Applicability of Annular Flow Model to Counter-Current Flow in Debris Beds

Counter-current flow limitation (CCFL) is dominant phenomena for dryout in a debris bed which may be formed during a severe accident as observed in the Three-Mile Island unit-2. Actual CCFL situation in debris bed is very complex. It is difficult to treat the CCFL in the debris bed as it is. On the other hand, an annular flow model was developed to predict CCFL in a pipe by assuming a two-dimensional turbulent flow. If hypothetical flow channel were assumed for CCFL in the debris bed, CCFL in the debris bed could be treated with the same manner as for CCFL in a pipe. 'The purpose of this study is to investigate whether the annular flow model developed for CCFL in a pipe is applicable for CCFL in the debris bed or not. As the results, it is clarified that qualitative tendency of the CCFL in the debris bed consisting of larger particles than 3 mm is estimated by the annular flow model developed for CCFL in a pipe, although the difference between the calculation and the data is large in higher and lower gas velocity. It is also clarified that wall friction factor calculated with the present analysis is twice to forth larger than that in the single phase flow through porous media.     

垂直管内气液两相逆流极限管径效应实验

在压水堆安全性分析中,需准确预测气液逆流极限(CCFL)工况下两相流动关系。本文采用水下淹没排气的实验方法,对相同管长不同管径垂直管的CCFL特性进行可视化实验,并对垂直管CCFL关联式模型进行分析,主要结论有:①在CCFL工况下垂直管内流型为环状流动;表观气速较大时,大管径管内液膜呈搅拌状,小管径管内液膜呈波动状;随表观气速减小,均转为液面光滑的自由降膜流动;②Wallis数模型过度关联了管径变化对垂直管CCFL特性的影响;Kutateladze数和Froude-Ohnesorge数模型也不能良好关联垂直管CCFL特性的管径效应;③提出了新的CCFL无量纲参数和相应的实验关联式,由此可使垂直管CCFL特性的管径效应得以统一表征,还可以关联物性参数变化的影响。     

AP1000稳压器波动管竖直管段空气-水CCFL实验研究

使用竖直管代替波动管模型开展稳压器波动管竖直管段内空气-水两相逆流限制(CCFL)特性可视化实验研究。实验现象表明:竖直管与上容器接口处的局部CCFL决定了进入竖直管内的液相流量;竖直管内的局部CCFL决定了从竖直管流出的液相流量;两处局部CCFL均随空气流量的增大而增强。在较低气量情况,进入竖直管内的液相能够完全或大部分流出,竖直管内的局部CCFL较弱,上容器和竖直管接口处的局部CCFL在整体CCFL中占主导地位,整体CCFL程度随着上容器液位升高而略有增强。在高气量情况,从上容器进入竖直管的液相大部分或者完全被限制而不能向下流出,竖直管内的局部CCFL强烈,在整体CCFL中占主导地位,整体CCFL特性不受上容器液位变化的影响。通过实验数据拟合得到了新的稳压器竖直管CCFL模型。稳压器波动管CCFL数据和稳压器竖直管CCFL数据基本重合,表明波动管CCFL主要由CCFL-U决定。     

Development of debris bed cooling evaluation code,DPCOOL, based on heating porous media submerged in two-phase pool

ABSTRACT

A framework of the modular code system, THERMOS, aiming to evaluate cooling of a debris bed having complex configurations was introduced with a focus on one of the major modules, DPCOOL, which models heating or non-heating porous media of particulate debris in a two-phase pool. In DPCOOL, pool and debris bed regions are discretized in a three-dimensional Cartesian coordinate system. A pool region is formulated based on the two-fluid model. A two-phase flow in the debris bed region is formulated based on the Tung & Dhir model with modifications for smaller particles proposed by Schmidt. In order to synthesize the momentum equations of the two regions, interpolation factors as piecewise linear functions of porosity are introduced. The interfacial friction model was validated based on Chu’s test using a debris bed composed of non-heating SUS spheres in a water pool with air injection from below where the net water flow in the layer became zero so that pressure loss of the layer was governed by interfacial friction. The sum of the two-phase flow friction and the interfacial friction models was validated based on top flooding and bottom flooding tests conducted in IKE’s DEBRIS test facility loaded with mixed steel and alumina spheres that were heated by an induction coil system.     

