Research on the mechanism and application of crystal deposition in corrugated drainage pipes
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摘要: 石灰岩地区的隧道经常面临排水管淤堵问题，采用模型模拟分析排水管淤堵形成过程和影响因素较为重要。为得到能够贴合现实工况的预测模型，考虑流场与化学反应耦合，同时结合物质传递过程，构建起对波纹管类型的曲线边界的计算与模拟模型。采用相场法与动网格结合的手段得到在自由液面情况下，结晶生成同时影响诱发流场变化的过程。结果表明：该模型对内壁摩擦系数为0.2~0.3的情况有较好的准确度，摩擦系数低于0.2时，模拟则出现较大误差，原因可能是低摩擦壁面需要调整壁面函数，同时对沉积公式进行系数修正。内壁摩擦系数高于0.3的情况则因为等效砂砾粗糙度过高，失去边界层，模拟效果较差，模型不再适用。根据上述结果，将对粤北某隧道排水管的应用进行模拟，并根据模型预测的淤堵时间来进行处治，将有效预防排水管的淤堵。Abstract:
The frequent clogging of drainage pipes of tunnel engineering in the limestone regions has significantly impacted the long-term operation and maintenance of tunnels. To better solve this problem, in this study, a multi-field coupled numerical model was constructed to thoroughly analyze the formation mechanisms and key influencing factors of drainage pipe clogging. In recent days, fluid simulation has become an important tool for solving such problems, thanks to the rapid development of computational power. At present, numerous simulation models have been developed to simulate pipeline scaling; however, the conditions they simulate are often far cry from the actual working conditions of tunnel drainage pipes. To be specific, most simulations of pipeline scaling are conducted under full-pipe flow conditions, while the actual tunnel drainage pipes are rarely operated under full-pipe conditions. Considering this situation, this study integrated Fick’s law of mass transfer with the Navier-Stokes equations, thereby coupling fluid dynamics with chemical reaction kinetics through flow velocity. This coupling was achieved by incorporating mass transfer processes, which allowed for the determination of flow velocity and the distribution of calcium carbonate content within the pipe. Subsequently, a computational and simulation model was established for the curved boundaries of corrugated pipe by integrating an equation for calculating deposition thickness. To further enhance the model’s accuracy, a combination of the phase-field method and dynamic mesh technology was employed. The phase-field method simulated the movement of the gas-liquid interface, while dynamic mesh technology simulated flow channel contraction changes due to deposition. Moreover, changes in flow channel contraction may alter the flow velocity and the distribution of calcium carbonate content within the pipe, which in turn affected the contraction of the flow channel. Additionally, to ensure smooth mesh movement, mesh smoothing conditions were set, and functions were applied at the inlet and outlet to transition the movement rate from zero displacement to a specified velocity. In terms of boundary conditions, this model adopted a turbulence model. The inner wall friction coefficient of the pipe was calculated by formulas from hydraulic design manuals. Subsequently, the inner wall friction coefficient obtained from experiments was converted into an equivalent sand-grain roughness height using the Nikuradse formula, which was then used to represent various wall conditions in the model. Given that the model involves corrugated pipes, further adjustments to the Nikuradse formula are required. From the perspective of energy conservation, the energy loss caused by corrugated pipe grooves in water flow can be divided into two parts: firstly, the energy dissipation caused by imparting rotation to the stagnant water within the grooves; secondly, similar to a smooth pipe, energy loss caused by friction along the pipe wall. This portion of energy loss is related to the length of the wall. In this