An experimental study on pressure drop and dryout heat flux of two-phase flow in packed beds of multi-sized and irregular particles

This paper is concerned with debris bed coolability in a postulated severe accident of light water reactors, where the debris particles are irregular and multi-sized. To obtain and verify the friction laws predicting the hydrodynamics of the debris beds, the drag characteristics of air/water single- and two-phase flow in a particulate bed packed with multi-sized spheres or irregular sand particles were investigated on the POMECO-FL test facility. The same types of particles were then loaded in the test section of the POMECO-HT facility to obtain the dryout heat fluxes of the particulate beds heated volumetrically. The effective (mean) particle diameter is 2.25 mm for the multi-sized spheres and 1.75 mm for the sand particles, determined from the Ergun equation and the measured pressure drop of single-phase flow through the packed bed. Given the effective particle diameter, both the pressure drop and the dryout heat flux of two-phase flow through the bed can be predicted by the Reed model. The experiment also shows that the bottom injection of coolant improves the dryout heat flux significantly and the first dryout position is moving upward with increasing bottom injection flowrate. Compared with top-flooding case, the dryout heat flux of the bed can be doubled if the superficial velocity of coolant injection is 0.21–0.27 mm/s. The experimental data provides insights for interpretation of debris bed coolability (how to deal with the multi-sized irregular particles), as well as high-quality data for validation of the coolability analysis models and codes.     

Gas–liquid two-phase flow in narrow horizontal annuli

Experimental data associated with the two-phase flow regimes, void fraction and pressure drop in horizontal, narrow, concentric annuli are presented. Two transparent test sections, one with inner and outer diameters of 6.6 and 8.6 mm, and an overall length of 46.0 cm; the other with 33.2 and 35.2 mm diameters and 43.0 cm length, respectively, were used. Near-atmospheric air and water constituted the gas and liquid phases, respectively. The gas and liquid superficial velocities were varied in the 0.02–57 and 0.1–6.1 m s⁻¹ ranges, respectively. The major two-phase flow patterns observed included bubbly, slug/plug, churn, stratified, and annular. Transitional regimes, where the characteristics of two distinct flow regimes could be observed in the test sections, included bubbly-plug, stratified-slug and annular-slug. The obtained flow regime maps were different than flow regime maps typical of large horizontal channels and microchannels with circular cross-sections. They were also different from the flow regimes in rectangular thin channels. The measured average void fractions for the two test sections were compared with predictions of several empirical correlations. Overall, a correlation proposed by Butterworth [Butterworth, D., 1975. A comparison of some void fraction relationships for co-current gas–liquid flow. Int. J. Multiphase Flow 1, 845–850] based on the results of Lockhart and Martinelli (1949) provided the most accurate prediction of the measured void fractions. The measured pressure drops were compared with predictions of several empirical correlations. The correlation of Friedel [Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. 3R Int. 18, 485–492] was found to provide the best overall agreement with the data.     

径向分层碎片床内流动特性研究

为研究非均质结构碎片床内的流动特性,采用两种尺寸颗粒构建了具有径向分层结构的颗粒堆积碎片床,为了对比分析,同时构建了均质结构颗粒堆积碎片床。实验研究了流体在不同堆积结构床内的流动阻力特性,并通过数值模拟揭示了流体在分层床分层界面处的流量再分配现象。研究结果表明,当流体自下而上通过碎片床时,对于均质结构颗粒堆积床,流体呈现一维流动特性;对于具有不同渗透率的径向分层床,除大部分流体自下而上通过分层床外,还存在部分流体从低渗透率层流向高渗透率层,呈现二维流动特性,且绝大部分横流仅发生在分层床的初始部分。     

Experimental characterization of the effective particle diameter of a particulate bed packed with multi-diameter spheres

This paper is concerned with uncertainty reduction in coolability analysis of a debris bed formed in fuel-coolant interactions (FCI) during a postulated severe accident of LWRs. A test facility named POMECO-FL was designed and set up to investigate the friction laws of adiabatic single and two-phase flow through particulate beds which have the characteristics of the prototypical debris bed, such as packed with particles of multiple sizes or irregular shapes. The emphasis of the present study is placed on quantification of effective particle diameter of a particulate bed composed of multi-diameter spheres. Pressure drops are measured for water/air flow through the particulate beds packed with various combinations of spheres, and the effective particle diameters of the beds are obtained based on the pressure gradients and the Ergun equation. The results show that at low flowrate (Re < 7) the effective particle diameters can be represented by the area mean diameters of the particles in the beds, while at high velocity (Re > 7) the effective particle diameters are closer to the length mean diameters. If the area mean diameters are chosen as the effective particle diameters, the frictional pressure drops of two-phase flow in the beds can be predicted by the Reed model with good agreements.     

