Pressure drop and friction factor of steady and oscillating flows in open-cell porous media

  • Li wen Jin
  • Kai Choong LeongEmail author


Open-cell metal foams are often used in heat exchangers and absorption equipment because they exhibit large specific surface area and present tortuous coolant flow paths. However, published research works on the characteristics of fluid flow in metal foams are relatively scarce, especially for the flow oscillation condition. The present experimental investigation attempts to uncover the behavior of steady and oscillating flows through metal foams with a tetrakaidecahedron structure. In the experiments, steady flow was supplied by an auto-balance compressor and flow oscillation was provided by an oscillating flow generator. The pressure drop and velocity were measured by the differential pressure transducer and hot-wire sensor, respectively. The friction factor of steady flow in metal foam channel was analyzed through the permeability and inertia coefficient of the porous medium. The results show that flow resistance in the metal foams increases with increasing form coefficient and decreasing permeability. The empirical equation obtained by the present study indicates that the maximum friction factor of oscillating flow through the tested aluminum foams with specific structure is governed by the hydraulic ligament diameter-based kinetic Reynolds number and the dimensionless flow amplitude.


Dimensionless flow amplitude Friction factor Inertia coefficient Kinetic Reynolds number Permeability Pressure drop 





Dimensionless flow amplitude


Form coefficient of porous media


Diameter of the pipe


Hydraulic ligament diameter of aluminum foam


Hydraulic diameter of channel


Ligament diameter of aluminum foam (μm)


Inertia coefficient of porous media (m−1)


Friction factor


Maximum friction factor


Height of the channel (m)


Permeability of the porous medium (m2)


Length of the tested foam (m)


Number of cycles


Pressure drop across the test section (Pa)


Maximum pressure drop across the test section (Pa)


Ligament diameter-based Reynolds number

Reω (Dh)

Kinetic Reynolds number


Maximum Reynolds number


Cycle time (s)


Maximum velocity of fluid in metal foam channel (m/s)


Mean velocity of fluid in porous channel (m/s)


Channel width (m)


Amplitude of flow displacement (mm)

Greek Symbols


Stokes number


Shape parameter of porous medium


Phase lag




Phase lag


Porosity of the porous media


Dynamic viscosity of fluid (kg/m s)


Kinematic viscosity of fluid (m2/s)


Density of fluid (kg/m3)


Angular frequency (rad/s)


Average value


  1. Bear J. (1988). Dynamics of Fluids in Porous Media. Dover publication, New York, N.Y. Google Scholar
  2. Boomsma K., Poulikakos D. and Zwick F. (2003a). Metal foams as compact high performance heat exchangers. Mech. Mater. 35: 1161–1176 CrossRefGoogle Scholar
  3. Boomsma K., Poulikakos D. and Ventikos Y. (2003b). Simulations of flow through open cell metal foams using an idealized periodic cell structure. Int. J. Heat Fluid Flow 24: 825–834 CrossRefGoogle Scholar
  4. Cortis A., Smeulders D.M.J., Guermond J.L. and Lafarge D. (2003). Influence of pore roughness on high-frequency permeability. Phys. Fluids 15: 1766–1775 CrossRefGoogle Scholar
  5. Fu H.L., Leong K.C., Huang X.Y. and Liu C.Y. (2001). An experimental study of heat transfer of a porous channel subjected to oscillating flow. ASME J. Heat Transfer 123: 162–170 CrossRefGoogle Scholar
  6. Hassanizadeh S.M. and Gray W.G. (1987). High velocity flow in porous media. Transport Porous Med 2: 521–531 CrossRefGoogle Scholar
  7. Lage J.L. (1998). The fundamental theory of flow through permeable media from Darcy to turbulence. In: Ingham, D.B. and Pop, I. (eds) Transport Phenomena in Porous Media, pp 1–30. Pergamon, Oxford Google Scholar
  8. Lage J.L., Weinert A.K. and Price D.C. (1996). Numerical study of a low permeability microporous heat sink for cooling phased-array radar systems. Int. J. Heat Mass Transfer 39: 3633–3647 CrossRefGoogle Scholar
  9. Lage J.L., Narasimhan A., Porneala D.C. and Price D.C. (2004). Experimental study of forced convection through microporous enhanced heat sinks: enhanced heat sinks for cooling airborne microwave phased-array radar antennas. Emerg. Technol. Tech. Porous Media 28: 433–452 Google Scholar
  10. Kaviany M. (1985). Laminar flow through a porous channel bounded by isothermal parallel plates. Int. J. Heat Mass Transfer 28: 815–858 Google Scholar
  11. Khodadadi J.M. (1991). Oscillatory fluid flow through a porous medium channel bounded by two impermeable parallel plates. ASME J. Fluids Eng. 113: 509–511 Google Scholar
  12. Kim S.Y., Kang B.H. and Kim J.H. (2001). Forced convection from aluminum foam materials in an asymmetrically heated channel. Int. J. Heat Mass Transfer 44: 1451–1454 CrossRefGoogle Scholar
  13. Leong K.C. and Jin L.W. (2005). An experimental study of heat transfer in oscillating flow through a channel filled with an aluminum foam. Int. J. Heat Mass Transfer 48: 243–253 CrossRefGoogle Scholar
  14. Lu T.J., Stone H.A. and Ashby M.F. (1998). Heat transfer in open-cell metal foams. Acta Mater. 46: 3619–3635 CrossRefGoogle Scholar
  15. Nield D.A. (1994). Modelling high speed flow of a compressible fluid in a saturated porous medium. Transport Porous Med. 14: 85–88 CrossRefGoogle Scholar
  16. Panda M.N. and Lake L. (1994). Estimation of single-phase permeability from parameters of particle-size distribution. AAPG Bull. 78: 1028–1039 Google Scholar
  17. Taylor, J.R.: An Introduction to Error Analysis, 2nd ed. University Science Books, California (1997)Google Scholar
  18. Uchida S. (1950). The pulsating viscous flow superposed on the steady laminar motion of an incompressible fluid in a circular pipe. ZAMP 7: 403–422 CrossRefGoogle Scholar
  19. Vafai K. and Tien C.L. (1981). Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Transfer 24: 195–203 CrossRefGoogle Scholar
  20. Vafai K. and Kim S.J. (1989). Forced convection in a channel filled with a porous medium: an exact solution. ASME J. Heat Transfer 111: 1103–1106 CrossRefGoogle Scholar
  21. Whitaker S. (1967). Diffusion and dispersion in porous medium. AIChE J. 13: 420–427 CrossRefGoogle Scholar
  22. Zhao T.S. and Cheng P. (1996a). Oscillatory pressure drops through a woven-screen packed column subjected to a cyclic flow. Cryogenics 36: 333–341 CrossRefGoogle Scholar
  23. Zhao T.S. and Cheng P. (1996b). The friction coefficient of a fully developed laminar reciprocating flow in a circular pipe. Int. J. Heat Fluid Flow 17: 167–172 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.School of Mechanical and Aerospace EngineeringNanyang Technological UniversitySingaporeRepublic of Singapore

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