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Flow Regimes in Packed Beds of Spheres from Pre-Darcy to Turbulent

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Abstract

Characteristics of flow regimes in porous media, along the processes of energy dissipation in each regime, are critical for applications of such media. The current work presents new experimental data for water flow in packed steel spheres of 1- and 3-mm diameters. The porosity of the porous media was about 35 % for both cases. The extensive dataset covered a broad range of flow Reynolds number such that several important flow regimes were encountered, including the elusive pre-Darcy regime, which is rarely or never seen in porous-media literature and turbulent regime. When compared to previous information, the results of this study are seen to add to the divergence of available data on pressure drop in packed beds of spheres. The divergence was also present in the coefficients of Ergun equation and in the Kozeny–Carman constant. The porous media of the current work were seen to exhibit different values of permeability and Forchheimer coefficient in each flow regime. The current data correlated well using the friction factor based on the permeability (measured in the Darcy regime) and the Reynolds number based on the same length scale. An attempt was made to apply recent theoretical results regarding the applicability of the quadratic and cubic Forchheimer corrections in the strong and weak inertia regime.

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Abbreviations

\(a\) :

Constant, Eq. (9)

\(b \) :

Constant, Eq. (9)

\(A \) :

Constant, Ergun equation

\(B \) :

Constant, Ergun equation

\(d\) :

Sphere diameter

\(d_{p}\) :

Particle diameter, Ergun equation

\(f_{K}\) :

Permeability-based friction factor \(=\frac{\left( {{\Delta p}/L} \right) \sqrt{K}}{\rho u^{2}}\)

F:

Forchheimer coefficient (dimensionless)

\(F_o \) :

Forchheimer number \(={\rho F\sqrt{K}u}/\mu \)

\(g\) :

Acceleration due to gravity

\(i\) :

Dimensionless hydraulic head \(={\Delta p}/{\rho gL}\)

\(K\) :

Permeability (m\(^{2})\)

L:

Length of porous medium (m)

\(m\) :

Parameter, Eq. (5)

\(n\) :

Parameter, Eq. (10)

p:

Static pressure (kPa)

\(\hbox {Re}_{loc} \) :

Local Reynolds number \(=\frac{\rho ud}{\mu \varepsilon \pi }\)

\(\hbox {Re}_d \) :

Reynolds number based on particle diameter\(=\frac{\rho ud}{\mu }\)

\(\hbox {Re}_K \) :

Reynolds number based on permeability\(=\frac{\rho u\sqrt{K}}{\mu }\)

u:

Average velocity

\(\alpha \) :

Parameter, Eq. (5)

\(\alpha ^{*}\) :

Parameter, Eq. (6)

\(\Delta \) :

Change

\(\varepsilon \) :

Porosity

\(\kappa \) :

Kozeny–Carman constant

\(\mu \) :

Viscosity

\(\rho \) :

Density

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Acknowledgments

This work was supported by the Scientific & Technological Research Council of Turkey (TUBİTAK) under program 2221: 1059B211301074, for which the authors are very thankful.

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Authors and Affiliations

  1. Makina Fakültesi, Istanbul Technical University, Gümüşsuyu, 34437 , Istanbul, Turkey

    Özer Bağcı & Mustafa Özdemir

  2. Department of Mechanical Engineering, University of Detroit Mercy, Detroit, MI , 48334, USA

    Nihad Dukhan

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  1. Özer Bağcı
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  2. Nihad Dukhan
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Correspondence to Nihad Dukhan.

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Bağcı, Ö., Dukhan, N. & Özdemir, M. Flow Regimes in Packed Beds of Spheres from Pre-Darcy to Turbulent. Transp Porous Med 104, 501–520 (2014). https://doi.org/10.1007/s11242-014-0345-0

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