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A discussion on the interpretation of the Darcy equation in case of open-cell metal foam based on numerical simulations

Sven De Schampheleire (UGent) , Kathleen De Kerpel (UGent) , Bernd Ameel (UGent) , Peter De Jaeger (UGent) , Özer Bağci (UGent) and Michel De Paepe (UGent)
(2016) MATERIALS. 9(6).
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Abstract
It is long known that for high-velocity fluid flow in porous media, the relation between the pressure drop and the superficial velocity is not linear. Indeed, the classical Darcy law for shear stress dominated flow needs to be extended with a quadratic term, resulting in the empirical Darcy–Forchheimer model. Another approach is to simulate the foam numerically through the volume averaging technique. This leads to a natural separation of the total drag force into the contribution of the shear forces and the contribution of the pressure forces. Both representations of the total drag lead to the same result. The physical correspondence between both approaches is investigated in this work. The contribution of the viscous and pressure forces on the total drag is investigated using direct numerical simulations. Special attention is paid to the dependency on the velocity of these forces. The separation of the drag into its constituent terms on experimental grounds and for the volume average approach is unified. It is shown that the common approach to identify the linear term with the viscous forces and the quadratic term with the pressure forces is not correct.
Keywords
volume averaging theory, permeability, inertial coefficient, Darcy, Forchheimer, metal foam, pressure drop, ALUMINUM FOAM, POROUS-MEDIA, FLOW REGIMES, PERMEABILITY, DERIVATION, TRANSPORT

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Chicago
De Schampheleire, Sven, Kathleen De Kerpel, Bernd Ameel, Peter De Jaeger, Özer Bağci, and Michel De Paepe. 2016. “A Discussion on the Interpretation of the Darcy Equation in Case of Open-cell Metal Foam Based on Numerical Simulations.” Materials 9 (6).
APA
De Schampheleire, S., De Kerpel, K., Ameel, B., De Jaeger, P., Bağci, Ö., & De Paepe, M. (2016). A discussion on the interpretation of the Darcy equation in case of open-cell metal foam based on numerical simulations. MATERIALS, 9(6).
Vancouver
1.
De Schampheleire S, De Kerpel K, Ameel B, De Jaeger P, Bağci Ö, De Paepe M. A discussion on the interpretation of the Darcy equation in case of open-cell metal foam based on numerical simulations. MATERIALS. Basel, Switserland: MDPI; 2016;9(6).
MLA
De Schampheleire, Sven, Kathleen De Kerpel, Bernd Ameel, et al. “A Discussion on the Interpretation of the Darcy Equation in Case of Open-cell Metal Foam Based on Numerical Simulations.” MATERIALS 9.6 (2016): n. pag. Print.
@article{7225718,
  abstract     = {It is long known that for high-velocity fluid flow in porous media, the relation between the pressure drop and the superficial velocity is not linear. Indeed, the classical Darcy law for shear stress dominated flow needs to be extended with a quadratic term, resulting in the empirical Darcy--Forchheimer model. Another approach is to simulate the foam numerically through the volume averaging technique. This leads to a natural separation of the total drag force into the contribution of the shear forces and the contribution of the pressure forces. Both representations of the total drag lead to the same result. The physical correspondence between both approaches is investigated in this work. The contribution of the viscous and pressure forces on the total drag is investigated using direct numerical simulations. Special attention is paid to the dependency on the velocity of these forces. The separation of the drag into its constituent terms on experimental grounds and for the volume average approach is unified. It is shown that the common approach to identify the linear term with the viscous forces and the quadratic term with the pressure forces is not correct.},
  articleno    = {409},
  author       = {De Schampheleire, Sven and De Kerpel, Kathleen and Ameel, Bernd and De Jaeger, Peter and Ba\u{g}ci, {\"O}zer and De Paepe, Michel},
  issn         = {1996-1944},
  journal      = {MATERIALS},
  keyword      = {volume averaging theory,permeability,inertial coefficient,Darcy,Forchheimer,metal foam,pressure drop,ALUMINUM FOAM,POROUS-MEDIA,FLOW REGIMES,PERMEABILITY,DERIVATION,TRANSPORT},
  language     = {eng},
  number       = {6},
  pages        = {15},
  publisher    = {MDPI},
  title        = {A discussion on the interpretation of the Darcy equation in case of open-cell metal foam based on numerical simulations},
  url          = {http://dx.doi.org/10.3390/ma9060409},
  volume       = {9},
  year         = {2016},
}

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