Upscaling of Navier–Stokes equations in porous media: Theoretical, numerical and experimental approach |
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Authors: | Guillermo A Narsilio Olivier Buzzi Stephen Fityus Tae Sup Yun David W Smith |
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Institution: | 1. Melbourne Engineering Research Institute (MERIT), Department of Civil and Environmental Engineering, The University of Melbourne, Parkville, VIC 3010, Australia;2. Centre for Geotechnical and Materials Modelling, The School of Engineering, The University of Newcastle, Callaghan, NSW 2308, Australia;3. Department of Civil and Environmental Engineering, Lehigh University, 13 East Packer Avenue, Bethlehem, PA 18015, USA;4. Faculty of Engineering, Computing and Mathematics, The University of Western Australia (M017), Crawley, WA 6009, Australia |
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Abstract: | The accurate estimation of hydraulic conductivity is important for many geotechnical engineering applications, as the presence of fluids affects all aspects of soil behaviour, including its strength. Darcy’s law is the key experimental (or phenomenological) equation employed to model ground water flow. Yet, this phenomenological equation can be linked to a more fundamental microscale model of flow through the pore spaces of the porous material. This paper provides an experimental verification of the relationships between Darcy’s law (macroscale) and the Navier–Stokes equations (microscale) for actual complex pore geometries of a granular material. The pore geometries are experimentally obtained through state-of-the-art X-ray computer assisted micro-tomography. From the numerical modelling of the microscale flow based on actual pore geometries, it is possible to quantify and visualize the development of pore-scale fluid preferential flow-paths through the porous material, and to assess the importance of pore connectivity in soil transport properties. |
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Keywords: | Fluid flow Porous media Navier– Stokes Darcy’ s law micro-CT Hydraulic conductivity |
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