Natural Convection Heat Transfer From Vertical 5 × 5 Rod Bundles in Liquid Sodium

Abstract

Natural convection heat transfer from vertical 5 × 5 rod bundles in liquid sodium was numerically analyzed for two types of the bundle geometry (equilateral square array (ESA) and equilateral triangle array (ETA)). 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 thermophysical properties concerned. The 5 × 5 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, (Rf,L)ij and (Rf,L)5×5,S/D, ranging from 3.08 × 104 to 4.19 × 107 (q = 1 × 104–7 × 106 W/m2) in liquid temperature (TL = 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 5 × 5 rod bundles were ranged from 1.8 to 6 on each bundle geometry. The spatial distribution of local and average Nusselt numbers, (Nuav)ij and (Nuav,B)5×5,S/D, on vertical rods of a bundle was clarified. The average value of Nusselt numbers, (Nuav)ij and (Nuav,B)5×5,S/D, for the two types of the bundle geometry with various values of S/D were calculated to examine the effect of the bundle geometry, S/D, (Rf,L)ij, and (Rf,L)5×5,S/D on heat transfer. The bundle geometry for the higher (Nuav,B)5×5,S/D value under the condition of S/D = constant was examined. The correlations for (Nuav,B)5×5,S/D for two types of bundle geometry above mentioned including the effects of (Rf,L)5×5,S/D and S/D were developed. The correlations can describe the theoretical values of (Nuav,B)5×5,S/D for the two types of the bundle geometry at S/D ranging from 1.8 to 6 within −12.64% to 7.73% difference.