Effects of fluid properties on CCFL characteristics at a vertical pipe lower end

The purpose of this study is to derive a counter-current flow limitation (CCFL) correlation and evaluate its uncertainty for steam generator (SG) U-tubes in a pressurized water reactor (PWR). Experiments were conducted to evaluate effects of the liquid viscosity on CCFL characteristics using air–40 wt% or air–60 wt% glycerol water solution and saturated steam–water at atmospheric pressure with vertical pipes simulating the lower part of the SG U-tubes. The steam–water experiments confirmed that CCFL characteristics could be expressed in terms of the Wallis parameters (J_G* and J_L*) for the pipe diameters of D = 14, 20, and 27 mm. A CCFL correlation was derived using the ratio μ_G/μ_L of the viscosities of the gas and liquid phases, μ_G and μ_L, as a correction term representing effects of fluid properties, where J_G^*1/2(μ_G/μ_L)^?0.07 was expressed by a cubic function of J_L^*1/2(μ_G/μ_L)^0.1. In the correlation, the constant C indicating the value of J_G^*1/2(μ_G/μ_L)^?0.07 at J_L* = 0 was (1.04 ± 0.05), and this uncertainty of ±0.05 would cover most of the previous experimental data including the ROSA-IV/LSTF data at 1, 3, and 7 MPa.     

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.     

Natural convection heat transfer from horizontal rod bundles in liquid sodium. Part 1: Correlations for two parallel horizontal cylinders based on experimental and theoretical results

Natural convection heat transfer coefficients on two parallel horizontal test cylinders in liquid sodium were obtained experimentally and theoretically for various setting angles, γ, between vertical direction and the plane including both of these cylinders’ axes, over the range of 0°–90°. Both test cylinders are 7.6 mm in diameter and 50 mm in heated length with the ratio of the distance between each cylinder axis to the cylinder diameter, S/D, of 2. Theoretical equations for laminar natural convection heat transfer from the two horizontal cylinders were numerically solved for the same conditions as the experimental ones. The average Nusselt numbers Nu on the cylinders obtained experimentally were compared with the corresponding theoretical values on the Nu versus modified Rayleigh number R_f [= Gr*Pr²/(4?+?9Pr^1/2?+ 10Pr)] graph. The experimental values of Nu for the upper cylinder are about 20% lower than those for the lower cylinder at γ = 0° for the range of R_f tested here. The value of Nu for the upper cylinder becomes higher and approaches that for the lower cylinder with the increase in γ over the range of 0°–90°: the values for each cylinder agree with each other at γ = 90°. The values of Nu for the lower cylinder at each γ are almost in agreement with those for a single cylinder. The theoretical values of Nu on two cylinders except those for R_f < 4 at γ = 0° are in agreement with the experimental data at each γ with the deviations less than 15%. Correlations for two cylinders were obtained as functions of S/D and γ based on the theoretical solutions. A combined correlation for multi-cylinders in a vertical array based on the correlations for two cylinders was developed. The values by the correlation agree with the theoretical solution for the multi-cylinders for R_f ranging from 4.7 to 63 within 10% difference.     

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.     

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%.     

Study of countercurrent flow limitation in a horizontal pipe connected to an inclined one

Experiments with air and water in small hot leg reproductions were carried out aiming to acquire a better understanding of the countercurrent flow limitation (CCFL) in this geometry. The effects of various geometrical parameters of the test section and of the inlet water flow rate on the onset of flooding, on the partial delivery of water and on the zero liquid penetration were investigated. It was observed that while the onset of flooding is affected by the inlet water flow rate, the zero liquid penetration is independent of this flow rate. The results with partial delivery showed that, for a fixed air velocity, an increase in the horizontal length, or in the inclined length, of the flow channel leads to an increase of the water carried over by the air. On the other hand, in pipes with larger diameters the drag of the water is smaller. The experimental results showed small differences in the results for tests with inclination of the riser lower than 90°. For an inclination equal to 90°, the water carried by the air tends to be lower than in the others angles for a fixed air velocity. The study led also to a new correlation for the flooding.     

