Flow Around a Crack in a Porous Matrix and Related Problems |
| |
Authors: | Ahmad Pouya Siavash Ghabezloo |
| |
Institution: | (1) Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Yuseong, Daejeon, 305-701, Korea |
| |
Abstract: | The equations governing plane steady-state flow in heterogeneous porous body containing cracks are presented first. Then,
a general transformation lemma is presented which allows extending a particular solution obtained for a given flow problem
to another configuration with different geometry, behaviour and boundary conditions. An existing potential solution in terms
of discharges along the cracks, established by Liolios and Exadaktylos (J Solids Struct 43:3960–3982, 2006) for non-intersecting
cracks in isotropic matrix, is extended to intersecting cracks in anisotropic matrix. The basic problem of a single straight
crack in an infinite body submitted to a pressure gradient at infinity is then investigated and a closed-form solution is
presented for the case of void cracks (infinite conductivity), as well as a semi-analytical solution for the case of cracks
with Poiseuille type conductivity. These solutions, derived first for an isotropic matrix, are then extended to anisotropic
matrices using the general transformation lemma. Finally, using the solution obtained for a single crack, a closed-form estimation
of the effective permeability of micro-cracked porous materials with weak crack density is derived from a self-consistent
upscaling scheme. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|