Transp Porous Med
DOI 10.1007/s11242-015-0488-7
A Numerical Study of the Flow Past an Impermeable
Sphere Embedded in a Porous Medium
Gheorghe Juncu
1
Received: 5 August 2014 / Accepted: 11 March 2015
© Springer Science+Business Media Dordrecht 2015
Abstract The flow past an impermeable sphere embedded in a fluid-saturated porous
medium was investigated numerically. The flow is considered viscous, laminar, axisymmet-
ric, steady and incompressible. The generalized model for fluid flow through an isotropic,
rigid and homogeneous porous medium was used. The stream function–vorticity equations
were solved numerically in spherical coordinates system by a defect correction multigrid
method. The computations were focused on the influence of the Darcy number (Da) and
Forchheimer constant on the flow field for two boundary conditions on the surface of the
sphere: slip and no-slip. The conditions when the macroscopic inertial terms of the general-
ized model can be neglected are presented. For high-porosity porous media, the macroscopic
inertial terms of the generalized model can be neglected if Da Re < 1(Re is the sphere
Reynolds number).
Keywords Saturated porous medium · Sphere · Axisymmetric flow · Stream function ·
Vorticity · No-slip boundary condition · Slip boundary condition
List of symbols
a Radius of the sphere
C
D
Total drag coefficient
C
D, F
Friction drag coefficient
C
D, P
Pressure drag coefficient
C
F
Forchheimer constant
d Diameter of the sphere, d = 2a
Da Darcy number, K /d
2
K Permeability of the porous medium
B Gheorghe Juncu
juncugh@netscape.net; juncu@easynet.ro
1
Department of Chemical and Biochemical Engineering, Politehnica University Bucharest,
Polizu 1, 011061 Bucharest, Romania
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