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本文目的是探讨金属型铸件在获得等轴晶的条件下数值模拟的一些规律。对于同一铸件,在获得等轴晶的相同条件下,采用有限差分交替方向隐式(I.A.D)、有限差分显式和有限元三种方法进行了计算,并对三种方法的优缺点作了比较。为了提高计算精度,对如何处理凝固潜热,铸件—铸型界面热性质和初始条件等问题进行了分析。采用了三种不同折合比热函数来模拟凝固阶段潜热的释放。调整了界面的各种参数观察其对温度场的影响。符号表 T 温度 (℃) b 蓄热系数 (cal/cm~2·S·1/2·℃) t 时间 (s) v 表面换热系数 c 比热 (cal/g℃) M =△τ·k/c·p·(△x)~2 p 容重 (g/cm~3) k 在T的右上角表示时间步长数 k 导热系数 (cal/s·cm·℃) i r或x方向空间步长数 J 潜热 (cal/g) j r或x方向空间步长数 f_B 凝固阶段固相析出量与总量之比 m 液相线斜率 cj =(-J)()(cal·/g·℃) C_o 溶质浓度 x,y 直角坐标系中空间变量 T_L 液相线温度(℃) r,z 柱坐标系中空间变量 T_s 固相线温度(℃) n 边界法线方向坐标变量α导温系数(cm~2/s) r 定义域的边界线下标含义 m或M 金属或铸件 s 铸型 sm 相对于铸件的铸型界面ms 相对于铸型的铸件界面i 界面
The purpose of this paper is to investigate some of the numerical simulations of metallic castings obtained with equiaxed grains. For the same castings, three methods of finite difference alternating direction implicit (IAD), finite difference explicit and finite element method were used under the same conditions of obtaining equiaxed grains, and the advantages and disadvantages of the three methods were compared . In order to improve the calculation accuracy, the issues of how to deal with the latent heat of solidification, the thermal properties of the casting-mold interface and the initial conditions are analyzed. Three different specific heat transfer functions were used to simulate the release of latent heat during the solidification stage. Adjust the various parameters of the interface to observe its impact on the temperature field. Symbol Table T Temperature (° C) b Heat storage coefficient (cal / cm 2 · S · 1/2 · ° C) t Time (s) v Surface heat transfer coefficient c Specific heat (cal / g ° C) M = k / c · p · (Δx) ~ 2 p Bulk density (g / cm ~ 3) k The time step in the upper right corner of T k Thermal conductivity (cal / s · cm · ° C) ir or space step in x direction Length J latent heat (cal / g) jr or space step in x direction f_B ratio of solid phase precipitation amount to total amount in solidification phase slope of liquidus cj = (- J) () (cal · / g · ° C) C_o Solute concentration x, y Spatial variables in Cartesian coordinates T_L Liquidus temperature (° C) r, z Spatial variables in the cylindrical coordinate system T_s Solidus temperature (° C) n Coordinates of the normal direction of the boundary Variant α Thermal conductivity coefficient (cm ~ 2 / s) Boundary line of the definition field Subscript Meaning m or M Metal or castings s Molds sm Mold surface relative to the casting ms Casting surface relative to the mold i Interface