裂隙岩体不稳定温度场的复合单元算法研究

基于复合单元法，结合三维热传导-对流方程和“充填模型”，提出了裂隙岩体不稳定温度场的复合单元模型。该模型前处理简便快捷，计算网格生成时无需考虑裂隙的存在，网格剖分不受限制，随后利用复合单元前处理程序，依据裂隙的位置和方位将其自动离散在单元内。对常规热传导-对流方程进行自伴随性调整，应用变分原理，推导出裂隙岩体不稳定温度场的复合单元算法，该算法可分别计算出岩块子单元和裂隙的温度值，且可真实反映裂隙中水流与相邻岩块间的热能量交换规律。将复合单元数值模型计算的不稳定温度场结果与相应的实测数据进行对比分析可知，数值计算结果与实测数据基本一致，验证了裂隙岩体不稳定温度场复合单元算法的可靠性与有效性。算例分析表明，裂隙中水流与相邻岩块间有明显的热传导和热对流作用。

Composite element algorithm for transient thermal field in fractured rock mass

Based on the composite element method, we propose a composite element model associated with a three-dimensional heat conduction-convection equation and a “filled model” for the determination of the transient thermal field in fractured rock mass. Although the existence of fractures is not considered during mesh generation, it is explicitly treated in the mapping composite element by means of the composite element pre-processing work program. There is no restriction on the computational mesh generation. A self-adjoint process is made to adjust the heat conduction-convection equation. The composite element algorithm is deduced by applying the variational principle for solving transient thermal field in fractured rock mass. The proposed method is applied to calculate the respective temperature of rock sub-elements and fracture segments, in which it also takes into account the thermal exchange characteristics of the fluid in fracture and the adjacent rock blocks. The obtained numerical results are consistent well with the experimental data. The reliability and validity of the proposed numerical method are verified with the measured results, which show that the thermal conduction and convection and obviously occur between the fluid in fracture and the adjacent rock blocks.