Validation of CFD RANS of an internally heated natural convection in a hemispherical geometry

In the context of severe accidents, one mitigation strategy that has been shown to work for low-to-intermediate power reactors is the In-Vessel Melt Retention (IVMR) of molten corium. For this reason, several efforts have been put forward to make this strategy feasible for high power reactors. In particular, the aim of the European H2020 IVMR project was to evaluate and improve current modeling strategies, such as the use of Computational Fluid Dynamics (CFD) codes for the prediction of flow and heat transfer in a homogeneous corium pool. Due to evident limitations, the validation was mainly performed against an available water-based experimental data, rather than a corium mixture. In order to overcome this limitation, complementary high fidelity numerical simulations, in the form of Direct Numerical Simulation (DNS), have been performed recently and are used in the current work as a reference for the validation purposes of the Reynolds Averaged Navier–Stokes (RANS) approach. More specifically, RANS numerical simulations of a three-dimensional hemispherical configuration are performed using the STAR-CCM+ software. Consistent with the DNS approach, the Boussinesq assumption is used to characterize the internally heated (IH) natural convection problem. The flow conditions correspond to a Rayleigh number of $1.6\cdot 10^{11}$ and a Prandtl number of 0.5. Several turbulence models available in STAR-CCM+, which are generally used for buoyancy driven flows, are compared and evaluated against the DNS results, in terms of velocity, temperature, buoyancy production of the turbulent kinetic energy and heat flux. Reasonable results are obtained by the RANS models, especially in predicting the main qualitative features of the flow configuration, such as thermal stratification, fast descending flow on the curved walls and high turbulence at the top of the domain. The main divergence between RANS and DNS is observed in the bulk region, where all the RANS computations present strong recirculation, while an extended nearly stagnant zone is predicted by DNS calculations. A quantitative analysis is performed as well, highlighting the limitations of the RANS approaches, especially for the turbulent heat flux modeling, and the need for the development of more advanced models as potential future efforts.