Abstract
The flow of an adiabatic gas through a porous media is treated analytically for steady one- and two-dimensional flows. The effect on a compressible Darcy flow by inertia and Forchheimer terms is studied. Finally, wave solutions are found which exhibit a cut-off frequency and a phase shift between pressure and velocity of the gas, with the velocity lagging behind the pressure.
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Abbreviations
- A :
-
area of tube for one-dimensional flow
- B :
-
drag coefficient associated with Forchheimer term
- c :
-
speed of sound
- M:
-
Mach number
- p * :
-
gas pressure
- p :
-
dimensionless gas pressure
- s :
-
coordinate along the axis of tube
- t * :
-
time variable
- t :
-
dimensionless time variable
- V* :
-
gas velocity in the porous media
- V:
-
dimensionless gas velocity
- γ:
-
ratio of specific heat capacities
- θ:
-
phase angle between gas pressure and velocity for linear waves
- λ:
-
parameter indicating the importance of the inertia term
- μ:
-
viscosity
- ωp :
-
natural frequency of the porous media
- ϱ* :
-
gas density
- ϱ:
-
dimensionless gas density
- σ:
-
parameter indicating the importance of the Forchheimer term
- φ:
-
porosity of porous media
- Φ:
-
velocity potential
- Ψ:
-
stream function
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De Ville, A. On the properties of compressible gas flow in a porous media. Transp Porous Med 22, 287–306 (1996). https://doi.org/10.1007/BF00161628
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DOI: https://doi.org/10.1007/BF00161628