FEATool Multiphysics
v1.10 Finite Element Analysis Toolbox |

Flow in Porous Media

Axisymmetric laminar fluid flow in a diffusor duct or reaction chamber blocked by sections of a porous material. The model features several partially active subdomains with the Brinkman equations governing the fluid flow. The flow field with and without the porous material is compared.

This model is available as an automated tutorial by selecting **Model Examples and Tutorials...** > **Multiphysics** > **Flow in Porous Media** from the **File** menu. Or alternatively, follow the step-by-step instructions below.

- To start a new model click the
**New Model**toolbar button, or select*New Model...*from the*File*menu. - Select the
**Axi 2D**radio button.

First is to solve a pure laminar flow problem without the porous domains.

- Select the
**Navier-Stokes Equations**physics mode from the*Select Physics*drop-down menu. - Press
**OK**to finish the physics mode selection. - Select
**Polygon**from the*Geometry*menu.

Enter the following data into the **Point coordinates** table.

r | z | |
---|---|---|

1 | 0 | 0 |

2 | 0.002 | 0 |

3 | 0.005 | 0.003 |

4 | 0.005 | 0.01 |

5 | 0.002 | 0.013 |

6 | 0 | 0.013 |

- Press
**OK**to finish and close the dialog box. - Select
**Rectangle**from the*Geometry*menu. - Enter
`4e-3`

into the*y*edit field._{min} - Enter
`8e-3`

into the*y*edit field._{max} - Enter
`1e-3`

into the*x*edit field._{max} - Press
**OK**to finish and close the dialog box. - Select
**Rectangle**from the*Geometry*menu. - Enter
`1.5e-3`

into the*x*edit field._{min} - Enter
`3.5e-3`

into the*x*edit field._{max} - Enter
`4e-3`

into the*y*edit field._{min} - Enter
`8e-3`

into the*y*edit field._{max} - Press
**OK**to finish and close the dialog box. - Select
**R1**in the geometry object*Selection*list box. - Press the
**Copy and/or transform selected geometry object***Toolbar*button. - Select the
**Make copy of geometry object**check box. - Enter
`4e-3 0`

into the*Space separated string of displacement lengths*edit field. - Press
**OK**to finish and close the dialog box. - Switch to
**Grid**mode by clicking on the corresponding*Mode Toolbar*button. - Press the
**Settings***Toolbar*button.

Specific grid sizes for subdomains and boundaries can be prescribed directly in the *Grid Settings* dialog box. Here the grid size in the outer domain is set to three times the porous domains.

- Enter
`1.5e-4*[1 1 1 3]`

into the*Subdomain Grid Size*edit field. - Press the
**Generate**button to call the grid generation algorithm. - Press
**OK**to finish and close the dialog box. - Switch to
**Equation**mode by clicking on the corresponding*Mode Toolbar*button. - Select
**1**,**2**,**3**, and**4**in the*Subdomains*list box. - Enter
`1.2`

into the*Density*edit field. - Enter
`1.8e-5`

into the*Viscosity*edit field. - Press
**OK**to finish the equation and subdomain settings specification. - Switch to
**Boundary**mode by clicking on the corresponding*Mode Toolbar*button. - Select
**3**in the*Boundaries*list box. - Select
**Inlet/velocity**from the*Navier-Stokes Equations*drop-down menu. - Enter
`2e-2`

into the*Velocity in z-direction*edit field. - Select
**7**in the*Boundaries*list box. - Select
**Outflow/pressure**from the*Navier-Stokes Equations*drop-down menu. - Select
**1**,**8**, and**9**in the*Boundaries*list box. - Select
**Symmetry/slip**from the*Navier-Stokes Equations*drop-down menu. - Press
**OK**to finish the boundary condition specification. - Switch to
**Solve**mode by clicking on the corresponding*Mode Toolbar*button. - Press the
**=***Toolbar*button to call the solver. After the problem has been solved FEATool will automatically switch to postprocessing mode and plot the computed solution. - Press the
**Plot Options***Toolbar*button. - Select the
**Contour Plot**check box. - Select
**Pressure**from the*Predefined contour plot expressions*drop-down menu. - Select the
**Arrow Plot**check box. - Press
**OK**to plot and visualize the selected postprocessing options.

