Nuclear energy has recently re-gained support as a reliable source of carbon-free electricity. However, the safety of nuclear plants is still questioned, particularly in the wake of the tragic events in Fukushima. In response to this, the adoption of passive safety systems, providing cooling to the plant even in the absence of any active power, has been accelerated. However, the confident assessment of their effectiveness is still constrained by the large spatial scales involved, which makes experimental validation difficult and expensive. Additionally, the many complexities intrinsic to the prediction of natural convection makes the mathematical modelling of such systems problematic. In this paper, the development of computational fluid dynamics (CFD) as a reliable method to ultimately prove, and eventually improve, the passive safety features of reactors is described. The focus of the paper is external reactor vessel cooling. In the case of a reactor core melting, the core is kept inside the reactor vessel, which is cooled from the outside by natural convection after flooding the region of the containment that houses the vessel. More specifically, a recent experiment that simulates, at a reduced scale, cooling of the horizontal calandria vessel of a pressurized heavy water reactor, submerged in a water pool, is modelled using CFD. For this situation, of major relevance is the correct prediction of boiling on the external surface of the reactor vessel, and thermal stratification in the water pool, which could prevent lower regions of the pool from performing any heat transfer duty. Results from standard Reynolds-averaged Navier-Stokes based turbulent flow simulations demonstrate that more advanced models are needed for accurate simulation, specifically in view of the excessive mixing predicted by such approaches. In contrast, the development of a more advanced tool based on large eddy simulation (LES) is started from the prediction of thermal stratification in the water pool, for which good accuracy is demonstrated through comparisons with available data. Although further improvements are needed, and discussed, it is demonstrated that LES can provide a reliable tool for the analysis and design of passive safety systems and strategies, and the assessment of passive cooling effectiveness and reactor safety. Although computational effort remains the main constraint in using LES, computation times are not prohibitive, particularly given the continual increase in available computing resources.