寒区隧道轴向及径向温度分布理论解

Analytical Solution to Axial and Radial Temperature of Tunnel in Cold Region

摘要:

考虑与隧道纵向深度及时间相关的非齐次对流边界条件，建立寒区圆形隧道传热模型，利用叠加原理及贝塞尔特征函数的正交及展开定理，得到了寒区隧道围岩径向温度的理论解.利用能量守恒法及经验公式法求得寒区隧道洞内气体年平均气温及年温度振幅沿隧道轴向随时间变化的解析表达式，并得出年平均温度在隧道轴线方向呈指数增长，而年温度振幅呈负指数增长.将隧道围岩轴向和径向温度场理论计算结果与实测值进行比较，两者吻合得非常好.在确定洞口外气温分布规律、风速及围岩的热物性参数后，通过围岩轴向及径向温度场理论解便可计算隧道洞内及围岩温度分布规律，并确定寒区隧道防寒保暖段的设防长度.同时，该解析法可用于验证其他数值方法的计算结果，也便于工程设计人员和施工人员对同类寒区隧道温度场的计算，因而具有一定的工程应用价值.

Abstract:

Based on superpositon principle and the orthogonal expansions of Bessel eigenfuncion,the analytical solution to radial temperature of circle tunnel in cold region was obtained subject to time and distance dependent boundary changes of the third kind.The analytical solutions of the annual mean temperature and temperature amplitude were obtained by energy banlance method and experiential method with a consideration of heat conduction/convection between the tunnel ground and the air flow in the tunnel.The annual mean temperature presented an exponential growth with the increasing distance from entry of tunnel,the annual temperature amplitude a negative exponential growth.Applicablity and accuracy of the equation were examined by comparing the calculated results with the mesaured results.It is found that the calculated values agree well with those measured in the field.In determining the temperature distribution outside the tunnel,wind speed and thermal properties parameters of surrounding rock,the axial and radial temperature can be calculated with the analytical solution.The necessary length of anti-icicle treatment from tunnel entrance area can also be determined.The analytical solution proves to be useful for engineers and technicians.