棒束通道内定位格架的两相流动局部阻力实验研究

在常温、常压条件下,对竖直3×3棒束通道内定位格架的单相及两相局部阻力特性进行了实验研究。单相流动实验时,水雷诺数的变化范围为290~18 007;两相实验时,气相、液相表观速度变化范围分别为0.013~3.763m/s和0.076~1.792m/s。利用单相实验数据得到的定位格架局部阻力系数计算关系式,用两相实验数据对均相流模型中8种不同的两相等效黏度计算方法进行了评价。Rel9 000时,Dukler模型的预测效果最好;Rel≥9 000时,McAdams计算方法预测效果最好;基于所有数据,Dukler模型的计算值与实验值吻合最好,平均相对误差为29.03%。考虑了质量含气率、两相雷诺数及气液相密度的影响,对Rel9 000时的实验数据进行了拟合,得到的经验关系式的计算值与实验值符合较好。     

Properties of disturbance waves in vertical annular two-phase flow

Disturbance waves play an important role in interfacial transfer of mass, momentum and energy in annular two-phase flow. In spite of their importance, majority of the experimental data available in literature on disturbance wave properties such as velocity, frequency, wavelength and amplitude are limited to near atmospheric conditions (Azzopardi, B.J., 1997. Drops in annular two-phase flow. International Journal of Multiphase Flow, 23, 1-53). In view of this, air-water annular flow experiments have been conducted at three pressure conditions (1.2, 4.0 and 5.8 bar) in a tubular test section having an inside diameter 9.4 mm. At each pressure condition liquid and gas phase flow rates are varied over a large range so that the effects of density ratio, liquid flow rate and gas flow rate on disturbance wave properties can be studied systematically. A liquid film thickness is measured by two flush mounted ring shaped conductance probes located 38.1 mm apart. Disturbance wave velocity, frequency, amplitude and wavelength are estimated from the liquid film thickness measurements by following the statistical analysis methods. Parametric trends in variations of disturbance wave properties are analyzed using the non-dimensional numbers; liquid phase Reynolds number (Re_f), gas phase Reynolds number (Re_g), Weber number (We) and Strouhal number (Sr). Finally, the existing correlations available for the prediction of disturbance wave velocity and frequency are analyzed and a new, improved correlation is proposed for the prediction of disturbance wave frequency. The new correlation satisfactorily predicted the current data and the data available in literature.     

Experimental investigation of coolability behaviour of irregularly shaped particulate debris bed

In case of a severe nuclear reactor accident, the core can melt and form a particulate debris bed in the lower plenum of the reactor pressure vessel (RPV). Due to the decay heat, the particle bed, if not cooled properly, can cause failure of the RPV. In order to avoid further propagation of the accident, complete coolability of the debris bed is necessary. For that, understanding of various phenomena taking place during the quenching is important. In the frame of the reactor safety research, fundamental experiments on the coolability of debris beds are carried out at IKE with the test facility “DEBRIS”. In the present paper, the boiling and dry-out experimental results on a particle bed with irregularly shaped particles mixed with stainless steel balls have been reported. The pressure drops and dry-out heat fluxes of the irregular-particle bed are very similar to those for the single-sized 3 mm spheres bed, despite the fact that the irregular-particle bed is composed of particles with equivalent diameters ranging from 2 to 10 mm. Under top-flooding conditions, the pressure gradients are all smaller than the hydrostatic pressure gradient of water, indicating an important role of the counter-current interfacial drag force. For bottom-flooding with a liquid inflow velocity higher than about 2.7 mm/s, the pressure gradient generally increases consistently with the vapour velocity and the fluid-particle drag becomes important. The system pressures (1 and 3 bar) have negligible effects on qualitative behaviour of the pressure gradients. The coolability of debris beds is mainly limited by the counter-current flooding limit (CCFL) even under bottom-flooding conditions with low flow rates. The system pressure and the flow rate are found to have a distinct effect on the dry-out heat flux.Different classical models have been used to predict the pressure drop characteristics and the dry-out heat flux (DHF). Comparisons are made among the models and experimental results for DHF and pressure drop characteristics. Considering the overall trend in prediction of DHF and two-phase pressure drop, it was observed that none of the models could provide accurate predictions for both DHF and pressure drop under top- and bottom-flooding conditions. This implies that developments of more accurate models are needed including the effects of non-uniform particle sizes and the multidimensional nature of particulate debris beds, which are not reflected so far in these models.     

