Recursive Coupling of Thermal and Mechanical FE-Models of a Creeping Pressure Vessel with a Heated Melt Pool

To gain a better understanding of the behavior of the reactor pres
sure vessel lower head in case of a core meltdown scenario in a light water reactor experiments have been conducted worldwide. Especially for experiments including a heated melt pool in the lower head like FOREVER (performed at the Royal Institute of Technology, Stockholm) it is necessary to model the melt pool convection and the temperature field within the vessel as well as creep and plasticity processes and the dislocation of the melt pool due to the expanding vessel.
Therefore a 2D Finite Element Model with 3 different sub models is developed based on the code ANSYS® Multiphysics. A thermal sub model includes planar and contact elements for conductive heat transfer. Additional surface elements are used to simulate convection and radiation from outer surface areas and a radiation matrix is used to account for internal radiative heat exchange. Normally a CFD-simulation would have been required for the natural convective heat transfer in the melt pool, but at very high internal Rayleigh numbers there is no turbulence model that correctly simulates the heat transfer. Therefore an Effective Conductivity Convectivity Model is implemented to simulate the heat transfer from the melt pool to its boundaries.
The resulting temperature field of the vessel wall is applied to the mechanical sub model of the vessel. To describe the visco-plastic deformation a numerical creep data base was developed where the creep strain rate is evaluated in dependence on the current total strain, temperature, and equivalent stress. For an evaluation of the failure times a damage model according to an approach of Lemaitre is applied. The third sub model uses hyperelasticity and contact elements to move the melt pool along with the creeping vessel wall.
In this paper the differences between the results of a simple coupled and a recursive coupled FE-simulation are highlighted. Due to the thermal expansion at the beginning and the accumulating creep strain later on the shape of the melt pool and of the vessel wall are changing. Despite the fact that these relative small geometrical changes take place relatively slowly over time, the effect on the temperature field is rather significant concerning the mechanical material behavior and the resulting failure time. Assuming the same loading conditions the change in the predicted failure time between the simple and the recursive coupled model is in the order of magnitude of the total failure time of the simple model. The comparison with results from the FOREVER-experiments shows that the recursive coupled model is closer to reality than the single step model.