This research has found a novel computationally efficient method of modelling flow at low Reynolds number through fracture networks. The numerical analysis was performed by connecting Hele-Shaw cells to investigate the effect of intersections on the pressure field and hydraulic resistance for given inlet and outlet pressure values. In this analysis, the impact of intersecting length, intersecting angle and fracture aperture on the fluid flow was studied. For this purpose, two models with different topologies were established. The Hele-Shaw simulation results for hydraulic resistance, pressure and velocity agreed well with results obtained by solving the full Navier–Stokes equations (NSE). The results indicated an approximately linear relationship between intersection length and hydraulic resistance. Specifically, an increase in the intersection length increases the flow rate and as a result, the pressure along the intersection length decreases. The error associated with employing the Hele-Shaw approximation in comparison with NSE is less than 2%. All investigations were performed in the Reynolds Number range of 1–10.

中文翻译：

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修补 Hele-Shaw 细胞以研究裂缝网络中低雷诺数下的流动

这项研究发现了一种新的计算效率高的方法，可以通过裂缝网络对低雷诺数下的流动进行建模。数值分析是通过连接 Hele-Shaw 单元进行的，以研究交叉点对给定入口和出口压力值的压力场和水力阻力的影响。在该分析中，研究了相交长度、相交角度和裂缝孔径对流体流动的影响。为此，建立了两个具有不同拓扑结构的模型。液压阻力、压力和速度的 Hele-Shaw 模拟结果与通过求解完整的 Navier-Stokes 方程 (NSE) 获得的结果非常吻合。结果表明交叉点长度和水力阻力之间近似线性关系。具体来说，交叉点长度的增加会增加流速，因此，沿着交叉点长度的压力会降低。与 NSE 相比，使用 Hele-Shaw 近似的相关误差小于 2%。所有调查均在 1-10 的雷诺数范围内进行。