Analytical solution for the steady-state temperature field of a linear three-pipe freezing system under hydrodynamic conditions
Analytical solution for the steady-state temperature field of a linear three-pipe freezing system under hydrodynamic conditions
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DOI：
10.1016/j.ijthermalsci.2023.108378
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发表时间：
2023
影响因子：
4.5
通讯作者：
Zhiming Li;A. Tang;Jian Chen;Yundong Zhou
中科院分区：
文献类型：
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作者：
Zhiming Li;A. Tang;Jian Chen;Yundong Zhou
水动力条件下的人工冻结施工通常需要较长的冻结幕形成周期，这给温度分布预测带来了独特的挑战。本文基于多管效应和势函数叠加原理，推导了线性三管系统冻结时稳态温度场的简单解析公式。采用“分区分段”方法，假设该系统在水动力条件下任意单条冻结稳态温度场的冻结锋形状，进一步确定单条冻结管的温度影响范围。为了考虑多管道的影响，提出了“叠加长度比”来量化相邻冻结管道的相互影响。并给出了冻结管间距和地下水流速随叠加长度比变化的经验公式。最后，结合水热耦合数值模型和不同水动力条件下的线性三管冻结模型试验，将分析结果与数值和实验结果进行比较。对比结果表明，该解析模型能有效预测不同水动力条件下线性三管系统的稳态温度场，为水动力条件下的人工冻结设计提供理论依据。
Artificial ground freezing construction under hydrodynamic conditions generally requires a longer period for the formation of a freezing curtain, bringing unique challenges in the prediction of the temperature distribution. In this study, a simple analytical formula for the steady-state temperature field in the freezing of a linear three-pipe system was derived based on the effect of multiple pipes and the principle of potential function superposition. The “partition and subsection” method was adopted to assume the freezing front shape of any single frozen steady-state temperature field in this system under hydrodynamic conditions and to further determine the temperature influence range of a single freezing pipe. To account for the effect of multiple pipes, the “superposition length ratio” was proposed to quantify the mutual effect of adjacent freezing pipes. An empirical formula for the superposition length ratio varying with different freezing pipe spacings and groundwater flow velocities was also presented. Finally, combined with a hydrothermal coupling numerical model and a linear three-pipe freezing model test under different hydrodynamic conditions, the analytical results were compared with the numerical and experimental results. The comparison results showed that the analytical model can effectively predict the steady-state temperature field of the linear three-pipe system under different hydrodynamic conditions, thus providing a theoretical basis for artificial freezing design under hydrodynamic conditions.