Wind Power Production in the Urban Environment

Abstract

The purpose of this study is to resolve accurate, local flow details around buildings in an urban environment using commercial computational fluid dynamic (CFD) software. At present, few recommendations have been published regarding the appropriate turbulence models to be used for modelling these flow conditions. Due to the uncertain reliability of the k-ε models ability to successfully simulate flow over buildings, the current objective is to assess how applicable the k-ε turbulence model is in resolving this type of flow. Flow around buildings in the atmospheric boundary layer are characterized as having points of separation, reattachment, stagnation and various types of vortices as well as being anisotropic and transient in nature. The complexity of this problem indicates that the turbulence model must be capable of handling many issues to correctly model this flow. In order to justify an applicable turbulence model, these models must be tested under relatively simple conditions and compared with well-documented, large-scale tests to ensure accuracy. The standard k-ε model was investigated in these conditions because of its relative robustness and past ability to capture the major flow details in this type of flow. Increasing the number of cells in the domain had various effects on the solution. An accurate solution was obtained for the initial mesh and then subsequently the solution diverged and then converged when refining the mesh. Very fine grids were required for a two-dimensional building to achieve accurate results, but the solution was not verified as being grid independent. Even if the solution is grid independent, implementation of the k-ε model in three-dimensional complex flows would not be practical due to the substantial increase in computational power required. Therefore alternative turbulence models are now being investigated for modelling flow over buildings in the atmospheric boundary layer.

Full text

Wind Power Production in the Urban Environment
S.J. Kooiman, S.W. Tullis
*
Department of Mechanical Engineering, McMaster University
Hamilton, ON, L8S 4L7, Canada
Email: kooimasj@mcmaster.ca
*
Tel.: +1-905-525-9140 ext. 27692; Fax: +1-905-525-7944; E-mail: stullis@mcmaster.ca
A
BSTRACT
The purpose of this study is to resolve accurate, local
flow details around buildings in an urban
environment using commercial computational fluid
dynamic (CFD) software. At present, few
recommendations have been published regarding the
appropriate turbulence models to be used for
modelling these flow conditions. Due to the
uncertain reliability of the k-
ε
models ability to
successfully simulate flow over buildings, the current
objective is to assess how applicable the k-
ε
turbulence model is in resolving this type of flow.
Flow around buildings in the atmospheric boundary
layer are characterized as having points of separation,
reattachment, stagnation and various types of vortices
as well as being anisotropic and transient in nature.
The complexity of this problem indicates that the
turbulence model must be capable of handling many
issues to correctly model this flow. In order to justify
an applicable turbulence model, these models must
be tested under relatively simple conditions and
compared with well-documented, large-scale tests to
ensure accuracy. The standard k-
ε
model was
investigated in these conditions because of its relative
robustness and past ability to capture the major flow
details in this type of flow. Increasing the number of
cells in the domain had various effects on the
solution. An accurate solution was obtained for the
initial mesh and then subsequently the solution
diverged and then converged when refining the mesh.
Very fine grids were required for a two-dimensional
building to achieve accurate results, but the solution
was not verified as being grid independent. Even if
the solution is grid independent, implementation of
the k-
ε
model in three-dimensional complex flows
would not be practical due to the substantial increase
in computational power required. Therefore
alternative turbulence models are now being
investigated for modelling flow over buildings in the
atmospheric boundary layer.
1. I
NTRODUCTION
With the growing demand for renewable clean power
production, implementing Vertical Axis Wind
Turbines (VAWTs) in urban settings is currently
being assessed. Initially, the placement of a wind
turbine on top of buildings may seem less than ideal
considering the complex flow structure, high
directional variability, large skew angles and
increased turbulence intensity, all of which are
typical deterrents to operating wind turbines.
However, with the aerodynamic performance
advantages of omni-directionality characteristics,
increased performance in the VAWT in skewed flows
and the heightened wind speeds around buildings, the
application for these turbines may be more
advantageous than originally considered. In addition,
there are practical benefits of power generation and
consumption in the same location. In order to
optimize the placement of the wind turbines on top of
buildings and minimize negative effects, details of
the flow around buildings must be resolved. CFD
offers a method of obtaining estimations of the flow
fields around various shaped buildings with various
fetch characteristics (i.e. the area in front of the
building), which are currently not available.
2. F
LOW
S
TRUCTURE
Flow over a building is multifaceted even in the most
simplest of cases when steady state flow is
perpendicular to the building’s face and no other
interferences are present. As the flow approaches the
building, a high pressure region is formed on the
front face of the structure. This high pressure region
directs the incoming air around and above the
building. This creates a standing vortex in front of
the building as well as a stagnation location

