Countercurrent Flow Limitation Research Articles

Experimental Study on Two-Phase Countercurrent Flow Limitation in Horizontal Circular Pipes

The two-phase countercurrent flow limitation (CCFL) in horizontal channels is important in relation to nuclear reactor safety. In this study, we aim to investigate the CCFL characteristics and the flow behaviors in horizontal circular pipes with small diameters. The effects of pipe diameter and the water head in the upper plenum on CCFL characteristics are experimentally studied. An image-processing technique and statistical treatments are implemented to analyze the horizontal countercurrent flow. The results show that the CCFL characteristics for the horizontal circular pipes with small diameters can be well correlated using the dimensionless parameters, which are based on adding fluid viscosity to the Wallis parameters. The CCFL characteristics are significantly affected by the pipe diameter and are slightly affected by the water head above the horizontal pipe. The gas–liquid interface fluctuates with certain periods, and flow pattern transitions happen in the horizontal air–water countercurrent flow. As the air flow rate increases, the occurrence location of the liquid slug appears to shift towards the water entrance. In addition, the further away from the water entrance, the lower the average of liquid holdup.

Experimental investigation of countercurrent flow limitation (CCFL) in a 1/19 scale of VVER-1000 geometry

Countercurrent flow limitation (CCFL) has been experimentally considered in a VVER-1000 hot-leg. The proposed test facility consists of a hot-leg pipe, a reactor vessel simulator (RVs), and a steam generator simulator (SGs). It was designed and constructed based on power-to-volume scaling approach by preserving the Froud number in the hot leg. The scaling ratio was considered 1/19 of the Bushehr NPP (VVER-1000) geometry. The hot leg of the proposed facility provides good optical observation of the gas/liquid interface. The SG simulator has also a side view for optical observation. Experimental results were captured at atmospheric pressure with air/water as fluid. CCFL was obtained by analyzing the pressure differences between RV and SG simulators.This CCFL data was compared with empirical data and correlations available in the literature. With increasing liquid superficial velocity, the gas superficial velocity curve is continuously decreased, which is consistent with Navarro's results. In this study, an experimental correlation is proposed and compared to other correlations. It was very close to the Navarro and Richter correlations.The results of experimental investigations clarified the onset of the CCFL phenomenon in a Bushehr NPP (VVER-1000) hot-leg geometry. Moreover, the achieved patterns and behaviors of the air/water mixture would be used in computational fluid dynamics (CFD) code validations.

Evaluation of temperatures and flow areas of the Phebus Test FPT0

The cladding temperatures and axial mass distribution computed by MAAP5 were compared with their measured values in the test bundle of the Phebus Test FPT0. The computed cladding temperatures were in good agreed with the measured values in the pre-transient phase. In the transient heat-up phase, the computed temperatures were overestimated by the Baker-Just correlation in MAAP5, but the computed temperatures could simulate the subsequently measured values. The computed mass distribution in the axial direction was in qualitative agreement with the measured one for post-test fuel damage observations. The calculated flow areas of inner and outer regions in the test bundle were compared with the photographic observations. MAAP5 computed them at the height of 0.2 m where the molten pool formed was in qualitative agreement with the photographic observations. It was found that the remaining steam flow paths might be caused by the gas-liquid two-phase flow counter-current flow limitation.

Experimental research on flow regime and transitional criterion of slug to churn-turbulent and churn-turbulent to annular flow in rectangular channels

As for two-phase flow in rectangular channels, the flow regimes especially like churn-turbulent and annular flow are significant for the physical problem like Countercurrent Flow Limitation (CCFL). In this study, the rectangular channels with cross-sections of 4 × 66 mm, 6 × 66 mm, 8 × 66 mm are adopted to investigate the flow regimes of air-water vertical upward two phase flow under adiabatic condition. The gas and liquid superficial velocities are 0≤jg≤20m/s and 0.25≤jf≤3m/s respectively which covering bubbly to annular flow. The flow regimes are identified by random forest algorithm and the flow regime maps are obtained. As the results, the transitional void fraction from slug to churn turbulent flow fluctuate from 0.47 to 0.58 which is significantly affected by the dimensional size of channel and flow rate. Besides, the void fraction at transitional points from churn-turbulent (slug) to annular flow are 0.66–0.67, which are independent with the gap size. Furthermore, a new criteria of slug to churn-turbulent flow is established in this study. In addition, by introducing the interfacial force model, the criteria of churn-turbulent (slug) flow to annular flow is verified.

