Why does the minimum velocity become negative only for the 40% porosity model?

[Shunsuke Takai]

Hello,

I am performing a FlowDict simulation on fibrous catalyst layer models and would like to ask about an unexpected simulation result.

To compare the effect of porosity on transport properties, I created five fibrous models with porosities of 40%, 50%, 60%, 70%, and 80%.

The dimensions of each model are:

Voxel size: 0.1 μm
Domain size: 200 × 200 × 200 voxels
(20 μm × 20 μm × 20 μm)

The purpose of this study is to investigate how structural properties such as flow velocity and pressure drop change with porosity.

However, after performing the FlowDict simulation, I found that only the 40% porosity model exhibits negative minimum velocity values, whereas the other porosity models do not.

I attached the graph of the minimum velocity through the thickness direction.

I would like to know:

Is it physically reasonable for the minimum velocity to become negative in this case?
Could this result be caused by the simulation settings or boundary conditions?
Are there any FlowDict settings that I should check first?

My simulation information is:

GeoDict version: 2025.5
Module: FlowDict
Models: Fibrous catalyst layer
Porosity: 40%, 50%, 60%, 70%, 80%
Voxel size: 0.1 μm
Domain size: 200 × 200 × 200 voxels

If additional information such as the FlowDict settings or result files would be helpful, I would be happy to provide them.

Thank you very much for your help.

Best regards,

Shunsuke Takai

[Jonas Schabernack]

Hello Shunsuke,

Thank you for your detailed inquiry. Here are answers to your questions regarding the negative minimum velocities in your 40% porosity model:

1. Physical Reasonableness
Yes, this is physically reasonable. Negative velocity indicates that fluid is locally moving toward the inlet rather than the outlet. Low porosity structures often feature labyrinth-like geometries with high tortuosity. These complex shapes can redirect flow backward into narrow channels or dead ends before it resumes toward the outlet.

2. Comparison with Higher Porosities
As porosity increases, the structure becomes more open and flow paths become more direct. This reduces the likelihood of backflow. You can also see small negative values in your 50% porosity plot. For higher porosities backflow does not occur anymore.

3. Simulation Settings
Since this behavior is physical and expected, you do not need to adjust your solver settings.

The result aligns with expectations for dense fibrous media. The negative values represent local backflow caused by complex geometry rather than a simulation error.

Best regards,
Jonas

[Shunsuke Takai]

Hello Jonas,

Thank you very much for your detailed explanation. It was very helpful and helped me better understand the physical meaning of the negative velocity values.

I have one additional question.

Would it be possible to create a visualization that makes the local backflow easier to observe? For example, is there a way to display the flow using streamlines or another visualization method so that the reverse flow can be seen more clearly?

Also, would reducing the number of voxels while using a smaller voxel length improve the visualization or the accuracy of the flow field?

Thank you very much for your time and support.

Best regards,

Shunsuke

[Jonas Schabernack]

Hello Shunsuke,

You can visualize local backflow by using thresholding on the velocity field:

• Load the flow volume field and select the relevant velocity component depending on the defined flow direction (e.g., Z).
• Apply a threshold to display only values smaller than 0. This will only show regions with reverse flow for clearer observation.

Streamlines do not support filtering for negative values alone, but if backflow is significant, it will naturally appear in the streamline visualization. I recommend first identifying backflow zones using the thresholded velocity field, then examining streamlines within those specific areas to confirm the behavior. 

Regarding voxel resolution:

• Reducing the number of voxels while decreasing voxel size shrinks the total sample volume. This may limit your view to a single fiber instead of multiple ones, potentially compromising representativeness.
• Smaller voxels improve accuracy only until geometric features (e.g., pore throats or fiber diameters) are sufficiently resolved. Beyond ~10 voxels per feature, further refinement yields negligible simulation result improvements but increases runtimes.
• Only reduce voxel count if necessary to save computational resources or runtime. Always ensure the remaining volume remains statistically representative of your sample geometry for reliable results.

Best regards,
Jonas