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以裂隙岩体高放射性核废物地下处置库性能评估为目标,提出了分布热源作用下单裂隙岩体渗流-传热的简化概念模型、控制微分方程和拉氏变换-格林函数半解析法,为进一步采用半解析法计算分布热源作用下多裂隙岩体的渗流-传热问题奠定了基础。针对单裂隙岩体的渗流-传热问题,建立考虑岩石内热源和二维热传导的控制微分方程,利用拉氏变换域微分方程的基本解建立格林函数积分方程,采用解析法处理其中的奇点,通过数值积分和拉氏数值逆变换求解,计算任意时刻裂隙水和岩石的温度分布。通过算例,与基于岩石一维热传导假定的解析解进行了对比,并计算分析了分布热源作用下单裂隙岩体的渗流-传热特征及其对裂隙开度、岩石热传导系数和热流集度的敏感度。算例表明,(1)就裂隙水温度而言,由于考虑了岩石的二维热传导,拉氏变换-格林函数半解析解小于基于岩石一维热传导假定的解析解;(2)裂隙水温度和岩石温度对裂隙开度和热流集度的敏感度较大,对岩石热传导系数的敏感度较小。
Aiming at the performance evaluation of the underground repository for high-level radionuclide nuclear waste in fractured rock masses, a simplified conceptual model of seepage-heat transfer in single-fracture rock mass under distributed heat source is proposed. The governing differential equation and Laplace transform-Green’s function semi-analytical method are Further, the semi-analytical method is used to calculate the seepage-heat transfer problem of the multi-fractured rock mass under the distributed heat source. Aiming at the seepage-heat transfer problem in single fractured rock mass, a governing differential equation considering heat source and two-dimensional heat conduction in rock is established. The integral equation of Green’s function is established by using the basic solution of differential equation in Laplace transform. The singularities , Through numerical integration and Laplace inverse numerical solution to calculate the temperature of fractured water and rock at any time. A case study is compared with the analytical solution based on the assumption of one-dimensional heat conduction in rocks. The seepage-heat transfer characteristics of single-fractured rock masses under different heat sources and their influences on fracture opening, rock thermal conductivity and heat flux concentration Sensitivity. The numerical results show that (1) in the case of fissure water temperature, Laplace transform - the semi-analytical solution of Green’s function is smaller than that based on the one-dimensional heat conduction assumption of rock due to considering the two-dimensional heat conduction of rock; (2) Rock temperature is more sensitive to fissure opening and heat flux concentration, and less susceptible to rock thermal conductivity.