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 $\approx$ 15 m) can lead to a rather intensive heat exchange process mostly by natural convection (Rayleigh number ($Ra$) $\approx 10^{15}$). Reliable heat transfer correlations exist to date only up to $Ra \approx 10^{12}$, 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 (Angeli et al., 2015). The simulation has considered the local variations of the fluid properties. Near wall mesh discretization is enough refined ($x^+ \approx 0.2$) 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 ($Ra \approx 10^{12}$) (Yang and Bieder, 2023). 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 ($Ra \approx 10^{15}$) simulations and measurements in a meter-size scaled setup. The numerical results concerning the heat transport process show a reasonable agreement with available reference data. It is found that current simulation can successfully reproduce the heat relations $Nu \propto Ra^{0.25}$ for the laminar scheme and $Nu \propto Ra^{1/3}$ for the turbulent regime. Moreover, the comparisons of mean temperature, mean velocity, and a series of turbulent statistics with available references also achieve a qualitative agreement. Through the analysis of the 2D contour of the instantaneous velocity and temperature, 3D complete vortex evolution in the boundary layer, it is found that the turbulent development and vortex evolution in the helium boundary layer are similar to the water boundary layer at high Rayleigh number. 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.