Abstract: The hydromatic computation of the helical flow for non-Newtonian fluid is an important task in petroleum drilling.Theoretical analysis shows that the helical flow of any fluid can be characterized by three parameteres which are dependent upon the axial average velocity,the angular velocity of inner cylinders and rheogical behavior of the fluid.In this paper,shear shree function is introduced,the exact solution of helical flow have been derived from the fluid motion and constitutive equation.As four constant constitutive equation cover Bingham,power-law,Casson,modified power-law and Robertson-stiff rheological models,general soliving process of helical flow for non-Newtonian fluid in petroleum industry has practically give.Numerical evalutions verify this conclusion.

Key words: non-Newtonian, fluid, annular, helical flow, iteration method, stress, function

摘要： 非牛顿液体环空螺旋流的水力计算在石油钻井中具有重要意义.理论分析指出螺旋流可由3个特征参数a、b和c完全描述,这些参数的大小由环空螺旋流的轴向平均速度V_cp、环空内圆旋转角速度ω₁和液体的流变常数决定;从液体流动的运动方程式和具有4个流变常数的本构方程式出发,引入应力函数的概念后导出了求解特征参数的新方法.该法实际上给出了石油工业中常见的宾汉液体、幂律液体、卡森液体、修正幂律液体及罗伯逊液体的环空流和螺旋流水力计算的统一程序,数值计算显示了新方法的优越性.

关键词: 非牛顿液体, 环形空间, 螺旋流动, 迭代法, 应力, 函数