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http://dx.doi.org/10.9719/EEG.2019.52.4.291

Critical Reynolds Number for the Occurrence of Nonlinear Flow in a Rough-walled Rock Fracture  

Kim, Dahye (Department of Geological and Environmental Sciences, Chonnam National University)
Yeo, In Wook (Department of Geological and Environmental Sciences, Chonnam National University)
Publication Information
Economic and Environmental Geology / v.52, no.4, 2019 , pp. 291-297 More about this Journal
Abstract
Fluid flow through rock fractures has been quantified using equations such as Stokes equations, Reynolds equation (or local cubic law), cubic law, etc. derived from the Navier-Stokes equations under the assumption that linear flow prevails. Therefore, these simplified equations are limited to linear flow regime, and cause errors in nonlinear flow regime. In this study, causal mechanism of nonlinear flow and critical Reynolds number were presented by carrying out fluid flow modeling with both the Navier-Stokes equations and the Stokes equations for a three-dimensional rough-walled rock fracture. This study showed that flow regimes changed from linear to nonlinear at the Reynolds number greater than 10. This is because the inertial forces, proportional to the square of the fluid velocity, increased enough to overwhelm the viscous forces. This tendency was also shown for the unmated (slightly sheared) rock fracture. It was found that nonlinear flow was caused by the rapid increase in the inertial forces with increasing fluid velocity, not by the growing eddies that have been ascribed to nonlinear flow.
Keywords
rock fracture; nonlinear flow; critical Reynolds number; Navier-Stokes equations; Stokes equations;
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