摘要
空间狭缝流道在粘弹性聚合物成型加工中较为常见.针对流道特点,仅仅在流动平面内对速度采用形函数插值,在厚度方向采用傅里叶级数逼近流动分布函数,推导弱解形式的单元方程后,通过坐标变换得到整体坐标下的有限元方程系数矩阵,再集合成整体系数矩阵,从而建立了空间狭缝流动的有限柱解法.分别采用有限柱法和三维有限元对积分型K-BKZ本构模型粘弹流体在L型流道的流动进行求解,发现有限柱法与三维有限元的结果在整体上十分吻合.出口处流量分布的误差小于2%,流量的结果仅仅在流道收敛处略有差异,但差异仅局限于很小的区域.相比与三维有限元方法,有限柱法的单元数、计算时间和对内存需求大大减少.研究表明有限柱法是一种分析狭缝流动的简便有效的方法.
Space slit channel is extremely common in viscoelastic polymer process. In light of the features of the channel, shape functions of finite element are adopted to approach velocity distributions merely inside the flow plane, and Fourier series were adopted in the through-thickness direction. After the weak formulation of element equation was deduced, the coefficient matrix was transformed from local member coordinate system to the global coordinate system through coordinate transformation. Thereafter they were integrated into an integral coefficient matrix. Thus the finite piece method of space slit flow was established. The flows of viscoelastic K-BKZ fluid in L-shaped channel were solved by using the finite piece method and three dimensional finite element method（3D FEM） respectively. It was found that the results of the finite piece method and 3D FEM were highly consistent as a whole. The error of flow distribution was smaller than 2% at the outlet. There is a minor discrepancy of the pressure in the convergence region of channel and they are restricted to a small region. Comparing with 3D FEM, the elements of finite piece method are very few. Accordingly, the calculation time and the memory requirement are substantially saved. It is suggested by studies that finite piece method is a convenient and effective method for solving slit flow.
出处
《力学季刊》
CSCD
北大核心
2014年第1期149-156,共8页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(11372111)
关键词
粘弹流体
有限柱法
数值模拟
狭缝流道
viscoelastic fluid
finite piece method
numerical simulation
slit channel
