POROUS MEDIA IN SOLIDWORKS FLOW SIMULATION

Porous Medium offers different ways of specifying the flow resistance, including calculation of the resistance from the channels and pores dimensions. The heat exchange is defined in terms of porous matrix properties.

Porous Medium can be defined in Engineering Database by providing different parameters such as Porosity, Permeability type, Resistance Calculation Formula, Pore Size etc.,

Porous Medium definition from SW Flow Simulation

Porosity:
The ratio of the volume of the interconnected pores to the total volume.

Permeability type:
Defines the permeability of the medium with respect to the flow direction. Four types of permeability are available in SOLIDWORKS Flow Simulation.

• Isotropic: The medium permeability is independent of the direction within the medium.
• Unidirectional: The medium is permeable in one direction only.
• Axisymmetrical: The medium permeability is fully governed by its axial (n) and transverse (r) components with respect to a specified direction.
• Orthotropic: The general case, when the medium permeability varies with direction and is fully governed by its three components determined along three principal directions.

Resistance Calculation Formula:
It is used to calculate the flow resistance of the porous medium. The flow resistance coefficient is calculated by

Where P, ρ, V are Fluid Pressure, density, and velocity respectively.

User can specify the k vector components from one on the following equations.

• Pressure drop, Flowrate, Dimensions
  
  Where ∆P: The Pressure difference between the opposite sides of a parallelepiped porous body
  m : Mass flow rate through the body
  S : Body cross-sectional area
  L : Length of the body in selected direction




• Pressure drop, Velocity, Dimensions
  
  Where ∆P : The Pressure difference between the opposite sides of a parallelepiped porous body
  V,ρ : Fluid Velocity and Density respectively
  L : Length of the body in selected direction




• Dependency on Velocity:
  
  Where V, ρ: Fluid Velocity and density respectively.
  A and B: Constants A [kg/m4] and B [kg/ (s· m3)]

The following formulae are used to specify the resistance of long narrow channel porous medium. This medium along with Unidirectional permeability type allows the user to simulate fluid flow through the arrays of tightly packed parallel thin tubes with high length – to- diameter ratio.

• Dependency on Pore Size
  
  Where m and r are the fluid dynamic viscosity and density
  D is the Pore size, which is defined as the hydraulic diameter of pore,
  ε is the porous medium’s porosity.




• Dependency on Pore Size and Reynolds Number
  
• Use effective density: (1 – ε) * Density of the porous matrix, ε – Porosity
• ρ, Density of the Porous Matrix
• Cm, Specific heat capacity of porous matrix
• Conductivity type: Isotropic, Unidirectional, Axisymmetrical, Orthotropic
• λi, Thermal Conductivity
• Matrix and Fluid Heat exchange defined by
  • Volumetric Heat Exchange Co-efficient
  • Heat Exchange Co-efficient and Specific Area

  Volumetric Heat Exchange Co-efficient is calculated by
  
  h: Heat Exchange Co-efficient between porous body’s inner surface and the fluid,
  

EXAMPLE:
Let’s see an example using the same concept in a Catalytic Converter to observe the flow patterns.

From the above image, we have defined two porous media in a catalytic converter. The first one (From right), a Unidirectional medium and the other, an Isotropic medium. The following image will show the flow pattern in each medium.

For the application of the catalytic converter, both the Unidirectional and Isotropic porous medium have their advantages.

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