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

암반단열에서 비선형유동이 발생하는 임계 레이놀즈수

  • Kim, Dahye (Department of Geological and Environmental Sciences, Chonnam National University) ;
  • Yeo, In Wook (Department of Geological and Environmental Sciences, Chonnam National University)
  • 김다혜 (전남대학교 지구환경과학부) ;
  • 여인욱 (전남대학교 지구환경과학부)
  • Received : 2019.07.29
  • Accepted : 2019.08.27
  • Published : 2019.08.28

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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