Computational study of the effect of trees on wind flow over a building
- Mohamed Arif Mohamed^{1} and
- David H Wood^{1}Email author
https://doi.org/10.1186/s40807-014-0002-9
© Mohamed and Wood; licensee Springer. 2015
Received: 18 June 2014
Accepted: 30 September 2014
Published: 20 January 2015
Abstract
A computational study was performed to investigate the effect of varying upwind tree heights on the wind flow over a 15-m high, flat-roof building. It is shown that trees can have a significant effect on the mean wind speed and turbulence over the roof and should be included when performing a computational fluid dynamics simulation. The calculations also provide guidance for undertaking wind tunnel experiments on simulated trees and buildings to investigate their interaction. The effect of the trees on the mean wind speed above the roof was not a monotonic function of ratio of tree-to-building height. Further, the trees reduced the level of turbulence over the roof. The study also confirmed that the production of turbulent kinetic energy by the trees and its subsequent advection over the building are the main causes of the modified flow.
Keywords
Background
The roofs of buildings provide many opportunities for renewable energy generation, all of which require knowledge of the wind flow and turbulence. This is obvious for building-mounted wind turbines, but photovoltaic and solar thermal installations can often experience high wind loads and may incur significant structural costs to withstand them. In many cases, buildings are close to trees which, if upwind of the building, can significantly alter the wind flow.
Wind flows around trees are characterized by vortex shedding, high drag, and complex wake turbulence. Surprisingly, many computational fluid dynamics (CFD) simulations involving the urban landscape do not model trees viz Blocken et al. (2012) and Tabrizi et al. (2014). In some cases, it is possible to treat trees as a porous surface (Hakimi and Lubitz 2014). Excluding trees will lead to errors because their wakes persist a long downstream distance in terms of velocity deficit and increased turbulence, (Ishikawa et al. 2006). Knowledge of the wake is likely to be important in deciding where to erect a small wind turbine whose hub height is comparable to that of surrounding trees. Kalmikov et al. (2010) modeled trees in a simulation over the Massachusetts Institute of Technology campus by introducing a sink term in the momentum equation but did not account for the effect on the turbulent kinetic energy, k.
Much work has been done on the effects of vegetative canopies on the atmospheric boundary layer, e.g., Raupach and Shaw (1982), Finnigan and Shaw (2008), etc. The introduction of form drag within a canopy is purported to convert the mean kinetic energy and large scale k to its form at smaller scales (Wilson and Shaw 1977). However, this paper will consider only individual trees and their effects on the wind flow over a single generic building. The study is entirely computational, using the well-known k−ε turbulence model, where ε is the dissipation. It has two major aims, first to demonstrate the importance of trees for the roof flow, and, second, to give guidance for further investigation by wind tunnel experiments.
The computational modeling of trees is described in the next section. ‘The modeled building and computational domain’ subsection outlines the generic building and the upwind trees of varying height. The results and discussion are contained in the ‘Results and discussion’ section which is followed by the conclusions.
Methods
Modeling of trees
Amorim et al. (2013) gave β _{ p }, β _{ d }, and the constant E _{1} in Equation (3) as 1, 4, and 1.5 respectively. These values were used in the present calculations.
Leaf area density
Characterization of z _{ m } for different trees
Type of trees | z _{ m } |
---|---|
Oak and silver birch | 0.2h |
Common maple | 0.2 h<z _{ m }<0.4h _{ t } |
Pine | 0.4 h _{ t } |
The leaf area index, which is an input to calculate the leave area density in Equation (4), was taken from the website (http:na.fs.fed.us/fhp/eab/pubs/chicago_ash/chic_ash.shtm).
The flow downstream of a single tree
The modeled building and computational domain
The maximum y ^{+}x on the roof of the building was 11.067 based on the k−ε turbulence model. The advection scheme and turbulence numerics were based on the high resolution scheme in ANSYS CFX 15. The convergence criterion was set to 1e−6.
The simulations with varying h _{ t }/h _{ b } ratio used the same mesh. The height of the tree, h _{ t }, was varied based on the formulation of Equation (4).
Results and discussion
Figure 12 shows that below z/h _{ b }∼1.5 the largest velocity reduction occurs for h _{ t }/h _{ b }=1 when compared to flow without trees. This was expected as was the largely monotonic increase in U as h _{ t } decreased. Although the profiles do not exhibit a negative ∂ U/∂ z, which is typical of mean flow over hills and buildings, e.g., Mohamed and Wood (2013), they do show that trees placed 40 m away from a 15-m building play an important part in determining the flow field over the front of the roof. The inset to Figure 12 shows that for z/h _{ b }<0.67, there is a small recirculation region immediately above the roof.
The vertical distribution of k in Figure 13 follows the reverse trend as in k reduces with increasing h _{ t }/h _{ b }. The mechanism for this loss of k when the trees increase the turbulence will be discussed below.
Figures 14 and 15 show the wind speed and turbulence at the midpoint of the roof. The interesting result here is that the velocity profile appears to be same for h _{ t }/h _{ b } less than 0.67 and then similar for h _{ t }/h _{ b }=1.0 with a significant increase for h _{ t }/h _{ b }=0.67.
The k profiles at x/d=0.5 show that h _{ t }/h _{ b }=0.67 has smaller turbulence near the roof compared to all other h _{ t }/h _{ b }. Despite the treeless flow again having the maximum k, the trend in k vs h _{ t }/h _{ b } is not monotonic as it was near the front of the building. The plots for x/d=0.75 are shown in Figures 16 and 17. Barring a slight discrepancy for h _{ t }/h _{ b }=1, all the wind speed profiles appear to collapse. The k profiles show the same trend as Figure 15 albeit with a positive sharp gradient in the region 0.4≤ z/h _{ b } ≥ 0.6.
The general, and somewhat surprising, result that trees reduce k can be analyzed further through the energy budget which we now compare for the treeless flow and h _{ t }/h _{ b }=1.
with the eddy viscosity ν _{ T }=C _{ μ } k ^{2}/ε.
Without trees, there is increased advection and larger production of k compared to the case with trees. Both results reflect the reduction in wind speed and its vertical gradient around z/h _{ b }=0.1 that is shown in Figure 12. The dissipation rate and diffusion of k do not deviate as much between the two cases.
Conclusions
This study analyzed the effect on the wind field above the roof of a 15-m high building 40×50 m in plan of trees of varying height placed 40 m upwind of the building. The trees were varied in height from up to 15 m. For comparison, the flow without trees was also calculated. Although the wind speed with trees does not exhibit a negative ∂ U/∂ z, it does show a considerable difference when compared to the case without trees. The fact that even trees of height 2 m placed 40 m upwind of a 15-m building can affect the flow above the roof suggests that they should be included when performing CFD simulations for buildings. The effect on wind speed was not monotonic with tree height as the greatest increase occurred for 12-m trees. The differences in wind speed, especially in Figure 12, and in the turbulent kinetic energy suggest that this generic geometry should be tested in a wind tunnel.
Generally, the trees decreased the turbulence over the roof which appears to be due to the reduction in production of turbulent energy as demonstrated by the energy balances in Figures 18, 19, 20 and 21.
Declarations
Acknowledgments
This paper reports on work sponsored by the Natural Science and Engineering Research Council and the ENMAX Corporation under the NSERC Industrial Research Chairs scheme.
Authors’ Affiliations
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Copyright
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