As part of the design and safety analyses of the KiPT accelerator driven subcritical assembly system of Ukraine, a passive cooled spent fuel pool has been conceived, designed and analyzed numerically. The total decay power of the pool is low and The maximum heat load is 0.5 kW. Air cooling of the spent fuel pool tank through a natural convection thermosiphon is deemed sufficient to provide sufficiently low temperatures. Natural convection of the water within the tank removes the decay heat from the fuel elements to the tank surface. The present work discusses the numerical simulations of such facility by the means of CFD. While the system has low power and it is relatively simple, it poses significant challenges for the CFD simulations. in fact the presence of two natural convection patterns is a source of numerical instability at such low power. These issues and the obtained solutions are discussed in this paper. Since the problem (the simulation of two coupled natural convection systems) is general and likely to be of significant relevance to the design of future power plants, this paper is targeted to a broader audience. Rather than the specific design the focus will be on the theoretical and the practical problems involved with this kind of simulations. The problem is analyzed theoretically and numerically. For CFD simulations, the range of meshes used ranges from 1 million points to 40 million points. Several turbulence models and wall modeling approaches have been tried and tested. Several set of simulations have been performed: sets of simplified simulations considering only the external air thermo-siphon assuming a constant heat flux at the tank wall as well as a set of simulations of the coupled system using a porous medium approach in the fuel tank. All simulations provided consistent predictions and helped confirm that the temperature within the pool is below boiling point.