scholarly journals A pore scale study on fluid flow through two dimensional dual scale porous media with small number of intraparticle pores

2016 ◽  
Vol 18 (1) ◽  
pp. 80-92 ◽  
Author(s):  
Safa Sabet ◽  
Moghtada Mobedi ◽  
Turkuler Ozgumus
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Permeability Tensor ◽  
Navier Stokes ◽  
Pore Scale ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Flow Through ◽  
Dual Scale

Abstract In the present study, the fluid flow in a periodic, non-isotropic dual scale porous media consisting of permeable square rods in inline arrangement is analyzed to determine permeability, numerically. The continuity and Navier-Stokes equations are solved to obtain the velocity and pressure distributions in the unit structures of the dual scale porous media for flows within Darcy region. Based on the obtained results, the intrinsic inter and intraparticle permeabilities and the bulk permeability tensor of the dual scale porous media are obtained for different values of inter and intraparticle porosities. The study is performed for interparticle porosities between 0.4 and 0.75 and for intraparticle porosities from 0.2 to 0.8. A correlation based on Kozeny-Carman relationship in terms of inter and intraparticle porosities and permeabilities is proposed to determine the bulk permeability tensor of the dual scale porous media.

Cellular‐automaton fluids: A model for flow in porous media

Geophysics ◽  
1988 ◽  
Vol 53 (4) ◽  
pp. 509-518 ◽  
Author(s):  
Daniel H. Rothman
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
Pressure Gradient ◽  
Cellular Automaton ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cellular Automaton Fluids

Numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties. The large‐scale viewpoint is perhaps the most prevalent. Darcy’s law relates the chief macroscopic parameters of interest—flow rate, permeability, viscosity, and pressure gradient—and may be invoked to solve for any of these parameters when the others are known. In practical situations, however, this solution may not be possible. Attention is then typically focused on the estimation of permeability, and numerous numerical methods based on knowledge of the microscopic pore‐space geometry have been proposed. Because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult, microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores, throats, and cracks. I propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries. This new method solves the Navier‐Stokes equations numerically using the cellular‐automaton fluid model introduced by Frisch, Hasslacher, and Pomeau. The cellular‐ automaton fluid is extraordinarily simple—particles of unit mass traveling with unit velocity reside on a triangular lattice and obey elementary collision rules—but is capable of modeling much of the rich complexity of real fluid flow. Cellular‐automaton fluids are applicable to the study of porous media. In particular, numerical methods can be used to apply the appropriate boundary conditions, create a pressure gradient, and measure the permeability. Scale of the cellular‐automaton lattice is an important issue; the linear dimension of a void region must be approximately twice the mean free path of a lattice gas particle. Finally, an example of flow in a 2-D porous medium demonstrates not only the numerical solution of the Navier‐Stokes equations in a highly irregular geometry, but also numerical estimation of permeability and a verification of Darcy’s law.

Numerical Investigation of the “Poor Man’s Navier–Stokes Equations” with Darcy and Forchheimer Terms

2016 ◽  
Vol 26 (05) ◽  
pp. 1650086
Author(s):  
Tingting Tang ◽  
Zhiyong Li ◽  
J. M. McDonough ◽  
P. D. Hislop
Keyword(s):  
Porous Media ◽  
Numerical Investigation ◽  
Stokes Equations ◽  
Discrete Dynamical System ◽  
Flow In Porous Media ◽  
Phase Portraits ◽  
Navier Stokes ◽  
Flow Through Porous Media ◽  
Navier Stokes Equations ◽  
Flow Through

In this paper, a discrete dynamical system (DDS) is derived from the generalized Navier–Stokes equations for incompressible flow in porous media via a Galerkin procedure. The main difference from the previously studied poor man’s Navier–Stokes equations is the addition of forcing terms accounting for linear and nonlinear drag forces of the medium — Darcy and Forchheimer terms. A detailed numerical investigation focusing on the bifurcation parameters due to these additional terms is provided in the form of regime maps, time series, power spectra, phase portraits and basins of attraction, which indicate system behaviors in agreement with expected physical fluid flow through porous media. As concluded from the previous studies, this DDS can be employed in subgrid-scale models of synthetic-velocity form for large-eddy simulation of turbulent flow through porous media.

