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目的:少量任意布置冻结管冻结的稳态温度场无解析解。建立任意布置少量管冻结稳态温度场模型,获得解析解,解决人工冻结温度场理论问题。创新点:1.基于势函数叠加原理,确立人工地层冻结中少量管冻结稳态温度场的通用求解方法;2.建立任意布置的3根和4根非等温冻结管下冻结稳态温度场数学模型,获得其解析解通解及特解。方法:1.通过理论分析,将冻结管简化为热汇点源,确定人工地层冻结热势的拉普拉斯方程表述;2.应用势函数叠加原理建立少量管冻结稳态温度场的通用求解方法;3.建立少量管冻结稳态温度场的数学模型,通过理论推导获得温度场解析解;4.通过数值模拟,验证所提方法、数学模型和解析解的正确性和准确性。结论:1.将冻结管简化为点源(热汇),其冻结形成的热势场服从拉普拉斯方程,其解即为热势函数;2.多根冻结管冻结时,将单根冻结管的热势函数叠加,由冻结管的位置决定每根冻结管的热流,再根据边界条件定解。这一方法(即势函数叠加法)可以用于任意布置冻结管冻结稳态温度场解析解的求解;3.将冻结管简化为点源导致获得的解析解存在一定的误差,但误差仅发生在冻结管附近极小的范围内,并且误差微小,完全满足工程上的精度要求。
Objective: There is no analytic solution for a small amount of steady-state temperature field in freezing tube. A steady-state temperature field model with a small amount of tube freezing is arbitrarily set up, and an analytical solution is obtained to solve the theoretical problem of artificial freezing temperature field. Innovations: 1. Based on the principle of superposition of potential functions, a general solution to the steady-state temperature field of a few tubes frozen in artificial ground freezing is established. 2. Establish the mathematical model of the steady-state temperature field of freezing under the random arrangement of 3 and 4 non-isothermal freezing tubes Model, access to its analytical solutions and special solutions. Methods: 1.According to the analysis of theory, simplify the freezing tube as the source point of the heat sink and determine the Laplace equation of the artificial formation’s freezing potential; 2. Apply the potential function superposition principle to establish the general solution of the steady tube temperature field 3. Establish a mathematical model of a small amount of steady-state temperature field of tube freezing, obtain the analytical solution of temperature field by theoretical derivation; 4. Verify the correctness and accuracy of the proposed method, mathematical model and analytical solution through numerical simulation. Conclusions: 1. To simplify the freezing tube as a point source (heat sink), its frozen potential field obeys the Laplace equation, the solution is the thermal function; 2. When freezing a number of frozen tubes, a single The thermal function of the frozen tube is superposed. The position of the frozen tube determines the heat flow of each frozen tube, and then the solution is based on the boundary conditions. This method (ie, potential function superposition method) can be used to solve the analytical solution of freezing steady-state temperature field of an arbitrary frozen pipe.3. There is a certain error in the analytical solution obtained when the frozen pipe is simplified as a point source, but the error only occurs In the vicinity of the freezing tube is very small, and the error is small, fully meet the engineering accuracy requirements.