The Effect of Vibration on Critical Heat Flux in a Vertical Round Tube

This paper deals with the results of experimental investigations on the effects of tube vibration on critical heat flux (CHF) in order to gain an understanding of the relationship between CHF and flow-induced vibration (FIV). The experiment was carried out in the following range of parameters: diameter (D)=0.008 m; heated length (L)=0.2, 0.4 m; pressure (P)=101 kPa; mass flux (G)=403–2,551 kg/m².s; quality (x)=-0.045–0.289; amplitude (a)=0.0001–0.001 m; frequency (f)=0–70Hz. The CHF generally increases with vibration intensity, which is represented by vibrational Reynolds number (Re _v ); the CHF enhancement is more dependent on amplitude than on frequency. CHF enhancement seems to come from the reinforced flow turbulent mixing effect by vibration in the vicinity of heat transfer surface. Based on the experimental results, an empirical correlation is proposed for the prediction of CHF enhancement by tube vibration. The correlation predicts the CHF enhancement ratio (En) with reasonable accuracy, with an average error rate of -2.18% and 27.75% for RMS.     

Natural convection heat transfer from horizontal rod bundles in liquid sodium. Part 2: Correlations for horizontal rod bundles based on theoretical results

Natural convection heat transfer from horizontal rod bundles in N_xm × N_ym arrays (N_xm, N_ym = 5–9) in liquid sodium was numerically analyzed for three types of the bundle geometry (in-line rows, staggered rows I and II). The unsteady laminar two-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady state. The PHOENICS code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, R_f, ranging from 0.0637 to 63.1 (q = 1×10⁴ to 7×10⁶ W/m²). S_x/D and S_y/D for the rod bundle, which are the ratios of the distance between center axes on the abscissa and the ordinate to the rod diameter, respectively, were ranged from 1.6 to 2.5 on each bundle geometry. The spatial distribution of Nusselt numbers, Nu, on horizontal rods of a bundle was clarified. The average value of Nusselt number, Nu_av, for three types of bundle geometry with various values of S_x/D and S_y/D were calculated to examine the effect of the array size, S/D and R_f on heat transfer. The bundle geometry for the higher Nu_av value under the condition of S_x/D×S_y/D = 4 was examined by changing the ratio of S_x/S_y. A correlation for Nu_av for the three types of bundle geometry above mentioned including the effects of S_x/D and S_y/D was developed. The correlation can describe the theoretical values of Nu_av for the three types of bundle geometry in N_xm × N_ym arrays (N_xm, N_ym = 5–9) for S_x/D and S_y/D ranging from 1.6 to 2.5 within 10% difference.     

Effect of steam condensation on countercurrent flow limiting in nearly horizontal two-phase flow

An analytical model that includes the steam condensation effect has been derived and a parametric study has been performed. In addition, a series of experiments were performed and a total of 34 experimental data for the onset of countercurrent flow limiting (CCFL) in nearly horizontal countercurrent two-phase flow have been obtained for various flow rates of water. Comparisons of the present CCFL data with slug formation models show that the agreement between the present as well as the existing model and the data is about the same. However, the deviation between Taitel and Dukler’s model predictions and the data is the largest when j_f<0.04 m s⁻¹. A parametric study of the effect of condensation using the present model shows that, when all local conditions are similar, the model predicted local gas velocities that cause the onset of flooding are slightly lower when condensation occurred. Based on the visual observation and the evaluation of the present work, it has been concluded that the criterion derived for the onset of slug flow can be directly used to predict the onset of inner flooding in nearly horizontal two-phase flow within the experimental ranges of the present work.     