approximately three quarters up the face of the
building. Separation of the flow occurs around the
sides and top of the building’s edges creating low
pressure recirculation zones that are referred to as the
separation bubbles. The size of the separation bubble
is dependent on the surface roughness, wind velocity
and turbulence intensities. The flow over and beside
the building will reattach, provided the building is
long enough, and will separate off of the back edges
of the structure. The normal flow characteristics are
schematically shown below in figure 1.
Figure 1: General flow visualization with flow
normal to building face. [1]
When the flow is not parallel to the face of the
building, cornering vortices form along the edges.
The size and angle of the vortex core is dependent on
the angle that the flow makes with the building.
These are considered delta-wing vortices which
develop due to the pressure difference between the
high pressure sides and the low pressure top of the
building.
The implications of mounting small-scale wind
turbines on building rooftops in the urban
environment have only briefly been studied. Mertens
[2] investigated the wind potential over one specific
building configuration and considered two fetch
roughness lengths. However, the results of this study
were not validated with measured data.
There have been few full-scale tests measuring wind
velocities over buildings. Detailed full-scale tests
have been performed on the Wind Engineering
Research Field Laboratory (WERFL) complex at
Texas Technology University. The building is a low-
rise rotatable building with a height of 4 m, a width
of 9.1 m and a length of 13.7 m. The fetch is
considered long grass with a roughness height of
0.024 m [3]. Visualization measurements of the
separation bubble and corner vortices and pressure on
the roof were performed [4, 5, 6]. This yielded
quantitative flow structure observations such as
height and location of the reattaching separation
bubble on the roof of the building.
From the smoke injection investigation, carried out
by Sarkar et al. [5], it was observed that the
separation bubble grew before collapsing and then
reforming and this continued in a cyclical pattern.
Observations from tuft visualization carried out by
Wagaman et al. [6] indicated that there was little
correlation of the size of the separation bubble to the
wind speed or turbulence intensity. The separation
bubble with the wind perpendicular to the long side
of the building was 1.04 m [ranging from 0.73 - 1.22
m] high and 4.42 m [ranging from 3.20 - 5.06 m]
long.
The separation bubble height H
c
, and length X
c
are defined as shown below in figure 2. Both Sarkar
et al. and Wagaman et al. saw similar results for the
flow perpendicular to the shorter side of the building,
indicating that the flow can be considered two-
dimensional when the flow is perpendicular to the
face of the building.
Figure 2: Building configuration with separation
bubble defined.
Efforts have been made to model the WERFL
building and reasonable results have been obtained
with moderate grid sizes using k-
ε
turbulence
models [3, 7, 8, 9]. In these studies, pressure profiles
over the length of the building were used as an
indicator of the accuracy of the numerical model.
Reasonable pressure profiles around the building
were obtained from these studies when compared to
the measured data.
Cowan et al. [10] examined the numerical accuracy
of the k-
ε
model with flow around buildings. In
their assessment, independent groups modelled flow
over buildings and dispersion models using
commercial code and standard numerical modelling
practices. It was determined that the numerical
results from independent developers varied
dramatically between one another and were highly
dependent on mesh design and the advection scheme

used. Coincidently, the results for a course mesh
were sometimes more accurate than using a refined
grid.
The poor performance of the k-
ε
model is perhaps
unsurprising given the high streamwise strain rates
and highly anisotropic conditions [11]. Reynolds
Stress Models (RSM) have shown better performance
for free shear flows with strong anisotropy and flows
with a sudden change in the mean shear rate making
the model a good candidate for this flow
configuration. RSM models have difficulty
converging and are more computationally expensive
[12].
3. N
UMERICAL
S
IMULATION
Due to the uncertain reliability of the k-
ε
models
ability to successfully simulate flow over buildings,
the current objective is to assess how applicable the
k-
ε
turbulence model is in resolving the flow over a
building. Due to the availability of a relatively large
amount of experimental data obtained at the WERFL
building, it will be used as a base case to verify the
results.
As previously mentioned, the flow around the
WERFL building, with the wind normal to the long
face, can be approximated as two-dimensional. In
order to simplify the simulation, a two-dimensional
model of the WERFL building is used as a base case
to verify the numerical results. An unstructured grid
is used with refined elements around the roof of the
building and the ground. These elements expand
away from the specified nodal lengths at a rate of
1.05. Recommendations specified by Hargreaves and
Wright [13] concerning boundary conditions were
applied. Inlet boundary conditions for an
atmospheric boundary layer were given by [13] as:
( )
0*
0
2
*
3
*
0
ln
z z
u
u
z
u
k
C
u
z z
µ
κ
ε
κ
+
=
=
=
+
 
