Improved natural convection heat transfer correlations for reactor cavity cooling systems of high-temperature gas-cooled reactors: From computational fluid dynamics to Pronghorn

Abstract

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 (∼80%) and natural convection (∼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 1×1011 in a rectangular cavity. Next, the selected model is used to perform simulations of an HTGR cavity at different high Rayleigh numbers ∈[6.1×1011,2.9×1013] 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.