Experimental investigation and CFD validation of countercurrent flow limitation (CCFL) in a large-diameter PWR hot-leg geometry

ABSTRACT

Countercurrent flow limitation (CCFL) is a phenomenon that consists of several flow patterns occurring simultaneously which produces a complex gas/liquid interface and interfacial momentum transfer, thus making it one of the most challenging two-phase flow configurations for computational fluid dynamics (CFD) validation. Numerous experimental investigations have been carried out in recent years regarding this, but most of those investigations were performed in small-diameter pipes or in non-pipe geometries (rectangular cross sections). A review of these experimental investigations has shown that the scale and geometry of the test section has a large impact upon the onset and characteristics of the CCFL. In order to provide a better understanding of this phenomenon in an actual pressurized water reactor (PWR) hot-leg geometry at a relatively large-diameter and scale, a test facility with a ～1/3.9 scale and a 190 mm inner diameter was constructed. Experiments were carried out at atmospheric pressure using water and air. High-speed recording was used to acquire high-quality images of the air/water interface. CCFL mechanisms, flow patterns, and the limits of the onset of CCFL and deflooding were experimentally identified. CFD simulations of two representative cases were carried out and assessed against experimental results. The analysis of the CFD simulations has provided insights into the improvements necessary for the accurate simulation of CCFL in large-scale geometries.     

Two-phase countercurrent flow in a model of a pressurized water reactor hot leg

The onset of flooding or countercurrent flow limitation (CCFL) determines the maximum rate at which one phase can flow countercurrently to another phase. In the present study, the experimental data of the CCFL for gas and liquid in a horizontal pipe with a bend are investigated. The different mechanisms that lead to flooding and that are dependent on the liquid flow rate are observed. For low and intermediate liquid flow rates, the onset of flooding appears simultaneously with the slugging of unstable waves that are formed at the crest of the hydraulic jump. At low liquid flow rates, slugging appears close to the bend; at higher liquid flow rates, it appears far away from the bend, in the horizontal section. For high liquid flow rates, no hydraulic jump is observed, and flooding occurs as a result of slug formation at the end of the horizontal pipe. The effects of the inclination angle of the bends, the liquid inlet conditions and the length of the horizontal pipes are of significance for the onset of flooding. A mathematical model of Ardron and Banerjee is modified to predict the onset of flooding. Flooding curves calculated by this model are compared with present experimental data and those of other researchers. The predictions of the onset of flooding as a function of the length-to-diameter ratio are in reasonable agreement with the experimental data.     

Experimental study of gas–liquid two-phase flow through packed bed under natural circulation conditions

Dry-out phenomena in packed beds or porous media may cause a significant digression of cooling/reaction performance in heat transfer/chemical reactor systems. One of the phenomena responsible for the dry-out in packed beds is known as the counter-current flow limitation (CCFL). In order to investigate the CCFL phenomena induced by gas–liquid two-phase flow in packed beds inside a pool, a natural circulation packed bed test facility was designed and constructed. A total of 27 experimental conditions covering various packing media sizes (sphere diameters: 3.0, 6.4 and 9.5 mm), packed bed heights (15, 35 and 50 cm) and water level heights (1.0, 1.5 and 2.0 m) were tested to examine the CCFL criteria with adiabatic air–water two-phase flow under natural circulation conditions. Both CCFL and flow reversal phenomena were observed, and the experimental data including instantaneous and time-averaged void fraction, differential pressure and superficial gas–liquid velocities were collected. The CCFL criteria were determined when periodical oscillations of void fraction and differential pressure appear. In addition, the Wallis correlation for CCFL was utilized for data analysis, and the Wallis coefficient, C, was determined experimentally from the packed bed CCFL tests. Compared to the existing data-sets in literature, the higher C values obtained in the present experiment suggest a possibly higher dry-out heat flux for natural circulation debris systems, which may be due to the water supply from both top and bottom surfaces of the packed beds. Considering the effects of bed height and hydraulic diameter of the packing media, a newly developed model for the Wallis coefficient, C, under natural circulation CCFL is presented. The present model can predict the experimental data with an averaged absolute error of ±7.9%.     