Analysis of RELAP5 prediction of countercurrent flow limitation in downcomer at upper plenum test facility

The relevance of the countercurrent flow limitation phenomenon is known in nuclear (emergency core cooling and accident situations) industries, such as a Loss of Coolant Accident (LOCA). The occurrence of countercurrent flow limitation (CCFL), which can exist in a host of places around the nuclear reactor system, will prevent the emergency cooling water, which is necessary to cool the core successfully flowing into the core from the downcomer of Pressurized Water Reactor (PWR) in the LOCA. Accurate prediction of the downcomer CCFL phenomenon is significant for the design and analysis of reactor safety. Among the experiments at Upper Plenum Test Facility (UPTF), various tests, test 6 and test 7 are studied in this research. Those tests are conservatively evaluated to predict the CCFL phenomenon at the downcomer. Above all, the methodology of node partition used in the RELAP5 model for the channels with cross-connections to represent the circumferential downcomer annulus was also studied. In particular, the nodes along the circumferential direction had a vital effect on the prediction of the steam velocity profile of downcomers. The influence of the CCFL model, including the most widely used Wallis-type and Kutateladze-type correlations, and the cooling-limited liquid-downflow behavior were analyzed. In addition, the pressure on the downcomer and steam flow rate of the break were monitored, and the predicted results were also analyzed.

Integral-Effect Test for Loss of Residual Heat Removal System During Mid-Loop Operation in ATLAS Facility

A test called B4.2 in the OECD-ATLAS2 project was performed to simulate loss of the residual heat removal system (RHRS) during mid-loop operation (MLO) using a thermal-hydraulic (T-H) integral-effect test facility: the Advanced Thermal-Hydraulic Test Loop for Accident Simulation (ATLAS). The main purpose of this test was to investigate a T-H transient in the reactor coolant system (RCS) during loss of the RHRS and to evaluate the effectiveness of reflux condensation and the capability of a safety injection tank (SIT) on shutdown coolability. The initial and boundary conditions for the B4.2 test were appropriately determined according to a state of MLO corresponding to 65 h after reactor trip in the Advanced Power Reactor 1400 MW(electric) (APR1400). During the loss of RHRS accident transient simulation, major T-H parameters such as system pressures, temperatures, and collapsed water levels in the RCS were measured, and unique T-H phenomena such as reflux/cocurrent condensations, off-take, countercurrent flow, and countercurrent flow limitation were investigated. In this paper, the overall T-H behavior in the RCS during a simulated loss of the RHRS with SITs is highlighted to provide a better understanding of T-H phenomena regarding coolability with reflux condensation.

Experimental Investigations and Numerical Studies of Two-Phase Countercurrent Flow Limitation in a Pressurized Water Reactor: A Review

Gas–liquid two-phase countercurrent flow limitation (CCFL) phenomena widely exist in nuclear power plants. In particular, the gas–liquid countercurrent flow limitation phenomena in a pressurized water reactor (PWR) during a loss-of-coolant accident (LOCA) or a small-break loss-of-coolant accident (SBLOCA) play an important role in nuclear reactor safety research. Over several decades, a series of experimental investigations and numerical studies have been carried out to study the CCFL phenomena in a PWR. For the experimental investigations, numerous experiments have been conducted, and different CCFL mechanisms and CCFL characteristics have been obtained in various test facilities simulating different scenarios in a PWR. The CCFL phenomena are affected by many factors, such as geometrical characteristics, liquid flow rates, and fluid properties. For the numerical studies, more and more numerical models were presented and applied to the calculations of two-phase countercurrent flow over the past several decades. It is considered that the computational fluid dynamics (CFD) tools can simulate most of the two-phase flow configurations encountered in nuclear power plants. In this paper, the experimental investigations and the numerical studies on two-phase countercurrent flow limitation in a PWR are comprehensively reviewed. This review provides a further understanding of CCFL in a PWR and gives directions regarding future studies. It is found that relatively fewer investigations using steam–water under high system pressures are performed due to the limitation of the test facilities and test conditions. There are a number of numerical studies on countercurrent two-phase flow in a PWR hot leg geometry, but the simulations in other flow channels were relatively rare. In addition, almost all of the numerical simulations do not include heat and mass transfer. Thus, it is necessary to investigate the effects of heat and mass transfer experimentally and numerically. Furthermore, it is of significance to perform numerical simulations for countercurrent two-phase flow with a fine computational grid and suitable models to predict the formation of small waves and the details in two-phase flow.

