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

Laminar natural convection heat transfer from vertical 7 x 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 x 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,Ra-L)(ij) and (Ra-f,Ra-L)(Nx x Ny,S/D), ranging from 3.08 x 10(4) to 4.28 x 10(7) (q = 1 x 10(4) similar to 7 x 10(6) W/m(2)) 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 x 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 x Ny,S/D), were clarified. The average values of Nusselt number, (Nu(av))(ij) and (Nu(av,B))(Nx x 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,Ra-L)(ij) and (Ra-f,Ra-L)(Nx x Ny,S/D) on heat transfer. The bundle geometry for the higher (Nu(av,B))(Nx x 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 x N-y rod bundle with the ESA and equilateral triangle array (ETA), including the effects of array size, (Ra-f,Ra-L)(Nx x Ny,S/D) and S/D were derived. The correlations for vertical N-x x N-y rod bundles can describe the theoretical values of (Nu(av,B))(Nx x 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,Ra-L)(Nx x Ny,S/D) = 3.08 x 10(4) to 4.28 x 10(7)) within x 9.49 to 10.6% differences.