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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.Origin of the Inertial Deviation from Darcy's Law: an 2 Investigation from a Microscopic Flow Analysis on 2D Model
http://hdl.handle.net/10985/12154
Origin of the Inertial Deviation from Darcy's Law: an 2 Investigation from a Microscopic Flow Analysis on 2D Model
AGNAOU, Mehrez; LASSEUX, Didier; AHMADI, Azita
Inertial flow in porous media occurs in many situations of practical relevance among which one can cite flows in column reactors, in filters, in aquifers, or near wells for hydrocarbon recovery. It is characterized by a deviation from Darcy’s law that leads to a nonlinear relationship between the pressure drop and the filtration velocity. In this work, this deviation, also known as the nonlinear, inertial, correction to Darcy’s law, which is subject to controversy upon its origin and dependence on the filtration velocity, is studied through numerical simulations. First, the microscopic flow problem was solved computationally for a wide range of Reynolds numbers up to the limit of steady flow within ordered and disordered porous structures. In a second step, the macroscopic characteristics of the porous medium and flow (permeability and inertial correction tensors) that appear in the macroscale model were computed. From these results, different flow regimes were identified: (1) the weak inertia regime where the inertial correction has a cubic dependence on the filtration velocity and (2) the strong inertia (Forchheimer) regime where the inertial correction depends on the square of the filtration velocity. However, the existence and origin of those regimes, which depend also on the microstructure and flow orientation, are still not well understood in terms of their physical interpretations, as many causes have been conjectured in the literature. In the present study, we provide an in-depth analysis of the flow structure to identify the origin of the deviation from Darcy’s law. For accuracy and clarity purposes, this is carried out on two-dimensional structures. Unlike the previous studies reported in the literature, where the origin of inertial effects is often identified on a heuristic basis, a theoretical ustification is presented in this work. Indeed, a decomposition of the convective inertial term into two components is carried out formally allowing the identification of a correlation between the flow structure and the different inertial regimes. These components correspond to the curvature of the flow streamlines weighted by the local fluid kinetic energy on the one hand and the distribution of the kinetic energy along these lines on the other hand. In addition, the role of the recirculation zones in the occurrence and in the form of the deviation from Darcy’s law was thoroughly analyzed. For the porous structures under consideration, it is shown that (1) the kinetic energy lost in the vortices is insignificant even at high filtration velocities and (2) the shape of the flow streamlines induced by the recirculation zones plays an important role in the variation of the flow structure, which is correlated itself to the different flow regimes.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/121542017-01-01T00:00:00ZAGNAOU, MehrezLASSEUX, DidierAHMADI, AzitaInertial flow in porous media occurs in many situations of practical relevance among which one can cite flows in column reactors, in filters, in aquifers, or near wells for hydrocarbon recovery. It is characterized by a deviation from Darcy’s law that leads to a nonlinear relationship between the pressure drop and the filtration velocity. In this work, this deviation, also known as the nonlinear, inertial, correction to Darcy’s law, which is subject to controversy upon its origin and dependence on the filtration velocity, is studied through numerical simulations. First, the microscopic flow problem was solved computationally for a wide range of Reynolds numbers up to the limit of steady flow within ordered and disordered porous structures. In a second step, the macroscopic characteristics of the porous medium and flow (permeability and inertial correction tensors) that appear in the macroscale model were computed. From these results, different flow regimes were identified: (1) the weak inertia regime where the inertial correction has a cubic dependence on the filtration velocity and (2) the strong inertia (Forchheimer) regime where the inertial correction depends on the square of the filtration velocity. However, the existence and origin of those regimes, which depend also on the microstructure and flow orientation, are still not well understood in terms of their physical interpretations, as many causes have been conjectured in the literature. In the present study, we provide an in-depth analysis of the flow structure to identify the origin of the deviation from Darcy’s law. For accuracy and clarity purposes, this is carried out on two-dimensional structures. Unlike the previous studies reported in the literature, where the origin of inertial effects is often identified on a heuristic basis, a theoretical ustification is presented in this work. Indeed, a decomposition of the convective inertial term into two components is carried out formally allowing the identification of a correlation between the flow structure and the different inertial regimes. These components correspond to the curvature of the flow streamlines weighted by the local fluid kinetic energy on the one hand and the distribution of the kinetic energy along these lines on the other hand. In addition, the role of the recirculation zones in the occurrence and in the form of the deviation from Darcy’s law was thoroughly analyzed. For the porous structures under consideration, it is shown that (1) the kinetic energy lost in the vortices is insignificant even at high filtration velocities and (2) the shape of the flow streamlines induced by the recirculation zones plays an important role in the variation of the flow structure, which is correlated itself to the different flow regimes.