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Beyond Poiseuille flow: A transient energy-conserving model for flow through fractures of varying aperture
Advances in Water Resources ( IF 4.7 ) Pub Date : 2022-04-12 , DOI: 10.1016/j.advwatres.2022.104192
Bruce Gee , Robert Gracie

Large-scale models of fluid flow through fractures are almost exclusively based on Poiseuille flow (the cubic law). When the fracture aperture is time and/or spatially varying, flow is transient, and/or flow rates are modest (Re1), Poiseuille flow predictions can deviate substantially from the full Navier–Stokes solution and generally do not satisfy conservation of energy. A new Reduced Dimension Fracture Flow (RDFF) model is derived which more accurately predicts transient fracture flow for incompressible fluids with modest Reynolds numbers. The RDFF model is derived from the two-dimensional Navier–Stokes equations and yields a two-field model (fluid flux and pressure) governed by conservation of mass and momentum. The RDFF model conserves energy and is shown to include both Poiseuille flow and Forchheimer flow as limiting cases. The performance of the RDFF model is compared to the existing Poiseuille flow model and the solution to the full Navier–Stokes equations in three benchmarks problems. The RDFF model demonstrates complex transient and inertial behaviours not previously captured and produces up to 400% improvements in error over Poiseuille flow in steady-state flow conditions for 1Re100. The RDFF model is demonstrated to be superior in application where the Reynold’s number is modest and when aperture varies in space and/or time.



中文翻译:

超越泊肃叶流:流经不同孔径裂缝的瞬态能量守恒模型

通过裂缝的流体流动的大规模模型几乎完全基于泊肃叶流动(三次定律)。当裂缝孔径随时间和/或空间变化时,流动是瞬态的,和/或流速适中(Re1),泊肃叶流预测可能会大大偏离完整的 Navier-Stokes 解,并且通常不满足能量守恒。导出了一种新的降维裂缝流动 (RDFF) 模型,该模型更准确地预测了具有适度雷诺数的不可压缩流体的瞬态裂缝流动。RDFF 模型源自二维 Navier-Stokes 方程,并产生由质量和动量守恒控制的两场模型(流体通量和压力)。RDFF 模型节省能量,并显示将 Poiseuille 流和 Forchheimer 流都包括为限制情况。RDFF 模型的性能与现有的 Poiseuille 流模型和三个基准问题中完整 Navier-Stokes 方程的解进行了比较。1Re100. RDFF 模型被证明在雷诺数适中以及孔径随空间和/或时间变化的应用中表现出色。

更新日期:2022-04-12
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