Advances in Nuclear Fuel 54 problem.A variable space network method developed by Murray & Landis (1959) and a front tracking ALE (Arbitrary Lagrangian Eulerian) method developed by Jaeger & Carin (1994) are also classified as the former group.While the moving mesh methods give high accuracy in predicting an interface position, there is the drawback that the algorithm of remeshing is complicated especially in the case of multi-dimensional problems.When a shape of the solid-liquid interface becomes complex, we have to pay attention to deformation of elements.Therefore, the moving mesh methods are frequently used for directional melting/solidification problems.The latter group (i.e. an enthalpy method) introduces an artificial heat capacity containing latent heat for phase change.This enables us to eliminate a boundary condition at the solid-liquid interface.The enthalpy method requires only a single energy equation.Numerical analysis using the enthalpy method may be found in the paper by Comini et al. (1974) or by Rolph & Bathe (1982).The enthalpy method is quite popular for multi-dimensional problems because re-meshing is not required.However, there is also the drawback that isothermal phase change phenomena cannot be modeled consistently.This is due to the inevitable assumption that phase change occurs within a certain range of temperature.Application of the above-mentioned two types of the methods is limited by their inherent drawbacks.In application to the actual problems of the nuclear fuel cycle, a numerical analysis method needs to be applicable to multi-dimensional problems which involve complex move of the solid-liquid interface.A numerical analysis method using a fixed mesh can be simply applied to multi-dimensional problems even if they involves complex move of the interface.However, existence of a discontinuous temperature gradient at the solid-liquid interface complicates calculation of heat conduction and interface tracking in a fixed mesh.The eXtended Finite Element Method (X-FEM), which is a fixed-mesh-based-method, can overcome this difficulty.This method introduces an enriched finite element interpolation to represent the discontinuous temperature gradient in the element.The enriched finite element interpolation consists of a standard shape function and a signed distance function.This makes it possible to track the moving solid-liquid interface accurately without remeshing.The X-FEM has the advantages of both the moving mesh method and the enthalpy method.Moës et al. (1999) developed the X-FEM for arbitrary crack growth problems.Merle &Dolbow (2002) andChessa et al. (2002) applied the X-FEM to melting/solidification problems.Further, Chessa & Belytschko (2003) simulated a two-phase flow problem involving bubble deformation successfully by using the X-FEM.These researches indicate that the X-FEM is widely applicable to moving interface problems.
A gas entrainment (GE) prediction method has been developed to establish design criteria for the largescale sodium-cooled fast reactor (JSFR) systems. The prototype of the GE prediction method was already confirmed to give reasonable gas core lengths by simple calculation procedures. However, for simplification, the surface tension effects were neglected. In this paper, the evaluation accuracy of gas core lengths is improved by introducing the surface tension effects into the prototype GE prediction method. First, the mechanical balance between gravitational, centrifugal, and surface tension forces is considered. Then, the shape of a gas core tip is approximated by a quadratic function. Finally, using the approximated gas core shape, the authors determine the gas core length satisfying the mechanical balance. This improved GE prediction method is validated by analyzing the gas core lengths observed in simple experiments. Results show that the analytical gas core lengths calculated by the improved GE prediction method become shorter in comparison to the prototype GE prediction method, and are in good agreement with the experimental data. In addition, the experimental data under different temperature and surfactant concentration conditions are reproduced by the improved GE prediction method.
If pressurized water/water-vapor leaks from a heat transfer tube in a steam generator (SG) in a sodium-cooled fast reactor, the leakage forms high-velocity, high-temperature, and corrosive jet due to the pressure difference and sodium-water reaction. It would damage the other tubes and might propagate the tube failure in a SG. Thus, it is important to evaluate the effect of the tube failure propagation for safety assessment of a sodium-cooled fast reactor. The computational code LEAP-III can evaluate water leak rate during the tube failure propagation with short calculation time, since it consists of empirical formulae and one-dimensional equations of conservation. One of its models, the temperature distribution evaluation model, evaluates the temperature distribution in SG as circular arc isolines determined by experiments and preliminary analyses instead of complicated real distribution. Although this model has advantages of short calculation time and good agreement about maximum temperature, it provides broader high temperature region than the real one in some case. In order to improve this model to get more realistic temperature distribution, we have developed the Lagrangian particle method based on engineering approaches. In this study, we have focused on evaluating gas flow in a tube bundle system and constructed new models for the gas-particles behavior around a tube to evaluate void fraction distribution near the tube. Through the test analysis simulating vapor discharge in one target tube system and comparison with an existing computational fluid dynamics code, SERAPHIM, it was confirmed that basic behaviors of these models, which is the particles spread out around the target tube without significant inflow into the tube inside, and finally these went along the buoyancy force direction.