model, the equivalent length of the corrugated pipe is 1.2 times that of a smooth pipe with the same length. In condition of energy dissipation, and based on a series of trial calculations, the logarithmic function with base 10 was adjusted to a logarithmic function with base 11.3. The dynamic impact of crystal formation on flow field changes under free surface conditions was successfully simulated using this method. Simulation results indicate that the model developed in this study exhibits high predictive accuracy when the inner wall friction coefficient is within the range of 0.2 to 0.3, with an overall deviation between 10% and 20%. However, when the friction coefficient is below 0.2, significant deviations occur in the simulation results, which are higher than the actual deposition results. This may be due to the need for further optimization of the coefficients in the wall functions and deposition formulas under low-friction wall conditions. Moreover, when the friction coefficient exceeds 0.3, this model becomes inapplicable due to the failure of the boundary layer, which is caused by excessively high height of equivalent sand-grain roughness. In conclusion, based on the above research findings, this study has further applied the model to simulate the actual working conditions of drainage pipes in a tunnel in northern Guangdong. By predicting the clogging time and formulating corresponding treatment plans, this study provides scientific basis and technical support for the optimal design and clogging prevention of tunnel drainage systems. -
图 3 管内初期液体流动情况
a－g分别表现0~0.54s内某一时刻管内液体流动情况
Figure 3. Initial liquid flow conditions inside the pipe
图 4 工况1
a－c为10d、20d、30d水流动情况 d－f为10d、20d、30d流速云图 g－i为10d、20d、30d碳酸钙浓度分布图
Figure 4. Condition 1
图 5 工况2
a－c为10d、20d、30d水流动情况 d－f为10d、20d、30d流速云图 g－i为10d、20d、30d碳酸钙浓度分布图
Figure 5. Condition 2
图 6 工况3
a－c为10d、20d、30d水流动情况 d－f为10d、20d、30d流速云图 g－i为10d、20d、30d碳酸钙浓度分布图
Figure 6. Condition 3
图 7 工况4
a－c为10d、20d、30d水流动情况 d－f为10d、20d、30d流速云图 g－i为10d、20d、30d碳酸钙浓度分布图
Figure 7. Condition 4
图 8 工况5
a－c为10d、20d、30d水流动情况 d－f为10d、20d、30d流速云图 g－i为10d、20d、30d碳酸钙浓度分布图
Figure 8. Condition 5
图 9 工况6
a－c为10d、20d、30d水流动情况 d－f为10d、20d、30d流速云图 g－i为10d、20d、30d碳酸钙浓度分布图
Figure 9. Condition 6
图 11 实验结果与模拟结果对比图
11a-工况1的实验结果与模拟对比 11b-工况1的实验结果与模拟对比 11c-工况1的实验结果与模拟对比 11d- 工况1的实验结果与模拟对比 11e-工况1的实验结果与模拟对比 11f-工况1的实验结果与模拟对比
Figure 11. Comparison of experimental and simulation results
表 1 各个模拟工况数据
Table 1. Data for various simulation conditions
管道编号
（工况）液面高度/mm 管道坡度/% 初始流速/
cm·s−1内壁摩擦系数 1 7.1 3 41.36 0.26 2 6.9 4 43.73 0.21 3 7.2 5 41.28 0.23 4 10.2 5 41.83 0.27 5 13.3 5 39.86 0.24 6 6.9 5 43.36 0.12 7 7.1 5 42.11 0.53 8 6.8 5 40.41 0.65 9 7.0 5 43.78 0.69 10 7.3 5 39.19 0.83 
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表 2 转换后数据
Table 2. Transformed data
管道编号 内壁摩擦系数 等效砂砾粗糙高度/μm 1 0.26 3.78 2 0.21 2.89 3 0.23 3.25 4 0.27 2.71 5 0.24 3.43 6 0.12 1.23 7 0.53 7.70 8 0.65 9.05 9 0.69 9.46 10 0.83 10.76
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表 3 平均沉积厚度对比
Table 3. Comparison of average sedimentary thickness
模拟工况 实验沉积厚度/
mm·d−1模拟沉积厚度/
mm·d−1相对误差/
%1 0.0260 0.0236 9.23 2 0.0230 0.0225 2.17 3 0.0207 0.0207 0 4 0.0210 0.0209 0.5 5 0.0177 0.0212 19.77 6 0.0160 0.0206 28.75
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表 4 现场测试流速与离子浓度数据
Table 4. On-site sampling data（On-site testing of flow rate and ion concentration data）
试样编号 钙离子浓度/mg·L−1 钠离子浓度/mg·L−1 镁离子浓度/mg·L−1 钡离子浓度/mg·L−1 流速/m·s−1 1-1 66.6316 1.0865 9.3366 0.1119 0.055 1-2 64.3725 0.7503 9.3031 0.1061 0.059
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