A review of CCFL phenomenon

Counter current flow limitation CCFL is an important phenomenon for numerous engineering applications and safety of light water reactors. In particular, the possible occurrence of CCFL in the hot-leg of a PWR during SBLOCA or LOCA accidents is of special interest for nuclear safety research. A review of the related literature has made in order to present the most important studies about the phenomenon and to reach common general understanding of the different factors that govern CCFL. Eventually this will allow explaining contradictions among different explanations provided by different authors. Most important factors were geometrical characteristics, liquid superficial velocity, and physical properties. The review shows that despite numerous experimental works, many scaling and geometrical effects are still not fully understood. For Instance there exist no consistent explanation of the channel diameter and inclined riser length effect upon results. The same can be stated-though to a minimum extent – for the inclination angle while channel length (or channel to diameter ratio) effect was clear and consistent. Since most experimental work was done in down-scaled hot-leg simulators, it becomes interesting to build a coherent knowledge about these effects and to explain arising contradictions in order to safely extrapolate results to full-scale hot-leg. The review has shown that many differences were simply due to geometrical effects, this leads to the need to “standardize” experimental data according to geometrical parameters. This should results in a better understanding of the phenomenon and corresponding scaling effects. Additionally, important variables such as: pressure drop, void fraction and shear stress were also investigated and discussed. A compilation of CCFL data was built and analyzed. Since the new simulation trends tend to use CFD codes where geometrical and spatial deviations are excluded by using 3D modeling, emphasis was placed upon introducing correlations for onset of CCFL out of collected data. Existing correlations for interfacial shear stress friction factor and the void fraction as a function of gas superficial velocity were also gathered and briefly discussed. The effect of condensation, physical parameters, and hysteresis upon CCFL was also introduced.     

Interfacial Friction Factor for High-Pressure Steam/Water Stratified-Wavy Flow in Horizontal Pipe

The interfacial friction was investigated for high-pressure (3 to 9 MPa) steam/water stratified-wavy flow, using the TPTF experimental data for 4 and 8-inch diameter horizontal pipe test sections. The interfacial waves observed in the stratified-wavy flow regime with void fractions typically <–0.6, became larger in r.m.s. amplitude and more irregular in both amplitude and wave length, as the transition boundary to slug flow was approached. A correlation to predict the interfacial friction factor has been obtained for the stratified-wavy flows including the vicinity of the transition boundary to slug flow. The correlation is based on two non-dimensional parameters related to the interfacial wave generation by the Kelvin-Helmholtz instability, and correlates the TPTF data taken under different pipe diameters and pressures.     

Condensation experiments for counter-current flow limitation in an inverted U-tube

In this study, we measured counter-current flow limitation (CCFL) characteristics in an inverted U-tube (18.4 mm diameter and 1.0 m straight-part length) simulating steam generator (SG) U-tubes under conditions of steam condensation at pressures of 0.1–0.14 MPa. Differential pressure ΔP between the top of the inverted U-tube and the lower tank was measured, and the flow patterns wave estimated by comparing the waveforms of ΔP with those in air–water experiments. As a result, we classified the flow patterns under CCFL conditions into CCFL-P, CCFL-L and CCFL-T. The falling water flow rate under CCFL conditions slightly increased as the pressure increased and the cooling water temperature decreased (subcooling of cooling water increased). In the case of CCFL-L, CCFL characteristics in the inverted U-tube were between those in air–water and saturated steam–water experiments at 0.1 MPa. Furthermore, we derived a Wallis type CCFL correlation and its uncertainty from CCFL data, including previously measured data, i.e., J*^1/2_G + 0.88J_L*^1/2 = 0.76 ± 0.05.     

