Development of drift–flux correlation for predicting void fraction in downcomer regions

Accurate prediction of interfacial drag in the downcomer annulus is crucial for the assessment of downcomer void fraction for the loss of coolant accident analysis. The downcomer annulus is the gap between reactor pressure vessel (RPV) exterior and the inner wall of pressure containment vessel (PCV). Based on the previous research, occurrence of the nonuniform two-phase flow in downcomer section is reported, which is partly due to the large wall temperature difference between RPV exterior and the inner wall of PCV. In RELAP5, interfacial drag term in downcomer section is calculated using Kataoka–Ishii and churn-turbulent drift–flux correlations. It has been pointed out that this traditional calculation approach for calculating downcomer void fraction needs modification. The purpose of the current study is to assess the behaviors of drift–flux parameters in downcomer section and to propose an improved distribution parameter model that is suitable for donwcomer boiling analysis.     

Numerical study on sodium–water reaction mechanism in the gas phase using counter-flow reaction region

Sodium water reaction (SWR) is a design basis accident of a sodium-cooled fast reactor (SFR). In a steam generator of the SFR, when a heat transfer tube fails, highly pressurized water and/or water vapor will leak into liquid sodium resulting in a chemical reaction between sodium and water or water vapor. In the previous works, mechanisms of the SWR have been researched on surface reaction and gas-phase reaction. The mechanisms, however, are complicated and have not been fully elucidated. The authors have developed a numerical code in which chemical reaction models of sodium and water vapor are coupled with thermal-hydraulics. Experiments of a counter-flow diffusion flame for the gas-phase reaction have also been carried out. In this article, the authors perform numerical simulations based on the experimental conditions to validate two chemical reaction models, the chemical equilibrium model and the Arrhenius model. With respect to the reaction products, the latter model gives more realistic results. In addition, sensitivity analyses are performed for various hydration numbers and main-flow velocities. It is founded that hydration reaction occurs somewhat in the gas-phase reaction and that influences of the main-flow velocity are not negligible mainly from the viewpoint of the reaction surface location.     

A study on self-terminating behavior of sodium–concrete reaction

A sodium–concrete reaction (SCR) is one of the important phenomena to cause the structural concrete ablation and the release of hydrogen (H₂) gas in the sodium (Na) leak accident. In this study, the long-time SCR test had been carried out to investigate the self-termination mechanism under the condition to keep the temperature of Na on the concrete more than the reaction threshold temperature during 24 hours. The test results showed the SCR terminated by itself even if enough amount of Na remained on the concrete. In addition, quantitative data were collected on the SCR terminating behavior such as the temperature, the concrete ablation depth, the H₂ generation behavior and the concentration profiles of Na, silicon (Si), aluminum (Al) and calcium (Ca) in the reaction products after the test. In the concentration profiles, the calculation by the sedimentation diffusion model of the steady state was comparable with the experimental results. Though the reaction products were suspended by H₂ bubbling and Na ablated the concrete surface with the high H₂ generation rate, the reaction products gradually settled down with decreasing of the H₂ generation rate. Therefore, the Na concentration decreases at the reaction front with time and the SCR terminates of itself.     

Development of unstructured mesh-based numerical method for sodium–water reaction phenomenon in steam generators of sodium-cooled fast reactors

When pressurized water or vapor leaks from a failed heat transfer tube in a steam generator of sodium-cooled fast reactors, a high-velocity and high-temperature jet with sodium–water chemical reaction may cause wastage on the adjacent tubes. For safety assessment of the steam generator, a computational fluid dynamics code called SERAPHIM calculating compressible multicomponent multiphase flow with sodium–water chemical reaction has been developed. The original SERAPHIM code is based on the finite difference method. In this study, unstructured mesh-based numerical method for the SERAPHIM code was developed to advance a numerical accuracy for the complex-shaped domain including multiple heat transfer tubes. Numerical analysis of an underexpanded jet experiment was performed as part of validation of the unstructured mesh-based SERAPHIM code. The calculated pressure profile showed good agreement with the experimental data. To investigate the effect of the introduction of the unstructured mesh and to confirm applicability of the numerical method for the actual situation, water vapor discharging into liquid sodium was analyzed. The calculated behavior of the reacting jet agreed with the previous experimental knowledge. It was demonstrated that the proposed numerical method could be applicable to evaluation of the sodium–water reaction phenomenon.     