Countercurrent Flow Limitation in a Pipeline with an Orifice

Countercurrent flow limitation (CCFL) refers to an important class of gravity-induced hydrodynamic processes that impose a serious restriction on the operation of gas–liquid two-phase systems. In a nuclear power plant, CCFL may occur in the liquid level measurement system where an orifice is applied in the pipeline, which may introduce error into the level measurement system. CCFL can occur in horizontal, vertical, inclined, and even much more complicated geometric patterns, and the hot-leg channel flow passage has been widely investigated; however, a pipeline with variable cross-sections, including an orifice, has not yet been investigated. An experimental investigation has been conducted in order to identify the phenomenon, pattern, and mechanism of CCFL onset in this type of geometry. Both visual and quantified experiments were carried out. A high-speed camera was applied to capture the flow pattern. Visual experiments were implemented at atmospheric pressure, while quantified pressurizer experiments were implemented at higher pressures. It was determined that if the condensate drainage is low and the liquid level is also low, with a stable stratified flow upstream of the orifice, there is no oscillation of the differential pressure. However, at higher condensate drainage levels, when the liquid level increases, a stratified wavy flow occurs. One of these waves can suddenly rise upstream of the orifice to choke it, which subsequently gives rise to differential pressure across the orifice, with periodic variation. This pattern alternately features stratified flow, stratified wavy flow, and slug flow, which indicates the occurrence of CCFL. The CCFL occurring under these experimental conditions can be expressed as a Wallis type correlation, where the coefficients m and C are 0.682 and 0.601, respectively.

An experimental study on the effect of liquid properties on the counter-current flow limitation (CCFL) during gas/liquid counter-current two-phase flow in a 1/30 scaled-down of Pressurized Water Reactor (PWR) hot leg geometry

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.

フラッディング条件における鉛直管での壁面摩擦係数とボイド率

We measured counter-current flow limitation (CCFL), pressure gradient dP/dz, and void fraction αG in a 40 mm diameter vertical pipe with the rounded top and bottom ends and working fluids of air and water under flooding conditions, and we obtained the wall and interface friction factors, fw and fi. We compared CCFL, dP/dz, αG, fw and fi with those obtained from our previous experiments in the vertical pipes with the rounded top and sharp-edged bottom ends, and the sharp-edged top and rounded bottom ends. As a result, the shape of the upper end affected flow characteristics in vertical pipes under flooding conditions stronger than the shape of the lower end did. fw was expressed by the correlation for single-phase flows in the region of a large liquid Reynolds number ReL, but was much larger than that from the fw correlation for single-phase flows in the region of a low ReL. Therefore, we obtained a fw correlation for the region of the low ReL as a function of ReL or the liquid Kutateladze number KL*, and we evaluated uncertainty of liquid volume fraction αL = 1－αG when αG was obtained from the fw correlation and dP/dz data.

