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Fluid flow through heterogeneous porous media in a rotating square channel

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Abstract

An analytical three-dimensional solution to the fluid flow problem through heterogeneous porous media in a rotating square channel is presented. The permeability of the fluid saturated porous domain varies in the vertical direction, thus affecting the imposed main flow in the channel. As a result of Coriolis acceleration, secondary circulation in a plane perpendicular to the main flow direction is created. A particular example of a monotonic distribution of the permeability function is analyzed leading to a single vortex secondary circulation. Nevertheless, multiple vortex secondary flow solutions are possible depending on the particular variation of the permeability in the vertical direction. No secondary motion is expected for isothermal flows in homogeneous porous media.

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Abbreviations

Ek:

porous media Ekman number, defined by equation (3)

Ê x :

unit vector in thex direction

Ê y :

unit vector in they direction

Ê z :

unit vector in thez direction

Êω :

unit vector in the direction of the angular velocity

H * :

The height/width of the square channel

k c :

a reference value of permeability

k :

dimensionless permeability function, equalsk */k c

p :

dimensionless reduced pressure generalized to include the centrifugal as well as the gravity accelerations

q :

specific flowrate vector (dimensionless), equalsuÊ x +vÊ y +wÊ z

u :

x component of the specific flowrate, (dimensionless)

v :

y component of the specific flowrate, (dimensionless)

w :

z component of the specific flowrate, (dimensionless)

x :

horizontal coordinate along the axis of the channel

y :

horizontal coordinate across the axis of the channel

z :

vertical coordinate

Φ :

porosity

Ω c :

angular velocity of the rotating channel

Ν 0 :

fluid's kinematic viscosity

Μ c :

fluid's dynamic viscosity

ψ :

a stream function

*:

dimensional values

c :

characteristic or reference values

0:

zeroth order

1:

first order

References

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Vadasz, P. Fluid flow through heterogeneous porous media in a rotating square channel. Transp Porous Med 12, 43–54 (1993). https://doi.org/10.1007/BF00616361

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Key words

  • Porous media
  • heterogeneous
  • rotating flow
  • square channel
  • Coriolis acceleration
  • secondary circulation