Ex-vessel boiling experiments: laboratory- and reactor-scale testing of the flooded cavity concept for in-vessel core retention Part I: Observation of quenching of downward-facing surfaces

This paper presents the results of a series of quenching experiments to examine the boiling curve of relative large downward-facing surfaces. The test masses are 61 cm in diameter and the downward-facing surface is either flat or curved. The work is motivated by the need to assess the ex-vessel boiling process for in-vessel core retention. The critical heat flux is found to be approximately 50 W cm⁻². The nucleate boiling regime and the critical heat flux regime are found to be characterized by cyclic two-phase flow patterns.     

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.     

Transformation and fragmentation behavior of molten metal drop in sodium pool

In order to clarify the fragmentation mechanism of a metallic alloy (U–Pu–Zr) fuel on liquid phase formed by metallurgical reactions (liquefaction temperature = 650 °C), which is important in evaluating the sequence of core disruptive accidents for metallic fuel fast reactors, a series of experiments was carried out using molten aluminum (melting point = 660 °C) and sodium mainly under the condition that the boiling of sodium does not occur. When the instantaneous contact interface temperature (T_i) between molten aluminum drop and sodium is lower than the boiling point of sodium (T_c,bp), the molten aluminum drop can be fragmented and the mass median diameter (D_m) of aluminum fragments becomes small with increasing T_i. When T_i is roughly equivalent to or higher than T_c,bp, the fragmentation of aluminum drop is promoted by thermal interaction caused by the boiling of sodium on the surface of the drop. Furthermore, even under the condition that the boiling of sodium does not occur and the solid crust is formed on the surface of the drop, it is confirmed from an analytical evaluation that the thermal fragmentation of molten aluminum drop with solid crust has a potential to be caused by the transient pressurization within the melt confined by the crust. These results indicate the possibility that the metallic alloy fuel on liquid phase formed by the metallurgical reactions can be fragmented without occurring the boiling of sodium on the surface of the melt.     

Numerical analysis of fragmentation mechanisms in vapor explosions

Fragmentation of molten metal is the key process in vapor explosions. However, this process is so rapid that the mechanisms have not yet been clarified in experimental studies. In addition, numerical simulation is difficult because we have to analyze water, steam and molten metal simultaneously with boiling and fragmentation. The authors have been developing a new numerical method, the moving particle semi-implicit (MPS) method, based on moving particles and their interactions. Grids are not necessary. Incompressible flows with fragmentation on free surfaces have been calculated successfully using the MPS method. In the present study, numerical simulation of the fragmentation processes using the MPS method is carried out to investigate the mechanisms. A numerical model to calculate boiling from water to steam is developed. In this model, new particles are generated on water–steam interfaces. A two-step pressure calculation algorithm is also developed. Pressure fields are separately calculated in both heavy and light fluids to maintain numerical stability with the water and steam system. The new model and algorithm are added to the MPS code. Water jet impingement on a molten tin pool is calculated using the MPS code as a simulation of collapse of a vapor film around a melt drop. Penetration of the water jet, which is assumed in Kim–Corradini’s model, is not observed. If the jet fluid density is hypothetically larger, the penetration appears. Next, impingement of two water jets is calculated. A filament of the molten metal is observed between the two water jets as assumed in Ciccarelli–Frost’s model. If the water density is hypothetically larger, the filament does not appear. The critical value of the density ratio of the jet fluid over the pool fluid is ρ_jet/ρ_pool=0.7 in this study. The density ratios of tin–water and UO₂–water are in the region of filament generation, Ciccarelli–Frost’s model. The effect of boiling is also investigated. Growth of the filament is not accelerated when the normal boiling is considered. This is because normal boiling requires more time than that of the jet impingement, although the filament growth is governed by an instant of the jet impingement. Next, rapid boiling based on spontaneous nucleation is considered. The filament growth is markedly accelerated. This result is consistent with the experimental fact that the spontaneous nucleation temperature is a necessary condition of vapor explosions.     

