Experimental investigation on water flow in cubic arrays of spheres

Huang, Kun; Wan, Junwei; Chen, C.X.; He, Linqing; Mei, Wu; Zhang, M.Y.

doi:10.1016/j.jhydrol.2013.03.039

Cited by 26 publications

(30 citation statements)

References 30 publications

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“…Hence, the permeability k is proportional to the particle diameter square d 2 . In contrast, the inertia effect reduced with an increase in particle diameter, i.e., the inertia factor β is inversely proportional to the particle diameter d. These relationships had been verified by Huang et al [33] (see their Figures 7 and 8) in their experiment for the case of fluid flow in cubic arrays of smooth spheres. A similar result has been reported by Sedghi-Asl et al [34] (see their Figure 5) for the case of rounded aggregates packed into a column.…”

Section: Permeability K (M 2 )supporting

confidence: 56%

“…Flow field division relies on flow behavior. Up to now, the relationship of flow behavior and particle diameter has mainly focused on either the 'wall effect' [29][30][31] or the functional relationship with linear term and quadratic term coefficients [27,[32][33][34]. Several investigators have studied the connection of porosity of packed beds and the ratio of bed-to-particle diameter [35,36].…”

Section: Introductionmentioning

confidence: 99%

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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: Permeability K (M 2 )supporting

confidence: 56%

Section: Introductionmentioning

confidence: 99%

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

Yang

et al. 2017

Energies

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“…Previous studies have shown that besides the particle diameter and porosity, also the particle shape and packing arrangement has a significant impact on nonlinear flow behavior (e.g., Engelund 1953;Allen et al 2013;Salahi et al 2015). Experimental studies on nonlinear flow behavior on cubic arrays of smooth glass spheres show that the flow resistance is drastically lower compared to granular material (Huang et al 2013). This study showed that the Ergun constants provided by Irmay (1964) with values A and B of, respectively, 180 and 0.6 suffice to predict the experimental data.…”

Section: Discussionmentioning

confidence: 99%

“…A wide variety of experimental studies on nonlinear flow behavior through packed beds of all kinds of material is provided in the literature. Investigation of fluid/gas flow through packed beds of artificial compounds is done, such as cubes, cylinders, ellipsoids, fibers, cubic arrays of spheres, as well rounded spheres of glass or metal (e.g., MacDonald et al 1979;Sidiropoulou et al 2007;Allen et al 2013;Huang et al 2013;Bağci et al 2014;Erdim et al 2015). Besides artificial compounds, the literature provides a broad dataset on nonlinear flow behavior through all kinds of granular material, ranging from sand to cobbles.…”

Section: Experimental Data From Previous Studiesmentioning

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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Experimental investigation on water flow in cubic arrays of spheres

Cited by 26 publications

References 30 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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