Flow structure and bubble characteristics of steam–water two-phase flow in a large-diameter pipe

The flow structure and bubble characteristics of steam–water two-phase upward flow were observed in a vertical pipe 155 mm in inner diameter. Experiments were conducted under volumetric flux conditions of J_G<0.25 m s⁻¹ and J_L<0.6 m s⁻¹, and three different inlet boundary conditions to investigate the developing state of the flow. The radial distributions of flow structure, such as void fraction, bubble chord length and gas velocity, were obtained by horizontally traversing optical dual void probes through the pipe. The spectra of bubble chord length and gas velocity were also obtained to study the characteristics of bubbles in detail. Overall, an empirical database of the multi-dimensional flow structure of two-phase flow in a large-diameter pipe was obtained. The void profiles converged to a so-called core-shaped distribution and the flow reached a quasi-developed state within a relatively short height-to-diameter aspect ratio of about H/D=4 compared to a small-diameter pipe flow. The PDF histogram profiles of bubble chord length and gas velocity could be approximated fairly well by a model function using a gamma distribution and log–normal distribution, respectively. Finally, the correlation of Sauter mean bubble diameter was derived as a function of local void fraction, pressure, surface tension and density. With this correlation, cross sectional averaged bubble diameter was predicted with high accuracy compared to the existing constitutive equation mainly being used in best-estimate codes.     

Some problems for bundle CHF prediction based on CHF measurements in simple flow geometries

A comparison of critical heat flux (CHF) fuel bundles data with CHF data obtained in simple flow geometries was made. The base for the comparison was primary experimental data obtained in annular, circular, rectangular, triangular, and dumb-bell shaped channels cooled with water and R-134a. The investigated range of flow parameters (pressure, mass flux, and critical quality) in R-134a was chosen to be equivalent to modern nuclear reactor water flow conditions (p=7 and 10 MPa, G=350–5000 kg (m² s)⁻¹, x_cr=−0.1–1). The proper scaling laws were applied to convert the data from water to R-134a equivalent conditions and vise versa. The effects of flow parameters (p, G, x_cr) and the effects of geometric parameters (D, L) were evaluated during comparison. The comparison showed that no one simple flow geometry can be used for accurate and reliable bundle CHF prediction in wide range of flow parameters based on local (critical) conditions approach. The comparison also showed that the limiting critical quality phenomenon is unique characteristic for each flow geometry which depends on many factors: flow conditions (pressure and mass flux), geometrical parameters (diameter or surface curvature, gap size, etc.), flow obstructions (spacers, appendages, turbulizers, etc.) and others.     

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.     

Light and heavy water dynamic structure factor for neutron transport codes

In this study, we report on recent neutron inelastic scattering experiments performed at the Institut Laue-Langevin (ILL) for H₂O and D₂O. The measured dynamic structure factors S(q, ω) have been reduced, normalised and transformed into the S(α, β) formalism, where α and β stand for the unit-less momentum and energy transfers, respectively. The measurements were complemented with molecular dynamics simulations. After processing with NJOY, new water neutron scattering cross-sections have been generated for use with e.g. the Monte Carlo N-Particle (MCNP) software in view to improve the accuracy of the nuclear facility models. As an example, we present improved accuracy calculations for the safety rod insertion impact on the criticality factor k_eff for the ILL high flux research reactor.     

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.     

Basic Studies on Two-Phase Flow with the Use of Electrical Void-Meter

Further basic knowledge has been gained on the behavior of two-phase flow through the following experiments. An electrical void-meter based on transducement of void fraction into impedance is employed to measure the void distribution along a heater in an annular channel.

Experiments have further been conducted on the “velocity slip ratio (V_g/V₁)” to correlate the void-fraction (R_g,) with the volume flow rate ratio (F_g). The resulting equation takes the form R_g= 0.92-F_g and the ratio V_g/V_g= 1.08, for slug flow in a vertical pipe.

