Porous media

Using SimScale
1

I am trying to understand the use of porosity: Porosity & Porous Media | Advanced Concepts | SimScale .
I have used a leafed tree (from trees by rtir | SimScale), but in winter the leafs are gone and thus one could simulate this with porosity (and even in summer there will be some porosity).
There are several ways to implement porosity (as the porous-media link says). I have now tried it using ‘Perforated Plate’ as I found it simple to configure: Zwiepse Molen by vreijs | SimScale
So I gave the tree this ‘Perforated Plate’, but how does this ‘plate’ look like (its dimensions?)? Is this ‘plate’ a ‘flat’ object that traced the contours of my tree (in the direction of the defined flow)?
Or should I use a different way of porosity (but then how do I configure its parameters)?
Any help/hint/link is welcome. Thanks.

All the best,

Victor

2

Hi Victor,
if you have access to the Incompressible (LBM) or Pedestrian Wind Comfort analysis types you can directly assign a tree species to the model of the crown and assign a porous media.
But also if you don’t, the documentation provides some good insights in how to model trees with porous media and how to derive the Darcy-Forchheimer coefficients for it: Surface Roughness & Porosity | Advanced Modelling PWC | SimScale

For getting the correct drag coefficient and Leaf Area Index values I can refer you to this global database of tree scpecies: A Global Database of Field-observed Leaf Area Index in Woody Plant Species, 1932-2011

Best,
Richard

3

THANKS Richard, you helped me a lot.
I have the Community Plan so LBM and PWC are not available for me.

So I have deducted the following, simulated by your links:

DF formula = Darcy + Forchheimer
DF formula = -mu/K * u - rho * Fe/sqrt(K) * u^2

From: Modelling trees with cfd - FreeCAD Forum
DF formula = -mu/k * u - rho/k1 * u^2
d=1/k
f=2/k1

Combining both links:
k=K
k1=sqrt(K)/Fe
d=1/k=1/K
f=2/k1=2*Fe/sqrt(K)

For simplified Darcy-Forchheimer, we make the Darcy component zero (d >> 1/mu >> 5e+4) (Surface Roughness & Porosity | Advanced Modelling PWC | SimScale ):
DF formula = -rho * Fe/sqrt(K) * u^2

Fe/sqrt(K)=Cd * LAD
f=2 * Cd * LAD
LAD=LAI/h
f=2 * Cd * LAI/h
with:
LAI: Leaf Area Index
h: height of tree [m]
Cd: draft coefficient

For filling in the Darcy-Forchheimer medium window in SIMSCALE:
dx=dy=dz=5e+10
fx=fy=fz=2 * Cd * LAI/h
For oka tree in summer: Cd=0.2 and LAIsummer=5.2:
For oak tree in winter: Cd=0.2 and LAIwinter = around 0.1*LAIsummer = 0.52 (assuming the branches will take over the ‘surface’ in winter)
REMARK: Nageli, 1946 [https://www.dora.lib4ri.ch/wsl/islandora/object/wsl%3A24067/datastream/PDF/Nägeli-1946-Weitere_Untersuchungen_über_die_Windverhältnisse-(published_version).pdf] saw a decrease of 50% of the windspeed-reduction behind a winter tree compared to summer tree. Don’t know if this LAIwinter matches this, need to check.

fx=fy=fz=2 * Cd * LAIsummer/h = 2.1/h
fx=fy=fz=2 * Cd * LAIwinter/h = 0.21/h (see remark)

Hope I interpreted all ok.

Thanks for your hints!

All the best,
Victor

5

This deduction of mine is wrong!!! d should be zero, thus:
dx=dy=dz=0

Checked the ‘transparency’ of my oak tree. With leaves (summer) it would be around 95% coverage with leaf/branches. Without leaves (winter) there looks to be some 20% of coverage with branches. So if 95% compares to a LAIsummer of 5.2, then LAIwinter is around 5.2/95*20=1.1…

And thus for winter fx=fy=fz=2 * Cd * LAIwinter/h = 0.44/h

But this is all guessing for me. So any help is wanted