My BTech thesis involved the modeling of air-flow in a passageway. One of its walls is covered with a dense tropical creeper. Since we planned to use a wall-function-invoked SST k-omega turbulence model, the boundary layer thickness needed to be calculated. This was done as follows:
The actual geometry did not explicitly model the foliage (i.e., the wall was a simple smooth wall). When wall-functions are being used, the first layer thickness of the mesh must be greater than the maximum boundary layer thickness. We chose a first layer thickness of 13 cm, which corresponded to a y-plus value of 15.This also ensured that the boundary layer was forced to stay under 13 cm even for the smooth wall in the numerical model. We understand that 15 is very close to the minimum allowed y-plus value of 11 for wall-function models.
My question is, is this the right approach to tackling this problem? Are there better ways of modeling this? Please find the paper attached for reference.
Thank you for your response.
Article On the Air Cleansing Efficiency of an Extended Green Wall: A...
I guess that the wall covered with vegetation could be treated as a rough wall rather than as a smooth wall with taking into account specific relationships for the roughness length and displacement height for the rough walls (i.e. see the reviews and book of Raupach, Finnigan and other experts in the field). However only with the help of measurements we can get answer of what approach is better
Thank you for your answer, Mr. Kovalets.
A rough wall would certainly take into account the irregularities of the vegetation surface. But wouldn't it fail to model the vegetation's porous nature? I mean, with roughness, the boundary layer thickness would be increased, instead of being reduced due to the porous nature of the foliage.
It's all about how deep the vegetation sticks into the boundaray layer - assuming there is a boundary layer at all. To me it seems that the specific situation is not modelled appropriately. This only would be the case when the vegetation always would be restricted in its extend to the inner part of the boundary layer. Then indeed it could be modelled as a wall roughness - but standard wall functions are not an option in this case.
May be an alternative approach would be to simply find out how a flow through a channel (as a model of the flow through the passageway) is affected by wall roughness. This would be something like an order of magnitute consideration - but more will not be available in this geometrically complicated situation.
At first I thought it was solid wall behind the vegetation layer. If this is not the case, i.e. if velocity doesn't goe to zero at some distance from the vegetation edge, it may be also appropriate to extend the computational domain to contain vegetation layer inside the domain and to model air flow within the vegetation using the area-averaged Navie-Stokes equations which effectively lead to drag force depending on vegetation density, etc (see the same books of Finnigan etc as mentioned above).
Thank you, Dr. Herwig and Dr. Kovalets. The vegetation is in the form of a 'sheet' of creepers that sticks to the wall (there is indeed a solid wall behind the vegetation) . So we can safely say that it lies in the inner part of the boundary layer. According to your and Dr. Kovalets' suggestion, I will try to find the effect of using wall roughness on the flow.
A possible approach to determine the appropriate modelling could be: Rather than making an educated guess, you solve a small representative section of the boundary layer with "resolved" vegetation. Once you have detailed results to tune the coarse model, i.e. adding appropriate surface roughness etc., to yield the same integral properties. This requirs some extra work, but you can much better justify your modelling later.
Following earlier suggestions, I agree that there are two ways of modelling: (i) represent the vegetated surface on the wall by a roughness length, and (ii) resolve the vegetation and represent the drag of the vegetation on the flow by drag coefficients.
In both case, there is a fundamental problem namely: how to find the roughness length or how to find the vegetation density combined with drag coefficients. It is virtually impossible to find such parameters without experimentation.
Regarding the roughness length, it is sufficient to measure the logarithmic profile which will exist at some distance from the vegetated surface. Extrapolation towards the surface will give an estimate of the roughness length. Atmospheric models have the same problem: estimates have to be made of the surface roughness in order to formulate the boundary condition in the form of a logarithmic profile (or relation between wind and stress) at some distance from the surface). Roughness length tables are used to relate roughness to vegetation type for atmospheric applications. I would expect a well maintained vegetation layer on a wall to give roughness lengths of the order of a few cm (say between 1 and 10 cm). A dense well trimmed surface will be more smooth and a open irregular surface will be more rough. The roughness length goes into the logarithmic profile, so an accuracy better than a factor 2 is often not achievable for practical applications.
Thank you everyone for your advice.
Following Dr. Class' recommendation, I am planning to set up a simple 2D test case to see how the flow happens. Please see the attached image for schematic.
For now, based on Dr. Beljaar's suggestion, I did the following calculation:
With the log-profile model, u(z) = (u*/k)ln(z/z0)
We need to find the distance zBL at which u(z) equals the free stream velocity of 1 m/s.
With k = 0.41, assuming z0 = 0.02 m and u* = 0.2 m/s (for freestream velocity of 1 m/s - please see attached graph), we get a value of zBL = 0.15 m. At least on paper it seems to (almost) fit the first layer thickness of 0.13 m.
I shall verify this value using the results of the simulation.
I would say 1. B.L. thickness, 2. the distance from the start of B.L., and 3. the thickness of
vegetation (normal to the wall) are all important characteristic lengths for this problem.
Of course, the first 2 depend on each other too.
I ran a simulation with a small 2D section of the vegetation. Details follow.
The domain of simulation is similar to the schematic in my previous post. I could only incorporate a 10 cm long vegetation section as I was unable to implement repeating boundaries in fluent. The wall region begins at the vegetation and extends beyond it. The y+ value is 0.9 (fully resolved boundary layer for SST k-omega turbulence with no wall functions).
The transition to turbulence is visible immediately after the vegetation layer (although according to flat-plate calculations, this must occur around 7 meters downstream). As shown, the boundary layer thickness (including the vegetated region is around 20 cm).
If some kind of Darcy's law is valid inside the vegetation region (at least for a range of velocities) I would suggest that a possible characteristic legth that can be used to calculate the Reynolds number is the square root of the permeability.
Please check in the relevant standard or code when modelling flow over vegetated region...I do not know about your part of the world but for Malaysia it is all specified in MS 15000. THe Australian have a good guide too. I am sure the DN ;EN have a good code too...
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