An experimental study on gas–liquid two-phase countercurrent flow limitations of vertical pipes

The gas–liquid two-phase countercurrent flow limitation (CCFL) of vertical pipes is an important subject of concern in various industries. Predicting the CCFL of vertical pipes, i.e. the flow rate relationship between the gas and liquid phases under CCFL conditions, has not yet been clearly determined on effects of the structural parameters of the pipe. In this study, a visualization experiment on the CCFL of vertical pipes was performed by using air and water as the two phases. The effects of pipe diameter and pipe length were tested in the ranges of 25–100 mm and 0.50–2.0 m, respectively. Based on the experimental result, the flow behaviors of the CCFL in vertical pipes were analyzed, and four existing CCFL correlation models were examined in their capabilities to correlate the effects of pipe diameter and pipe length. The result shows that the flow patterns in vertical pipes are essentially annular flows and annular-mist flows under CCFL conditions, and the flow behaviors on gas–liquid interface present different features as the pipe differed in diameters. Examination of the available CCFL models indicates that none of them has reached a satisfactory correlation on the effects of pipe diameter and pipe length. Consequently, based on a reasonable fluid mechanics analysis, a novel CCFL correlation model that can correlate the effects of pipe diameter and pipe length was advanced. This model provides a reasonable and accurate prediction of the CCFL of vertical pipes when the pipe varies in structural parameters, which is of great significance to the safe and efficient operation of the related equipment in nuclear power generation, natural gas extraction and chemical industries.

Development of a dimensionless flooding correlation based on experimental study on air-water countercurrent flow limitation in a vertical tube

The flooding phenomenon has an important influence on the safety of equipment, especially the nuclear power plant. A new semi-empirical correlation for flooding was proposed based on the experimental investigation of the physical characteristics of the flooding in our previous work. The model was derived from the momentum equations in the annular flow model. The liquid volume fraction, the wall and interfacial friction have been taken into account. The interfacial friction factor is emphatically discussed in this study since the interfacial friction has a significant influence on flooding. A modified model of interfacial friction factor was presented containing the Bond number since the Bond number can remove the influence of the geometry. The predicting error was basically within 20% compared with the existing experimental data obtained in different geometries and sizes.

Research on Countercurrent Flow Limitation in Reactor Hot Leg at the Loss of Coolant Accident-Thermohydraulic Calculation With System Code RELAP5

Since the counter current flow limitation (CCFL) of the two-phase flow has an important influence on the safety analysis of the reactor, it is also of great significance to study some characteristics and flow pattern transitions of the two-phase flow. In order to explore the characteristics and influencing factors of two-phase counter current flow in the hot leg under the condition of the Loss of Coolant Accident, this research, using RELAP5 simulation calculation, analyzed the effect of the lengths of the flow path of the hot leg, the shapes of the upper outlet of the inclined pipe, and the shapes of the elbow connecting the horizontal pipe and the inclined pipe on the characteristics of the CCFL. This research also evaluated the limitation of the model. The simulation founded that under the same liquid flow rate, the longer the horizontal pipe, the lower the gas flow rate at the beginning of the counter current flow; the effect of the elbow on the CCFL was not great; compared with the sharp outlet shape, the Jf of the gentle circle was slightly larger. The method established in this study is suitable for the prediction of CCFL in the hot leg during Loss of Coolant Accident.

Experimental Investigation of the Heat Transfer Characteristics and Operation Limits of a Fork-Type Heat Pipe for Passive Cooling of a Spent Fuel Pool

A fork-type heat pipe (FHP) is a passive heat-transport and air-cooling device used to remove the decay heat of spent nuclear fuels stored in a liquid pool during a station blackout. FHPs have a unique geometrical design to resolve the significant mismatch between the convective heat transfer coefficients of the evaporator and condenser parts. The evaporator at the bottom is a single heat-exchanger tube, whereas the condenser at the top consists of multiple finned tubes to maximize the heat transfer area. In this study, the heat transfer characteristics and operating limits of an FHP device were investigated experimentally. A laboratory-scale model of an FHP was manufactured, and a series of tests were conducted while the temperature was varied to simulate a spent fuel pool. As an index of the average heat transfer performance, the loop conductance was computed from the measurement data. The results show that the loop conductance of the FHP increased with the heat transfer rate but deteriorated significantly at the operating limit. The maximum attainable heat transfer rate of the unit FHP model was accurately predicted by the existing correlations of the counter-current flow limit for a single-rod-type heat pipe. In addition, the instant heat transfer behaviors of the FHP model under different temperature conditions were examined to interpret the measured loop conductance variation and operating limit.

