定向渗流诱导的非对称冻结帷幕稳态温度场解析解

Analytical Solution of Steady-state Temperature Field of Asymmetric Frozen Wall Induced by Directional Seepage

受水流对流传热及冻结管热传导叠加影响,渗流场作用下人工冻结帷幕的形状具有明显的非对称性。为解决冻结帷幕形状不规则给冻结温度场计算带来的困难,以直线排布的3管冻结温度场为研究对象,采用分段等效的方法,对该类冻结帷幕的形状进行简化;基于稳态温度场的求解理论,推导得出定向渗流作用下非对称冻结帷幕稳态温度场解析解,以及冻结帷幕厚度、平均温度的计算公式;自主构建水热耦合物理模型试验系统,并开展不同流速条件下3管冻结温度场演化规律的模型试验,对公式的合理性进行验证。结果表明:关键轴线上冻结温度的计算值与试验结果吻合程度较高,解析解的合理性得到模型试验的验证;冻结帷幕的交圈时间及非对称系数随着流速的增加急剧增大;当地层中存在渗流场时,冻结温度场变化过程较为复杂,但冻结帷幕的平均温度整体仍然表现出随冻结帷幕厚度的增加而降低的规律。本文得出的解析解能够对渗流场作用下人工冻结温度场进行较为准确的数学描述,为大流速渗透地层人工冻结温度场的计算提供参考。

Due to the superposition of convection heat transfer of water flow and heat conduction of freezing pipes,the shape of the artificial frozen wall was obviously asymmetrical under the action of the seepage field.To solve the difficulty in the calculation of the freezing temperature field caused by the irregular shape of a frozen wall under the action of a seepage field,the freezing temperature field of three pipes arranged in a straight line was taken as the research object,the shape of the freezing front was simplified by the method of subsection equivalence.The analytical solution of steady-state temperature field of asymmetric frozen wall induced by directional seepage,the calculation formulas of thickness and average temperature of the frozen wall were derived based on the solution theory of steady-state temperature field.To verify the rationality of the formulas,the evolution law of the freezing temperature field of three pipes under the action of the seepage field was experimentally studied by using the self-constructed hydrothermal coupling physical model test system.The following conclusions were drawn from the research:the calculation results of freezing temperature on the key axis agreed well with the experimental results,the rationality of the analytical solution was verified by the model test;the closure time and asymmetry coefficient of the frozen wall were increased sharply with the increase of flow velocity under the action of the seepage field.When there was seepage in the formation,the temperature change process of the frozen wall was complicated,however,there was still a law that the average temperature decreased with the increase of thickness of the frozen wall.The formulas obtained in this paper could achieve an accurate mathematical description of the artificial freezing temperature field under the action of the seepage field,and it would provide a reference for the calculation of the artificial freezing temperature field of high-velocity permeation formation.