Experiments on microgravity boiling heat transfer by using transparent heaters

To clarify the relation between the liquid–vapor behavior and the heat transfer characteristics in the boiling phenomena, the structures of transparent heaters were developed for both flow boiling and pool boiling experiments and were applied to the microgravity environment realized by the parabolic flight of aircraft. In the flow boiling experiment, a transparent heated tube makes the heating, the observation of liquid–vapor behavior and the measurement of heat transfer data simultaneously possible. The heat transfer coefficient in the annular flow regime at moderate quality has distinct dependence on gravity provided that the mass velocity is not so high, while no noticeable gravity effect is seen at high quality and in the bubbly flow regime. The measured gravity effect was directly related to the behavior of annular liquid film observed through the transparent tube wall. In the pool boiling experiment, a structure of transparent heating surface realizes both the observation of the macrolayer or microlayer behavior from underneath and the measurements of local surface temperatures and the layer thickness. It was clarified in the microgravity experiments that no vapor stem exists but tiny bubbles are observed in the macrolayer underneath a large coalesced bubble at high heat flux. The heat flux evaluated by the heat conduction across the layer assumes less than 30% of the total to be transferred. The evaporation of the microlayers underneath primary bubbles just after the generation dominates the heat transfer in the microgravity, not only in the isolated bubble region but also in the coalesced bubble region.     

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.     

Water boiling on the corium melt surface under VVER severe accident conditions

Experimental results are presented on the interaction of corium melt with water supplied on its surface. The tests were conducted in the ‘Rasplav-2’ experimental facility. Corium melt was generated by induction melting in the cold crucible. The following data were obtained: heat transfer at boiling water-melt surface interaction, gas and aerosol release, post-interaction solidified corium structure. The corium melt charge had the following composition, mass%: 60% UO_2+x–16% ZrO₂–15% Fe₂O₃–6% Cr₂O₃–3% Ni₂O₃. The melt surface temperature ranged within 1920–1970 K.     

Two phase flow 1D turbulence model for poly-disperse upward flow in a vertical pipe

A 1D test-solver was developed in recent years for modeling of two phase bubbly flows in pipe geometry. The solver considers a number of bubble classes and calculates bubble-size resolved void fraction profiles in the radial direction. A successful implementation was achieved regarding bubble forces models (non-drag forces). Discrepancies appeared when coalescence and breakup rates were significant. These rates depend upon local turbulence quantities, which are possible reason for discrepancies. Originally the test-solver is equipped by Sato model (Sato, Y., Sadatomi, M., Sekoguchi, K., 1981. Momentum and heat transfer in two-phase bubble flow. I. International Journal Multiphase Flow 7, 167–177 .) which accounts for turbulence via shear- and bubble-induced viscosities calculated out of empirical correlations. One equation for the turbulent kinetic energy was solved, while the dissipation rate was calculated out of a correlation. In order to improve calculation of the local turbulence parameters, a two-phase k– turbulence model was adopted instead. The account for the bubble-induced turbulence was made via a source term taken out of literature. Comparisons between new and old turbulence modeling against experimental data showed better agreement for the new model. The experiments covered a wide range of water and air superficial velocities for upward bubbly flow in two pipe's diameters: 50 and 200 mm. The main feature of the new model is providing more reliable values of turbulence parameters for application in coalescence and breakup models. A comparison with CFX 5.7 calculations in a 50 mm pipe showed better calculation results when the source term was considered in the k– equations. An implementation into CFX is planned.     

Dynamic analysis of a nuclear reactor with fluid–structure interaction: Part II: Shock loading, influence of fluid compressibility

The present paper is related to the dynamic (shock) analysis of a naval propulsion (on-board) reactor with fluid–structure interaction modelling. In a previous study, low frequency analysis has been performed; the present study deals with high frequency analysis, i.e. taking into account compressibility effects in the fluid medium. Elasto-acoustic coupling effects are studied and described in the industrial case. The coupled problem is formulated using the so-called (u, p, φ) formulation which yields symmetric matrices. A modal analysis is first performed on the fluid problem alone, then for the coupled fluid–structure problem in the following cases: (i) with incompressible fluid; (ii) with compressible fluid at standard pressure and temperature conditions; (iii) with compressible fluid at the operating pressure and temperature conditions. Elasto-coupling effects are then highlighted, in particular through the calculation of an elastic energy ratio. As a general conclusion, compressibility effects are proved significant in the dynamic response of the reactor in the high frequency range.     

