Journal of Porous Materials

, Volume 18, Issue 6, pp 655–665 | Cite as

Effect of sample’s length on flow properties of open-cell metal foam and pressure-drop correlations



Many applications require fluid flow through the open pores of metal foam. The foam is usually treated as a porous medium for which the Darcy law and the Hazen-Dupuit-Darcy (or Forchheimer) equation are used to describe the pressure drop, and for obtaining the two important flow properties, i.e., the permeability and the form drag coefficient. Little or no attention is paid to the length (or thickness) of the porous medium in the flow direction. This paper establishes a minimum length necessary for the foam to have length-independent (or bulk) permeability and form drag coefficient. This minimum length is obtained experimentally for various types of open-cell aluminum foam subjected to airflow in the Forchheimer regime. Below this thickness values of the two key flow properties are not constant, and they include entrance/exit effects, which may explain some of the discrepancies in the reported values in the literature. The Forchheimer equation was recast in two different manners, which resulted in new non-dimensional numbers- one representing the form drag and the other the viscous drag. These numbers correlated very well with the thickness of the porous medium. The obtained correlations allow for determining the pressure drop given only the velocity and the thickness of an aluminum foam sample.


Metal foam Porous metals Permeability Entrance/exit Pressure drop Length effect 

List of symbols


Form drag coefficient (m−1)


Dimensionless form drag coefficient


Dimensionless viscous drag coefficient


Universal drag coefficient (dimensionless)


Friction factor (dimensionless)


Viscous friction factor (dimensionless)


Permeability (m2)


Thickness of foam sample in the flow direction (m or cells)


Static pressure (Pa)


Inlet pressure (Pa)


Exit pressure (Pa)


Reynolds number


Darcy velocity (m/s)



Uncertainty (%)




Porosity (%)


Kinematic viscosity of air (kg/m.s)


Density of air (kg/m3)