Experimental study and kinetic analysis on sodium oxide–silica reaction

ABSTRACT

In a sodium-cooled fast reactor (SFR), if considering hypothetical severe accidental condition such as the steel liner failure of structural concrete caused by intensive leakage of liquid sodium (Na) coolant, the liquid sodium–concrete reaction (SCR) may take place. The major consequences of SCR are hydrogen release, energy release and concrete ablation. Thus, it is important to understand the phenomenology and kinetic behavior of SCR. As a part of a series of studies on SCR, this study focused on the reaction between sodium oxide (Na₂O) and silica (SiO₂), which is dealt with possible formation of Na₂O as the result of sodium–water reaction in the initial stage of SCR. Through thermoanalytical and X-ray diffraction measurements, it was revealed that Na₂O–SiO₂ reaction to form sodium orthosilicate (Na₄SiO₄) occurs at significantly lower temperature in comparison with Na–SiO₂ reaction. The reaction is kinetically characterized as a largely overlapping multistep reaction, which is composed of at least three reaction steps. On the basis of the observations, the impact of Na₂O–SiO₂ reaction in the overall SCR and the significance of the conventional kinetic analysis using the Kissinger method are discussed.     

Numerical and theoretical investigations of heat transfer characteristics in helium–xenon cooled microreactor core

Helium–xenon cooled microreactors are a vital technological solution for portable nuclear reactor power sources. To examine the convective heat transfer behavior of helium–xenon gas mixtures in a core environment, numerical simulations are conducted on a cylindrical coolant channel and its surrounding solid regions. Validated numerical methods are used to determine the effect and mechanisms of power and its distribution, inlet temperature and velocity, and outlet pressure on the distribution and...     

Transient behavior of the sodium–potassium alloy heat pipe in passive residual heat removal system of molten salt reactor

High temperature heat pipes, as highly-effective heat transfer elements, have been extensively employed in thermal management for their remarkable advantages in conductivity, isothermality and self-actuating. It is of significance to apply heat pipes to new concept passive residual heat removal system (PRHRS) of molten salt reactor (MSR). In this paper, the new concept PRHRS of MSR using sodium–potassium alloy (NaK) heat pipes is proposed in detail, and then the transient behavior of high temperature NaK heat pipe is numerically investigated using the Finite Element Method (FEM) in the case of MSR accident. The two-dimensional transient conduction model for the heat pipe wall and wick structure is coupled with the one-dimensional quasi-steady model for the vapor flow when vaporization and condensation occur at the liquid–vapor interface. The governing equations coupled with boundary conditions are solved by FORTRAN code to obtain the distributions of the temperature, velocity and pressure for the heat pipe transient operation. Numerical results indicated that high temperature NaK heat pipe had a good operating performance and removed the residual heat of fuel salt significantly for the accident of MSR.     

A review of nanofluid heat transfer and critical heat flux enhancement—Research gap to engineering application

As a novel strategy to improve heat transfer characteristics of fluids by the addition of solid particles with diameters below 100 nm, nanofluids exhibit unprecedented heat transfer properties and are being considered as potential working fluids to be used in high heat flux systems such as electronic cooling systems, solar collectors, heat pipes, and nuclear reactors. The present paper reviews the state-of-the-art nanofluid studies on such topics as thermo-physical properties, convective heat transfer performance, boiling heat transfer performance, and critical heat flux (CHF) enhancement. It is indicated that the current experimental data of nanofluids thermal properties are neither sufficient nor reliable for engineering applications. Some inconsistent or contradictory results related to thermo-physical properties, convective heat transfer performance, boiling heat transfer performance, and CHF enhancement of nanofluids are found in data published in the literature. No comprehensive theory explains the energy transfer processes in nanofluids. To bridge the research gaps for nanofluids' engineering application, the urgent work are suggested as follows. (1) Nanofluid stability under both quiescent and flow conditions should be evaluated carefully; (2) A nanofluid database of thermo-physical properties, including detailed characterization of nanoparticle sizes, distribution, and additives or stabilizers (if used), should be established, in a worldwide cooperation of researchers; (3) More experimental and numerical studies on the interaction of suspended nanoparticles and boundary layers should be performed to uncover the mechanism behind convective heat transfer enhancement by nanofluids; (4) Bubble dynamics of boiling nanofluids should be investigated experimentally and numerically, together with surface tension effects, by considering the influences of nanoparticles and additives if used, to identify the exact contributions of solid surface modifications and suspended nanoparticles to CHF enhancement in boiling heat transfer. Once we acquire such details about the above key issues, we will gain more confidence in conducting application studies of nanofluids in different areas with more efficiency.     

