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

  • Nihad Dukhan
  • Krunal Patel


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)


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of Detroit MercyDetroitUSA

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