纤维悬浮剪切湍流中纤维脉动取向张量变化率分析

根据张量运算原理,推导了纤维悬浮剪切湍流中纤维脉动取向张量变化率的表达式,该式由流场脉动速度梯度的二阶关联和由方位角与纤维长径比表示的关联值系数组成.基于不同的流场脉动速度梯度二阶关联值量级相当的考虑,计算了二维流场中不同长径比和方位角情况下关联值系数的值,发现一般情况下纤维脉动取向变化率取决于流场的剪切与拉伸,当纤维长径比为1时,则只取决于流场的剪切.对长径比大于1的纤维而言,不同长径比下关联值系数的变化趋势一致,大长径比情况下,长径比对纤维脉动取向变化率没有影响.纯拉伸项对于纤维脉动取向变化率的作用在θ=45°处最显著.由拉伸项与剪切项乘积构成的速度梯度项,其对应的关联系数的最大值出现在θ=30°或60°的位置.

Analysis on the variation rate of fiber fluctuating orientation tensor in the turbulent shear fiber suspension

Based on the operation principle of tensor, the expression of fiber fluctuating orientation tensor in the turbulent shear fiber suspension derived. The expression consisted of the second correlation of the fluctuating velocity gradient in the flow and the correlation coefficient which includes the orientation angle and fiber aspect ratio. On the assumption that different second correlations of the fluctuating velocity gradient were roughly same in quantity, values of correlation coefficient calculated for the different orientation angles and fiber aspect ratios in a two-dimensional flow. It found the variation rate of fiber fluctuating orientation generally depends on the fluid shear and tension, but only on the fluid shear when the aspect ratio was larger than 1. The variation trends of correlation coefficient are consistent in the cases with 1. The aspect ratio has no effect on the variation rate different aspect ratios when the aspect ratio was larger than of fiber fluctuating orientation in the cases with large aspect ratio. The effect of pure tension on the variation rate of fiber fluctuating orientation is most predominant at θ=45. The maximum of correlation coefficient which corresponds to the velocity gradient with the product of fluid tension and shear appears at θ= 30 or 60. Conclusions are helpful for the understand of distribution of fiber fluctuating orientation tensor in the turbulent shear fiber suspension.