Natural Convection Heat Transfer From Vertical 7x7 Rod Bundles in Liquid Sodium

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 PHOENICS code was used for the calculation considering the temperature dependence of thermo-physical properties concerned. The 7×7 test rods for diameter (D = 7.6 mm), heated length (L = 200 mm) and L/d (= 26.32) were used in this work. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, (R_f,L)_ij and (R_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 S/D, which are ratios of the diameter of flow channel for bundle geometry to the rod diameter, for vertical 7×7 rod bundle were ranged from 1.8 to 6 on the bundle geometry with equilateral square array. 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 value 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, (R_f,L)_ij and (R_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 equilateral square and triangle arrays including the effects of array size, (R_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 to 6) and the modified Rayleigh number ((R_f,L)_Nx×Ny,S/D = 3.08×10⁴ to 4.28×10⁷) within −9.49 to 10.6 % differences.