The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion
The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion
复制标题
DOI：
10.1002/hyp.10745
复制
发表时间：
2016-05
影响因子：
3.2
通讯作者：
Jiazhong Qian;Lei Ma;Hongbin Zhan;Q. Luo;Xiao Wang;Mu Wang
中科院分区：
文献类型：
--
作者：
Jiazhong Qian;Lei Ma;Hongbin Zhan;Q. Luo;Xiao Wang;Mu Wang
单裂隙渗流是地下水水文学、水利工程、放射性核废料处置库和岩土工程中的重要研究课题。突然变化的光圈是一种独特的SF类型。本文讨论了流动对称性破缺的临界雷诺数（Rec）与SF的膨胀比（E）之间的关系。SF的膨胀比定义为出口孔径（D）与入口孔径（d）之间的比值。本研究还使用有限体积法研究了入口孔径d对突然变化孔径SF（SF-ACA）中流动Rec的影响。早期的数值和实验结果表明，在小雷诺数（Re）时，流动相对于SF-ACA的中心平面是对称的，但当Re足够大时，流动变得不对称。我们的模拟表明，Rec的值随着E的增加而减小，并且Rec和E的对数之间的关系可以使用二次多项式函数或对数函数来准确地描述。然而，对于给定的E值，Rec和d的关系是模糊的，并且当E增加时，Rec对d变得更不敏感。这项研究还表明，水力梯度（J）和流速（v）遵循超线性关系，几乎可以通过Forchheimer方程完美拟合。J的惯性分量（Ji）随Re单调增加，而J的粘性分量（Jv）随Re单调减少。当E增大时，对应于J的惯性分量和粘性分量相等的Re值（称为过渡点Re）减小，该过渡点Re应与临界雷诺数Rec密切相关，但尚无严格的理论证明。版权所有© 2015约翰威利父子有限公司
Flow in a single fracture (SF) is an important research subject in groundwater hydrology, hydraulic engineering, radioactive nuclear waste repository and geotechnical engineering. An abruptly changing aperture is a unique type of SF. This study discusses the relation between the values of the critical Reynolds number (Rec) for the onset of symmetry breaking of flow and the expansion ratio (E) of SF, which is defined as the ratio between the outlet (D) and inlet (d) apertures. This study also investigates the effect of inlet aperture d on Rec for flow in an SF with abruptly changing apertures (SF‐ACA) using the finite volume method. Earlier numerical and experimental results showed that flow is symmetric in respect to the central plane of the SF‐ACA at small Reynolds number (Re) but becomes asymmetric when Re is sufficiently large. Our simulations show that the value of Rec decreases with the increasing E, and the relationship between the logarithm of Rec and E can be described accurately using either a quadratic polynomial function or a logarithmic function. However, the relationship of Rec and d for a given E value is vague, and Rec becomes even less sensitive to d when E increases. This study also reveals that the hydraulic gradient (J) and flow velocity (v) follow a super‐linear relationship that can be fitted almost perfectly by the Forchheimer equation. The inertial component (Ji) of J increases monotonically with Re, whereas the viscous component (Jv) of J decreases monotonically with Re. The Re value corresponding to equal inertial and viscous components of J (named as the transitional point Re) decreases when E increases, and such a transitional point Re should be closely related to the critical Reynolds number Rec, although a rigorous theoretical proof is not yet available. Copyright © 2015 John Wiley & Sons, Ltd.