An utilization of liquid sublayer dryout mechanism in predicting critical heat flux under low pressure and low velocity conditions in round tubes

From a theoretical assessment of extensive critical heat flux (CHF) data under low pressure and low velocity (LPLV) conditions, it was found out that lots of CHF data would not be well predicted by a normal annular film dryout (AFD) mechanism, although their flow patterns were identified as annular–mist flow. To predict these CHF data, a liquid sublayer dryout (LSD) mechanism has been newly utilized in developing the mechanistic CHF model based on each identified CHF mechanism. This mechanism postulates that the CHF occurrence is caused by dryout of the thin liquid sublayer resulting from the annular film separation or breaking down due to nucleate boiling in annular film or hydrodynamic fluctuation. In principle, this mechanism well supports the experimental evidence of residual film flow rate at the CHF location, which can not be explained by the AFD mechanism. For a comparative assessment of each mechanism, the CHF model based on the LSD mechanism is developed together with that based on the AFD mechanism. The validation of these models is performed on the 1406 CHF data points ranging over P=0.1–2 MPa, G=4–499 kg m⁻² s⁻¹, L/D=4–402. This model validation shows that 1055 and 231 CHF data are predicted within ±30 error bound by the LSD mechanism and the AFD mechanism, respectively. However, some CHF data whose critical qualities are <0.4 or whose tube length-to-diameter ratios are <70 are considerably overestimated by the CHF model based on the LSD mechanism. These overestimations seem to be caused by an inadequate CHF mechanism classification and an insufficient consideration of the flow instability effect on CHF. Further studies for a new classification criterion screening the CHF data affected by flow instabilities as well as a new bubble detachment model for LPLV conditions, are needed to improve the model accuracy.     

Study on flow characteristics in gas-molten metal mixture pool

As part of basic research on the flow characteristics of a two-phase mixture pool under severe accident of fast breeder reactor (FBR), visualization and measurement of nitrogen gas-molten lead/bismuth two-phase flow in a rectangular pool were performed by using the neutron radiography technique. Measurements of drag coefficient of a single bubble and bubble shape regime showed that the relationship between the shape, size and the rising velocity of a single isolated nitrogen bubble in the molten lead/bismuth was not much different from that for an ordinary one. Appropriate correlation for drift velocity and drag coefficient between phases were recommended based on the drift flux correlation of measured pool void fraction. One- and two-dimensional analyses were performed by using a next generation computational code for safety analysis of severe accident of FBRs, SIMMER-III with various drag coefficient models. It was revealed that Kataoka–Ishii’s equation was suitable basically for estimation of drift velocity, namely, drag force between phases.     

A 3-D Lagrangian stochastic model for the meso-scale atmospheric dispersion applications

A fully 3-D Lagrangian stochastic particle trajectory model is presented and applied to the meso-scale atmospheric dispersion and ground concentration calculations. The use of Gaussian plume model (GPM) with Pasquill–Gifford σ's for downwind distances exceeding 10 km is critically viewed. Further, the effect of variation in release height on the ground concentration and dispersion parameters (σ_y,σ_z) is studied for continuous releases. A continuous release of a non-buoyant gas in a neutral stratified atmosphere is simulated for various stack heights. The turbulent atmospheric parameters like vertical profiles of the fluctuating wind component and the eddy lifetimes for the horizontal and vertical directions, etc. were calculated using a semi-empirical mathematical model and compared with a E–ε model. The numerically calculated horizontal and vertical dispersion coefficients (σ_y,σ_z) are compared with the Pasquill–Gifford empirical σ's and with the Pasquill-modified σ_y. The ground concentration values as a function of downwind distance, have been compared with the Green Glow data and with a GPM for various release heights. The comparison of the results demonstrate a need of using a 3-D model over the simple GPM for meso-scale atmospheric dispersion applications. The GPM overpredicts the ground concentration because it cannot take into account the vertical wind shear, which is observed in the atmosphere under all stability conditions. A weak dependence on the release height in the numerically calculated dispersion coefficients σ's, is also observed.     

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.     

