The effect of the macroscopic local inertial term on the non-Newtonian fluid flow in channels filled with porous medium (original) (raw)
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International Journal of Heat and Mass Transfer, 2001
The transient hydrodynamics behavior of the¯uid¯ow in parallel-plate channels partially ®lled with porous material is investigated numerically. The role of the local macroscopic inertial term in the porous domain momentum equation is studied. It is found that the eect of the local inertial term on the channel hydrodynamics behavior is insigni®cant when Da`1 Â 10 À6 , over the entire range of 0X1`l R`1 0, 0`A`10 4 , and for all porous substrate thicknesses. Also, it is found that the deviation between the predictions of the transient and the quasi-steady models is more signi®cant in the porous domain and the deviation decreases as the time proceeds. Ó
Numerical analysis of non-Newtonian fluid in a non-Darcy porous channel
Modelling, Measurement and Control B
In this work, non-Newtonian fluid properties in a non-Darcy porous channel, specifically Darcy-Forchheimer porous channel is investigated with focus on a numerical analysis of Eyring-Powell type of non-Newtonian fluid. The unsteady state problem is considered under the influence of thermal radiation and transversely applied magnetic field. The governing non-linear partial differential equations were non-dimensionalized and then solved using Crank-Nicolson concept. Significance of non-Newtonian fluid properties as well as other fluid parameters is considered on the velocity, temperature and concentration profiles with the aid of graphs.
A Semi-Analytical Solution for a Porous Channel Flow of a Non-Newtonian Fluid
Journal of Applied Fluid Mechanics, 2016
A theoretical study of steady laminar two-dimensional flow of a non-Newtonian fluid in a parallel porous channel with variable permeable walls is carried out. Solution by Differential Transform Method (DTM) is obtained and the flow behavior is studied. The non-Newtonian fluid considered for the study is couple stress fluid. Thus, in addition to the effects of inertia and permeabilities on the flow, the couple stress effects are also analyzed. Results are presented and comparisons are made between the behaviour of Newtonian and non-Newtonian fluids.
Effect of Inertial Terms on Fluid–Porous Medium Flow Coupling
Transport in Porous Media, 2017
The study considers an effect of the nonlinear inertial terms in the Brinkman filtration equation on the characteristics of coupled flows in a pure fluid and porous medium in the frameworks of two independent problems. The first problem is the forced boundarylayer flow overlying the Darcy-Brinkman porous medium. The Prandtl theory is used, and the self-similar equations are built to describe it. It is shown that the inertial terms have a valuable effect on the boundary-layer structure because of the large velocity gradient in the transition zone. The boundary-layer thickness in a porous medium rapidly grows at large Reynolds numbers. The velocity magnitude and gradient at the interface also change. The second independent problem is an analysis of the inertial terms effect on the flow stability. The neutral curves of the full and linearized flow models are built using the shooting method. They have different shortwave asymptotic, but there are no significant changes in the critical Reynolds numbers and corresponding wave numbers.
An investigation of inertial one-phase flow in homogeneous model porous media
2009
Our interest in this work is the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates requirin g the introduction of the inertial forces at the pore-scale. At the macroscale, this impli es a nonlinear correction to Darcy’s law i.e. a nonlinear relationship between the filtration velo city and the pressure gradient. The objective here is to analyze the nonlinear correction on som e periodic models of porous media with respect to the Reynolds number and the pressure gradi ent orientation relative to the principal axes of the periodic unit cell. Our results show th at, in the general case, for ordered structures, the inertial correction to the Darcy’s law, i) i nvolves a non-symmetric tensor even if the structure is isotropic in the Darcy regime (i.e. is chara cterized by a spherical permeability tensor); ii) is neither aligned with the applied pressure gra dient nor with the mean flow indicating that the macroscopic force exerted on the...