Numerical simulation using CFD software of countercurrent gas-liquid flow in a PWR hot leg under reflux condensation

In order to improve the countercurrent flow model of a transient analysis code, countercurrent air-water tests were previously conducted using a 1/15 scale model of the PWR hot leg and numerical simulations of the tests were carried out using the two-fluid model implemented in the CFD software FLUENT 6.3.26. The predicted flow patterns and CCFL characteristics agreed well with the experimental data. However, the validation of the interfacial drag correlation used in the two-fluid model was still insufficient, especially regarding the applicability to actual PWR conditions. In this study, we measured water levels and wave heights in the 1/15 scale setup to understand the characteristics of the interfacial drag, and we considered a relationship between the wave height and the interfacial drag coefficient. Numerical simulations to examine the effects of cell size and interfacial drag correlations on numerical predictions were conducted under PWR plant conditions. Wave heights strongly related with the water level and interfacial drag coefficient, which indicates that the interfacial drag force mainly consists of form drag. The cell size affected the gas velocity at the onset of flooding in the process of increasing gas flow rate. The gas volumetric fluxes at CCFL predicted using fine cells were higher than those using normal cells. On the other hand, the cell size did not have a significant influence on the process of decreasing gas flow rate. The predictions for the PWR condition using a reference set of interfacial drag correlations agreed well with the Upper Plenum Test Facility data of the PWR scale experiment in the region of medium gas volumetric fluxes. The reference interfacial drag correlations employed in this study can be applied to the PWR conditions.     

Upward vertical two-phase flow local flow regime identification using neural network techniques

Traditionally, the flow regimes in two-phase flow are considered in a global sense. However, a local flow regime is required to understand and model the interfacial structures present in the flow. In this work, a new approach has been used to identify both global and local flow regimes in a two-phase upward flow in a 50.8 mm internal diameter pipe under adiabatic conditions. In the present method, the bubble chord length distributions, which are measured simultaneously with three double-sensor conductivity probes, have been used to feed a self-organized neural network. The global flow regime identification results show a reasonable agreement with the visual observation for all the flow conditions. Nonetheless, only the local flow regimes measured at the center of the pipe agree with the global ones. The local flow regime combinations found are analyzed using the flow map information, cross-correlations between the probe signals, and previous correlations. In this way, it is possible to identify eight different global flow regime configurations.     

Single Scattering Calculations of Sky-Shine with Cylindrical Container Penetrations

Loss by deposition of aerosol particles in an air sampling pipe causes error in the estimation of aerosol concentration in the atmosphere.

For a horizontal pipe, the deposition fraction for laminar flow can be estimated by equations of deposition governed by gravity settling and diffusion. For turbulent flow, there are two methods available—one using the equation by Yoshioka et al, to express deposition velocity, the other being the “extrapolation method” proposed by the present authors.

The present paper examines the validity of the two methods, with particular reference to the contribution of gravity settling to the deposition, and the effect of roughness of the pipe wall on the deposition from turbulent flow.

The deposition fraction in a horizontal straight metal pipe can be estimated with deviation from experimental values not exceeding a factor of 2, throughout the whole region covered by the study, extending over both laminar and turbulent ranges. Use of a suitable friction factor to account for the roughness of the pipe wall gives a reasonable value of deposition fraction in the turbulent region. The deposition from turbulent flow is mainly governed by gravity settling when the Reynolds number is not very large (Re?10⁴).     

Correlation for countercurrent flow limitation in a PWR hot leg

Numerical simulations were done to evaluate countercurrent flow limitation (CCFL) characteristics in a pressurized water reactor (PWR) hot leg with the diameter of 750 mm by using a volume of fluid (VOF) method implemented in the CFD software, FLUENT6.3.26. The calculated CCFL characteristics agreed well with known values including the UPTF data at 1.5 MPa. Sensitivity analyses for system pressures up to 8 MPa showed that the calculated CCFL characteristics in the Wallis diagram were slightly mitigated from 0.1 MPa to 1.5 MPa with increasing system pressure, but they did not change from 1.5 MPa to 8MPa. Using the CCFLs calculated in this study and values measured under air–water and steam–water conditions, a CCFL correlation and its uncertainty were derived.     

