On the numerical modelling of Corium spreading using Volume-of-Fluid methods

This paper investigates the numerical simulation of Corium spreading, focussing on modelling the two fluid Corium/air system. The complex Corium spreading flow is simplified by assuming the Corium is a homogeneous non-reactive fluid with a strongly temperature-dependent viscosity. A detailed investigation of the numerical methods most suitable to simulate Corium spreading flows is conducted, focusing on numerical errors, such as numerical diffusion, associated with the spatial discretisation of the governing equations. Numerical errors in the prediction of temperature may significantly affect the flow prediction because of the temperature-dependency of the viscosity. To this end, advection schemes to discretise the energy equation widely applied in the literature are found to be too diffusive to model the flow of interest, and the application of a discretisation scheme originally developed for the discretisation of sharp interfaces is shown to greatly reduce the numerical diffusion of temperature at the interface between the two immiscible fluids. While numerical diffusion can be limited using a suitable discretisation scheme, additional numerical errors in the calculation of the temperature-dependent viscosity arise as a result of the implicit temperature averaging inherent to the VOF method. Various viscosity averaging and smoothing strategies are tested, with the aim to mitigate errors associated with the viscosity calculation at the interface, and an algorithm to improve the calculation of the temperature-dependent viscosity of Corium in interfacial cells is proposed. The different discretisation schemes, viscosity calculation methods and smoothing strategies are tested on a spreading test case where a hot dense fluid with temperature-dependent viscosity, similar to Corium, spreads under the influence of gravity in a domain filled with a light cold fluid, highlighting the significant influence of the applied numerical methods for the simulation of Corium spreading.