为了检验纤维取向各封闭格式对三维剪切流场的适用性情况,对6种封闭格式进行了研究.将6种封闭格式分别代入二阶取向张量的控制方程进行数值求解,将求得的二阶取向张量的5个分量分别与根据定义直接积分求得的分量作比较.结果发现,封闭格式的动态特性高度依赖于纤维相互作用系数和长径比的取值.当忽略纤维之间的相互作用,且纤维的长径比趋于无限大时,除了线性封闭,其他5种封闭格式差别很小.当相互作用系数大于0.01时,H&L第一复合封闭呈现较好的动态和稳态行为.
Six closure models of fiber orientation were used to solve numerically the controlling equation of the second-order orientation tensor in order to determine the applicability of different closure models to simulating three-dimensional shear flows. Then five independent components of the second-order orientation tensor were compared with the integrally calculated values according to definition. Results show that the dynamic characteristic of every closure relies strongly on the values of fiber's interaction coefficient and aspect ratio. When the interaction of fibers is ignored and the aspect ratio tends to infinite, the differences of the closure models are small except the linear closure. When the interaction coefficient is larger than 0.01, the first composite closure proposed by Hinch and Leal exhibits good transient behavior and accurate steady-state value.