  1. 1.
    J. Zhou, W.O. Soboyejo, C. Mercer, Metall. Mater. Trans. 33A(5), 413–1427 (2002)Google Scholar
  2. 2.
    M.F. Ashby, A.G. Evans, N.A. Fleck, L.J. Gibson, J.W. Hutchinson, H.N.G. Wadley, Metal Foams, a Design Guide (Butterworth-Heinemann, Woburn, 2000)Google Scholar
  3. 3.
    W. Azzi, W.L. Roberts, A. Rabiei, Mater. Des. 28, 569–574 (2007)CrossRefGoogle Scholar
  4. 4.
    J.J. Hwang, G.J. Hwang, R.H. Yeh, C.H. Chao, J. Heat Trans. 124, 120–129 (2002)CrossRefGoogle Scholar
  5. 5.
    J.L. Lage, B.V. Antohe, D.A. Nield, J. Fluids Eng. 119, 700–706 (1997)CrossRefGoogle Scholar
  6. 6.
    D. Seguin, A. Montillet, J. Comiti, Chem. Eng. Sci. 53(21), 3751–3761 (1998)CrossRefGoogle Scholar
  7. 7.
    L. Tadrist, M. Miscevic, O. Rahli, F. Topin, Exp. Therm. Fluid Sci. 28, 193–199 (2004)CrossRefGoogle Scholar
  8. 8.
    S.Y. Kim, J.W. Paek, B.H. Kang, J. Heat Trans. 122, 572–578 (2000)CrossRefGoogle Scholar
  9. 9.
    J.W. Paek, B.H. Kang, S.Y. Kim, J.M. Hyun, Int. J. Thermophys. 21(2), 453–464 (2000)CrossRefGoogle Scholar
  10. 10.
    J.S. Noh, K.B. Lee, C.G. Lee, Int. Commun. Heat Mass. Trans. 33, 434–444 (2006)CrossRefGoogle Scholar
  11. 11.
    A. Bhattacharya, V.V. Calmidi, R.L. Mahajan, Int. J. Heat Mass. Trans. 45, 1017–1031 (2002)CrossRefGoogle Scholar
  12. 12.
    J.P. du Plessis, A. Montillet, J. Comiti, J. Legrand, Chem. Eng. Sci. 49, 3545–3553 (1994)CrossRefGoogle Scholar
  13. 13.
    J.G. Fourie, J.P. du Plessis, Chem. Eng. Sci. 57, 2781–2789 (2002)CrossRefGoogle Scholar
  14. 14.
    J.F. Despois, A. Mortensen, Acta Mater. 53, 1381–1388 (2005)CrossRefGoogle Scholar
  15. 15.
    K. Boomsma, D. Poulikakos, Y. Ventikos, Int. J. Heat Fluid Flow 24, 825–834 (2003)CrossRefGoogle Scholar
  16. 16.
    K. Boomsma, D. Poulikakos, J. Fluids Eng. 124, 263–272 (2002)CrossRefGoogle Scholar
  17. 17.
    B. Antohe, J.L. Lage, D.C. Price, R.M. Weber, J. Fluids Eng. 11, 404–412 (1997)CrossRefGoogle Scholar
  18. 18.
    C. Naakteboren, P.S. Krueger, J.L. Lage, in Proceedings of the International Conference on Porous Media and Applications, Evora, Portugal, 24–27 May 2004Google Scholar
  19. 19.
    C. Naakteboren, P.S. Krueger, J.L. Lage, in Proceedings of the ASME Fluids Engineering Summer Meeting and Exhibit, Houston, TX, 19–20 June 2005Google Scholar
  20. 20.
    M. Medraj, E. Baril, V. Loya, L.P. Lefebvre, J. Mat. Sci. 42, 4372–4383 (2007)CrossRefGoogle Scholar
  21. 21.
    M.D.M. Innocentini, L.P. Lefebvre, R. V. Meloni, E. Baril (2009) J. Porous Mat. doi:  10.1007/s10934-009-9312-5
  22. 22.
    E. Baril, A. Mostafid, L.P. Lefebvre, M. Medraj, Adv. Eng. Mat. 10(9), 889–894 (2008)CrossRefGoogle Scholar
  23. 23.
    K.C. Leong, L.W. Jin, Int. J. Ht. Fld. Fl. 27, 144–153 (2006)CrossRefGoogle Scholar
  24. 24.
    A. Bhattacharya, R.L. Mahajan, J. Elec. Pack 124, 155–163 (2002)CrossRefGoogle Scholar
  25. 25.
    K. Boomsma, D. Poulikakos, F. Zwick, Mech. Mat. 35, 1161–1176 (2003)CrossRefGoogle Scholar
  26. 26.
    J.F. Liu, W.T. Wu, W.C. Chiu, W.H. Hsieh, Exp. Therm. Fld. Sci. 30, 329–336 (2006)CrossRefGoogle Scholar
  27. 27.
    O. Reutter, E. Smirnova, J. Sauerhering, S. Angel, T. Fend, R. Pitz-Paal, J. Fluids Eng. 130, 201–205 (2008)CrossRefGoogle Scholar
  28. 28.
    J.P. Bonnet, F. Topin, L. Tadrist, Transp. Porous Media. 73, 233–254 (2008)CrossRefGoogle Scholar
  29. 29.
    ISO 4638:1984—Polymeric materials, cellular flexible—Determination of air flow permeabilityGoogle Scholar
  30. 30.
    ISO 7231:1984—Polymeric materials, cellular flexible—Method of assessment of air flow value at constant pressure-dropGoogle Scholar
  31. 31.
    ASTM D737 Standard test method for air permeability of textile fabricsGoogle Scholar
  32. 32.
    ASTM F 778–88 Standard methods for gas flow resistance testing of filtration mediaGoogle Scholar
  33. 33.
    ASTM D3574-03 Standard test methods for flexible cellular Materials—slab, bonded, and molded urethane foamsGoogle Scholar
  34. 34.
    J.P. du Plessis, S. Woudberg, Chem. Eng. Sci. 63, 2576 (2008)CrossRefGoogle Scholar
  35. 35.
    J.L. Lage, B. Antohe, J. Fluids Eng. 122, 619–625 (2000)CrossRefGoogle Scholar
  36. 36.
    S. Ergun, Chem. Eng. Progress 48(2), 89–94 (1952)Google Scholar
  37. 37.
    N. Dukhan, P. Patel, Exp. Therm. Fluid Sci. 32, 1059–1067 (2008)CrossRefGoogle Scholar
  38. 38.
    ERG Materials and Aerospace, Oakland, CA. Accessed March 2010
  39. 39.
    R. Figliola, D. Beasly, Theory and Design for Mechanical Measurements (Wiley, New York, 2000)Google Scholar
  40. 40.
    K. Vafai, C.L. Tien, Int. J. Heat Mass. Trans. 25(8), 1183–1190 (1982)CrossRefGoogle Scholar
  41. 41.
    I.H. Shams, Mechanics of Fluids (Wiley, New York, 1992), p. 674Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of Detroit MercyDetroitUSA

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