The reactor cavity cooling system (RCCS) is a common reactor safety system in high-temperature gas-cooled Reactors (HTGR) that removes heat from the reactor pressure vessel (RPV) by radiation ($\sim 80\%$) and natural convection ($\sim 20\%$). For the simulation of accident scenarios of HTGRs, intermediate fidelity and system codes models must be employed to limit the models’ execution time. While an accurate quantification of the radiative heat transfer is available in these models, the quantification of natural convection must rely on correlations of questionable accuracy for the Nusselt number. Commonly used correlations are based in experiments performed at low Rayleigh numbers and/or using isothermal walls in simplified geometries. This work improves on the accuracy of natural convection heat transfer correlations to support HTGR designs.These correlations include both local and average Nusselt numbers as a function of the global Rayleigh number, the local Rayleigh number, and the temperature profile at the hot wall of the RCCS. In the absence of dedicated experiments and the difficulty of performing high-fidelity simulations at realistic Rayleigh numbers, the data to fit the correlations are generated with computational fluid dynamics (CFD) using Reynolds Averaged Navier-Stokes (RANS) models. First, a careful selection of the RANS turbulence model is performed by comparing the results obtained with different RANS turbulence models against high-fidelity simulations of natural convection at Ra $1\times {10}^{11}$ in a rectangular cavity. Next, the selected model is used to perform simulations of an HTGR cavity at different high Rayleigh numbers $\in [6.1\times {10}^{11},2.9\times {10}^{13}]$ to encompass several HTGR designs, assuming an isothermal RPV wall. The results obtained are used to fit a correlation for the average and space-varying Nusselt number as a function of the global and local Rayleigh numbers via a sparsity-promoting, least-squares method. The selected RANS model is then used to perform simulations of a PBMR-400 (Pebble Bed Modular Reactor) HTGR cavity with the temperature profiles at the RPV wall obtained during a PLOFC (Pressurized loss of forced cooling) transient. We use the results obtained to fit a temperature-dependent correction to the space-varying Nusselt number with the sparsity-promoting, least-squares method. The results obtained in this work enable system-level codes, such as Pronghorn, to perform higher-fidelity simulations of the heat exchange process in the RCCS while still maintaining a low computational cost.

反应堆腔体冷却系统（RCCS）是高温气冷堆（HTGR）中常见的反应堆安全系统，它通过辐射从反应堆压力容器（RPV）中带走热量（$～80\%$) 和自然对流 ($～20\%$）。对于高温气冷堆事故场景的模拟，必须采用中等保真度和系统代码模型来限制模型的执行时间。虽然在这些模型中可以准确量化辐射传热，但自然对流的量化必须依赖于 Nusselt 数有问题的准确性的相关性。常用的相关性基于在低瑞利数和/或在简化几何结构中使用等温壁进行的实验。这项工作提高了自然对流热传递相关性的准确性，以支持 HTGR 设计。这些相关性包括作为全局瑞利数、局部瑞利数和热壁温度分布的局部和平均 Nusselt 数。 RCCS。在没有专门的实验并且难以在现实瑞利数下执行高保真模拟的情况下，拟合相关性的数据是使用雷诺平均纳维 - 斯托克斯 (RANS) 模型通过计算流体动力学 (CFD) 生成的。首先，通过将不同 RANS 湍流模型获得的结果与 Ra 处自然对流的高保真模拟结果进行比较，对 RANS 湍流模型进行了仔细选择。$1\times {10}^{11}$在一个矩形腔中。接下来，所选模型用于在不同的高瑞利数下对 HTGR 腔进行仿真$\in [6.1\times {10}^{11},2.9\times {10}^{13}]$包含几个 HTGR 设计，假设一个等温 RPV 墙。获得的结果用于通过稀疏促进最小二乘法拟合作为全局和局部瑞利数的函数的平均和空间变化的 Nusselt 数的相关性。然后使用选定的 RANS 模型对 PBMR-400（球床模块化反应器）HTGR 腔进行模拟，其中 RPV 壁的温度分布在 PLOFC（强制冷却的加压损失）瞬变期间获得。我们使用获得的结果通过稀疏促进最小二乘法对随空间变化的 Nusselt 数进行温度相关校正。在这项工作中获得的结果启用了系统级代码，例如 Pronghorn、