Mass Dispersion Coefficients for Turbulent Flow in an Infinite Porous Medium

Volume 1 ◽  
2004 ◽  
Author(s):  
Maximilian S. Mesquita ◽  
Marcelo J. S. de Lemos

In this work, mass dispersion tensors were calculated within an infinite porous medium formed by a spatially periodic array of longitudinally-displaced cylindrical rods. For the sake of simplicity, just one unit-cell, together with periodic boundary conditions for mass and momentum equations, and Neumann conditions for the mass concentration, was used to represent such medium. The numerical methodology herein employed is based on the control volume approach. Turbulence is assumed to exist within the fluid phase. High and low Reynolds k-e models were used to model such non-linear effects. The flow equations at the pore-scale were numerically solved using the SIMPLE method applied to a non-orthogonal boundary-fitted coordinate system. Integrated mass fraction results were compared with existing data in the literature.

Author(s):  
Maximilian S. Mesquita ◽  
Marcelo J. S. de Lemos

In this work, results for a macroscopic mass transport model are presented for a parallel plate channel filled with a fluid saturated heterogeneous porous medium. The numerical methodology herein employed is based on the control volume approach. Turbulence is assumed to exist within the fluid phase. High and low Reynolds k-e models were used to model such non-linear effects. The flow equations at the pore-scale were numerically solved using the SIMPLE method applied to a non-orthogonal boundary-fitted coordinate system. Integrated mass fraction results were compiled leading to correlations for the mass dispersion coefficients in the x and y directions. Application of the macroscopic model using the proposed correlations showed the role of dispersion mechanism in the overall transport in porous media.


2000 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Marcos H. J. Pedras

Abstract Turbulent flow in a channel, totally and partially filled with a porous medium, is simulated with a proposed turbulence model. Two cases are analyzed, namely clear flow past a porous obstacle and flow through a porous medium having a cavity with a higher porosity. Mean and turbulence quantities were solved within both computational domains using a single numerical technique. The control volume approach was used to discretize the governing equations. In the first case analyzed, the flow penetration into the porous substrate is accompanied by generation of turbulence kinetic energy within the obstacle. In the second geometry, the flow is pushed towards the cavity as porosity increases.


2012 ◽  
Vol 694 ◽  
pp. 399-407 ◽  
Author(s):  
Yulii D. Shikhmurzaev ◽  
James E. Sprittles

AbstractA new approach to the modelling of wetting fronts in porous media on the Darcy scale is developed, based on considering the types (modes) of motion the menisci go through on the pore scale. This approach is illustrated using a simple model case of imbibition of a viscous incompressible liquid into an isotropic porous matrix with two modes of motion for the menisci, the wetting mode and the threshold mode. The latter makes it necessary to introduce an essentially new technique of conjugate problems that allows one to link threshold phenomena on the pore scale with the motion on the Darcy scale. The developed approach (a) makes room for incorporating the actual physics of wetting on the pore scale, (b) brings in the physics associated with pore-scale thresholds, which determine when sections of the wetting front will be brought to a halt (pinned), and, importantly, (c) provides a regular framework for constructing models of increasing complexity.


2008 ◽  
Vol 130 (11) ◽  
Author(s):  
O. D. Makinde ◽  
P. Sibanda

The problem of steady laminar hydromagnetic heat transfer by mixed convection flow over a vertical plate embedded in a uniform porous medium in the presence of a uniform normal magnetic field is studied. Convective heat transfer through porous media has wide applications in engineering problems such as in high temperature heat exchangers and in insulation problems. We construct solutions for the free convection boundary-layer flow equations using an Adomian–Padé approximation method that in the recent past has proven to be an able alternative to the traditional numerical techniques. The effects of the various flow parameters such as the Eckert, Hartmann, and Schmidt numbers on the skin friction coefficient and the concentration, velocity, and temperature profiles are discussed and presented graphically. A comparison of our results with those obtained using traditional numerical methods in earlier studies is made, and the results show an excellent agreement. The results demonstrate the reliability and the efficiency of the Adomian–Padé method in an unbounded domain.


