交叉裂隙水力学开度的计算及非线性水力特性研究

基于人工交叉裂隙模型，通过室内透水试验，得到了不同进口与出口组合时的流量和压力变化的关系曲线。同时结合串联裂隙水力学开度的计算公式，利用最小二乘法求解超静定方程组，计算交叉裂隙中每个裂隙单元的水力学开度。通过拓扑得到裂隙交叉点的几何尺寸，并求解Navier-Stokes方程，研究裂隙交叉对其水力特性的影响。结果表明，通过室内试验和串联裂隙水力学开度计算公式相结合的方法，可以准确计算每个裂隙单元的水力学开度。当雷诺数Re较小时，交叉点内部的流体成稳态层流流动；当雷诺数较大（比如Re≥100）时，可以观测到明显的漩涡，说明流体的惯性力远大于黏性力，经典的立方定律不再适用。对于1个进口2个出口的情况，出口的流量分配比率与雷诺数成二次函数关系，随着雷诺数的增大，流量分配比率的非线性越来越明显，其最大分配比率变化超过15%。出口的水力学开度e与初始水力学开度（即力学开度E0）的比值e/E0和雷诺数Re也具有二次函数关系。当Re10时，e/E0呈现出较强的非线性；利用该关系式可以得到修正的立方定律，从而进一步求解交叉裂隙的水力特性问题。

Study of nonlinear hydraulic characteristics and hydraulic aperture calculation of crossed fracture

Fluid flow tests are conducted on an artificial crossed fracture model. The relations between flux and pressure are obtained under different combinations of inlets and outlets. For these connected fractures, indeterminate equations are utilized to calculate the hydraulic aperture of each fracture element with the least squares method. The geometry of the fracture intersection is reproduced with topology method. The effect of fracture intersection on hydraulic characteristics is researched by solving Navier-Stokes equations. The results show that the fracture aperture for each fracture element can be accurately calculated based on flow test results and equations of hydraulic aperture. Within the fracture intersection, static flow and vortexes are observed respectively at lower Reynolds numbers and higher Reynolds numbers(Re≥100). It is shown that the inertial force is far larger than the viscous force and the cubic law is no longer applicative. For the cases with one inlet and two outlets, the normalized flow rate exhibits a quadratic relationship with the Reynolds number, especially when Reynolds number is large. The flow rate difference between the two outlets can be as much as 15%. The ratio of hydraulic aperture e to mechanical aperture E0, i.e. e/E0, varies with the increase of Reynolds number at the inlet. The value of e/E0 shows linear, little nonlinear and strong nonlinear relations respectively when Re10. A nonlinear modified cubic law is obtained with the relation between e/E0 and Re. This modified cubic law can be utilized to solve the nonlinear hydraulic characteristics caused by fracture intersections.