# Tree model used in PWC

**URL:** <https://www.simscale.com/forum/t/tree-model-used-in-pwc/99546>\
**Category:** Fluid Flow / CFD\
**Created:** [December 5, 2024, 4:30pm UTC](https://www.simscale.com/forum/t/tree-model-used-in-pwc/99546 "2024-12-05T16:30:58Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![jjansman](https://www.simscale.com/forum/letter_avatar/jjansman/32/5_5575768a8748004e209b776fc1b2916d.png) [@jjansman](https://www.simscale.com/forum/u/jjansman)\
**Post date:** [December 5, 2024, 4:30pm UTC](https://www.simscale.com/forum/t/tree-model-used-in-pwc/99546/1 "2024-12-05T16:30:59Z")

</div>

I have had a few earlier queries in the forum about the used Tree model in PWC. I think I am now starting to get a more consistent story in my head.  
I want to verify that and see if some questions I still have can be answered by someone.

In literature (see e.g. here my inventory: [Simulating a tree](https://www.archaeocosmology.org/eng/Boomsim.htm#contribution)):

- When measuring the drag in e.g. a windtunnel: Cd is depending on wind velocity and on the leaf coverage (LAI) of the tree [Koizuma, 2010, Fig. 5: [https://www.researchgate.net/publication/44385014\_Evaluation\_of\_drag\_coefficients\_of\_poplar-tree\_crowns\_by\_a\_field\_test\_method](https://www.researchgate.net/publication/44385014_Evaluation_of_drag_coefficients_of_poplar-tree_crowns_by_a_field_test_method) ].
- A leafless tree is around Cd=0.18 (migth be quite velocity indepepdent). And a leafed tree has an average Cd between 0.2 and 1.5 depending on wind velocity [Koizuma, 2010, Fig. 5]

In SIMSCALE PWC doc: [Surface Roughness & Porosity | Advanced Modelling PWC | SimScale](https://www.simscale.com/docs/analysis-types/pedestrian-wind-comfort-analysis/advanced-modelling/) ad related spreadsheet:

- SIMSCALE uses: fsim = 2_LAI/H_Cdsim
- Cdsim (=0.2) is independant on leaf coverage (LAI) and it looks to be independing on wind velocity.
- Correct?

So questions:

- What Cdsim is to be used (aka how derived from literature Cd’s?)? At what velocity and what leaf coverage?
- What height H is to be used? Is it the tree heigth or the crown height?
- Depending on the above height definition: How would one model a tree with a cylinder: a) of crown height and raised with stem height or b) tree height (not raised). I would think the a) choice would most logical, but this is not shown in the Tree model section of WPC (Figure 10). Sten height quite commenly upto 50% of the tree height.
- Is velocity somewhere included in the fsim?

I hope someone can help me getting a view of how the fsim is defined/derived.

Thanks for your help.

---

<div class="post-metadata">

**Author:** ![RicardoParis](https://www.simscale.com/forum/user_avatar/www.simscale.com/ricardoparis/32/30222_2.png) [@RicardoParis](https://www.simscale.com/forum/u/RicardoParis)\
**Post date:** [December 5, 2024, 7:13pm UTC](https://www.simscale.com/forum/t/tree-model-used-in-pwc/99546/2 "2024-12-05T19:13:14Z")

</div>

All porous media models that involve polynomial approximations are based on the same formulation, but the formula involves different parameters.

The basic polynomial approximation looks like this:  
 ![image](https://www.simscale.com/forum/uploads/default/original/3X/9/f/9f56718544b6c45265569c4c8c5fca9bd2769f16.png)  
With C\_1 and C\_2 being constants, and U velocity.

For Darcy-Forchheimer you’d have something like this:

 ![image](https://www.simscale.com/forum/uploads/default/original/3X/a/b/abaccced331d464418fd8f7d8a7b3c212ded9f14.png)

And for the tree model you’d have what the documentation page that you posted says:

 ![image](https://www.simscale.com/forum/uploads/default/original/3X/9/2/922449e7322b3c77d81cf65b850a8778b5cd806c.png)

All in all, it’s the same base equation but written with different terms. For the tree model you can see that the Darcy term is zero.

- Cd is assumed, by default, to be fixed at 0.2 for all cases but you can change it with a custom definition.
- [Figure 10](https://www.simscale.com/docs/analysis-types/pedestrian-wind-comfort-analysis/advanced-modelling/#:~:text=500%20different%20locations.-,Figure%2010,-%3A%20Visual%20Description%20of) in the documentation that you posted shows how to obtain the height
- I normally model a solid trunk (as a solid wall) and a separate volume for the leaves (as a porous media)

Cheers

---

<div class="post-metadata">

**Author:** ![jjansman](https://www.simscale.com/forum/letter_avatar/jjansman/32/5_5575768a8748004e209b776fc1b2916d.png) [@jjansman](https://www.simscale.com/forum/u/jjansman)\
**Post date:** [December 5, 2024, 7:24pm UTC](https://www.simscale.com/forum/t/tree-model-used-in-pwc/99546/3 "2024-12-05T19:24:44Z")

</div>

Thanks for your answer. I try to use papers/aticles to backup the chosen values, so that is why I come back:

> [@RicardoParis](#):
>
> - Cd is assumed, by default, to be fixed at 0.2 for all cases but you can change it with a custom definition

Were is this value 0.2 coming from? It looks to be close to the drag coefficient measured for a leafless decidious tree; but is that the origin of the 0.2?

> [@RicardoParis](#):
>
> - [Figure 10](https://www.simscale.com/docs/analysis-types/pedestrian-wind-comfort-analysis/advanced-modelling/#:~:text=500%20different%20locations.-,Figure%2010,-%3A%20Visual%20Description%20of) in the documentation that you posted shows how to obtain the height
> - I normally model a solid trunk (as a solid wall) and a separate volume for the leaves (as a porous media)

In your case: I assume you use as H, the height of the ‘seperate volume for the leaves’. Correct?

Sorry for this elaboration. But I get the feel, my picture becomes more and more consistent. Thanks.

All the best,