Natural Convection Heat Transfer from Horizontal Rod Bundles in Liquid Sodium

在0 ~ 90℃范围内，通过实验和理论计算得到了两个平行的水平测试柱在钠液中垂直方向与包括两个圆柱体轴线在内的平面之间的不同设置角度下的自然对流换热系数。两个试验钢瓶的直径为7.6 mm，加热长度为50mm，各钢瓶轴线之间的距离与钢瓶直径之比S/D为2。采用PHOENICS程序对两水平圆柱层流自然对流换热理论方程进行了与实验相同条件下的数值求解。在修正瑞利数R_f范围为0.0637至63.1 （q=1*10^4-7*10^6 W/m^2）的情况下，每个圆柱体的表面热通量相等。将实验得到的圆柱体上的平均努塞尔数Nu与修正瑞利数R_f [=Gr^<**>Pr^…More 2/ (4+9Pr^<1/2>+10Pr)]图上相应的理论值进行了比较。除了R_f<4在γ =0￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣两个圆柱体上Nu的理论值与各γ￣￣￣￣￣￣的实验值基本一致，偏差小于15%。在理论解的基础上，以S/D和γ为函数，得到了两个圆柱体的相关性。在两圆柱相关的基础上，建立了垂直阵列中五圆柱的联合相关。R_f在4.7 ~ 63范围内的相关值与理论解一致，差值在10%以内。对Nx*Ny阵列（Nx, Ny=5-9）中水平棒束的自然对流换热进行了数值分析，得到了三种棒束几何形式（直线排列和两种交错排列）。杆束的S_x/D和S_y/D是横坐标上中心轴与杆直径的距离之比，在每个杆束几何上的取值范围为1.6 ~ 2.5。计算了不同S_x/D和S_y/D值下三种束形结构的努塞尔数平均值Nu_<av>，考察了阵列尺寸、S/D和R_f对传热的影响。Nu_<av>随R_f值的减小而减小，随S_x/D和S_y/D值的增大而增大。在S_x/D和S_y/D值组合相同的情况下，Nu_<av>的值几乎一致，与束的几何形状无关。在(S_x/D) * (S_y/D)=4的条件下，通过改变S_x/S_y的比值，检验了较高Nu_<av>值的束几何形状。建立了包括S_x/D和S_y/D影响在内的三种束形的Nu_<av>的相关关系。该相关性可以描述Nx*Ny阵列（Nx, Ny=5-9）中三种束形的S_x/D和S_y/D的Nu_<av>的理论值在1.6 ~ 2.5之间，差值在10%以内。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