Developing Fluid Flow and Heat Transfer in a Semi-Porous Square Channel

2003 ◽  
Author(s):  
Tien-Chien Jen ◽  
Tuan-Zhou Yan ◽  
S. H. Chan
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Porous Channel ◽  
Navier Stokes ◽  
Axial Position ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer

A three-dimensional computational model is developed to analyze fluid flow in a semi-porous channel. In order to understand the developing fluid flow and heat transfer process inside the semi-porous channels, the conventional Navier-Stokes equations for gas channel, and volume-averaged Navier-Stokes equations for porous media layer are adopted individually in this study. Conservation of mass, momentum and energy equations are solved numerically in a coupled gas and porous media domain in a channel using the vorticity-velocity method with power law scheme. Detailed development of axial velocity, secondary flow and temperature fields at various axial positions in the entrance region are presented. The friction factor and Nusselt number are presented as a function of axial position, and the effects of the size of porous media inside semi-porous channel are also analyzed in the present study.

Fluid Flow in an Annular Microchannel Subjected to Uniform Wall Injections

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Mohammad Layeghi ◽  
Hamid Reza Seyf
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Analytical Results ◽  
Uniform Wall ◽  
Change Of Variable ◽  
Wall Injection

Analytical analysis of fluid flow in an annular microchannel subjected to uniform wall injection at various Reynolds numbers is presented. The classical Navier–Stokes equations are used in the present study. Mathematically, using an appropriate change of variable, Navier–Stokes equations are transformed to a set of nonlinear ordinary differential equations. The governing equations are analytically solved using series solution method. Some analytical results are given for the prediction of velocity profiles and pressure distributions in annular microchannels. The agreement between the computational fluid dynamics and the analytical predictions is very good. However, the analytical results are valid in a limited range of radius ratios and needs more study.

scholarly journals Application of Navier – Stokes Equation to Solve Fluid Flow Problems

2020 ◽  
pp. 101-114
Author(s):  
Ebiendele Ebosole Peter ◽  
Adamu Bala
Keyword(s):  
Fluid Flow ◽  
Laminar Flow ◽  
Velocity Profile ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Flow Through

The Navier – Stokes equations were used to obtain the velocity profile for two different fluid flow problems, firstly to a laminar flow through a pipe and secondly to flow of incompressible fluid between two boundaries, one boundary is the air and the other boundary moving with a velocity, inclined at an angle . The velocity profiles were obtained and presented in a diagram of showing how the fluid flow through the channels.

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

Modelling Turbulent Flow in Deformable Highly Porous Seabed and Structures

2018 ◽  
Author(s):  
Hisham Elsafti ◽  
Hocine Oumeraci
Keyword(s):  
Porous Media ◽  
Transient Flow ◽  
Stokes Equations ◽  
Pore Fluid ◽  
Navier Stokes ◽  
Model Parameters ◽  
Navier Stokes Equations ◽  
Deformable Porous Media ◽  
Physical Experiments ◽  
Fluid Coupling

In this study, the fully-coupled and fully-dynamic Biot governing equations in the open-source geotechFoam solver are extended to account for pore fluid viscous stresses. Additionally, turbulent pore fluid flow in deformable porous media is modeled by means of the conventional eddy viscosity concept without the need to resolve all turbulence scales. A new approach is presented to account for porous media resistance to flow (solid-to-fluid coupling) by means of an effective viscosity, which accounts for tortuosity, grain shape and local turbulences induced by flow through porous media. The new model is compared to an implemented extended Darcy-Forchheimer model in the Navier-Stokes equations, which accounts for laminar, transitional, turbulent and transient flow regimes. Further, to account for skeleton deformation, the porosity and other model parameters are updated with regard to strain of geomaterials. The presented model is calibrated by means of available results of physical experiments of unidirectional and oscillatory flows.

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