非牛顿液体螺旋流场的数值解

本文采用近代物理中的格林函数,把非线性常微分方程组的解表示成非齐次项的定积分迭代式,对两种有代表性的物质——塑性液体和幂律液体进行了数值计算,并与Savins方法的计算结果进行了对比,其结果令人满意。本文把钻杆与井壁之间(环形空间)的钻井液的流动视为螺旋流,考虑了钻杆转动对水力因素的影响,比不考虑钻杆旋转的环空流更符合钻井实际;并且本方法避免了传统数值解法在解边值问题时的诸多不便,是一种新的积分方法。但在有刚性流核的场合,本方法不适用。

NUMERICAL METHOD FOR HELICAL FLOW FIELD OF NON-NEWTONIAN FLUIDS IN ANNULUS

Helical flow of a Newtonian fluid such as plastic fluid or power-law fluid is contained between the two coaxial cylinders having radius R_2 and R_1(R_2>R_1), respectively, which rotates about their common axis with an angular velocity. The helical flow field of the two kinds of fluid is evaluated numerically by expressing the solution of ordinary differential equations as definite integral of non-homogeneous terms by means of Green's function. The results of this method is compared with those of the Savins's method showing that both these results are in good agreement. Moreover, for drilling fluids flowing in the annulus, helical flow in consideration of rotation of drill pipe is more true for practics than annular flow. Hence, this method has made an improvement in solving boundary value problems over the typical numerical method, but it does not hold true inthc presence of plug flow occuring in a flow field.