Resistance to the Flow of Fluids Through Simple and Complex Porous Media Whose Matrices Are Composed of Randomly Packed Spheres

1987 ◽  
Vol 109 (3) ◽  
pp. 268-273 ◽  
Author(s):  
R. M. Fand ◽  
B. Y. K. Kim ◽  
A. C. C. Lam ◽  
R. T. Phan
Keyword(s):  
Porous Media ◽  
Turbulent Flow ◽  
Turbulent Regime ◽  
Complex Media ◽  
Simple Method ◽  
Forchheimer’S Equation ◽  
The Matrix ◽  
Fully Developed Turbulent Flow ◽  
Uniform Diameter ◽  
Different Diameters

Experimental data relating to the flow of fluids through simple and complex porous media whose matrices are composed of randomly packed spheres have been obtained. In this context the term “simple” refers to porous media whose matrices are composed of spheres of uniform diameter, while “complex” refers to matrices composed of spheres having different diameters. It was found that Darcy’s law is valid for simple media within a range of the Reynolds number, Re, whose upper bound is 2.3. The upper bounds of Darcy flow for complex media were found to be consistent with this value. It is shown that the resistance to flow in the Darcy regime can be characterized by taking the Kozeny-Carman constant equal to 5.34 if the characteristic dimension is taken equal to the weighted harmonic mean diameter of the spheres that comprise the matrix. Forchheimer’s equation was found to be valid for simple media within the range 5 ≤ Re ≤ 80. The corresponding bounds for complex media were found to be consistent with this range. It is shown that the resistance to flow in the Forchheimer regime for both simple and complex media can be characterized by adopting the following values of the Ergun constants: A = 182 and B = 1.92. Finally, it is shown that fully developed turbulent flow exists when Re > 120 and that the resistance to flow in the turbulent regime can be calculated using Forchheimer’s equation by adopting the following values of the Ergun constants: A′ = 225 and B′ = 1.61. A simple method for characterizing the behavior of porous media in the transition regions between Darcy and Forchheimer and between Forchheimer and turbulent flow is presented.

A General Macroscopic Model for Turbulent Flow in Porous Media

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Nima F. Jouybari ◽  
Mehdi Maerefat ◽  
T. Staffan Lundström ◽  
Majid E. Nimvari ◽  
Zahra Gholami
Keyword(s):  
Porous Media ◽  
Turbulent Flow ◽  
Present Model ◽  
Flow Characteristics ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Solid Matrix ◽  
Turbulent Regime ◽  
Rod Bundles ◽  
Capillary Model

The present study deals with the generalization of a macroscopic turbulence model in porous media using a capillary model. The additional source terms associated with the production and dissipation of turbulent kinetic energy due to the presence of solid matrix are calculated using the capillary model. The present model does not require any prior pore scale simulation of turbulent flow in a specific porous geometry in order to close the macroscopic turbulence equations. Validation of the results in packed beds, periodic arrangement of square cylinders, synthetic foams, and longitudinal flows such as pipes, channels, and rod bundles against available data in the literature reveals the ability of the present model in predicting turbulent flow characteristics in different types of porous media. Transition to the fully turbulent regime in porous media and different approaches to treat this phenomenon are also discussed in the present study. Finally, the general model is modified so that it can be applied to lower Reynolds numbers below the range of fully turbulent regime in porous media.

scholarly journals Symmetry breaking of turbulent flow in porous media composed of periodically arranged solid obstacles

2021 ◽  
Vol 929 ◽  
Author(s):  
Vishal Srikanth ◽  
Ching-Wei Huang ◽  
Timothy S. Su ◽  
Andrey V. Kuznetsov
Keyword(s):  
Numerical Simulation ◽  
Porous Medium ◽  
Porous Media ◽  
Symmetry Breaking ◽  
Turbulent Flow ◽  
Vortex Shedding ◽  
Flow Instability ◽  
Flow In Porous Media ◽  
Turbulent Regime ◽  
Solid Obstacles

