The passive safety concept of Small Modular Reactors (SMR) is based on the extraction of residual heat from the reactor to a surrounding water pool. However, the large scale of the reactor vessel (height ~ 15 m) can lead to a rather intensive heat exchange process mostly by natural convection (Rayleigh number (Ra) ~ 10¹⁵). Reliable heat transfer correlations exist to date only up to Ra ~ 10¹², with uncertainties in the extrapolation to higher Ra. To improve the understanding of natural convection at high Ra number and find a valid heat transfer correlation, the three-dimensional turbulent natural convection boundary layer (TNCBL) along a side-heated vertical wall in a cryogenic helium tank is simulated with Large Eddy Simulation method in the CEA in-house code TrioCFD [1]. The simulation has taken into account the local variations of the fluid properties. Near wall mesh discretization is enough refined (x⁺ ~ 0.2) to resolve the thin boundary layers. Our preliminary analysis with water as a working fluid have shown the ability of the computational model in recovering the heat transfer behavior at moderate Rayleigh number (Ra ~ 10¹²) [2]. As the second step, cryogenic helium is selected as a working fluid for its special physical properties (low viscosity, high thermal expansion...), which allows to perform high Rayleigh (Ra ~ 10¹⁵) simulations and measurements in a meter-size scale setup. The numerical results concerning the heat transport process show a reasonable agreement with available reference data. Moreover, the mean temperature and mean velocity in the boundary layer at different Rayleigh number are also presented. The vortex evolution in the boundary layer is visualized to enhance the understanding of the turbulence developing procedure. Current work can shed more light on the understanding of the turbulent natural convection along the vertical wall at high Rayleigh number and support the design of new experiments at CEA to validate these results.