By Kurt Kugeler and Nader Sanei, Institute for Reactor Safety and Technology, Aachen Technical University, Aachen,Germany; and Wolfgang Timm, Fluent Germany

View the pdf of this Supplement

Although a subject of ongoing controversy, nuclear power generation and nuclear fuel will continue to be indispensable to future energy supply strategies. The decreasing availability of fossil fuels, the greenhouse effect, and growing energy demands in fast-developing countries like China will very likely lead to the construction of new nuclear power plants in the years to come. Because of limited fissile material reserves, there is an associated need to develop innovative and more efficient nuclear power generation techniques, especially for fast breeders. Fast breeders are nuclear reactors that are used for power generation as well as the simultaneous breeding of fissile materials. Since the safe operation of each new type of power plant must be guaranteed to avoid accidents like those at Chernobyl and Three Mile Island, a project has been underway at Aachen Technical University to study failure scenarios for a fast breeder reactor. Researchers in the Reactor Safety and Technology Group have undertaken the task of assessing the thermal performance of the core catcher of an 875 MW_th fast breeder following a core meltdown. The core catcher is a well-insulated container at the base of the reactor cavern. In the unlikely event of a core meltdown, the core catcher has to encapsulate the molten radioactive materials (melt) in a safe way for a long period of time until sufficient cooling has taken place.

Core catcher for an 875 MWth Fast Breeder

Using FLUENT, a complete reactor core meltdown was assumed, and the behavior of this melt in the core catcher was simulated. The core catcher is a graphite hemisphere with an inner radius of 3 m, and a shell thickness of 0.3 m. It is embedded in a twolayer block composed of concrete and zirconium dioxide, which serve as thermal insulators. The graphite is surrounded with a steel liner on which cooling channels are mounted to provide an outer shell temperature of 410 K throughout the process. Inside the graphite shell there is a solid steel bed initially kept at 580 K. At the beginning of the simulation, two liquid phases are assumed to be present: uranium dioxide and contaminated molten steel, both at a temperature of 3275 K. In both phases there is an internal heat source due to the radioactive decay of the fission products present. This heat source power, PN_' is a function of the reactor thermal power (P_th = 875 MW_th in this case), the time that the reactor has been operating under normal conditions, t0_' and the time after shut-down, t:

where C is a constant.

The complex flow field in the melt

The simulation was done using the volume of fluid (VOF) and phase change models. The fluid zone was defined as one consisting of three phases: the uranium dioxide and contaminated steel phases (initially molten) and an uncontaminated steel phase (the initially solid steel bed in the core catcher). The heat source term applied to the uranium dioxide and contaminated steel phases was supplied by a user-defined function (UDF) in which P_N was computed for each time step and multiplied by the volume fraction of each phase in each cell. When accounting for solidification and melting, the mushy-zone capability in the phase change model was used. Heat transfer in the melt pool was assumed to take place through a mixed convection and conduction mechanism, consisting of natural convection near the side walls causing a downward flow of colder melt adjacent to the walls, natural convection in the upper zone of the bulk creating the main flow circulation in the system, and heat conduction in the lower (stratified) zone of the molten pool. The resulting flow field is more complicated than the classical case of Rayleigh-Bénard natural convection. On one hand, this is due to the existence of internal heat sources, and on the other hand, it is due to the solidification and melting processes and the corresponding movement of the melt front. Because of the high internal Rayleigh numbers characteristic of the system (10⁹ to 10¹²), the flow was considered turbulent, even though the velocity magnitudes in the liquid melt were not very high. The RNG k-ε model was chosen. A 2D axisymmetric solution was performed and 26 hours of real-time were simulated using a time step size of less than a second.

Contours of solid/liquid (blue/red, left); uranium dioxide (yellow=maximum, middle); and temperarture (red=maximum, right) after 2, 4, and 26 hours (top to bottom)

Neither experimental nor theoretical data for a nuclear meltdown of this type is available in the literature. However there are some basic flow features that can be expected, and the simulation results have successfully captured these features. In particular, once the core melt is in the core catcher, the steel bed begins to melt, and the flow can be roughly divided into three zones: a colder flow falling downward near the side walls, an unstable zone in the bulk with strong turbulence, and a stratified zone beneath it where heat transfer is dominated by conduction. After two hours, a large part of the steel bed is molten, with the melting front moving downward as the denser uranium dioxide sinks due to the gravitational force. During this time, the uranium solidifies and sinks down in chunks that are surrounded by liquid steel.

The 4-hour-mark serves as a turning point for the meltdown process. Before this time, energy is constantly being transferred from the uranium dioxide to the steel, causing the amount of molten steel to increase and the uranium dioxide to cool and solidify. The solidified uranium dioxide chunks reach the bottom after about 4 hours, and remarkably, some of them begin to melt again. This happens because there is neither sufficient upward convective heat transfer through the molten steel nor enough downward conductive heat transfer to maintain a temperature below the uranium dioxide melting point. The thermal conductivity of the uranium dioxide is too low, and the surface area of contact with the steel container is too small for it to be able to remove the heat generated by continued radioactive decay. Thus, re-melting occurs.

After 26 hours, a quasi-steady state is achieved in which both phases remain at their respective melting temperatures. A crust of considerable thickness forms and covers the molten steel and uranium dioxide beneath it. The temperature distribution at this time can be assumed to remain somewhat stable in the core catcher for a time frame of several months. The process will take place in a safe manner, however, since it will be encapsulated in the huge block of steel, concrete, and zirconium dioxide.

FluentNEWS Supplement