Numerical Analysis of Pressure Effects on Heavy Water Separation Characteristics for a Pair of Dual Temperature Multistage-Type H2/H2O-Exchange Columns

In order to study how the operating pressure has influence on the heavy water separation characteristics for a pair of dual temperature multistage-type H₂/H₂O-exchange columns, the authors utilized the analytical expressions derived from the finite difference equation describing the material balance in the exchange column. The separation characteristics of the system were studied theoretically under the conditions where the temperature in a hot column t_h=200°C, the pressure in a hot column π≦50atm and the pressure in a cold column π = 5–50atm.

As the results, the optimum modified specific column volume v^*_opt decreases with the increase of π and then keeps the nearly constant value, and is smaller at ≦=50atm than at ≦=30atm in the case where the temperature in a cold column t_c is constant. Other important parameters such as the optimum operating temperature in a cold column t_copt the optimum numbers of stages in a hot column M_opt and in a cold column t_opt, the optimum hydrogen to feed water molar flow ratio γ _opt and the optimum degradation ratio δ_opt were also calculated.     

Theoretical study of the adsorption of Cs,Cs+, I,I−, and CsI on C60 fullerene

Theoretical investigation for the adsorption of the cesium atom (Cs), the cesium iodide molecule (CsI), the iodine atom (I), the cesium cation (Cs⁺), and the iodide anion (I^?) onto the surface of a single fullerene molecule (C₆₀) are reported. A hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) is employed. The adsorption energies, i.e., the opposite of enthalpy change through adsorption, are calculated to be 143, 12, 9, 46, and 49 kJ mol^?1 for Cs, CsI, I, Cs⁺, and I^?, respectively. The equilibrium constant for Cs is calculated to be 7×10³ atm^?1 at the temperature of 1000 K and is seven orders of magnitude higher than that for CsI, indicating that the C₆₀ molecule adsorb the Cs atom highly selectively against the CsI molecule.     

Experimental Study on Gas Carry-Under in Liquid Down Flow from a Two-Phase Mixture

The gas carry-under characteristics in liquid down flow from a two-phase mixture flow have been studied for various flow parameters, based on experiments with a small scale air- water system simulating the concept of a natural circulation BWR with no separators. For high void fraction in the riser, as the liquid superficial velocity jf increased to 0.17 m/s, the void fraction in the lower part of the downcomer αd increased sharply due to the descent of comparatively large bubbles (diameter: about 4–6mm). In the region of jf> 0.17m/s, on increasing jf, the void fraction αd increased until it reached a maximum value at jf.3. For liquid descending velocities higher than 0.3 m/s, αd became almost constant and the level of the mixture above the riser had little effect on the void fraction ad due to the phase separation of the large bubbles formed by bubble coalescence in the upper part of the downcomer. The void fraction αd increased as the void fraction αr increased until bubble coalescence occurred in the upper part of the downcomer, and αd became constant and independent of αr after the occurrence of bubble coalescence. Under the conditions of high void fractions in the riser, 0.4<αr<0.64 (upper limit of the tests), and high liquid descending velocities in the down-comer, 0.3 m/s<jf.<0.4 m/s (upper limit of the tests), the void fraction αd was represented by a dimensionless number (G = η⁴ g/σ³ pf) and by the upper limit of void fractions in bubbly flow, αd=0.3.     

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

This paper replaces the paper published in the journal by Deendarlianto et al. (2008). Because of an error in the implementation of the air flow meter some of the data given by Deendarlianto et al. (2008) 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 (0.25 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. 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.     

In-Pile and Out-of-Pile Grain Growth Behavior of Sintered UO2 and (U,Gd)O2 Pellets

Grain growth behavior of UO₂ and (U, Gd)O₂ fuel pellets was investigated with the data from the out-of-pile isothermal heating experiments and the irradiation test at the Halden Boiling Water Reactor. The laboratory data gave best-fitted equations by employing the following fourth power rate equations :

UO₂ : D²-D⁴ ₀=3.79×10¹⁸ exp(-142,000/RT)t,

(U, Gd) : D²-D⁴ ₀=4.98×10¹⁷ exp(-140,000/RT)t,

where, D ₀ and D are initial and final three-dimensional diameters (μm), respectively, R the gas constant (=1.987 cal/mole/K), T the absolute temperature (K) and t the time (h) (gadolinia content: 3~10%, temperature range: 1,700~2,000°C).

