Implementation of the SP₃ Solver with Gray Boundary Conditions in OpenFOAM for Thermal Radiation Modeling: Application to Molten Salt Reactors

Evaluating heat radiation in new-generation molten salt reactors with significant optical thicknesses demands employing a high-fidelity approach for solving the radiative transfer equation (RTE). Furthermore, it is imperative to develop a boundary condition that considers the surface emissivity of metals in these systems. In this study, a P₃ approach (named SP₃) incorporating Marshak gray boundary conditions is implemented in OpenFOAM using C++ object-oriented programming to integrate with fluid mechanics and other physical phenomena.

To assess the performance of the SP₃ library, it undergoes verification against an analytical solution and validation using experimental data from Sandia flame D. Additionally, this study evaluates the impact of different methods for solving the RTE by comparing the SP₃ library with the standard heat radiation models in OpenFOAM (P₁ and fvDOM). Finally, the SP₃ library is utilized to analyze the impact of including thermal radiation in the modeling of the molten salt fast reactor (MSFR). The results show that although SP₃ estimates the radiation ratio better than P₁ for the turbulent jet flame, the discrete ordinates method (DOM) had the best prediction for this system.

In two-dimensional geometry, DOM yields temperatures different from those of SP₃ and P₁. The sensitivity analysis revealed that the trend in the sensitivity measure of SP₃ to changes in the scattering coefficient were opposite that of P₁. Moreover, the MSFR modeling results showed that considering thermal radiation can significantly impact the temperature field, particularly along the centerline and at the reactor boundaries.