Adoption of Manning's equation to 1D non-Darcy flow problems

Sedghi-Asl, Mohammad; Rahimi, Hassan

doi:10.1080/00221686.2011.629911

Cited by 38 publications

(10 citation statements)

References 10 publications

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“…A similar behavior to this is essentially depicted in Figure 3 of Sedghi-Asl et al and Rahimi et al [60]. They suggested that the voids and the angular sediment edges become larger, which leads to an increase in flow resistance.…”

Section: Influence Of Particle Diameter On Friction Factorsupporting

confidence: 74%

Experimental Investigation of Flow Domain Division in Beds Packed with Different Sized Particles

Yang

et al. 2017

Energies

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Seepage in a medium packed with particles of variable granular size can be seen in many fields of engineering applications. Due to the relative complex spatial aspect of pore geometry, there are notable differences in the critical parameters of flow transition (Reynolds number and Forchheimer number) between different structures. It is difficult to distinguish the available range of seepage equations and predict the water flux accurately. This work aims to establish the relationship between particle size and flow transition. This is conducted according to the results of flow region division, which obtains the application range for seepage equations. Experiments were carried out in sand columns with nine different particle sizes of sand with mean diameters of 0.0375, 0.1125, 0.225, 0.45, 0.8, 1.5, 2.18, 3.555 and 7.125 mm. Four flow regimes were identified (pre-Darcy regime, Darcy regime, Forchheimer regime and turbulent regime). The experimental data indicate that the permeability increases exponentially and the inertia factor reduces exponentially with an increase in particle diameter. The inertial effect becomes more significant in the medium with larger particles than with finer particles when the flow transition occurs.

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Section: Influence Of Particle Diameter On Friction Factorsupporting

confidence: 74%

Experimental Investigation of Flow Domain Division in Beds Packed with Different Sized Particles

Yang

et al. 2017

Energies

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“…These are the nonlinear laminar flow regime (also known as Forchheimer regime or transition flow regime) and the fully turbulent flow regime (Andersen and Burcharth 1995;Lage 1998;Houben 2015). This is done by flow visualization studies in porous media that determined the onset of turbulent flow (e.g., Dybbs and Edwards 1984;Seguin et al 1998), as well as analysis of macroscale flow experiments on packed beds (e.g., Venkataraman and Rao 1998;Sedghi-Asl and Rahimi 2011;Bağci et al 2014). This transition between the different flow regimes in the post-Darcian flow regime is hard to define for natural irregular and graded granular materials such as used in this study (Andersen and Burcharth 1995).…”

Section: Discussionmentioning

confidence: 99%

“…where g [m/s 2 ] is the acceleration due to gravity, d [m] is the characteristic pore length by means of the particle diameter, v [m 2 /s] is the kinematic viscosity of the fluid, n [−] is the porosity, A is the Ergun constant that equals 150 and B is the Ergun constant that equals 1.75 (Ergun 1952). Many variations on the Ergun relation for different kinds of porous media and flow regimes are given in the literature (e.g., Engelund 1953;Irmay 1964;Mac-Donald et al 1979;Du Plessis 1994;Sedghi-Asl and Rahimi 2011;Erdim et al 2015;Guo et al 2019).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

et al. 2019

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Under certain flow conditions, fluid flow through porous media starts to deviate from the linear relationship between flow rate and hydraulic gradient. At such flow conditions, Darcy's law for laminar flow can no longer be assumed and nonlinear relationships are required to predict flow in the Forchheimer regime. To date, most of the nonlinear flow behavior data is obtained from flow experiments on packed beds of uniformly graded granular materials (C u = d 60 /d 10 < 2) with various average grain sizes, ranging from sands to cobbles. However, natural deposits of sand and gravel in the subsurface could have a wide variety of grain size distributions. Therefore, in the present study we investigated the impact of variable grain size distributions on the extent of nonlinear flow behavior through 18 different packed beds of natural sand and gravel deposits, as well as composite filter sand and gravel mixtures within the investigated range of uniformity (2.0 < C u < 17.35) and porosity values (0.23 < n < 0.36). Increased flow resistance is observed for the sand and gravel with high C u values and low porosity values. The present study shows that for granular material with wider grain size distributions (C u > 2), the d 10 instead of the average grain size (d 50) as characteristic pore length should be used. Ergun constants A and B with values of 63.1 and 1.72, respectively, resulted in a reasonable prediction of the Forchheimer coefficients for the investigated granular materials.

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“…Many experimental data on (post-Darcy) nonlinear flow in porous media are available for coarser porous media, such as coarse sands, gravels and glass beads (Sidiropoulou et al 2007;Moutsopoulos et al 2009;Sedghi-Asl and Rahimi 2011;Huang et al 2013;Bagci et al 2014;Salahi et al (2015); Sedghi-Asl et al 2014;Li et al 2017). A relatively small amount of experimental data is available for finer unconsolidated sandy porous media.…”

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confidence: 99%

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

et al. 2017

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The current study provides new experimental data on nonlinear flow behavior in various uniformly graded granular materials (20 samples) ranging from medium sands (d 50 > 0.39 mm) to gravel (d 50 = 6.3 mm). Generally, theoretical equations relate the Forchheimer parameters a and b to the porosity, as well as the characteristic pore length, which is assumed to be the median grain size (d 50 ) of the porous medium. However, numerical and experimental studies show that flow resistance in porous media is largely determined by the geometry of the pore structure. In this study, the effect of the grain size distribution was analyzed using subangular-subrounded sands and approximately equal compaction grades. We have used a reference dataset of 11 uniformly graded filter sands. Mixtures of filter sands were used to obtain a slightly more well-graded composite sand (increased C u values by a factor of 1.19 up to 2.32) with respect to its associated reference sand at equal median grain size (d 50 ) and porosity. For all composite sands, the observed flow resistance was higher than in the corresponding reference sand at equal d 50 , resulting in increased a coefficients by factors up to 1.68, as well as increased b coefficients by factors up to 1.44. A modified Ergun relationship with Ergun constants of 139.1 for A and 2.2 for B, as well as the use of d m − σ as characteristic pore length predicted the coefficients a and b accurately.

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Adoption of Manning's equation to 1D non-Darcy flow problems

Cited by 38 publications

References 10 publications

Experimental Investigation of Flow Domain Division in Beds Packed with Different Sized Particles

Experimental Investigation of Flow Domain Division in Beds Packed with Different Sized Particles

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

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