Void Fraction and Interfacial Friction in Vertical Circular Pipes with the Square Top End under Flooding Conditions

The objective of this study was to reduce the uncertainties of correlations for flow characteristics in vertical pipes under flooding at the top end. The void fraction α, pressure gradient dP/dz, and countercurrent flow limitation (CCFL) were previously measured with diameter D = 40 mm and working fluid of air and water. The wall friction and interfacial friction factors (fw and fi) were obtained based on the annular flow model, and CCFL and fw were evaluated in detail. Hence, attention was turned to detailed evaluations of α and fi. Liquid film thickness δ and interfacial friction factor fi for smooth film (SF) due to flooding at the top end were obtained using the previously derived fw correlation and existing dP/dz data with D = 20 to 50.8 mm and pressure P = 0.1 to 4.1 MPa, and empirical correlations for δ and fi were derived. The δ term was well expressed by a function of the liquid Reynolds number ReL, and the uncertainty of the δ correlation was ±0.0062 for α = 0.87 to 0.98. fi was expressed by a function of δ/L (where L is the Laplace length) or the Kutateladze parameter KG*, the dimensionless diameter D* (=D/L), and the density ratio of the gas and liquid phases ρG/ρL. The applicability of the derived correlations to conditions of D = 300 mm and P = 7 MPa was evaluated, and the fi correlation was modified based on fi values computed with the δ correlation. The drift-flux parameters for SF were also considered.

Assessing the effects of switching from multi-channel to three-dimensional nodalisations of the core in TRACE

Modern thermal-hydraulics (TH) systems analysis codes are increasingly being updated to include three-dimensional (3D) TH components towards capturing the complex flow phenomena in large components of light water reactors (LWRs). These are becoming increasingly popular for modelling reactor pressure vessels and cores since they potentially offer a more realistic representation of, for example, the effects of asymmetric loop flows and injection, which cannot be captured using traditional multi-channel models. Experience suggests, however, there may be unexpected side effects of upgrading from traditional multi-channel models. In this paper, we present comparative results demonstrating our experiences in switching to 3D components using the US-NRC system code TRACE. We present a series of studies in which 1D and 3D nodalisations are compared for representative PWR loss-of-coolant-accident (LOCA) scenarios. We see a clear trend for many of the LOCA scenarios considered. In particular, the peak cladding temperature (PCT) for 3D nodalisations is significantly lower than for traditional multi-channel models in many cases. Counter current flow limitation (CCFL) at the core upper tie plate appears to be one of the driving phenomena for many of the observed differences. This trend is, however, not universal; For a surge line break in the large scale test facility (LSTF), heterogeneities in the core upper tie plate lead to hot regions in the core, which are not captured in the multi-channel model. For large PWR cores, 3D nodalisations appear to represent the reality more closely. For smaller cross-sections, however, the validity of the TRACE’s CCFL prediction for 3D nodalisations is questionable. Specific guidelines are therefore needed to help TRACE users select the most appropriate 3D nodalisation for different geometries.

Effects of Water Levels in Upper Tank on Flow Characteristics in a Vertical Pipe under Flooding at Its Top End

In order to evaluate effects of water levels in the upper tank hut on flow characteristics in a vertical pipe under flooding at its top end, counter-current flow limitation (CCFL characteristics), void fraction and pressure gradient were measured for counter-current flows of air and water in a vertical pipe with the diameter of 40 mm at hut = 200 and 300 mm in addition to data at hut = 100 mm measured in our previous study, and the wall and interfacial friction factors were obtained from the data. As a result, the falling water flow rate decreased with increasing hut, and a Wallis-type CCFL correlation with the Kutateladze parameters was derived as a function of hut. With increasing hut, the thickness of the falling water film decreased due to decrease in the falling water flow rate, and the wall and interfacial friction factors decreased due to decrease in the water film thickness. The annular flow model with correlations for CCFL, and the wall and interfacial friction factors could predict the effects of hut on the liquid volume fraction αL and the transition from αL decrease regime to αL increase regime with increasing the gas volumetric flux.

