Directional Loss model in Porous Media
 

Hello everybody,

I'm asking for help to calculate corretly the permeability and resistance loss coefficient in a porous media that mimics the behavior of an architectural feature of a building. It's also called in question the possibility to parameterize those fields.

I’m simulating the cross-ventilation effect caused by the interaction between a low-rise building and the wind present at a specific site. My aim is to get reasonable accurate results about velocity and direction fields inside the building in three different scenarios (each with its own typical wind direction and speed). A whole-field simulation approach was enforced due to high-porosity façades, as I must avoid heavily distorted results that would be caused by a decoupled method (envelope, and then interior space) in this situation.

https://image.ibb.co/fThLsc/Planta_1.jpg
Natural ventilation occurs in the highlighted green area. Grey areas are gardens. Northwest and southeast facades have a high porosity.

The northwest façade is a single curvature wall that was simplified to
ten straight segments. Each segment is composed by an assembly made of one of three different types of perforated blocks. Those blocks (called cobogós) have square orifices, the same depth and thickness, and only its dimensions varies, allowing the unchecked passage of wind.

https://image.ibb.co/d2xydH/Tipos_Cobogo.jpg
Types of cobogós used in this building.

https://image.ibb.co/cE7aQx/Panos_Cobogo.jpg
Assemblage of cobogós.

https://image.ibb.co/gGvekx/20170223_151915_800x600.jpg
Indoor photo. Cobogó type 1.

During my first test I’ve tried to model all blocks’ geometry, but as computational costs soared, I´ve switched to a model that uses porous medium to mimic the assembly’s behavior and effectively simulate a cross-ventilation effect inside the building.

At this points, I have ten straight segments each composed by a specific type of block. So in CFX I have modelled ten different solids to act as porous domains. The main questions are about permeability and resistance loss coefficient, further complicated by such curved wall.

Loss Model

The directional loss model was selected as these elements effectively narrows the fluid’s passage to only one direction. True Velocity type has been selected, although Superficial Velocity may yield the same result to me. All vectorial components from each face normal were correctly drawn from the original geometric model.

Streamwise Loss

Here some questions arise about Permeability and Resistance Loss Coefficient.

1 - In the simplest hypothesis, may I ask: Does the directional loss model allows the permeability value be the total free area available to the flow in this domain, as calculated through an frontal view of each face? Should this value be then the sum of all blocks’ void areas?

If that is the case, all ten porous domains will use just three different permeability values (as they are made of only three block types). As such, they would also use three different Resistance Loss coefficient.

However the wind will never have a perpendicular incidence to all faces at the same time because the wall is curved, so Permeability (and Resistance Loss coefficient) should vary as a function of this angle of incidence.

2 – Is this variation in Permeability covered up by the directional loss model or should I parameterize this field? In the latter case, is it even possible to calculate the angle of incidence between the face normal and the incoming air direction?

As far as i know the permeability is the ratio of free volume in your porous domain to the whole volume or in your case ratio of free surface to whole surface at a frontal view. That being said the permeability shouldn't change with angle of incidence.

The Problem in your case is probably, that your cavity-size is relatively big compared to the depth of the wall (for Type 3 at least), usually you would just set the loss coefficients in the transverse direction to a big number to prevent transverse flow. But i don't know if that is applicable in your case because slight transverse flow is actually possible.

Maybe you can simulate a basic validation-case with just a wall as a porosity model and one with the actual cobogós-geometry for various velocity-vectors and compare them.

Shouldn't this be Porosity? CFX asks for an adimensional value for it (it also doesn't give another option if not isotropic area porosity).

Although the third type is the largest of them, as an isolated object in a wall its small size only allow unidirectional flow, as pointed in Etheridge. I used 100 as Streamwise coefficient multiplier to prevent any bidirectional flow. However, if the wall is made entirely of them its performance may be different. I'll perform an experiment to verify it, but it isn't my main concern right now.

I've carried an CFD test to evalute the Discharge Coefficient from a single cobogó. In the next step I may try to model a wall as an actual porous domain and also as a geometric model to compare both cases. However, any advice to avoid unnecessary tests would greatly appreciated, as I would rather avoid making deductions about CFX's inner workings.

Thanks

As you already recognised, i confused permeability with porosity. Unfortunately i don't have much knowledge about CFXs inner working either, i solely rely on the Information given in the documentation.
In my case the streamwise permeability, assuming a laminar flow, can be approximated to be

hydraulicDiameter^2 * porosity / 32

which should be a general approximation, applicable to your case aswell. But in my case the porous domain is much longer which renders the inflow conditions less significant. Your flow is probably not laminar aswell making it far more complicated.

Thanks. You are right, the flow is fully turbulent and this complicates a bit. I'm still stuck at this permeability issue, though...