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

摘要

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?×?10 ~( 4 ) to 4.28?×?10 ~( 7 ) (q?= ? 1?×?10 ~( 4 ) ～7?×?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?×?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?×?10 ~( 4 ) to 4.28?×?10 ~( 7 ) ) within ?9.49 to 10.6% differences.