The calculated grain diameter with the above equations revealed an overestimation on specimens which involved noticeable fission gas bubbles on their grain boundaries. It was demonstrated that the in-pile grain growth model, as was given in the following equation, which took account of the retarding effects of growth by precipitated intergranular bubbles could describe the grain growth of the irradiated samples :

where f: Grain boundary fractional coverage (-).     

Applications of Artificial Neural Network for the Prediction of Flow Boiling Curves

An artificial neural network (ANN) was applied successfully to predict flow boiling curves. The databases used in the analysis are from the 1960's, including 1,305 data points which cover these parameter ranges: pressure P=100–1,000 kPa, mass flow rate G=40–500 kg/m²-s, inlet subcooling ΔT_sub =0–35°C, wall superheat ΔT_w = 10–300°C and heat flux Q=20–8,000kW/m². The proposed methodology allows us to achieve accurate results, thus it is suitable for the processing of the boiling curve data. The effects of the main parameters on flow boiling curves were analyzed using the ANN. The heat flux increases with increasing inlet subcooling for all heat transfer modes. Mass flow rate has no significant effects on nucleate boiling curves. The transition boiling and film boiling heat fluxes will increase with an increase in the mass flow rate. Pressure plays a predominant role and improves heat transfer in all boiling regions except the film boiling region. There are slight differences between the steady and the transient boiling curves in all boiling regions except the nucleate region. The transient boiling curve lies below the corresponding steady boiling curve.     

A Nuclear Magnetic Resonance Study on Ligand Exchange Reactions in La(III), Nd(III), and U(VI) Nitrato Complexes with n-Octyl(pheny1)-N,N-Diisobutylcarbamoylmethylphosphine Oxide in Non-aqueous Solvents

The exchange reactions of n-octyl(pheny1)-N, N-diisobutylcarbamoylmethylphosphine oxide (CMPO) in La(III), Nd(III), and U(VI) nitrate complexes with CMPO (La(III)-, Nd(III)-, and U(VI)-CMPO complexes) have been studied in CD₃COCD₃ by means of ³¹P NMR method. The number of CMPO coordinated to the first coordination sphere of La(III) ion was directly determined to be 3 by the area integrations of ³¹P NMR signals of free and coordinated CMPO molecules. The same coordination number of 3 was also obtained for the U(VI)-CMPO complex. The coordination number was not determined for the Nd(III)-CMPO complex, because of its paramagnetic behavior. The exchange rate constants of CMPO in La(III)- and U(VI)- CMPO complexes were obtained by the two-site exchange model. Paramagnetic line broadening was observed in the Nd(III)-CMPO complex and the rate constant for the exchange of CMPO was determined by the line-broadening method. The exchange rates of CMPO in La(III)- and Nd(III)-CMPO complexes depend on the free CMPO concentration ([CMPO]), while that in U(VI)-CMPO complex is independent of [CMPO]. The dissociative (D) and dissociative interchange (I_d ) mechanisms were proposed for the exchange reactions in the La(III)- and Nd(III)-CMPO complexes, and dissociative (D) or I_d mechanism was proposed for the U(VI)-CMPO complex. The dissociative rate constants (s^?1) at 25°C and activation parameters ΔH^# (kJ·mol^?1) and ΔS^# (J·K^?1·mol^?1) are 4.76x10³, 28.7±0.1, ?78.4±0.2 for La(III)-CMPO complex, 4.72x10³, 42.6±0.4, ?31.7±1.3 for Nd(III)-CMPO complex, and 3.20x10³, 46.9±0.6, ?20.5±2.2 for U(VI)-CMPO complex, respectively.     