By plotting the *Velocity field* at the mid point one can see that the flow decreases smoothly towards the edges.

- Select
**Point/Line Evaluation...**from the*Post*menu. - Select
**Velocity field**from the*Evaluation Expression*drop-down menu. - Enter
`0:0.005/100:0.005`

into the*Evaluation coordinates in r-direction*edit field. - Enter
`0.006`

into the*Evaluation coordinates in z-direction*edit field. - Press
**OK**to finish and close the dialog box.

Now go back to *Equation* mode and add the *Brinkman Equations* physics mode which will account for the porous domains.

- Switch to
**Equation**mode by clicking on the corresponding*Mode Toolbar*button. - Switch to the
**+**tab. - Select the
**Brinkman Equations**physics mode from the*Select Physics*drop-down menu. - Press the
**Add Physics >>>**button. - Select
**1**,**2**, and**3**in the*Subdomains*list box. - Enter
`1.2`

into the*Density*edit field. - Enter
`1.8e-5`

into the*Viscosity*edit field. - Enter
`2e-7`

into the*Permeability*edit field.

Deactivate the *Brinkman Equations* physics mode in the outer domain.

- Select
**4**in the*Subdomains*list box. - Press the
**active**toggle button.

Similarly, deactivate the *Navier-Stokes Equations* physics mode in the inner porous domains.

- Switch to the
**ns**tab. - Select
**1**,**2**, and**3**in the*Subdomains*list box. - Press the
**active**toggle button. - Press
**OK**to finish the equation and subdomain settings specification. - Switch to
**Boundary**mode by clicking on the corresponding*Mode Toolbar*button.

The two physics modes are coupled via setting the corresponding velocities equal at the shared boundaries.

- Select
**11**,**12**,**13**,**14**,**15**,**16**,**17**,**18**,**19**, and**20**in the*Boundaries*list box. - Select
**Inlet/velocity**from the*Navier-Stokes Equations*drop-down menu. - Enter
`u2`

into the*Velocity in r-direction*edit field. - Enter
`w2`

into the*Velocity in z-direction*edit field. - Switch to the
**br**tab. - Select
**Inlet/velocity**from the*Brinkman Equations*drop-down menu. - Enter
`u`

into the*Velocity in r-direction*edit field. - Enter
`w`

into the*Velocity in z-direction*edit field. - Select
**1**in the*Boundaries*list box. - Select
**Symmetry/slip**from the*Brinkman Equations*drop-down menu. - Press
**OK**to finish the boundary condition specification. - Switch to
**Solve**mode by clicking on the corresponding*Mode Toolbar*button. - Press the
**=***Toolbar*button to call the solver. After the problem has been solved FEATool will automatically switch to postprocessing mode and plot the computed solution.

There now exists two sets of postprocessing variables, one for each physics mode. Plot and compare the magnitude of the *Velocity field* for both the porous and outer domains.

- Press the
**Plot Options***Toolbar*button. - Select
**Velocity field**from the*Predefined surface plot expressions*drop-down menu. - Press
**OK**to plot and visualize the selected postprocessing options.

Also again plot magnitude of the *Velocity field* at the mid point line. As *nan* values are returned for queries outside the valid domain, one can use the *setnan* function to plot both curves together.

- Select
**Point/Line Evaluation...**from the*Post*menu. - Enter
`setnan(sqrt(u^2+w^2),0) + setnan(sqrt(u2^2+w2^2),0)`

into the edit field. - Enter
`0:0.005/100:0.005`

into the*Evaluation coordinates in r-direction*edit field. - Enter
`0.006`

into the*Evaluation coordinates in z-direction*edit field. - Press
**OK**to finish and close the dialog box.

Compared to the smooth flow before, the flow now is irregular with two peaks between the porous domains.

The *flow in porous media* multiphysics model has now been completed and can be saved as a binary (.fea) model file, or exported as a programmable MATLAB m-script text file, or GUI script (.fes) file.