Abstract
To quantitatively analyze the macroscopic properties of the flow in porous media by means of the continuum approach, detailed information (velocity and pressure fields) on the microscopic scale is necessary. In this paper, the numerical solution for incompressible, Newtonian flow in a diverging-converging representative unit cell (RUC) is presented. A new solution procedure for the problem is introduced. A review of the accuracy of the computational method is given.
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Abbreviations
- A *ff :
-
area of entrance and exit of RUC
- A *fs :
-
interfacial area between the fluid and solid phases
- d :
-
throat diameter of RUC (m)
- D :
-
pore diameter of RUC (m)
- i, j :
-
unit vector for RUC
- L * :
-
wave length of a unit cell
- L p :
-
pore length of RUC (m)
- L t :
-
throat length of RUC (m)
- n :
-
unit outwardly directed vector for the fluid phase
- p * :
-
fluid pressure
- \(\bar P\) * :
-
cross-sectional mean pressure
- \(\bar P\) *en :
-
entrance cross-sectional mean pressure
- Re d :
-
Reynolds number
- x *, r* :
-
cylindrical coordinates
- u *, v* :
-
velocity
- u *cl :
-
centerline velocity
- \(\bar U\) d :
-
mean velocity at the throat of RUC (m/s)
- \(\bar U\) D :
-
mean velocity at the large segment of RUC (m/s)
- Μ :
-
viscosity coefficient (Ns/m2)
- ξ p :
-
excess momentum loss factor defined in (4.1)
- ρ :
-
fluid density (kg/m3)
- ψ * :
-
stream function
- Ω* :
-
vorticity
- г:
-
dimensionless circulation defined in (2.7)
- -:
-
the mean value
- *:
-
dimensionless quantities
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Ruth, D.W., Ma, H. Numerical analysis of viscous, incompressible flow in a diverging-converging RUC. Transp Porous Med 13, 161–177 (1993). https://doi.org/10.1007/BF00654408
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DOI: https://doi.org/10.1007/BF00654408