Laminar Natural Convection Heat Transfer From Vertical 7 × 7 Rod Bundles in Liquid Sodium

Laminar natural convection heat transfer from vertical 7 × 7 rod bundle in liquid sodium was numerically analyzed to optimize the thermal–hydraulic design for the bundle geometry with equilateral square array (ESA). The unsteady laminar three-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady-state. The code of the parabolic hyperbolic or elliptic numerical integration code series (PHOENICS) was used for the calculation considering the temperature dependence of thermophysical properties concerned. The 7 × 7 heated rods for diameter (D = 0.0076 m), length (L = 0.2 m) and L/D (=26.32) were used in this work. The surface heat fluxes for each cylinder, which was uniformly heated along the length, were equally given for a modified Rayleigh number, (Ra_f,L)_ij and (Ra_f,L)_Nx×Ny,S/D, ranging from 3.08 × 10⁴ to 4.28 × 10⁷ (q = 1 × 10⁴∼7 × 10⁶ W/m²) in liquid temperature (T_L = 673.15 K). The values of ratio of the diagonal center-line distance between rods for bundle geometry to the rod diameter (S/D) for vertical 7 × 7 rod bundle were ranged from 1.8 to 6 on the bundle geometry with ESA. The spatial distribution of average Nusselt numbers for a vertical single cylinder of a rod bundle, (Nu_av)_ij, and average Nusselt numbers for a vertical rod bundle, (Nu_av,B)_Nx×Ny,S/D, were clarified. The average values of Nusselt number, (Nu_av)_ij and (Nu_av,B)_Nx×Ny,S/D, for the bundle geometry with various values of S/D were calculated to examine the effect of array size, bundle geometry, S/D, (Ra_f,L)_ij and (Ra_f,L)_Nx×Ny,S/D on heat transfer. The bundle geometry for the higher (Nu_av,B)_Nx×Ny,S/D value under the condition of S/D = constant was examined. The general correlations for natural convection heat transfer from a vertical N_x×N_y rod bundle with the ESA and equilateral triangle array (ETA), including the effects of array size, (Ra_f,L)_Nx×Ny,S/D and S/D were derived. The correlations for vertical N_x×N_y rod bundles can describe the theoretical values of (Nu_av,B)_Nx×Ny,S/D for each bundle geometry in the wide analytical range of S/D (=1.8–6) and the modified Rayleigh number ((Ra_f,L)_Nx×Ny,S/D = 3.08 × 10⁴ to 4.28 × 10⁷) within −9.49 to 10.6% differences.