Non-Newtonian fluid pipeline flow equation and its approximate solution

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.