Roller转子密炼机聚合物流体的混沌混合特性

Chaotic Mixing of Polymer Melt in Internal Mixer with Roller Rotors

建立了Roller转子密炼机二维有限元模型,利用网格重叠技术,对密炼机流体的流动过程进行了数值模拟。利用粒子示踪技术,采用4阶Runge-Kutta法计算了不同转数和不同流体粒子释放位置的密炼机Poincaré截面、平均对数线拉伸及Lyapunov指数等混沌混合参数。从非线性混沌理论的视角研究了Roller转子密炼机的混沌混合机理。结果表明,在双转子周期性扰动的作用下,聚合物流体在密炼机内被反复地拉伸、折叠,且啮合区的Poincaré截面出现了典型的"马蹄形"混沌结构。随着混合周期的增加,平均线拉伸以指数形式增长,且Lyapunov指数大于零。Roller转子密炼机流体具有混沌对流的特征。

The 2D finite element model of an internal mixer with Roller rotors was established by the mesh superposition technique. Based on the particles tracking technique, the chaotic mixing parameters, such as Poincar~ section map, mean logarithm of line stretch and Lyapunov exponents were calculated by 4th-order-Runge-Kutta method. From the point of view of the nonlinear chaotic theory, the chaotic mixing mechanism in the internal mixer was studied. The results show that the polymer melt in the internal mixer undergoes the repeated actions of stretching and folding under the periodic disturbance by the two rotors. And the typical ＂Smale horseshoe＂ structure appears in the Poincare section. With increasing of mixing periods, the mean logarithm of line stretch increases exponentially and Lyapunov exponent is above zero. The fluid in internal mixer presents the characteristics of chaotic convection mixing.