Coupling effect between film boiling heat transfer and evaporation drag around a hot-particle in cold liquid

Extremely rapid evaporation could occur when high-temperature particles contact withlow-temperature liquid. This kind of phenomenon is associated with the engineering safety and the problems in high-transient multi-phase fluid and heat transfer. The aim of our study was to design and build an observable experiment facility. The first series of experiments were performed by pouring one or six high-temperature particles into a low saturated temperature liquid pool. The particle's falling-down speed was recorded by a high-speed camera, thus we can find the special resistant feature of the moving high-temperature particles, which is induced by the high-speed evaporation surrounding the particles. The study has experimentally verified the theory of evaporation drag model.     

Study of heat transfer by using DEM–CFD method in a randomly packed pebble-bed reactor

The pebble-bed reactor is one of the most promising designs for the nuclear energy industry. In this paper,a discrete element method-computational fluid dynamics(DEM-CFD) approach that includes thermal conduction, radiation, and natural convection mechanisms was proposed to simulate the thermal-fluid phenomena after the failure of forced circulation cooling system in a pebble-bed core. The whole large-scale packed bed was created using the DEM technique, and the calculated radial porosity of the bed was validated with empirical correlations reported by researchers. To reduce computational costs, a segment of the bed was extracted, which served as a good representative of the large-scale packed bed for CFD calculation. The temperature distributions simulated with two different fluids in this DEM-CFD approach were in good agreement with SANA experimental data. The influence of the natural convection mechanism on heat transfer must be taken into account for coolants with strong convective capacity. The proposed DEM-CFD methodology offers a computationally efficient and widely applied method for understanding the heat transfer process in a pebble-bed core. The method can also be easily extended to assess the passive safety features of newly designed fluoride-salt-cooled pebble-bed reactors.     

Void reactivity coefficient benchmark results for a 10 × 10 BWR assembly in the full 0–100% void fraction range

A boiling water reactor SVEA-96+ fresh fuel lattice has been used as the basis for a benchmark study of the void reactivity coefficient at assembly level in the full voidage range. Results have been obtained using the deterministic codes CASMO-4, HELIOS, PHOENIX, BOXER and the probabilistic code MCNP4C, combined for almost all cases with different cross section libraries. A statistical analysis of the results obtained showed that the void reactivity coefficient tends to become less negative beyond 80% void and that the discrepancies between codes tend to increase from less than 15% at voidages lower than 40% to more than 25% at voidages higher than 70%. The void reactivity coefficient results and the corresponding differences between codes were isotopically decomposed to interpret discrepancies. The isotopic decomposition shows that the minimum observed in the void reactivity coefficient between 80% and 90% void is largely due to the decrease in the relative importance of the ¹⁵⁷Gd(n, γ) rate with increasing voidage, and that the fundamental discrepancies between codes or libraries are mainly governed by the different predictions of the ²³⁸U(n, γ) variation with voidage.     

Cathodic polarization curves of the oxygen reduction reaction on various structural materials of boiling water reactors in high temperature–high purity water

Cathodic polarization curves of the O₂ reduction reaction were measured by using electrodes made from typical structural materials of boiling water reactors (BWRs) to evaluate the effects of kind of material on the electrochemical corrosion potential (ECP) calculation. To estimate ECPs at any region in the BWRs on the basis of the BWR environmental conditions, anodic and cathodic polarization curves should be obtained in advance under relevant conditions. The concentration of oxidants such as O₂ and H₂O₂ in coolant changes depending on the region in which they exist. As well, reduction reaction rates might differ depending on the kind of materials. In this work, the cathodic polarization curves of type 316L stainless steel (316L SS) and Alloy 182 were measured in high purity water at 553 K with different O₂ concentrations and compared with those of type 304 SS (304 SS). The results showed that the cathodic polarization curves differed depending on the kind of materials at the activation-controlled region. But, the difference in the ECP vs. O₂ concentration relationship was small when the ECPs were calculated by using both anodic and cathodic polarization curves measured on the objective material.     

Phase relations for reactions of hydrogen with sodium oxide between 500 and 900°C

The equilibrium pressure technique, commonly used for investigating the phase relations in binary gas-condensed phase equilibria, was applied to the Na-Na₂O-NaOH-NaH corner of the ternary Na-O-H system. Measured amounts of hydrogen were reacted with Na₂O (sealed in vacuo in a thin-walled nickel crucible) and the equilibrium hydrogen pressure (0.03 < P < 100 kPa) was determined as a function of temperature(510 < T < 879°C) and hydrogen atom fraction(0 < X_H < 0.275). Discontinuities encountered in the isothermal(√P vs X_H) or fixed-hydrogen-concentration (InP vs 1/T) plots were used to delineate the condensed-phase boundaries that occur within theP-T-X_H ranges studied. Data were fitted to analytical equations which permitted construction of a portion of the phase diagram and yielded pertinent thermodynamic information. Limitations of the technique in applications to other similar systems are discussed.     