The focus of this paper is a numerical simulation study of the flow dynamics in a periodic porous medium to analyse the physics of a symmetry-breaking phenomenon, which causes a deviation in the direction of the macroscale flow from that of the applied pressure gradient. The phenomenon is prominent in the range of porosity from 0.43 to 0.72 for circular solid obstacles. It is the result of the flow instabilities formed when the surface forces on the solid obstacles compete with the inertial force of the fluid flow in the turbulent regime. We report the origin and mechanism of the symmetry-breaking phenomenon in periodic porous media. Large-eddy simulation (LES) is used to simulate turbulent flow in a homogeneous porous medium consisting of a periodic, square lattice arrangement of cylindrical solid obstacles. Direct numerical simulation is used to simulate the transient stages during symmetry breakdown and also to validate the LES method. Quantitative and qualitative observations are made from the following approaches: (1) macroscale momentum budget and (2) two- and three-dimensional flow visualization. The phenomenon draws its roots from the amplification of a flow instability that emerges from the vortex shedding process. The symmetry-breaking phenomenon is a pitchfork bifurcation that can exhibit multiple modes depending on the local vortex shedding process. The phenomenon is observed to be sensitive to the porosity, solid obstacle shape and Reynolds number. It is a source of macroscale turbulence anisotropy in porous media for symmetric solid-obstacle geometries. In the macroscale, the principal axis of the Reynolds stress tensor is not aligned with any of the geometric axes of symmetry, nor with the direction of flow. Thus, symmetry breaking in porous media involves unresolved flow physics that should be taken into consideration while modelling flow inhomogeneity in the macroscale.

Tip region of a hydraulic fracture driven by a laminar-to-turbulent fluid flow

2016 ◽  
Vol 797 ◽  
Author(s):  
E. V. Dontsov
Keyword(s):  
Fluid Flow ◽  
Turbulent Flow ◽  
Numerical Solution ◽  
Hydraulic Fracture ◽  
Asymptotic Solutions ◽  
Turbulent Regime ◽  
Zone Size ◽  
Turbulent Fluid Flow ◽  
Fully Developed Turbulent Flow ◽  
Steady Propagation

The focus of this study is to analyse the tip region of a hydraulic fracture, for which a fluid flow inside the crack transitions from the laminar to the turbulent regime away from the tip. To tackle the problem, a phenomenological formula for flow in pipes has been adapted to describe flow in a fracture through the concept of a hydraulic diameter. The selected model is able to capture laminar, turbulent and transition regimes of the flow. The near-tip region of a hydraulic fracture is analysed by focusing on steady propagation of a semi-infinite hydraulic fracture with leak-off, for which the aforementioned phenomenological formula for the fluid flow is utilized. First, the distance from the tip within which a laminar solution applies is estimated. Then, expressions for asymptotic solutions that are associated with fully developed turbulent flow inside the semi-infinite hydraulic fracture are derived. Finally, the laminar zone size and the asymptotic solutions are compared with the numerical solution, where the latter captures all regimes of the fluid flow.

scholarly journals Prediction of Effective Thermal Conductivities of Four-Directional Carbon/Carbon Composites by Unit Cells with Different Sizes

2021 ◽  
Vol 11 (3) ◽  
pp. 1171
Author(s):  
Chang Xu ◽  
Zhihong Sun ◽  
Guowei Shao
Keyword(s):  
Carbon Fiber ◽  
Longitudinal Direction ◽  
Unit Cell ◽  
Carbon Composites ◽  
Temperature Boundary ◽  
The Matrix ◽  
Unit Cells ◽  
Experimental Values ◽  
Different Diameters ◽  
Thermal Conductivities

Two-unit cells developed to predict the effective thermal conductivities of four-directional carbon/carbon composites with the finite element method are proposed in this paper. The smaller-size unit cell is formulated from the larger-size unit cell by two 180° rotational transformations. The temperature boundary conditions corresponding to the two-unit cells are derived, and the validity is verified by the temperature and heat flux distributions at specific positions of the larger-size unit cell and the smaller-size unit cell. The thermal conductivities of the carbon fiber bundles and carbon fiber rods are measured firstly. Then, combined with the properties of the matrix, the effective thermal conductivities of the four-directional carbon/carbon composites are numerically predicted. The results in transverse direction predicted by the larger-size unit cell and the smaller-size unit cell are both higher than experimental values, which are 5.8 to 6.2% and 7.3 to 8.2%, respectively. In longitudinal direction, the calculated thermal conductivities of the larger-size unit cell and the smaller-size unit cell are 6.8% and 6.2% higher than the experimental results, respectively. In addition, carbon fiber rods with different diameters are set to clarify the influence on the effective thermal conductivities of the four-directional carbon/carbon composites.

scholarly journals Fully developed turbulent flow in a square duct with a rough wall.

1987 ◽  
Vol 53 (492) ◽  
pp. 2370-2376 ◽  
Author(s):  
Hideomi FUJITA ◽  
Hajime YOKOSAWA ◽  
Masafumi HIROTA ◽  
Satoru NISHIGAKI
Keyword(s):  
Turbulent Flow ◽  
Rough Wall ◽  
Square Duct ◽  
Fully Developed Turbulent Flow
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