Natural Convection Heat Transfer from Horizontal Rod Bundles in Liquid Sodium

在0~90ﾟ的范围内，从实验和理论上得到了两个平行的水平试验圆筒在液钠中的自然对流换热系数，在不同的竖直方向与包括两个圆筒轴线的平面之间的夹角Gamma。两个测试圆柱体的直径为7.6 mm，加热长度为50 mm，每个圆柱体轴线与圆柱体直径的距离之比S/D为2。利用PHOENICS程序，在与实验值相同的条件下，对水平圆柱体层流自然对流换热的理论方程进行了数值求解。修正的瑞利数Rf为0.0637~63.1时，每个圆柱体的表面热流密度相等，Q=1*10^4~7*10^6 W/m^2。将实验得到的圆柱上的平均努塞尔数Nu与相应的Nu上的理论值以及修正的瑞利数Rf[=Gr^&lt；**&gt；Pr^…]进行了比较更多2/(4+9Pr^&lt；1/2&gt；+10Pr)]图表。除R_f&lt；4AT伽马=0ﾟ外，其余两个圆柱体上的Nu理论值与实验值符合较好，偏差小于15%。基于理论解，得到了两个圆柱体的关联式，它们是S/D和伽马的函数。基于两个圆柱体的相关关系，提出了垂直阵列中五个圆柱体的组合关联式。对于R_f在4.7-63范围内的五个圆柱体，关联值与理论解在10%的误差范围内是一致的。对NX*NY(NX，NY=5-9)阵列中水平棒束的自然对流换热进行了数值分析，得到了三种不同的棒束几何形状(顺排和两种错列)。在每个杆束几何形状上，杆束的S_x/D和S_y/D，即横坐标轴上中心轴与纵轴与杆径的距离之比，在1.6~2.5之间变化。为了考察阵列尺寸、S/D和Rf对换热的影响，计算了具有不同S_x/D和S_y/D值的三种束几何形状的努塞尔数的平均值Nu&lt；av和gt；。Nu_t；av&gt；随R_f的减小而减小，随S_x/D和S_y/D的增大而增大。S_x/D和S_y/D的相同组合的Nu_t；av&gt；与丛的几何形状无关。本文通过改变S_x/S_y的比值，考察了在(S_x/D)*(S_y/D)=4的条件下，具有较高Nu_&lt；av&gt；值的丛几何形状，建立了考虑S_x/D和S_y/D影响的三种丛几何形状的Nu&lt；av&gt；关联式。对于S_x/D和S_y/D在1.6%到2.5%范围内的Nx*NY阵列(Nx，NY=5-9)中的三种束几何形状，该关联式可以描述其Nu&lt；av和gt；的理论值，相差10%。较少

Natural convection heat transfer coefficients on two parallel horizontal test cylinders in liquid sodium were obtained experimentally and theoretically for various setting angles, gamma, between vertical direction and the plane including both of these cylinder axis, over the range of zero to 90ﾟ. Both test cylinders are 7.6 mm in diameter and 50 mm in heated length with the ratio of the distance between each cylinder axis to the cylinder diameter, S/D,of2. Theoretical equations for laminar natural convection heat transfer from the two horizontal cylinders were numerically solved for the same conditions as the experimental ones by using the PHOENICS code. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, R_f, ranging from 0.0637 to 63.1 (q=1*10^4-7*10^6 W/m^2). The average Nusselt numbers Nu on the cylinders obtained experimentally were compared with the corresponding theoretical values on the Nu versus modified Rayleigh number R_f [=Gr^<**>Pr^ … More 2/ (4+9Pr^<1/2>+10Pr)] graph. The theoretical values of Nu on two cylinders except those for R_f<4at gamma=0ﾟ are in agreement with the experimental data at each gamma with the deviations less than 15 %. Correlations for two cylinders were obtained as functions of S/D and gamma based on the theoretical solutions. A combined correlation for five cylinders in a vertical array based on the correlations for two cylinders was developed. The values by the correlation agree with the theoretical solution for the five cylinders for R_f ranging from 4.7 to 63 within 10% difference. Natural convection heat transfer from horizontal rod bundles in Nx*Ny arrays (Nx, Ny=5-9) was numerically analyzed for three types of the bundle geometry (in-line rows, two kinds of staggered rows). S_x/D and S_y/D for the rod bundle which are ratio of the distance between center axs on the abscissa and the ordinate to the rod diameter were ranged from 1.6 to 2.5 on each bundle geometry. The average value of Nusselt number, Nu_<av>, for three types of the bundle geometry with various values of S_x/D and S_y/D were calculated to examine the effect of the array size, S/D and R_f on heat transfer. The Nu_<av> becomes lower with the decrease in the value of R_f and higher with the increase in the value of S_x/D and S_y/D.The values of Nu_<av> with the same combinations of S_x/D and S_y/D values are almost in agreement independent of the bundle geometry. The bundle geometry for the higher Nu_<av> value under the condition of (S_x/D) * (S_y/D)=4 was examined by changing the ratio of S_x/S_y. A correlation for Nu_<av> for three types of bundle geometry above mentioned including the effects of S_x/D and S_y/D was developed. The correlation can describe the theoretical values of Nu_<av> for three types of the bundle geometry in Nx*Ny arrays (Nx, Ny=5-9) for S_x/D and S_y/D ranging from 1.6 to 2.5 within 10% difference. Less