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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 10 Apr 2020 06:31:09 GMT2020-04-10T06:31:09ZFrom steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation
http://hdl.handle.net/10985/10895
From steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation
AGNAOU, Mehrez; LASSEUX, Didier; AHMADI-SENICHAULT, Azita
This work focuses on the occurrence of the first Hopf bifurcation, corresponding to the transition from steady to unsteady flow conditions, on 2D periodic ordered and disordered non-deformable porous structures. The structures under concern, representative of real systems for many applications, are composed of cylinders of square cross section for values of the porosity ranging from 15% to 96%. The critical Reynolds number at the bifurcation is determined for incompressible isothermal Newtonian fluid flow by Direct Numerical Simulations (DNS) based on a finite volume discretization method that is second order accurate in space and time. It is shown that for ordered square periodic structures, the critical Reynolds number increases when the porosity decreases and strongly depends on the choice of the Representative Elementary Volume on which periodic boundary conditions are employed. The flow orientation with respect to the principal axes of the structure is also shown to have a very important impact on the value of the Reynolds number of the bifurcation. When structural disorder is introduced, the critical Reynolds number decreases very significantly in comparison to the ordered structure having the same porosity. Correlations between the critical Reynolds number and the porosity are obtained on both ordered and disordered structures over wide range of porosities. A frequency analysis is performed on one of the velocity components to investigate pre- and post-bifurcation flow characteristics.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/108952016-01-01T00:00:00ZAGNAOU, MehrezLASSEUX, DidierAHMADI-SENICHAULT, AzitaThis work focuses on the occurrence of the first Hopf bifurcation, corresponding to the transition from steady to unsteady flow conditions, on 2D periodic ordered and disordered non-deformable porous structures. The structures under concern, representative of real systems for many applications, are composed of cylinders of square cross section for values of the porosity ranging from 15% to 96%. The critical Reynolds number at the bifurcation is determined for incompressible isothermal Newtonian fluid flow by Direct Numerical Simulations (DNS) based on a finite volume discretization method that is second order accurate in space and time. It is shown that for ordered square periodic structures, the critical Reynolds number increases when the porosity decreases and strongly depends on the choice of the Representative Elementary Volume on which periodic boundary conditions are employed. The flow orientation with respect to the principal axes of the structure is also shown to have a very important impact on the value of the Reynolds number of the bifurcation. When structural disorder is introduced, the critical Reynolds number decreases very significantly in comparison to the ordered structure having the same porosity. Correlations between the critical Reynolds number and the porosity are obtained on both ordered and disordered structures over wide range of porosities. A frequency analysis is performed on one of the velocity components to investigate pre- and post-bifurcation flow characteristics.Inertial flow in porous media: A numerical investigation on model structures
http://hdl.handle.net/10985/9888
Inertial flow in porous media: A numerical investigation on model structures
AGNAOU, Mehrez; LASSEUX, Didier; AHMADI-SENICHAULT, Azita
The aim of this work is to study the correction to Darcy's law for inertial flow in porous media. In many situations encountered in industrial applications such as flow in column reactors, gas flow near wells for hydrocarbon recovery and CO2 sequestration, flow in filters... , Reynolds numbers are large enough to lead to a non-linear relationship between the filtration velocity and the pressure gradient. In this work, a numerical analysis of the non linear -inertial- correction to Darcy's law is carried out for the stationary inertial flow of a one-phase Newtonian incompressible fluid on model 2D and 3D structures. Effective properties appearing in the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scale are determined using the microscopic flow fields and solving the closure problems resulting from up-scaling. From the numerical simulations, the dependence of the correction to Darcy's law on the geometrical properties of the 3D structure is studied. These properties are the shape of the solid grains which may be cubic or spherical and the degree of disorder in their arrangement in the domain. Weak disorder corresponds to a random placement of the grains of identical shape and size within each cell of a regular 3D lattice, while for strong disorder, grain size is also randomly distributed.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/98882013-01-01T00:00:00ZAGNAOU, MehrezLASSEUX, DidierAHMADI-SENICHAULT, AzitaThe aim of this work is to study the correction to Darcy's law for inertial flow in porous media. In many situations encountered in industrial applications such as flow in column reactors, gas flow near wells for hydrocarbon recovery and CO2 sequestration, flow in filters... , Reynolds numbers are large enough to lead to a non-linear relationship between the filtration velocity and the pressure gradient. In this work, a numerical analysis of the non linear -inertial- correction to Darcy's law is carried out for the stationary inertial flow of a one-phase Newtonian incompressible fluid on model 2D and 3D structures. Effective properties appearing in the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scale are determined using the microscopic flow fields and solving the closure problems resulting from up-scaling. From the numerical simulations, the dependence of the correction to Darcy's law on the geometrical properties of the 3D structure is studied. These properties are the shape of the solid grains which may be cubic or spherical and the degree of disorder in their arrangement in the domain. Weak disorder corresponds to a random placement of the grains of identical shape and size within each cell of a regular 3D lattice, while for strong disorder, grain size is also randomly distributed.