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Transition of effective hydraulic properties from low to high Reynolds number flow in porous media
Author(s) -
Sivanesapillai R.,
Steeb H.,
Hartmaier A.
Publication year - 2014
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/2014gl060232
Subject(s) - reynolds number , inertia , turbulence , laminar flow , darcy's law , mechanics , darcy number , porous medium , tortuosity , drag , physics , hele shaw flow , classical mechanics , porosity , geology , geotechnical engineering , nusselt number
We numerically analyze fluid flow through porous media up to a limiting Reynolds number of O ( 1 0 3 ) . Due to inertial effects, such processes exhibit a gradual transition from laminar to turbulent flow for increasing magnitudes of R e . On the macroscopic scale, inertial transition implies nonlinearities in the relationship between the effective macroscopic pressure gradient and the filter velocity, typically accounted for in terms of the quadratic Forchheimer equation. However, various inertia‐based extensions to the linear Darcy equation have been discussed in the literature; most prominently cubic polynomials in velocity. The numerical results presented in this contribution indicate that inertial transition, as observed in the apparent permeability, hydraulic tortuosity, and interfacial drag, is inherently of sigmoidal shape. Based on this observation, we derive a novel filtration law which is consistent with Darcy's law at small R e , reproduces Forchheimer's law at large R e , and exhibits higher‐order leading terms in the weak inertia regime.