Statistical methods have been applied in analyzing the two-phase flow. It is shown that the speed of voids in a two-phase flow can be determined with a cross-correlation function calculated from two time series of void-fraction fluctuation measured at two points along the channel.     

Structure of Flow Fields in Low Pressure Impactor

In order to clarify the detailed flow fields of impinging jets in a low pressure impactor, nitrogen and argon flow fields are investigated experimentally and numerically at a relatively small range of P _down/P _up, where P _down is the downstream stagnation pressure and P _up the upstream stagnation pressure. The pressure at the center of collection plate, P _c, is measured in addition to the flow visualization by Laser Induced Fluorescence (LIF) technique, which is used in previous study. Furthermore, the flow fields in a low pressure impactor have been simulated by solving the axisymmetric Euler equation through Harten-Yee TVD method. The effects of P _down/P _up and H/D on flow fields are examined in detail, where H is the jet-to-plate distance and D the nozzle diameter. The calculated shock wave position on jet axis and the pressure at the center of collection plate are in reasonable agreement with the experimental results. It is found that the structure of flow fields changes drastically at a certain value of P _down/P _up and there exist hysteresis phenomena in the relationship between the value of P _c/P _up and that of P _dowb/P _up for both gases. The formation of the separation bubble at a certain value of H/D is discussed.     

Analytical prediction of friction factors and Nusselt numbers of turbulent forced convection in rod bundles with smooth and rough surfaces

A simple analytical method was developed for the prediction of the friction factor, f, of fully developed turbulent flow and the Nusselt number, Nu, of fully developed turbulent forced convection in rod bundles arranged in square or hexagonal arrays. The friction factor equation for smooth rod bundles was presented in a form similar to the friction factor equation for turbulent flow in a circular pipe. An explicit equation for the Nusselt number of turbulent forced convection in rod bundles with smooth surface was developed. In addition, we extended the analysis to rod bundles with rough surface and provided a method for the prediction of the friction factor and the Nusselt number. The method was based on the law of the wall for velocity and the law of the wall for the temperature, which were integrated over the entire flow area to yield algebraic equations for the prediction of f and Nu. The present method is applicable to infinite rod bundles in square and hexagonal arrays with low pitch to rod diameter ratio, P/D<1.2.     

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.     

Effects of water-to-cement ratio and temperature on diffusion of water in hardened cement pastes

Apparent diffusion coefficients (D_a) of water and activation energies (E_a) of diffusion in hardened cement pastes (HCPs) were determined as a function of water-to-cement (w/c) ratio (0.36–0.60) and temperature (293–323 K) using HTO and H₂¹⁸O as tracers. The values of D_a and E_a ranged from 1.1×10^?11 to 1.7×10^?10 m² s^?1 and from 21.5 to 31.3 kJ mol^?1, respectively. No significant difference between the D_a values of HTO and H₂¹⁸O suggests that water predominantly diffuses as H₂O molecule and dissociation of water is not significant even at high pH range in HCP. The values of E_a at low w/c ratio were higher than in bulk liquid water, suggesting a contribution of a different water regime, such as supercooled bulk water. Two simple models consisting of capillary and gel pores were considered to estimate the volume ratio of gel pores to total pores by optimizing the model to fit with the experimental data. The result suggests that HCP has a pore network mostly consisting of capillary pores with some very narrow pores plugged with hydrates, where HTO must diffuse through gel pores. This view of the HCP pore network was made available through analysis of E_a values.     