Physical Phenomena in Nuclear Thermal Hydraulics and Current Status

116 nuclear Thermal-Hydraulic Phenomena T-HP are identified in the present paper, following documents issued during the last three decades by the Committee on the Safety of Nuclear Installations of Nuclear Energy Agency of the Organization for Economic Cooperation and Development (OECD/NEA/CSNI) and by the International Atomic Energy Agency (IAEA). The derived T-HP list includes consideration of experiments performed in Separate Effect Test (SET) and Integral Effect Test (IET) facilities relevant to reactor coolant system and containment of Water Cooled Nuclear Reactors (WCNR). We consider a dozen WCNR types: Pressurized Water Reactors (PWR), Boiling Water Reactors (BWR), Russian reactors (VVER-440, VVER-1000 and RBMK), pressure tube heavy water reactors by Canada (CANDU) and India (PHWR) and so-called ‘advanced’ reactors (e.g. AP-1000 and APR-1400 designed in US and Korea, respectively). We envisage a variety of applications for the T-HP list. Four of the phenomena are helpful to characterize the current state of art in nuclear thermal-hydraulics: Counter Current Flow Limitation (CCFL), Critical Heat Flux (CHF), reflood and Two-Phase Critical Flow (TPCF). Furthermore, the T-HP identification contributes to addressing the scaling issue, performing uncertainty evaluations, developing constitutive equations and ‘special models’ in codes and prioritizing the research.

Numerical Simulation Study on the Air/Water Counter- current Flow Limitation in Nuclear Reactors

After a loss-of-coolant accident (LOCA) in a Pressurized Water Reactor (PWR), the temperature of the fuel elements cladding increases dramatically due to the heat produced by the fission products decay, which is not adequately removed by the vapor contained in the core. In order to avoid this sharp rise in temperature and consequent melting of the core, the Emergency Core Cooling System is activated. This system initially injects borated water from accumulator tanks of the reactor through the inlet pipe (cold leg) and the outlet pipe (hot leg), or through the cold leg only, depending on the plant manufacturer. Some manufacturers add to this, direct injection into the upper plenum of the reactor. The penetration of water into the reactor core is a complex thermofluidodynamic process because it involves the mixing of water with the vapor contained in the reactor, added to that generated in the contact of the water with the still hot surfaces in various geometries. In some critical locations, the vapor flowing in the opposite direction of the water can control the penetration of this into the core. This phenomenon is known as Countercurrent Flow Limitation (CCFL) or Flooding, and it are characterized by the control that a gas exerts in the liquid flow in the opposite direction. This work presents a proposal to use a CFD to simulate the CCFL phenomenon. Numerical computing can provide important information and data that is difficult or expensive to measure or test experimentally. Given the importance of computational science today, it can be considered a third and independent branch of science on an equal footing with the theoretical and experimental sciences.

Fork-end heat pipe for passive air cooling of spent nuclear fuel pool

When a station blackout accident occurs in a nuclear power plant, active cooling of spent nuclear fuels stored in a water pool using pumps is not available. As a result, the stagnant water in the pool gradually heats up via decay heat from the spent fuels and evaporates, thus exposing the spent fuels to air. This rapidly overheats the spent fuels and produces hydrogen gas due to oxidation of the zircaloy cladding. Accumulation of hydrogen gas can result in harmful detonation in the spent fuel storage building similar to what occurred in the Fukushima accident. In this study, a new concept of a gravity-assisted heat pipe that removes decay heat of spent fuels in a water pool by natural convection of ambient air is proposed. In the design, the condenser at the top of the heat pipe consists of several finned tubes for passive air cooling while the evaporator at the bottom is a single rod submerged in the spent fuel pool, which is called fork-end heat pipe (FEHP). A theoretical analysis model of a FEHP was developed and a laboratory-scale specimen was manufactured and tested for validation. It was found that the developed theoretical analysis model reasonably predicted the heat transfer rate of the FEHP specimen at diverse operating conditions and the operating limit point where the heat transfer rate is maximized due to the counter-current flow limit phenomenon.