On a Simple Expression of Reynolds Number, and Lower Critical Reynolds Number for Pseudo-Plastic Fluid Flow in Concentric Annular Tubes
On a Simple Expression of Reynolds Number, and Lower Critical Reynolds Number for Pseudo-Plastic Fluid Flow in Concentric Annular Tubes
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关于同心环形管中拟塑性流体流动的雷诺数和下临界雷诺数的简单表达
DOI：
10.2473/shigentosozai.119.410
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
N. Hatakeyama
中科院分区：
文献类型：
--
作者：
T. Masuyama;N. Hatakeyama
本文的目的是推导出一个简单的表达式的假塑性流体在同心环空中流动的钻井泥浆流模型假设的雷诺数和低临界雷诺数的估计方法，因为雷诺数的计算中使用插值方法，需要的低临界雷诺数的理论估计方法。根据Fredrickson和Bird（1977）给出的假塑性流体流动的理论函数，得到了雷诺数的简单表达式：(20)其能够在任何流变学常数值下估计1的理论值，误差在2%以内，其中管直径比的值大于0.2，并且为零。应用Masuyama和Kawashima（1977）给出的流动稳定性参数估算较低临界雷诺数的方法如方程所示。(32)和等式（三十三）。当流变常数的倒数为正整数时，方程的解析解为正整数。(32)是推导出来的，并显示为Eqs。(A-4)（A-12）在附录中。将同心环管内假塑性流体流动的低临界雷诺数的实验值与预测值进行了比较，结果表明，预测值与实验值在20%的误差范围内是一致的。
The aim of this paper is to derive a simple expression of the Reynolds number and an estimation method of the lower critical Reynolds number for the pseudo-plastic fluid flow in concentric annular tubes assumed the model of drilling mud flow in a well, because interpolation methods are used in the calculation of the Reynolds number and the theoretical estimation methods of the lower critical Reynolds number are needed. Based on the theoretical function for the pseudo-plastic fluid flow given by Fredrickson and Bird(1977), the simple expression for the Reynolds number is obtained as Eq.(20) that is capable of estimating the theoretical value of one within 2% error at any rheology constant values where the values of the pipe diameter ratio are more than 0.2, and zero. The estimation method of the lower critical Reynolds number by applying the flow stability parameter given by Masuyama and Kawashima(1977) is shown as Eq.(32) and Eq.(33). When the reciprocal number of the rheology constant is positive integer, the analytical solution of Eq.(32) is derived and shown as Eqs.(A-4) to (A-12) in the appendix. It appears from the comparison of experimental and predicted lower critical Reynolds numbers for pseudo-plastic fluid flow in concentric annular tubes that the estimated values show agreement with the experimental ones within 20% error.