Phase distribution in horizontal gas-liquid two-phase bubbly flow

1IntroductionTwo-phasebubblyflowisencounteredinawidevaxietyofindustrialapplications;Suchasintheproductionofelectricalpowerandpetrochendcajsindustry.Oneofthemosttwortantandyetleastunderstandingaspectsoftwo-phaseflowislateralphasedistribution.Theinformationonphasedistributionisarequiredparameterforhydrodynalincandthermalcalculationsinmanypracticalapplications.Considerableexperimentalandseal-theoreticalresearchhasbeenconductedbymanyresearchersinverticalupwaxdsordownwaxdsbubblynow.[1-7]However,L…     

Evaluation of leak flow rate and jet impingement related to leak before break

Leak flow rate and jet impingement load are experimentally evaluated using very narrow and short artificial slits which simulate a through-wall fatigue crack. The following items are clarified in the experiments under BWR fluid conditions: (1) the leak flow rate from the rectangular slit is experimentally clarified and it agrees well with the analytical result when the estimated thermodynamic nonequilibrium parameter N in the present experiment is introduced; (2) the orifice effects are experimentally evaluated concerning the through-wall fatigue crack, in which the discharge coefficients C_D between 0.75 and 0.25 are obtained as a function of the exit to the stagnation area ratio A_e/A_o; (3) when very narrow and short slits are used in the jet impingement experiments, the maximum pressure on the target is higher than that of a large diameter pipe and it increases with the decrease of the flow path length to hydraulic diameter ratio L/D of the slit because of the thermodynamic nonequilibrium effect.     

Leak-before-break and plastic collapse behaviour of statically indeterminate pipe system with circumferential crack

Much research has been carried out on Leak-Before-Break (LBB) behavior of pipes with cracks. However, most studies have been made on statically determinate pipe systems. Few studies have been made on LBB behavior of statically indeterminate pipe systems. Most pipe systems in nuclear power plants have supports and restraints, thus they can be considered as statically indeterminate pipe systems. From above points of view, LBB and plastic collapse behaviors of statically indeterminate pipe with circumferential crack and compliance were studied in this paper. A new method is proposed to analyze and evaluate the LBB and plastic collapse behavior of a statically indeterminate structure. The pipe system of which one end is clamped and the other is supported with compliance was analyzed. The main results obtained are as follows: (1) By combining the limit analysis theory and elastic–plastic fracture mechanics, the effects of crack size, compliance and fracture toughness on load deflection behaviors to failure and structural integrity of statically indeterminate pipe system have been analyzed quantitatively and easily. (2) When a crack grows in a statically indeterminate pipe before plastic collapse, load drop conditions can be derived quantitatively, as a function of J_IC, dJ/da, flow stress, crack size, pipe span length, compliance and flexural rigidity of the pipe. (3) The analytic method developed in this research is useful and convenient to evaluate the LBB and tearing instability behavior of a statically indeterminate pipe system. (4) LBB resolves easily for statically indeterminate pipes with a crack, even when it does not resolve for statically determinate pipes with the same crack. That results from the fact that bending moment redistribution during the fracture process occurs easily for statically indeterminate pipe systems, and its redistribution restrains plastic deformation of the cracked weak section.     

Experimental Study of Counter-Current Two-Phase Flow in Horizontal Tube Connected to Inclined Riser

In order to determine the Counter-Current Flow Limitation (CCFL) in hot legs of PWRS, CCFL characteristics of air-water and saturated steam-water flow were experimentally investigated in a modeled flow path of a horizontal tube connected to an inclined riser. The ranges of dimensions of experimental tubes were as follows: diameter D 0.026–0.076 m, length of horizontal tube H 0.01–0.4 m, length of inclined riser I 0.038–0.6 m and inclination angle of inclined riser θ 40° or 45°.

Wallis-type correlation (J _g ^*1/2+mJ _i ^*1/2=C) was applicable to the data during a steady separated flow. An analysis based on envelope theory showed that the constant C should be a function of H/D and I. A function of C with those parameters was empirically determined by using data obtained in this study. The developed function correlated well with the results of Richter et al. (D = 0.203 m, H = 1.26 m, I = 0.5 m and θ = 45°). The constant m in the Wallis-type correlation was almost constant 0.75. The problems were discussed, which should be made clear to apply the correlation obtained in this study to an actual PWR hot leg.     

