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New correlations for non-Darcy flow in porous media

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Abstract

In this paper, a general power form of head-loss (pressure-drop) equation and the concept of shear velocity were used to study non-Darcy filtration through coarse granular materials. Using new laboratory data, the validity of four widely-used power form pressure-drop equations were evaluated. The results indicated that for the lower size of grain diameter (d ≤ 8.7 mm) the Wilkins (in: Proceedings of the 2nd Australia-New Zealand Conference on Soil Mechanics and Foundation Engineering, Christchurch, 1956) method has predicted satisfactorily the hydraulic gradient, while for the higher size of grain diameter (d ≥ 15.6 mm), the Stephenson (Rockfill in Hydraulic Engineering, Elsevier Science Publishers B.V., Amsterdam, 1979) method predicted acceptably the pressure gradient. The results also indicated that the best estimation for the Izbash coefficient a is the Wilkins method. Finally, new correlations for friction factor, shear velocity and Reynolds number as well as new threshold limits for Darcy, partially-turbulent, and fully-turbulent flow regimes are presented and discussed.

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Abbreviations

\(A\) :

Cross-sectional area of cylinder (L2)

\(a,b\) :

Coefficients of Izbash equation (−)

C :

Constant coefficient of f - Re relationship (−)

\(d\) :

Mean diameter of the grains (L)

\(f\) :

Friction factor the porous media (−)

\(g\) :

Gravitational constant (L/T2)

\(h_{f}\) :

Pressure-loss (L)

\(i\) :

Pressure (hydraulic) gradient (−)

\(L\) :

Length of media (L)

\(M\) :

Power constant of f - Re relationship (−)

\(n\) :

Porosity of the aggregates (−)

R :

Hydraulic mean radius of the porous media (L)

Re:

Reynolds number (−)

\(V\) :

Bulk flow velocity (L/T)

X :

The mean of experimental data

x i :

The values of every step of equations

y i :

The values of every step of the experimental data

u * :

Shear velocity (L/T)

\(\rho\) :

Water density (FT2/L4)

\(\tau\) :

Tortuosity factor (−)

\(\tau_{0}\) :

Shear stress (F/L2)

\(\nu\) :

Kinematic viscosity of water (L2/T)

NOF:

Normalized objective function

RMSE:

Root mean square error

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Acknowledgements

The authors wish to express their deepest gratitude to Yasouj University and the University of Tehran for the support of the research. Unfortunately, Prof. Hassan Rahimi (1946–2022), the late professor of the University of Tehran, and the third author of this article, passed away. His efforts to publish this article are commendable. Rest in Peace.

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  1. Deceased: Hassan Rahimi.

Authors and Affiliations

  1. Soil Science Department, College of Agriculture, Yasouj University, Yasouj, 75918-74831, Iran

    Mohammad Sedghi-Asl & Banafsheh Afrasiabi

  2. Department of Irrigation and Reclamation Engineering, University of Tehran, Karaj, Iran

    Hassan Rahimi

  3. Civil Section, ESI, Sydney Trains, Sydney, Australia

    Hassan Rahimi

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  1. Mohammad Sedghi-Asl
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Correspondence to Mohammad Sedghi-Asl.

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Sedghi-Asl, M., Afrasiabi, B. & Rahimi, H. New correlations for non-Darcy flow in porous media. Acta Mech 234, 4559–4572 (2023). https://doi.org/10.1007/s00707-023-03586-3

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