The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion
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2016 John Wiley & Sons, Ltd. 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.
