In the prospect of a safe use of hydrogen in our society, one important task is to evaluate under which conditions the storage of hydrogen systems can reach a sufficient level of safety. One of the most important issues is the use of such system in closed area, for example a private garage or an industrial facility. In the scope of this paper, we are mainly interested in the following scenario: a relatively slow release of hydrogen (around 5Nl/min) in a closed and almost cubic box, representing either a fuel cell at normal scale, or a private garage at a smaller scale. For practical reasons, helium was used instead of hydrogen in the experiments on which are based our comparisons. This kind of situation leads to the fundamental problem of the dispersion of hydrogen due to a simple vertical source in an enclosure. Many numerical and experimental studies have already been conducted on this problem showing the formation of either a stably stratified distribution of concentration or the formation of a homogeneous layer due to high enough convective flows at the top of the enclosure. Nevertheless, most of them consider the cases of accidental situation in which the flow rate is relatively important (higher than 10Nl/min). Numerical simulations carried out with the CEA code Cast3M and a LES turbulence model confirm the differences of results already observed in experimental helium concentration measurments for a same injection flow rate and two different injection nozzle diameters, contradicting simple physical models used in safety calculations.