Two-phase flow resistance in flexible metal hoses

This study presents the two-phase flow resistance, hence the friction factor and the pressure drop for air–water mixture flowing in flexible metal hoses. Experiments were performed under the following conditions of two-phase parameters; mass flux from 200 to 1150 kg/m² s, gas quality from 1 to 60% and system pressure from 3 to 10 bar. The inner diameters of the tested hoses were 25, 40, 50 and 65 mm with a ratio of ridge depth to inner diameter (r/d) from 0.02 to 0.1 and a ratio of pitch to inner diameter (p/d) from 0.06 to 0.3. The results demonstrate that the two-phase flow resistance, energy dissipation and friction losses in flexible metal hoses are perceptible greater than that in pipes. Therefore, the two-phase pressure drops of the hoses are two to five times greater than that in smooth pipes. The two-phase friction factor of such hoses increased from 0.035 up to 0.2 in dependence on the influencing flow and geometrical parameters. Based on the energy balance and the presented experimental results, a new model has been developed to calculate the two-phase pressure drops and hence the friction factor of flexible metal hoses. The model includes the relevant primary parameters, fit the data well and is sufficiently accurate for engineering purposes. The results reported enable practical designs with standard products and optimization of the hose geometry for specific conditions.     

Pressure Drop Experiments using Tight-Lattice 37-Rod Bundles

In order to design a Reduced-Moderation Water Reactor (RMWR) core from a thermal-hydraulic point of view, an evaluation method on the pressure drop in a tight-lattice rod bundle is required. In this study, axial pressure drops in tight-lattice 37-rod bundles were measured under conditions of 2-9 MPa in exit pressure and 200-1,000 kg/(m²·s) in mass velocity. The measured pressure drops were compared with calculated ones by the evaluation method with the Martinelli-Nelson's correlation. The comparison shows that a single-phase friction factor can be applied not only to a circular tube but also to a tight-lattice bundle except for an extremely small gap width. Then two-phase friction loss is a dominant component and accounts for about 60% of the pressure drop under an RMWR nominal operating condition. The evaluation method can evaluate effects of the flow area configuration (rod number, rod diameter, gap width) and axial power distribution under a wide range of flow conditions, and it can yield a good prediction of the pressure drop in a tight-lattice bundle.     

Scaling of two-phase flow transients using reduced pressure system and simulant fluid

Scaling criteria for a natural circulation loop under single-phase and two-phase flow conditions are derived. Based on these criteria, practical applications for designing a scaled-down model are considered. Particular emphasis is placed on scaling a test model at reduced pressure levels compared to a prototype and on fluid-to-fluid scaling. The large number of similarity groups which are to be matched between model and prototype makes the design of a scale model a challenging task. The present study demonstrates a new approach to this classical problem using two-phase flow scaling parameters. It indicates that a real time scaling is not a practical solution and a scaled-down model should have an accelerated (shortened) time scale. An important result is the proposed new scaling methodology for simulating pressure transients. It is obtained by considering the changes of the fluid property groups which appear within the two-phase similarity parameters and the single-phase to two-phase flow transition parameters.Sample calculations are performed for modeling two-phase flow transients of a high-pressure water system by a low-pressure water system or a Freon system. It is shown that modeling is possible for both cases for simulating pressure transients. However, simulation of phase change transitions is not possible by a reduced pressure water system without distortion in either power or time.     

