非规则边界相变温度场奇异摄动解

A Singular Perturbation Method of Phase Change Temperature of Petroleum Pipeline in Seasonally Frozen Ground Regions for Irregular Boundary Configuration

研究了季节冻土地区集 (输 )油管线基础土体在冬季冻结期间的相变温度场的奇异摄动解法 .通过共形映射将非规则区域进行规则化 ,导出映射后坐标系中非线性、非稳定热传导方程和相变界面热通量连续性方程 ;采用奇异摄动方法和变分原理对映射坐标系中的热传导问题进行近似分析计算 ,获得集 (输 )油管线基础土体在冬季冻结过程中的非线性温度场近似解 .

The two-dimensional phase change temperature field of petroleum pipelines in seasonally frozen ground regions under severe climate conditions is studied. Through conformal mapping w=F(z) , the irregular boundary configuration is adjusted into regular one and general form of unsteady phase change heat conduction and interface energy-balance equation on mapping coordinate are derived as following:α-iΔT-i=dwdz+{-2}T-it1h-r(k-sT-sγ-k-lT-lγ)=ρLdwdz+{-2}s(θ, t)t Singular perturbation method is used to solve unsteady phase change temperature question. The perturbation parameter ε used in the expansion solution is as ε=c-s(T-f-T-w)/L. The zero-order expansion term of frozen and thawed phase and interface equation are solved. Because the factor of the term vt in the zero-order thawed phase equation is a function of dwdz, Galerkin's method is used to solve the perturbation equation. Besides researching the temperature field of oil-pipeline system, the thermal parameter relating to temperature and numerical examples are also discussed.