Study on the characteristic points of boiling curve by using wavelet analysis and genetic neural network

Local singularity of a signal includes a lot of important information. Wavelet transform can overcome the shortages of Fourier analysis, i.e., the weak localization in the local time- and frequency-domains. It has the capacity to detect the characteristic points of boiling curves. Based on the wavelet analysis theory of signal singularity detection, Critical Heat Flux (CHF) and Minimum Film Boiling Starting Point (q_min) of boiling curves can be detected by using the wavelet modulus maxima detection. Moreover, a genetic neural network (GNN) model for predicting CHF is set up in this paper. The database used in the analysis is from the 1960s, including 2365 data points which cover a range of pressure (P), from 100 to 1000 kPa, mass flow rate (G) from 40 to 500 kg m⁻² s⁻¹, inlet sub-cooling (ΔT_sub) from 0 to 35 K, wall superheat (ΔT_sat) from 10 to 500 K and heat flux (Q) from 20 to 8000 kW m⁻². GNN mode has some advantages of its global optimal searching, quick convergence speed and solving non-linear problem. The methods of establishing the model and training of GNN are discussed particularly. The characteristic point predictions of boiling curve are investigated in detail by GNN. The results predicted by GNN have a good agreement with experimental data. At last, the main parametric trends of the CHF are analyzed by applying GNN. Simulation and analysis results show that the network model can effectively predict CHF.     

Fracture toughness of welded joints materials for main pipelines at Ignalina NPP

This paper deals with an investigation of mechanical and fracture toughness characteristics of welded joint materials used in Ignalina Nuclear Power Plant (NPP) reactor main circulating circuit (MCC) and steam pipelines. Basic metal of MCC group distributing header (GDH) steel 08Ch18N10T (Du-300), its weld metal welded by manual and automatic arc method using the wire SV-04Ch19N11M3 and electrodes EA-100/10U or EA-100/10T, this joint heat-affected zone metal and base metal of the main steam system—steel 16GS (DU-630) and its weld metal welded by manual arc method using the wire SV-08GS2 and electrodes UONI-13/55 were tested.Mechanical properties of welded joints materials—proportional limit (σ_pl), yield (σ_y) and ultimate (σ_u) strength, fracture stress (σ_f) and ductility (Z) (percent reduction of area) of the specimens were determined. Investigation of relative critical stress intensity factor for fixed thickness of the specimen and critical J-integral, J_IC, was performed.The probabilistic investigation of influence of the mechanical properties (σ_pl, σ_y, σ_u) onto fracture toughness characteristics and J_IC for tested materials by using linear regression model with three independent variables was performed.Research enabled to conclude that proposed multivariable regression model with 80% probability (confidence coefficient α = 0.05) has explained reasonably well the dependence of with σ_pl, σ_y, σ_u and it has shown the non-acceptability of probabilistic evaluation of the model with respect to J_IC.     

Two-phase flow and boiling heat transfer in two vertical narrow annuli

Experimental study associated with two-phase flow and heat transfer during flow boiling in two vertical narrow annuli has been conducted. The parameters examined were: mass flux from 38.8 to 163.1 kg/m² s; heat flux from 4.9 to 50.7 kW/m² for inside tube and from 4.2 to 78.8 kW/m² for outside tube; equilibrium mass quality from 0.02 to 0.88; system pressure from 1.5 to 6.0 MPa. It was found that the boiling heat transfer was strongly influenced by heat flux, while the effect of mass velocity and mass quality were not very significant. This suggested that the boiling heat transfer was mainly via nucleate boiling. The data were used to develop a new correlation for boiling heat transfer in the narrow annuli. In the two-phase flow study, the comparison with the correlation of Chisholm [Chisholm, D., 1967. A theoretical basis for the Lockhart–Martinelli correlation for two-phase flow. Int. J. Heat Mass Transfer 10, 1767–1778] and Mishima and Hibiki [Mishima, K., Hibiki, T., 1996. Some characteristics of air–water two-phase flow in small diameter vertical tubes. Int. J. Multiphase Flow 22, 703–712] indicated that the existing correlations could not predict the two-phase multiplier in the narrow annuli well. Based on the experimental data, a new correlation was developed.     

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.     

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.