotonically decreases with the increase of the liquid velocity. At high liquid flow rates, it is noticed that with the increase of glycerol percentage, the gas flow rate needed to initiate the flooding significantly decrease due to either the increase in liquid viscosity or the decrease in corresponding surface tension. Here under the same flow condition, the flooding is initiated faster by the higher glycerol percentage. Moreover, instead of the well-known Wallis superficial velocity, the Kutateladze-type parameter or a combination of the Wallis parameter and liquid property numbers by Zapke & Kröger (1996) which were previously proposed by numerous authors to investigate the effects of liquid properties on CCFL characteristics, a modified non-dimensional Wallis parameter combined with the inverse viscosity number introduced by Ma et al. (2020) is found herein to more accurately correlate the present experimental data. Through a dimensional similarity analysis, a new empirical correlation reveals that the liquid Froude number is the greatest determinant of CCFL characteristics with respect to the effect of the liquid properties. [ABSTRACT FROM AUTHOR]

• The experiment was conducted during the liquid–gas counter-current two-phase flow in a 1/30 scaled-down of PWR hot leg. • The liquid thickening on the upper edge of the hydraulic jump triggers the liquid blockage to initiate the CCFL. • The statistical characterizations were investigated on the basis of both the locus and the flow parameters. • The time-domain and frequency-domain analyses implies a good agreement with the visual observations, while the wavelet analysis is able to differ the obtained flow regimes. The present work investigates the statistical characteristics of the fluctuations of the liquid film thickness obtained by resistive-conductance probe signals of a complex geometry representing a 1/30 down-scaled of a PWR hot leg. Here, four locations at the horizontal part of the test section were assessed, while the flow development was investigated through a close observation by using a high-speed video camera. Next, the normalized voltages, indicating the liquid film thickness fluctuations, are shown in the time-series. From the fluctuations, the amplitudes representing the film thickness were recorded. Hence, such statistical diagnostic tools were applied on the basis of time-domain, frequency-domain and also time–frequency domain analyses. From the probability density function, the distributions of the fluctuations were assessed, whereas the power spectral density function describes the dominant frequencies. In addition, the Kolmogorov entropy denotes the chaotic level of the signal, meanwhile the wavelet energy corresponds to several details on the wavy interfaces on the basis of its frequency scales. Next, those parameters were statistically employed to elaborate the interfacial behaviors due to the signal characteristics. The results indicate that the low dominant frequency corresponds to the occurrence of either liquid blockage or slugs during the acquisition, meanwhile the largest scale fluctuations reveal the wave movements. [ABSTRACT FROM AUTHOR]