Quasi 3-D measurements of turbulence structure in horizontal air–water bubbly flow

Quasi 3-D measurements of the turbulence structure of air–water bubbly flow in a horizontal tube with 35 mm i.d. are undertaken with two TSI “X”-type hot-film probes. The turbulent fluctuations, u_f,v_f,w_f, in axial, radial and circumferential directions, respectively, and Reynolds stresses and are obtained. It is found that in the lower portion of the tube, the profiles of turbulent fluctuation and Reynolds stress resemble those of single phase flow; whereas in the upper portion of the tube, where the bubble population is high, the turbulence, especially the circumferential fluctuation w_f, is substantially enhanced, and the radial turbulence assumes highest value in the radial position −0.7<r/R<0.5. The magnitudes of Reynolds stresses and in our measurements are in the same level except in the lower portion of the tube where assumes a value close to zero as is the case in single phase flow and vertical air–water bubbly flow.     

Geometric effects of 90-degree Elbow in the development of interfacial structures in horizontal bubbly flow

Present study investigates the geometric effects of flow obstruction on the distribution of local two-phase flow parameters and their transport characteristics in horizontal bubbly flow. The round glass tubes of 50.3 mm in inner diameter are employed as test sections, along which a 90-degree Elbow is located at L/D = 206.6 from the two-phase mixture inlet. In total, 15 different flow conditions are examined within the air–water bubbly flow regime. The detailed local two-phase flow parameters are acquired by the double-sensor conductivity probe at four different axial locations. The effect of elbow is found to be evident in both the distribution of local parameters and their development. The elbow clearly promotes bubble interactions resulting in significant changes in interfacial area concentration. It is also found that the elbow-effect propagates to be more significant further downstream (L/D = 250) than immediate downstream (L/D = 225) of the elbow. Furthermore, it is shown that the elbow induces significant oscillations in the flow in both vertical and horizontal directions of the tube cross-section. Characteristic geometric effects due to the existence of elbow are also shown clearly in the transport of one-dimensional interfacial area concentration and void fraction along the flow.     

Investigation of the ductile fracture properties of type 304 stainless steel plate, welds, and 4-inch pipe

J-integral fracture toughness tests were performed on welded 304 stainless steel 2-inch plate and 4-inch diameter pipe. The 2-inch plate was welded using a hot-wire automatic gas tungsten arc process. This weldment was machined into 1T and 2T compact specimens for single specimen unloading compliance J-integral tests. The specimens were cut to measure the fracure toughness of the base metal, weld metal and the heat affected zone (HAZ). The tests were performed at 550°F, 300°F and room temperature. The results of the J-integral tests indicate that the J_Ic of the base plate ranged from 4400 to 6100 in lbs/in² at 550°F. The J_Ic values for the tests performed at 300°F and room temperature were beyond the measurement capacity of the specimens and appear to indicate that J_Ic was greater than 8000 in lb/in². The J-integral tests performed on the weld metal specimens indicate that the J_Ic values ranged from 930 to 2150 in lbs/in² at 550°F. The J_Ic values of the weld metal specimens tested at 300°F and room temperature were 2300 and 3000 in lbs/in² respectively. One HAZ specimen was tested at 550°F and found to have a J_Ic value of 2980 in lbs/in² which indicates that the HAZ is an average of the base metal and weld metal thoughness. These test results indicate that there is a significant reduction in the initiation fracture toughness as a result of welding.The second phase of this task dealt with the fracture toughness testing of 4-inch diameter 304 stainless steel pipes containing a gas tungsten arc weld. The pipes were tested at 550°F in four point bending. Three tests were performed, two with a through wall flaw growing circumferentially and the third pipe had a part through radial flaw in combination with the circumferential flaw. These tests were performed using unloading compliance and d.c. potential drop crack length estimate methods. The results of these test indicate that the presence of a complex crack (radial and circumferential) reduces in the initiation toughness and the tearing modulus of the pipe material compared to a pipe with only a circumferentially growing crack.     

