The passive safety concept of Small Modular Reactors (SMR) is based on the transfer of residual heat from the reactor to a water pool. Since the height of the reactor vessel reaches approximately 15 $\mathrm{m}$, this leads to a strong heat exchange between the wall and the water by the way of natural convection. The maximum Rayleigh number ($\mathit{Ra}$) reaches ${10}^{14}$ or ${10}^{15}$. Reliable heat transfer correlations exist only up to $\mathit{Ra}\approx {10}^{12}$, still along with uncertainties in the extrapolation to higher Rayleigh number values. To improve the understanding of natural convection at high Rayleigh number values, the turbulent natural convection boundary layer (TNCBL) along a 15 $\mathrm{m}$ high, side-heated vertical wall in a water tank is simulated by employing the Large Eddy Simulation method with the CEA in-house code Triocfd (Angeli et al., 2015). The numerical results in terms of heat transfer correlation, mean temperature and mean velocity, second moment variables show a reasonable agreement with available experimental data in the range of $\mathit{Ra}$ < ${10}^{12}$. It is observed in the simulation that the powers of the heat transfer correlations in the laminar $({\mathit{Nu}}_y={0.56\left({\mathit{Gr}}_y\bullet \mathrm{P}\mathrm{r}\right)}^{0.25})$ and the turbulent regimes $({\mathit{Nu}}_y={0.114\left({\mathit{Gr}}_y\bullet \mathrm{P}\mathrm{r}\right)}^{1/3})$ correspond well to the classical regimes at $\mathit{Ra}<2\times {10}^{12}$. A slight deviation from the classical exponent (1/3) is found at higher Rayleigh number ($2\times {10}^{12}$ < $\mathit{Ra}$< ${1.8\times 10}^{15}$), namely ${\mathit{Nu}}_y=0.114{({\mathit{Gr}}_y\bullet \mathrm{P}\mathrm{r})}^{0.33}$ . Through the analysis of turbulent kinetic energy budget, it is found that turbulent contribution from shear stress increases continuously with the increase of Rayleigh number. However, the turbulence contribution from buoyancy keeps increasing until $\mathit{Ra}\approx {6.6\times 10}^{13}$, then decreases gradually at higher Rayleigh number. The behavior of the maximum buoyant force shifts slowly from the inner boundary layer to the outer boundary layer may indicate the potential transition of the buoyancy-dominated regime to the shear stress dominated regime, thus confirming previous theoretical prediction (Wells Andrew and Worster, 2008). The increasing scale of the streak-like turbulent structures with the increase of Rayleigh number are clearly demonstrated through visualization process.

小型模块化反应堆（SMR）的非能动安全概念基于将反应堆的余热传递到水池。由于反应堆容器的高度达到约15$\mathrm{米}$，这导致壁与水通过自然对流的方式进行强烈的热交换。最大瑞利数（$\mathit{拉}$) 达到${10}^{14}$或者${10}^{15}$。可靠的传热相关性仅存在于$\mathit{拉}\approx {10}^{12}$，仍然存在外推至更高瑞利数值的不确定性。为了提高对高瑞利数值下自然对流的理解，沿 15 的湍流自然对流边界层 (TNCBL)$\mathrm{米}$通过使用大涡模拟方法和 CEA 内部代码 Triocfd（Angeli 等人，2015）来模拟水箱中的高侧加热垂直壁。传热相关性、平均温度和平均速度、二阶矩变量方面的数值结果与现有实验数据在以下范围内表现出合理的一致性：$\mathit{拉}$ < ${10}^{12}$。在模拟中观察到，层流中传热的幂相关性$（{\mathit{努}}_y={0.56\left({\mathit{组}}_y\bullet \mathrm{磷}\mathrm{r}\right)}^{0.25}）$和动荡的政权$（{\mathit{努}}_y={0.114\left({\mathit{组}}_y\bullet \mathrm{磷}\mathrm{r}\right)}^{1/3}）$与经典制度很好地对应$\mathit{拉}<2\times {10}^{12}$。在较高瑞利数处发现与经典指数 (1/3) 略有偏差 ($2\times {10}^{12}$<$\mathit{拉}$<${1.8\times 10}^{15}$），即${\mathit{努}}_y=0.114{（{\mathit{组}}_y\bullet \mathrm{磷}\mathrm{r}）}^{0.33}$。通过对湍流动能收支的分析发现，剪应力对湍流的贡献随着瑞利数的增加而不断增加。然而，浮力对湍流的贡献不断增加，直到$\mathit{拉}\approx {6.6\times 10}^{13}$，然后在较高的瑞利数处逐渐减小。最大浮力从内边界层缓慢转移到外边界层的行为可能表明浮力主导状态到剪应力主导状态的潜在转变，从而证实了先前的理论预测（Wells Andrew和Worster，2008） 。通过可视化过程清楚地证明了随着瑞利数的增加，条纹状湍流结构的规模不断增大。