Investigation of radiation-induced surface activation effect in austenitic stainless steel under ultraviolet and γ-ray irradiations

The radiation-induced surface activation (RISA) effect will be applied to the core design in supercritical light water reactor (SCWR) in order to achieve a high performance with excellent economy and safety. The purpose of the present study is to investigate the RISA effect in the candidate fuel cladding materials in SCWR such as PNC1520. The change of weldability due to RISA effect and the related microstructure analysis were performed in oxidized PNC1520 and 304 stainless steel with various oxidization periods. The phases contained in the surface oxide layer of the present specimen were identified as Fe₂CrO₄, γ-Fe₂O₃, and Fe₂O₃. The lifetime of 13.8 days for wettability improving factor was confirmed in the ultraviolet (UV) irradiation. Meanwhile, the long life of 13.8 days and short life of 0.8 days for wettability improving factors were identified in the γ-ray irradiation. Based on the fact that the band gap energies of Fe₂CrO₄, γ-Fe₂O₃, and Fe₂O₃ were, respectively, 2.1, 2.0, and 2.2 eV, and the photo energies of UV and γ-ray irradiation were 4.48 eV and 13.3 MeV, it is therefore clarified that the hydrophilization on the oxide layer is ascribed to the RISA effect.     

Numerical study of in-vessel retention under the gallium–water external reactor vessel cooling system using MARS-LMR

To confirm the feasibility of the gallium–water IVR-ERVCS (in-vessel retention-external reactor vessel cooling system), this paper focuses on the numerical simulation of severe accidents in APR 1400 using MARS-LMR (multidimensional analysis of reactor safety-liquid metal reactor). To analyze the gallium-cooled systems, the properties of liquid gallium were added to the MARS-LMR code used in our previous work. In this system, the generated decay heat is transferred to liquid gallium through the reactor pressure vessel and then removed from the water pool as a heat sink. The numerical analyses results show that the temperature range of the liquid gallium is much lower than its boiling point and confirm the natural convection. Sensitivity studies were also performed by changing several parameters such as the initial temperature of gallium and water pool inventory and their results indicated that the working time of the gallium–water IVR-ERVCS depends on the inventory of the water pool. Because liquid gallium in this system does not have a phase change, unlike water, the gallium–water IVR-ERVCS can provide stable and reliable cooling capability. To solve the limitation due to critical heat flux in IVR-ERVCS and to ensure the sufficient thermal margin, it is confirmed that the gallium–water IVR-ERVCS can be a successful severe accident mitigation strategy in nuclear power plants.     

A model of silver–iodine reactions in a light water reactor containment sump under severe accident conditions

Metallic silver and iodine form insoluble AgI in the containment sump which has a major impact on iodine volatility and hence on the source term to the environment. Resistance-in-series models are developed and validated against separate-effects tests. The reaction between I₂ and Ag is limited by mass transfer in the liquid. The rate does not follow a parabolic law for the duration of the experiments. The extent of oxidation of the silver sample seems to play a decisive role for reactions with I⁻ which proceed via a two-step process. The initial, rapid step is controlled by the reaction with the surface silver oxide with a contribution of mass transfer in the liquid. The subsequent, slow step is limited by reaction between I⁻ and Ag⁺ at the solid–liquid interface. The reaction is probably negligible for pH > 7 and in the absence of oxidising conditions.     

Investigation of the symmetry properties and level density parameters of some superdeformed light even–even nuclei

In this study we have investigated the symmetry properties and R_4/2 energy ratio of energy bands for superdeformed light even–even nuclei from Z = 10 to 30 by the use of a simple and valid analytical relation obtained in terms of a K-quantum number, which is the projection of the total angular momentum on the axis of symmetry of a nucleus. Moreover, the nuclear level density parameters of the nuclei of interest have been calculated by considering different excitation bands of the observed nuclear spectra. The method used assumes equidistant spacing of the collective coupled state bands of the nuclei considered. The values of the calculated nuclear level density parameters and R_4/2 energy ratio have been compared with those of the experimental and compiled values and are in quite good agreement with the experimental and compiled results.     

Simulations of air–water flow and subcooled boiling flow using the CUPID code

This paper summarizes the physical models and a modified numerical procedure for the lift force of the CUPID code to simulate a subcooled boiling flow. A part of these physical models and the numerical procedure were verified through a calculation of air–water flow tests. A subcooled boiling flow was then calculated to assess the whole implementation. These assessments indicate that the implementation of the physical models and a modified numerical scheme are appropriate, and that the calculated primary variables of a subcooled boiling flow such as the liquid velocity and void fraction profiles can be acceptable in general, though IATE and a turbulence model for a two-phase flow are needed to be improved for a better prediction.