Integrated sorption and diffusion model for bentonite. Part 2: porewater chemistry,sorption and diffusion modeling in compacted systems

It is important to understand the coupled processes of sorption and diffusion of radionuclides (RNs) in compacted bentonite, and to develop mechanistic models that can aid in the prediction of the long-term performance of geological disposal systems of radioactive waste. The integrated sorption and diffusion (ISD) model was developed based on the consistent combination of clay–water interaction, sorption and diffusion models. The diffusion model based on the electrical double layer theory describing relative ionic concentrations and viscoelectric effects at the negatively charged clay surface was coupled with porewater chemistry and sorption models. This ISD model was successfully tested for various actinides with a complex chemistry (Np(V), Am(III), U(VI) under conditions where variably charged carbonate complexes are formed) considered in Part 1, by using published diffusion and sorption data (D_a, D_e, K_d) as a function of partial montmorillonite density. Quantitative agreements were observed by considering uncertainty in porewater chemistry and dominant aqueous species. It can therefore be concluded that the ISD model developed here is able to adequately explain the sorption and diffusion behavior of various RNs with a complex chemistry in compacted bentonites. The performed modeling indicates that uncertainties are mainly related to porewater chemistry and RN speciation and that these parameters need to be carefully evaluated.     

Numerical investigation of heat transfer in upward flows of supercritical water in circular tubes and tight fuel rod bundles

Heat transfer in upward flows of supercritical water in circular tubes and in tight fuel rod bundles is numerically investigated by using the commercial CFD code STAR-CD 3.24. The objective is to have more understandings about the phenomena happening in supercritical water and for designs of supercritical water cooled reactors. Some turbulence models are selected to carry out numerical simulations and the results are compared with experimental data and other correlations to find suitable models to predict heat transfer in supercritical water. The comparisons are not only in the low bulk temperature region, but also in the high bulk temperature region. The two-layer model (Hassid and Poreh) gives a better prediction to the heat transfer than other models, and the standard k– high Re model with the standard wall function also shows an acceptable predicting capability. Three-dimensional simulations are carried out in sub-channels of tight square lattice and triangular lattice fuel rod bundles at supercritical pressure. Results show that there is a strong non-uniformity of the circumferential distribution of the cladding surface temperature, in the square lattice bundle with a small pitch-to-diameter ratio (P/D). However, it does not occur in the triangular lattice bundle with a small P/D. It is found that this phenomenon is caused by the large non-uniformity of the flow area in the cross-section of sub-channels. Some improved designs are numerically studied and proved to be effective to avoid the large circumferential temperature gradient at the cladding surface.     

Hydrogen Concentration Dependence of Tritium Tracer Diffusion Coefficient in Alpha Phase of Niobium

In order to examine influences of coexistent hydrogen isotopes on diffusion behavior of tritium in niobium, tracer diffusion coefficients D_t of tritium in alpha phase of hydrogenated and deuterized niobium (α-NbH_xT_y and α-NbD_xT_y (x<0,8,y<<x)) have been measured at 473 K, 493 K and 553 K. The data on D_t show typical hydrogen concentration dependence: D_t of tritium for both α-NbH_xT_y, and α-NbD_xT_y, decreases with hydrogen concentration under all experimental conditions. The obtained concentration dependence of D_t of tritium differs from that of D_t of protium in α-NbH_x or of deuterium in α-NbH_xT_y. On the other hand, no appreciable differences in the concentration dependence of D_t of tritium between α-NbH_xT_y, and α-NbD_xT_y, are observed: there are no definite isotope effects due to the coexisting hydrogen isotopes. This result suggests that D_t of tritium for a tritiated niobium (α-NbT_x) is not very different from that for α-NbH_xT_y and α-NbD_xT_y. The chemical diffusion coefficient D* of tritium is also evaluated on the basis of the obtained D_t of tritium and of a literature value of a thermodynamic factor F for Nb-H and Nb-D systems.