Steady-state performances and scaling analyses for an open flashing-driven natural circulation system

Simulating investigations are carried out to study the steady-state performances, the pressure resistance distributions and the scaling methods of the single-phase and flashing-induced two-phase flow in the open natural circulation system, which is designed for the passive containment cooling system. The results show that the steady-state mass flow rate changes with the heat transfer regularly both in the single-phase and flashing-induced two-phase flow under a certain inlet subcooling. From the sensitivity analysis, it can be found that the riser height only has impact on the single-phase flow but has little influence on the flashing-driven two-phase flow. Both increasing the diameters of the riser and downcomer can enhance the flow and heat transfer in sing-phase and two-phase flow when keeping the structure of the heat exchanger unchanged, but the influence degree for each flow type is different. The flow resistance distributions of the loops under different flow modes have been studied to provide the foundation for improving the heat transfer capacity by choosing the structural parameters reasonably. The pressure resistance distribution of the steady single-phase flow only relates to the geometrical, but the pressure resistance distribution of the two-phase flow relates both to the pipe diameters and to the external conditions. The acceleration pressure resistance in the riser section is the main resistance under the higher-quality two-phase conditions. Therefore, the influence of the riser diameter on the flashing-induced two-phase flow is far greater than that of downcomer diameter and the most effective method to improve the two-phase flow and heat transfer is to increase the diameter of the riser. Finally, the scaling analysis is performed for the penetration and economy considerations after selecting the optimal dimensions. The scaling of the cold and hot sections is considered separately to insure the driven force of the system unchanged, and different scaling criterions are given for the single-phase and flashing-induced two-phase flow according to the analyses of the pressure resistance distributions. The results show that the scaling criterion of the two-phase flow can deal with the scaling problem accurately both in the single-phase and two-phase flow. However, the scaling criterion of the single-phase flow only can solve the single-phase scaling problem, but it will overestimate the operating results in the scaling model.     

Critical heat flux and flow pattern for water flow in annular geometry

An experimental study on critical heat flux (CHF) and two-phase flow visualization has been performed for water flow in internally-heated, vertical, concentric annuli under near atmospheric pressure. Tests have been done under stable forced-circulation, upward and downward flow conditions with three test sections of relatively large gap widths (heated LENGTH = 0.6 m, inner DIAMETER = 19 mm, outer DIAMETER = 29, 35 and 51 mm). The outer wall of the test section was made up of the transparent Pyrex tube to allow the observation of flow patterns near the CHF occurrence. The CHF mechanism was changed in the order of flooding, churn-to-annular flow transition and local dryout under a large bubble in churn flow as the flow rate was increased from zero to higher values. Observed parametric trends are consistent with the previous understanding except that the CHF for downward flow is considerably lower than that for the upward flow. In addition to the experiment, selected CHF correlations for annuli are assessed based on 1156 experimental data from various sources. The Doerffer et al. (1994); Barnett (1966); Jannsen and Kervinen (1963); Levitan and Lantsman (1977) correlations show reasonable predictions for wide parameter ranges, among which the Doerffer et al. (1994) correlation shows the widest parameter ranges and a possibility of further improvement. However, there is no correlation predicting the low-pressure, low-flow CHF satisfactorily.     

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.     

矩形通道高宽比对两相流动阻力和流型关系的影响

在可视化观察的基础上,实验研究了矩形通道高宽比对两相流动阻力和流型关系的影响。实验选择了3种通道尺寸的实验段,截面宽度相同,全部为43 mm,高度分别为1.41、3和10 mm,根据受限因子C_o,前两个实验段属于窄通道,第3个属于常规通道。实验结果表明：高宽比不同时,随着气相流速的增加,通道内两相流动压降呈不同的变化趋势。对于10 mm通道,低气相流量时重位压降占主要成分,而对于1.41 mm和3 mm通道,摩擦压降占主要成分;随着气相流量的增大,总压降中摩擦压降的比例也增大;对于10 mm矩形通道,可利用压降变化规律确定搅混流的发生范围。     

Flow excursion instability in downward flow systems: Part I. Single-phase instability

A procedure for predicting the onset of flow excursion instability in downward flows at low-pressure and low-flow conditions without boiling is presented. It is generally accepted that the onset of significant void in subcooled boiling precedes, and is a precondition to, the occurrence of static flow instability. A detailed analysis of the pressure drop components for a downward flow in a heated channel reveals the possibility of unstable transition from single-phase flow to high-quality two-phase flow, i.e. flow excursion. Low flow rate and high subcooling are the two important conditions for the occurrence of this type of instability. The unstable transition occurs when the resistance to the downward flow caused by local (orifice), frictional, and thermal expansion pressure drops equalizes the driving force of the gravitational pressure drop. The inclusion of the thermal expansion pressure drop is essential to account for this type of transition. Experimental data have still to be produced to verify the prediction of the present analysis.     

