Carreau-Extended非牛顿流体圆管层流流动的摄动解

Perturbation Solution for Laminar Flow of Carreau-Extended Non-Newtonian Fluid in Pipe

非牛顿流体在工业生产中应用广泛。文中基于同时包含屈服应力、时间常数和幂律指数的Carreau-Extended(简称Carreau-E)复杂流变方程及剪切应力与压降平衡关系,建立了圆管内充分发展的稳定Carreau-E流体层流管流的运动方程,并采用摄动方法推导出相应运动方程的一阶渐近解,获得了不同类型流体管流的速度分布以及压力梯度、流核宽度、屈服应力和时间常数对Carreau-E流体管流流场分布的影响规律,该研究对Carreau-E流体及其他复杂非牛顿流体管流特性研究具有参考价值。

Non-Newtonian fluids are widely used in industrial production.Based on the complex Carreau-Extended(shorted as Carreau-E)rheological equation with three parameters of yield stress,time constant and power-law index,and the equilibrium relationship of shear stress and pressure drop,motion equation for fully developed,steady and laminar flow of Carreau-E fluid in a pipe was established and its first-order asymptotic solution was derived by using perturbation method.The laws of velocity distribution of different types of fluid flow and the influences of pressure gradient,flow core width,yield stress and time constant on the flow field distribution of the Carreau-E fluid pipe flow were obtained.This study has reference value for the flow characteristics of Carreau-E fluid and other complex non-Newtonian fluids.