A gas entrainment (GE) prediction method has been developed to establish design criteria for the largescale sodium-cooled fast reactor (JSFR) systems. The prototype of the GE prediction method was already confirmed to give reasonable gas core lengths by simple calculation procedures. However, for simplification, the surface tension effects were neglected. In this paper, the evaluation accuracy of gas core lengths is improved by introducing the surface tension effects into the prototype GE prediction method. First, the mechanical balance between gravitational, centrifugal, and surface tension forces is considered. Then, the shape of a gas core tip is approximated by a quadratic function. Finally, using the approximated gas core shape, the authors determine the gas core length satisfying the mechanical balance. This improved GE prediction method is validated by analyzing the gas core lengths observed in simple experiments. Results show that the analytical gas core lengths calculated by the improved GE prediction method become shorter in comparison to the prototype GE prediction method, and are in good agreement with the experimental data. In addition, the experimental data under different temperature and surfactant concentration conditions are reproduced by the improved GE prediction method.
This report discusses the progress on the collaboration between Sandia National Laboratories (Sandia) and Japan Atomic Energy Agency (JAEA) on the sodium fire research in fiscal year 2019. First, the current sodium pool fire model in MELCOR, which is adapted from CONTAIN-LMR code, is discussed. The associated sodium fire input requirements are also presented. A proposed model improvement developed at Sandia is discussed. Finally, the validation study of the sodium pool fire model in MELCOR carried out by a JAEA's staff is described. To validate this model, a JAEA sodium pool fire experiment (F7-1 test) is used. A preliminary calculation is performed using a modified MELCOR model from a previous experiment simulation. The results of the calculation are discussed as well as suggestions for improvement. Finally, recommendations are made for new MELCOR simulations for next fiscal year, 2020.
Abstract A numerical method for the thermal hydraulic phenomena in a narrow flow passage is developed to evaluate the gap cooling capability. Based on a drift flux model, the two-dimensional gas-liquid two-phase flow in the annular and hemispherical heated narrow flow passages is modeled. The drift velocity correlation is combined with the flooding correlation, which describes physical phenomena under cooling limits. Experiment on thermal hydraulic phenomena in the heated narrow flow passage is performed. Boiling two-phase flow behavior and dryout phenomena are observed. The critical heat flux data is obtained from measurement of the heating surface temperature. Counter-current two-phase flow, which is a key phenomenon in the gap cooling mechanism, is reproduced by the numerical analysis appropriately. The critical heat flux is predicted by assuming that deficiency of the liquid supply against the gas upward flow leads to occurrence of dryout. Validity of the newly developed numerical method is demonstrated through comparison of the predicted critical heat flux with the present and existing data in the gap width range from 0.5 to 5 mm and the pressure range from 1 to 50 bar. KEYWORDS: severe accidentin-vessel molten core retentionnarrow gapthermal hydraulicsgas-liquid two-phase flowdrift flux modelfloodingcooling capabilitycritical heat flux
Sodium-cooled fast breeder reactors use liquid sodium as a moderator and coolant to transfer heat from the reactor core. The main hazard associated with sodium is its rapid reaction with water. Sodium–water reaction (SWR) takes place when water or vapor leak into the sodium side through a crack on a heat-transfer tube in a steam generator. If the SWR continues for some time, the SWR will damage the surface of the defective area, causing it to enlarge. This self-enlargement of the crack is called “self-wastage phenomena.” A stepwise numerical evaluation model of the self-wastage phenomena was devised using a computational code of multicomponent multiphase flow involving a sodium–water chemical reaction: sodiumwater reaction analysis physics of interdisciplinary multiphase flow (SERAPHIM). The temperature of gas mixture and the concentration of NaOH at the surface of the tube wall are obtained by a numerical calculation using SERAPHIM. Averaged thermophysical properties are used to assess the local wastage depth at the tube surface. By reflecting the wastage depth to the computational grid, the self-wastage phenomena are evaluated. A two-dimensional benchmark analysis of an SWAT (Sodium-Water reAction Test rig) experiment is carried out to evaluate the feasibility of the numerical model. Numerical results show that the geometry and scale of enlarged cracks show good agreement with the experimental result. Enlarged cracks appear to taper inward to a significantly smaller opening on the inside of the tube wall. The enlarged outer diameter of the crack is 4.72 mm, which shows good agreement with the experimental data (4.96 mm).