2021 ◽  
Author(s):  
Hanbang Zou ◽  
Pelle Ohlsson ◽  
Edith Hammer

<p>Carbon sequestration has been a popular research topic in recent years as the rapid elevation of carbon emission has significantly impacted our climate. Apart from carbon capture and storage in e.g. oil reservoirs, soil carbon sequestration offers a long term and safe solution for the environment and human beings. The net soil carbon budget is determined by the balance between terrestrial ecosystem sink and sources of respiration to atmospheric carbon dioxide. Carbon can be long term stored as organic matters in the soil whereas it can be released from the decomposition of organic matter. The complex pore networks in the soil are believed to be able to "protect" microbial-derived organic matter from decomposition. Therefore, it is important to understand how soil structure impacts organic matter cycling at the pore scale. However, there are limited experimental studies on understanding the mechanism of physical stabilization of organic matter. Hence, my project plan is to create a heterogeneous microfluidic porous microenvironment to mimic the complex soil pore network which allows us to investigate the ability of organisms to access spaces starting from an initial ecophysiological precondition to changes of spatial accessibility mediated by interactions with the microbial community.</p><p>Microfluidics is a powerful tool that enables studies of fundamental physics, rapid measurements and real-time visualisation in a complex spatial microstructure that can be designed and controlled. Many complex processes can now be visualized enabled by the development of microfluidics and photolithography, such as microbial dynamics in pore-scale soil systems and pore network modification mimicking different soil environments – earlier considered impossible to achieve experimentally. The microfluidic channel used in this project contains a random distribution of cylindrical pillars of different sizes so as to mimic the variations found in real soil. The randomness in the design creates various spatial availability for microbes (preferential flow paths with dead-end or continuous flow) as an invasion of liquids proceeds into the pore with the lowest capillary entry pressure. In order to study the impact of different porosity in isolation of varying heterogeneity of the porous medium, different pore size chips that use the same randomly generated pore network is created. Those chips have the same location of the pillars, but the relative size of each pillar is scaled. The experiments will be carried out using sterile cultures of fluorescent bacteria, fungi and protists, synthetic communities of combinations of these, or a whole soil community inoculum. We will quantify the consumption of organic matter from the different areas via fluorescent substrates, and the bio-/necromass produced. We hypothesise that lower porosity will reduce the net decomposition of organic matter as the narrower pore throat limits the access, and that net decomposition rate at the main preferential path will be higher than inside branches</p>


Author(s):  
Eslam Ezzatneshan ◽  
Reza Goharimehr

In the present study, a pore-scale multicomponent lattice Boltzmann method (LBM) is employed for the investigation of the immiscible-phase fluid displacement in a homogeneous porous medium. The viscous fingering and the stable displacement regimes of the invading fluid in the medium are quantified which is beneficial for predicting flow patterns in pore-scale structures, where an experimental study is extremely difficult. Herein, the Shan-Chen (S-C) model is incorporated with an appropriate collision model for computing the interparticle interaction between the immiscible fluids and the interfacial dynamics. Firstly, the computational technique is validated by a comparison of the present results obtained for different benchmark flow problems with those reported in the literature. Then, the penetration of an invading fluid into the porous medium is studied at different flow conditions. The effect of the capillary number (Ca), dynamic viscosity ratio (M), and the surface wettability defined by the contact angle (θ) are investigated on the flow regimes and characteristics. The obtained results show that for M<1, the viscous fingering regime appears by driving the invading fluid through the pore structures due to the viscous force and capillary force. However, by increasing the dynamic viscosity ratio and the capillary number, the invading fluid penetrates even in smaller pores and the stable displacement regime occurs. By the increment of the capillary number, the pressure difference between the two sides of the porous medium increases, so that the pressure drop Δp along with the domain at θ=40∘ is more than that of computed for θ=80∘. The present study shows that the value of wetting fluid saturation Sw at θ=40∘ is larger than its value computed with θ=80∘ that is due to the more tendency of the hydrophilic medium to absorb the wetting fluid at θ=40∘. Also, it is found that the magnitude of Sw computed for both the contact angles is decreased by the increment of the viscosity ratio from Log(M)=−1 to 1. The present study demonstrates that the S-C LBM is an efficient and accurate computational method to quantitatively estimate the flow characteristics and interfacial dynamics through the porous medium.


2016 ◽  
Vol 5 (1) ◽  
pp. 29
Author(s):  
Madhura K R ◽  
Uma M S

<p><span lang="EN-IN">The flow of an unsteady incompressible electrically conducting fluid with uniform distribution of dust particles in a constricted channel has been studied. The medium is assumed to be porous in nature. The governing equations of motion are treated analytically and the expressions are obtained by using variable separable and Laplace transform techniques. The influence of the dust particles on the velocity distributions of the fluid are investigated for various cases and the results are illustrated by varying parameters like Hartmann number, deposition thickness on the walls of the cylinder and the permeability of the porous medium on the velocity of dust and fluid phase.</span></p>


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