# PermeabIlity of wire-net porous media determined by a simple Darcy-Forchheimer equation

## Main Article Content

## Abstract

The permeability (K) of porous media is the most significant parameter for describing the fluid flow mechanism within porous matrix. A simple experiment to investigate the K of wire-net porous media based on Darcy – Forchheimer principle is proposed. The stainless ASUS304 with four PPIs (Pores per inch), i.e., PPI = 4, 8, 10 and 12, are examined and reported in the form of porosity (e) yielding as 0.943, 0.898, 0.822 and 0.794 respectively. Five thicknesses (H) consisting of 1.2, 2.4, 3.6, 4.8 and 6.0 mm, are tested. Regarding to the Darcy – Forchheimer method, the equation of relation between pressure drop (DP) and velocity (u) is in the 2^{nd} polynomial form: DP = au+bu^{2}. To simplify this equation, the linear form is discussed: DP = a+bu. The DP as measured by U-tube manometer is conducted in varying the velocity (u) from 0.225 m/s to 1.578 m/s. From the experiment, it is found that the value of K is depended on e (PPI) and H. Thus, the equation of K estimated by multi-regression method can be reported by K =(89.401e - 66.412)/H x 10^{-7} which determination coefficient (R^{2}) has 0.889. To validate the present regression, three available models consisting of Kozeny-Carman correlation, Gebart equation and a nonlinear equation of Koponen are compared. Good agreement is obtained in comparison. Therefore, it can be said that the present regression form is highly believable and it is easily used.

## Article Details

*Journal of Research and Applications in Mechanical Engineering*,

*6*(1), 63–70. Retrieved from https://ph01.tci-thaijo.org/index.php/jrame/article/view/136547

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

## References

[2] Arash, K., Mehdi, S., Amir, H.M. and Deresh, R. Reliable method for the determination of surfactant retention in porous media during chemical flooding oil recovery, Fuel, Vol. 158, 2015, pp. 122-128.

[3] Bernard, D. and John, W.M. Groundwater age in fractured porous media: analytical solution for parallel fractures, Adv. Water Resour., Vol. 37, 2012, pp. 127-135.

[4] Alessio, F and Anna, S. A numerical method for two-phase flow in fractured porous media with non-matching grids, Adv. Water Resour., Vol. 62, 2013, pp. 454-464.

[5] Ali, F. and Faical, L. Two-phase flow hydrodynamic study in micro-packed beds – effect of bed geometry and particle size, Chem. Eng. Process., Vol. 78, 2014, pp. 27-36

[6] Zhao, T.F. and Chen, C.Q. The shear properties and deformation mechanisms of porous metal fiber sintered sheets, Mech. Mater., Vol. 70, 2014, pp. 33-40.

[7] Kim, K.N., Kang, J.H., Lee, S.G., Nam, J.H. and Kim, C.J. Lattice Boltzmann simulation of liquid water transport in microporous and gas diffusion layers of polymer electrolyte membrane fuel cells, J. Power Sources, Vol. 278, 2015, pp. 703-717.

[8] Molaeimanesh, G.R. and Akbari, M.H. A three-dimensional pore-scale model of the cathode electrode in polymer-electrolyte membrane fuel cell by lattice Boltzmann method, J. Power Sources, Vol. 258, 2014, pp. 89-97.

[9] Scheidegger, A.E. The physics of flow through porous media, 1974, University of Toronto Press, Toronto.

[10] Chai, Z., Shi, B., Lu, J. and Guo, Z. Non-Darcy flow in disordered porous media: A lattice Boltzmann study, Computers and Fluids, Vol. 39, 2010, pp. 2069-2077.

[11] Nabovati, A., Llewellin, E. W. and Sousa, Antonio C.M. A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method, Composites: Part A, Vol. 40, 2009, pp. 860-869.

[12] Kozeny, J. Ueber kapillare Leitung des Wassers in Boden, Stizungsber Akad Wiss Wien., Vol. 136, 1927, pp. 271-306.

[13] Carman, P.C. Permeability of saturated sands, soils and clays, J. Agric. Sci., Vol. 18, 1939, pp. 262-273.

[14] Ergun, S. Fluid flow through packed column, Chem. Eng. Sci., Vol. 48, 1952, pp. 89-94.

[15] Gebart, B.R. Permeability of unidirectional reinforcements for RTM, J. Compos. Mater., Vol. 26(8), 1992, pp. 1100-1133.

[16] Aminu, M.D. and Ardo. B.U. A novel approach for determining permeability in porous media, J. Pet. Environ. Biotechnol, Vol. 6(4), 2015, pp. 1-5.

[17] Koponen, A., Kandhai, D. and Hellen, E. Permeability of three-dimensional random fiber webs, Phys. Rev. Lett., Vol. 80, 1998, pp. 716-719.

[18] Eshghinejadfard, A., Daroczy, L. Janiga, G. and Thevenin, D. Calculation of the permeability in porous media using the lattice Boltzmann method, Int. J. Heat & Fluid Flow, Vol. 62, 2016, pp. 93-103.

[19] Yang, P., Wen, Z., Duo, R. and Lui, X. Permeability in multi-size structures of random packed porous media using three-dimensional lattice Boltzmann method, Int. J. Heat & Mass Trans., Vol. 106, 2017, pp.1368-1375.

[20] Krittacom, B. and Amatachaya, P. A simplified method based on Darcy – Forchheimer equation for investigating the permeability of wire-net porous media, paper presented in the 2018 International Conference on Power, Energy and Electrical Engineering (CPEEE 2018), Tokyo, Japan.

[21] Krittacom, B., Amatachaya, P., Srimuang W. and Inla, K. The combustion of diesel oil on porous burner installed porous emitter downstream, paper presented in the 8th KSME-JSME Thermal and Fluids Engineering Conference, Songdo Convensia Center, 2012, Incheon, Korea.

[22] Krittacom, B. and Klamnoi, A. A simplified linear scattering phase function for solving equation of radiative heat transfer, paper presented in the 4th International Symposium on Engineering, Energy and Environments, 2015, Pattaya, Thailand.

[23] Kaewchart, K. and Krittacom, B. Comparison of combustion behavior between solid porous burners installed the porous emitter and non-porous emitter, Energy Procedia, Vol. 138, 2017, pp. 2-7.

[24] Mohamad, A.A. Heat transfer enhancements in heat exchangers fitted with porous media Part I: constant wall temperature, Int. J.Ther. Sci., Vol. 42(4), 2003, pp. 385-395.

[25] Pavel, B.I. and Mohamad, A.A. An experimental and numerical study on heat transfer enhancement for gas heat exchangers fitted with porous media, Int. J. Heat & Mass Trans., Vol. 47(23), 2004, pp. 4939-4952.

[26] Cengel, Y.A. and Ghajar, A.F. Heat and Mass Transfer: Fundamental and Applications, 4th edition, 2011, McGraw-Hill, Singapore.

[27] Cheney, W. and Kincaid, D. Numerical Mathematics and Computing, 7th edition, 2013, Brooks/Cole, Cengage Learning, USA.

[28] Green, L. Jr. Fluid flow though porous metals, J. Appl. Mechanics, Vol. 18, 1951, pp. 39-45.

[29] Kaiany, M. Principle of Heat Transfer in Porous Media. 2nd edition, 1996, Springer-Verlag, New York.