Experimental investigation of inertial flow processes in porous media
Journal of Hydrology, 2009
s u m m a r y 23 The hydraulic behavior of inertial flows in porous media is experimentally investigated. A vertical metal 24 column was constructed, of dimensions 0.5 m in diameter and 2.30 m in height. Eight different porous 25 media were used in the experiments. Head loss was measured. A total of 454 experimental data were col-26 lected. The experimental data indicate that, for a wide spectrum of velocities, both the Forchheimer and 27 Izbash equations offer excellent descriptions of the flow processes. For moderate values of the Reynolds 28 number, a discontinuity in the velocity-hydraulic gradient curve was detected, a behavior also predicted 29 by former numerical studies. The analysis of the hydraulic behavior of bidisperse media indicate the 30 influence of wall effects taking place at the interface between small and large grains. The data are used 31 to validate semi-empirical relations, and give also some insight on the flow processes taking place at the 32 pore-scale for the case of non-Darcian flows. 33 Ó 2009 Published by Elsevier B.V. 34 35 36 Introduction 37 In most studies examining flow processes in groundwater, it is 38 assumed that flow is described by the linear Darcy's law; standard 39 software and theoretical descriptions are based on this assumption 40 (McDonald and Harbaugh, 1988; Bear, 1979). 41 As problems involving flow and transport processes in coarse 42 porous media and fractures emerged, an adequate description of 43 these processes became crucial. Therefore, recently, a substantial 44 research effort is focused on ''non-conventional" groundwater prob-45 lems, including coupled flow and transport processes in individual 46 fractures or fracture networks, and inertial flows in groundwater. 47 High-velocity flows in underground geological formations occur in 48 many real-world problems, including the exploitation of hot dry 49 rock formations (Kohl et al., 1997), simulation of pollutant transport 50 in waste rock deposits (Greenly and Joy, 1996), and water extraction 51 issues (Wen et al., 2006, 2008a,b; Mathias et al., 2008), while other 52 applications include design of constructed wetlands (Economopou-53 lou and Tsihrintzis, 2003; Akratos and Tsihrintzis, 2007). 54 For both coarse porous media and fractures, this type of flow 55 can be adequately described either by the Forchheimer or the Iz-56 bash law . For the 57 one-dimensional case, these equations read, respectively:
Inertia Effects in High-Rate Flow Through Heterogeneous Porous Media
Transport in Porous Media, 2005
The paper deals with the effects of large scale permeability-heterogeneity on flows at high velocities through porous media. The media is made of a large number of homogeneous blocks where the flow is assumed to be governed by the Forchheimer equation with a constant inertial coefficient. By assuming the validity of the Forchheimer equation at the large scale, an effective inertial coefficient is deduced from numerical simulations. Different media are investigated: serial-layers, parallel-layers and correlated media. The numerical results show that: (i) for the serial-layers, the effective inertial coefficient is independent of the Reynolds number and decreases when the variance and the mean permeability ratio increases; (ii) for the parallel-layers and the correlated media, the effective inertial coefficient is function of the Reynolds number and increases when the variance and the mean permeability ratio increases. Theoretical relationships are proposed for the inertial coefficient as function of the Reynolds number and the characteristics of the media.
Inertial Effects on Fluid Flow through Porous Media in Disordered Porous Media
We investigate the origin of the deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media. We apply the Forchheimer equation as a phenomenological model to correlate the variations of the friction factor for different porosities and flow conditions. At sufficiently high Reynolds numbers, when inertia becomes relevant, we observe a transition from linear to nonlinear behavior which is typical of experiments. We find that such a transition can be understood and statistically characterized in terms of the spatial distribution of kinetic energy in the system. [S0031-9007(99)09541-1]
The Canadian Journal of Chemical Engineering, 1993
The present analysis investigates non-Darcy forced convective heat transfer in a channel confined by two parallel walls subjected to uniform heat flux in a highly porous medium saturated with a non-Newtonian power-law fluid. Extensive numerical integrations have been carried out utilizing the Brinkman-Forchheimer extension of the Darcy model in order to study the effects of pseudoplasticity, and Brinkman and Forchheimer terms on the heat transfer characteristics.