Evolution of interfacial area concentration in a vertical air–water flow measured by wire–mesh sensors

An application of wire–mesh sensors to obtain the interfacial area concentration in vertical pipes is presented as an alternative to the widely used multiple-tip electrical or optical fibre probes. The measuring data of a mesh sensor consists of a three-dimensional matrix of local instantaneous gas fractions measured at each crossing point of the wires and recorded as a time sequence. Bubbles are clearly distinguishable in this data matrix, since they represent regions of interconnected elements containing the gaseous phase. The method to deduce the interfacial area concentration from this data is based on a full reconstruction of the gas–liquid interface, where the interfacial area of each bubble is recovered as the sum of the surface area of all surface elements belonging to the given bubble. The new method can be applied to large bubbles with an arbitrary shape. To study the change of the interfacial area concentration along the pipe the distance between sensor and gas injection was varied. The axial development of the interfacial area density measured in the test pipe of 195.3 mm inner diameter was compared to the measurements carried out by Sun et al. [Sun, X., Smith, T., Kim, S., Ishii, M., Uhle, J., 2002. Interfacial area of bubbly flow in a relatively large diameter pipe. Exp. Thermal Fluid Sci. 27, 97–109] in a pipe of 101.6 mm diameter, which is the largest pipe for which interfacial area densities are presented in literature. An acceptable agreement was found, whereas deviations are consistent with the differences in the boundary conditions of both experiments.     

Boiling experiments for the validation of dryout models used in reactor safety

The coolability of fragmented corium is a major issue in reactor safety. Since the long-term coolability of such particle beds is limited by the availability of coolant inside the bed and not by heat transfer limitations from the particles to the coolant, the pressure field inside the debris has a strong effect on the cooling potential in multi-dimensional cases as expected in severe accidents in light water reactors (LWR). Therefore, the determination of the pressure field for two-phase flows in porous media is one central point of interest.In this context simulation models and in particular dryout models were developed for reactor safety analyses which have to be validated by reliable experimental data. Therefore, basic experimental investigations have been carried out with inductively heated steel balls of 6 or 3 mm diameter to provide a database for the validation and modification of the friction laws included in these dryout models.The performed boiling and dryout experiments show clearly that models without the explicit consideration of the interfacial drag cannot predict the pressure distribution inside a boiling particle bed, not even qualitatively. Against it, models with an explicit consideration of the interfacial drag can describe the distribution of pressure inside a boiling particle bed.     

New explicit correlations for turbulent flow friction factor

Two new correlations of single-phase friction factor for turbulent pipe flow are shown in this paper. These two formulas are actually explicit approximations of iterative Colebrook's relation for calculation of flow friction factor. Calculated friction factors are valid for whole turbulent flow including hydraulically smooth and rough pipes with special attention on transient zone of turbulence between them. Hydraulically smooth regime of turbulence does not occur only in total absence of roughness of inner pipe surface, but also, four new relations for this theoretical regime are presented. Some recent formulas for turbulent flow friction calculation are also commented.     

Hydraulic Performance of Small Bending Radius Helical Coil-Pipe

Helical steam generator or helical heat exchanger is extensively used in high-temperature gas cooling reactor, fast breeder reactor, pressurized water reactor using in ship propulsion and areas of electro-power, chemical industry and petroleum industry. The purpose of this paper is to research the hydraulic performance of small bending radius helical coil-pipe used in HTR-10. Research for hydraulic performance of small bending radius helical pipe was carried out on the HTR-10 steam generator experimental facility. Based on the experimental results, it was confirmed that for helical pipe the critical Reynolds number (Re) is much greater than in a straight pipe and is a function of De. Formulas for Re of single-phase flow structure transition, friction coefficient of single-phase flow, and two-phase flow friction factor are obtained. Experience formulas of small bending radius helical pipe are recommended for design and research.     

Experimental study on the air/water counter-current flow limitation in a model of the hot leg of a pressurized water reactor

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 (0.25 m × 0.05 m) and 2.59 m, 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.     

Flooding in the pressurizer surge line of AP600 plant and analyses of APEX data

For the passive AP600 plant, the three stages of ADS (automatic depressurization system) valves are attached to the top of pressurizer. The existence of these valves makes liquid flow into and out of the pressurizer an important part of the dynamics during a small break loss-of-coolant accident. In this paper, counter-current flow limit (CCFL) in the surge line was analyzed. Specifically, CCFL in vertical piping, in slightly inclined horizontal piping, and in horizontal and vertical elbows were compared. The CCFL in the vertical section of the surge line was found to be the most limiting section. That is, the vertical CCFL controls the pressurizer liquid drain rate. This conclusion was tested and verified by comparing the predicted vertical CCFL against the counter-current flow states in the surge line, observed in small break LOCA tests conducted at the AP600 scaled test facility (APEX).