Numerical simulation of corium cooling driven by natural convection in case of in-vessel retention and time-dependent heat generation

Represented study considers numerical simulation of corium cooling driven by natural convection within a horizontal hemicylindrical cavity, boundaries of which are assumed isothermal. Corium is a melt of ceramic fuel of a nuclear reactor and oxides of construction materials.
Corium cooling is a process occurring during severe accident associated with core melt. According to in-vessel retention conception, the accident may be restrained and localized, if the corium is contained within the vessel, only if it is cooled externally. This conception has a clear advantage over the melt trap, it can be implemented at already operating nuclear power plants. Thereby proper numerical analysis of the corium cooling has become such a relevant area of studies.
In the research, we assume the corium is contained within a horizontal semitube. The corium initially has temperature of the walls. In spite of reactor shutdown, the corium still generates heat owing to radioactive decays, and the amount of heat released decreases with time accordingly to Way-Wigner formula. The system of equations in Boussinesq approximation including momentum equation, continuity equation and energy equation, describes the natural convection within the cavity. Convective flows are taken to be laminar and two-dimensional.
The boundary-value problem of mathematical physics is formulated using the non-dimensional non-primitive variables «stream function – vorticity». The obtained differential equations are solved numerically using the finite difference method and locally one-dimensional Samarskii scheme for the equations of parabolic type.
As a result of the present research, we have obtained the time behavior of mean Nusselt number at top and bottom walls for Rayleigh number ranged from $10^3$ to $10^6$. These mentioned dependences have been analyzed for various dimensionless operation periods before the accident. Investigations have been performed using stream-lines and isotherms as well as time dependences for convective flow and heat transfer rates.