CAJ | 학술논문

应用投影算法与相场法相结合的数学模型，采用基于非均匀网格的自适应有限元法求解该模型，并对强制流动作用下镍过冷熔体中枝晶生长行为进行模拟。模拟结果表明，强迫对流的引入导致枝晶生长的不对称性。当流速小于临界值时，流动对枝晶的不对称生长影响较小；当流速达到或超过临界值时，枝晶生长的控制因素逐渐从热扩散过渡到对流。随着流速的增大，流动法向的一次枝晶臂朝逆流方向倾斜角度增大。而枝晶生长对熔体流动具有明显的影响。随着枝晶尺寸的增大，在顺流区域产生涡流效应，涡流区逐渐扩大并在枝晶尖端出现重熔现象。此外，非均匀网格的自适应有限元方法的 CPU 耗费时间比均匀网格方法降低一个数量级，并且加速比与计算域尺寸成正比。
응용투영산법여상장법상결합적수학모형，채용기우비균균망격적자괄응유한원법구해해모형，병대강제류동작용하얼과랭용체중지정생장행위진행모의。모의결과표명，강박대류적인입도치지정생장적불대칭성。당류속소우림계치시，류동대지정적불대칭생장영향교소；당류속체도혹초과림계치시，지정생장적공제인소축점종열확산과도도대류。수착류속적증대，류동법향적일차지정비조역류방향경사각도증대。이지정생장대용체류동구유명현적영향。수착지정척촌적증대，재순류구역산생와류효응，와류구축점확대병재지정첨단출현중용현상。차외，비균균망격적자괄응유한원방법적 CPU 모비시간비균균망격방법강저일개수량급，병차가속비여계산역척촌성정비。
A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.