The analysis of CCFL using drift-flux models

Counter-current flow limited (CCFL) situations can be analyzed using one-dimensional drift-flux techniques. Indeed such techniques can be used to prove that CCFL conditions occur at the point of kinematic ‘choking.’ This paper derives drift-flux parameters (C₀ and V_gj) which automatically predict CCFL conditions. These parameters are applied to the special case of simulated inlet flow blockage, and are shown to accurately predict internal flooding.     

Lattice Parameters of Mixed Oxides in Sm-U-O System

The oxidation-reduction properties of mixed oxides in the system Sm-U-O and the variation of their lattice parameters due to oxidation and reduction were examined by means of thermogravimetry and X-ray diffraction. For mixed oxides Sm_yU_1-yO_2±x prepared in air, the O/M ratio decreased linearly from 2.667 at y= 0 to nearly stoichiometric 2.02 at y=0.5. The 0/M ratios at y>0.5 were on the line connecting 2.667 at y= 0 with 1.50 at y =1. The single phase region of the fluorite structure was between y = 0.5 and 0.6. The lattice parameters of the fluorite phase at ≤0.6 were constant, 5.418×10^?10m. For mixed oxides prepared in hydrogen, the 0/M ratio decreased linearly from 2.00 at y = 0 to 1.84 at y = 0.5, and from 1.84 at y = 0.5 to 1.50 at y = 1. The quenched oxides were single phase compounds except those for y = 0.1, 0.6 and 0.9. The lattice parameter of the fluorite structure decreased from 5.4700 at y = 0 to 5.427 × 10^?10 m of Smo.₄U0.6O_1.854. and was kept constant between y = 0.4 and 0.5, then increased to 5.466 × m at y = 0.7. The Sm-U-O phase diagram at 1,000°C was constructed on the basis of the X-ray diffraction work.     

反应堆失水事故条件下热管段内的两相流逆向流动研究

对反应堆失水事故条件下热管段内的两相流逆向流动过程进行了实验研究和理论分析。实验回路由竖直管、倾斜管和水平管三段组成 ,研究发现在这种回路中水平管的长度对逆向流动的溢流开始点影响较大。对逆向流动的溢流开始点进行了实验研究和理论分析 ,对现有的国外计算模型进行了分析和比较 ,推荐了热管段内溢流开始点的计算关系式。     

Droplet entrainment correlation in vertical upward co-current annular two-phase flow

Upward annular two-phase flow in a vertical tube is characterized by the presence of liquid film on the tube wall and entrained droplet laden gas phase flowing through the tube core. Entrainment fraction in annular flow is defined as a fraction of the total liquid flow flowing in the form of droplets through the central gas core. Its prediction is important for the estimation of pressure drop and dryout in annular flow. In the following study, measurements of entrainment fraction have been obtained in vertical upward co-current air–water annular flow covering wide ranges of pressure and flow conditions. Comparison of the experimental data with the existing entrainment fraction prediction correlations revealed their inadequacies in simulating the trends observed under high flow and high pressure conditions. Furthermore, several correlations available in the literature are implicit and require iterative calculations.Analysis of the experimental data showed that the non-dimensional numbers, Weber number (We = ρ_gj_g²D/σ(Δρ/ρ_g)^1/4) and liquid phase Reynolds number (Re_f = ρ_fj_fD/μ_f), successfully collapse the data. In view of this, simple, explicit correlation was developed based on these non-dimensional numbers for the prediction of entrainment fraction. The new correlation successfully predicted the trends under the high flow and high pressure conditions observed in the current experimental data and the data available in open literature. However, in order to use the proposed correlation it is necessary to predict the maximum possible entrainment fraction (or limiting entrainment fraction). In the current analysis, an experimental data based correlation was used for this purpose. However, a better model or correlation is necessary for the maximum possible entrainment fraction. A theoretical discussion on the mechanism and modeling of the maximum possible entrainment fraction condition is presented.