Direct numerical simulation of sodium in vertical channel flow: From forced convection to natural convection at friction Reynolds number 180

The buoyancy-aided sodium flow in a vertical channel is investigated using direct numerical simulation (DNS) to study turbulent flow and heat transfer at six different Richardson numbers (Ri = 0, Ri = 0.025, Ri = 0.25, Ri = 2.5, Ri = 7.5, and Ri = 15) with a fixed friction Reynolds number (Reτ = 180). The results reveal that the velocity profile shows an “M” shape under buoyancy effect and reverses at the center under strong buoyancy. Additionally, the temperature profile exhibits a thicker boundary layer compared to the velocity profile. Global coefficients, such as the skin friction coefficient and the Nusselt number, are analyzed using Fukagata, Iwamoto, and Kasai (FIK) decomposition to elucidate their respective contributions. Furthermore, anisotropy analysis indicates that buoyancy makes the turbulence more isotropic, and the buoyancy also makes the turbulent Prandtl number (Prt) unpredictable; however, a comparison among the molecular heat flux, the definition of turbulent heat flux, and the calculation of the standard gradient diffusion hypothesis (SGDH) model suggests that the turbulent heat flux can be neglected without significant influence in this study. Finally, the turbulent structures in the viscous layer are presented, and the quadrant analysis is performed to quantitatively analyze the influence of buoyancy on the turbulent structure.