Experimental measurement of frictional law under CCFL in porous debris

Counter-current flow limitation (CCFL) is the dominant phenomena for dryout in porous debris, which would be formed during a severe accident of a nuclear power plant. Since flow at CCFL in porous debris is far away from normal two-phase flow in a pipe, it is not clear whether the interfacial friction laws in a pipe can be applied to the CCFL in porous debris. In the present experimental research, the void fraction in porous debris is measured simultaneously with the differential pressure and flow rates for gas and liquid. The combination of these simultaneously measured data makes it possible to estimate the shear stresses and friction factors in a porous debris at CCFL. It results that the wall friction factor estimated is larger than the Ergun equation proposed for single-phase flow in a porous bed. Furthermore, the interfacial friction factor estimated is well correlated by the theoretical correlation derived here from a force balance for a hypothetical flow channel in porous debris at CCFL.     

Pressure drops for steam and water flow in heated tubes

Measurements of pressure drop for a steam and water flow inside several heated tubes were obtained at two different laboratories (Chalk River Laboratories and École Polytechnique). The test sections used to carry out the experiments were constructed with Inconel-600 tubes, and were cooled internally with an upward flow of water. A reduction in frictional pressure gradient with an increase in heat flux was observed for single-phase flows at the same cross-sectional-average conditions. After boiling was initiated, the two-phase friction multiplier increased with increasing heat flux in the bubbly-flow region, but decreased in the annular-flow region. As the heated surface approached dryout, the two-phase friction multiplier exhibited a maximum value and decreased with increasing thermodynamic quality, until dryout occurred. The decreasing trend was attributed to a reduction in the liquid-film thickness and the termination of liquid entrainment. Following the occurrence of critical heat flux, a significant drop in frictional pressure gradient was noted, caused by the change in the near-wall sublayer to a low-viscosity vapor blanket.     

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%.     

Structure of air–water two-phase flow in helically coiled tubes

Air–water two-phase flow in helically coiled tubes is investigated experimentally to elucidate the effects of centrifugal acceleration on the flow regime map and the spatial and the temporal flow structure distribution. Three kinds of test tubes with 20 mm inner diameters including a straight tube are used to compare the turbulent flow structure. Superficial velocities up to 6 m/s are tested so that the centrifugal Froude number covers a range from 0 to 3. The interfacial structure is photographed from two directions by a high-speed video system with synchronized measurement of local pressure fluctuations. The results reveal that the flow transition line alters due to centrifugal force acting on the liquid phase in the tube. In particular, the bubbly flow regime is narrowed significantly. The pressure fluctuation amplitude gets large relatively to the average pressure loss as void fraction increases. The frequency spectra of the pressure fluctuation have plural peaks in the case of strong curvature, implying that the periodicity of slugging two-phase flow is collapsed by an internal secondary flow activated inside the liquid phase. Moreover, under large Froude number conditions, the substantial velocity of the gas phase that biases to the inner side of the helical coil is slower than the total superficial velocity because the liquid flow is allowed to pass through the outer side and so resembles a radial stratified flow.     

Fluorination of UF4 in a mini-tapered fluidized bed and mathematical modeling

A mini-tapered fluidized bed reactor can be used for fluorination reaction of UF₄ to produce uranium hexafluoride. By adopting the mini-tapered bed the problems associated with fluidization in a cylindrical bed such as entrainment of particles and the limitation of operating velocity can be overcome, consequently the performance of the reactor can be enhanced. Simulation of the reactor was performed employing two-phase models, bubble phase with piston flow and emulsion phase with piston (D.P-P model) or perfectly mixed flow (D.P-M model). The voidage of the emulsion and bubble phases were estimated from the distribution two-phase structure hydrodynamic model. The model predictions have been compared with the results from a pilot-scale experiment. The D.P-P model gives good agreement between computed and empirical results. The effects of various parameters on the reactor performance are discussed using the model.