非牛顿流体管道流动方程及其近似解

Non-Newtonian fluid pipeline flow equation and its approximate solution

摘要:

为准确计算非牛顿流体充填料浆在不同工况条件下的充填流量和沿程阻力并以之指导充填工程实践,对非牛顿流体充填料浆在管道内的流动行为进行了研究.首先根据流变学以及流体力学理论,对充填料浆在管道内的流动状态进行分析,确定了非牛顿流体管道输送的层流临界条件；然后推导出近似管道流量方程,大幅度的降低了计算量、简化了计算过程；最后根据所构建的非牛顿流体管道流量方程组和近似管道流量方程组,以铜矿选厂全尾砂和325普通硅酸盐水泥制备了固体质量分数为71%、水泥掺量为11%的非牛顿流体充填料浆进行了环管试验,并分别以精确解法和近似解法对其屈服应力τ_B、稠度系数K和幂率指数n进行了计算. 研究结果表明:试验料浆在管道半径R为0.75 m、管道总长L为26 m及压差ΔP分别152 376、132 219、109 576 Pa时,流量Q分别为119.6、73.1、24.3 m³/h；基于试验结果以精确解法所求解的τ_B为128.098 3 Pa、K为0.450 6、n为1.109 7,以近似解法所求解的τ_B为138.965 2 Pa、K为1.244 4、n为0.905 7；以方程可视化方法绘制的三维图像对比证明精确解法和近似解法所求得的管道流量数值大小基本一致,且有相似的变化规律,证明了近似管道流量方程的准确性；因此,非牛顿流体管道流动方程及其近似解适用于非牛顿流体管道输送工程实践,是白金汉（Buckingham）流动方程和泊肃叶定律（Poiseuille law）的有力补充.

Abstract:

To accurately calculate the filling flow rate and on-way resistance of non-Newtonian fluid filling slurry in different working conditions and to guide filling engineering practice, the flow behavior of non-Newtonian fluid filling slurry in pipeline was studied. Firstly, according to rheology and fluid mechanics theory, the flow state of filling slurry in the pipeline was analyzed, and the critical condition of laminar flow in non-Newtonian fluid pipeline transportation was determined. Then, the approximate pipe flow equation was deduced, which greatly reduced the amount of calculation and simplified the calculation process. Finally, the non-Newtonian fluid filling slurry with mass concentration of 71% and cement content of 11% was prepared from the total tailings of copper concentrator and 325 Portland cement. Loop test was carried out based on the established non-Newtonian fluid pipeline flow equation and approximate pipeline flow equation, and the yield stress τ_B, consistency coefficient K, and power exponent n were calculated by the exact solution and approximate solution, respectively. Results show that when R was 0.75 m, L was 26 m, and ΔP were 152 6,2 219, and 109 576 Pa, then Q were 119.6,3.1, and 24.3 m³/h. The τ_B solved by the exact solution in the loop test was 128.098 3 Pa, K was 0.450 6, and n was 1.109 7, while the τ_B value solved by the approximate solution was 138.965 2 Pa, K was 1.244 4, and n was 0.905 7. The comparison of 3D images drawn by equation visualization method demonstrates that the values of pipeline flow obtained by the exact solution and the approximate solution were basically the same and had similar variations, indicating the accuracy of the approximate pipeline flow equation. Therefore, the flow equation of non-Newtonian fluid pipeline is suitable for the engineering practice of non-Newtonian fluid pipeline transportation and is a strong supplement to Buckingham flow equation and Poiseuille law.