 
 
Where u
*
is the friction velocity,
κ
is the von Karman
constant (0.41), z is the height above the surface and
z
0
is the aerodynamic surface roughness, in this case
0.02 m. Symmetry conditions were imposed at the
top of the domain. A first order upwind differencing
scheme was used. The commercial code
ANSYS/CFX 11.0 was used for this study.
In order to accurately model the ground roughness a
relationship between roughness specified in
commercial software, based on sand grain particle
roughness, and aerodynamic surface roughness is
required. This has often been neglected in many
previous investigations but is necessary to properly
model the surface roughness. This relationship has
been investigated by Hargreaves and Wright [13] and
they concluded that the relationship k
s
=29.6z
0
is valid
for the commercial software used in this study, where
k
s
is the roughness height based on sand particles and
z
0
is the aerodynamic roughness.
From supportive literature, Cowan et. al. [10]
recommends that the upwind and downwind
dimensions should be 5H and 15H +-4H respectively,
where H is the building height. In this analysis, the
height H was defined as a characteristic height
H
c
=B
s
0.66
B
L
0.33
where B
s
and B
L
are the respective
smaller and larger dimensions of the building
windward face. In the subsequent simulations a
domain sized with a fetch of 7H, a height of 8H and a
downwind dimension of 20H was applied. The
domain dimensions are shown below in figure 3.
Figure 3: Domain used in the subsequent analysis.
To simplify the atmospheric conditions, it is assumed
that the atmosphere is stable, i.e. the buoyancy
turbulence generation is negligible compared to the
mechanical turbulence production. Also, it is
assumed that the buildings are smooth and the flow is
fully turbulent.
4. R
ESULTS
To justify the applicability of the k-
ε
, the results
must be physically realistic and thus must agree with
full scale experimental results. To obtain accurate
results the numerical solution must be independent of
the choice of domain and grid size given that these
constraints are satisfactory prescribed. Typical grid
sizes for the building configuration were initially
chosen from previous studies. Subsequent grid
refinement was done to determine grid independence.
Each consecutive grid refinement was produced by
halving the number of specified cells over the

building and ground while retaining the specified
expansion ratio in the domain.
An initial grid was generated with the cell length of
0.01H
c
along the top of the building and 0.1H
c
along
the ground. These successive grid refinements led to
significant changes in the flow structure around the
building. A summary of the results is shown in
figure 4, indicating the reattachment location on the
roof of the building for the k-
ε
model. With the
initial coarse grid, the separation bubble formed and
was quite accurate in size and shape for the upwind
scheme. A further refinement of the mesh led to a
complete change in the flow structure with no
reattachment zone on the roof of the building.
Subsequent grid refinement led to a reattachment on
the roof but over predicted the roof separation bubble
reattachment location. Further grid refinement leads
to quite accurate results with the solution attaining a
reattachment location within the experimental
variation. The resulting velocity field around the
building for the final grid refinement is presented in
figure 5.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
40000 100000 150000 250000
Grid Size [Number of Nodes]
Reattachment Location [Xc/Xb]
Numerical Experimental
Figure 4: Non-dimensional reattachment locations on
the roof of the building where Xc is the reattachment
location and Xb is the building depth. Error bars
indicate the experimental variation.
The pressure profiles obtained for the final grid
refinement were quite similar to the experimental
measurements and numerical results obtained in other
investigations. The pressure distribution is plotted
down the centre of the building and is displayed in
figure 6. The non-dimensionalized pressure
coefficient is the pressure nominal to the building
divided by the dynamic pressure equivalent to,
½ρV
H
2
where ρ is the density of air and V
H
is the free
stream velocity at the height of the building. The
distance along the x-axis begins at the bottom centre
of the windward wall and progresses over the
building to the bottom centre of the leeward side.
Experimental results were obtained from Paterson
and Holms [8]
-2
-1.5
-1
-0.5
0
0.5
1
0 2 4 6 8 10 12 14
Distance Along the Building [m]
Nondimensional Pressure Coefficient Cp
Minimum
Experimental Pressure
Maximum
Experimental Pressure
Grid 250000 Elements
Figure 6: Pressure distribution over the building for
the finest grid compared to experimental data.
Transient solutions were run on the highest refined
grid and reattachment settled to steady oscillations
after 10 seconds. Oscillations were small with a
peak-to-peak range of 0.32 m and a period of two
seconds with a mean value equivalent to the steady
state solution. The transient response is expected as
the flow is unsteady indicated by the range of values
for reattachment locations and pressure distribution
The domain size was doubled in height and doubled
in downstream length to test for domain dependence.
It was seen that the size of the domain had little effect
on the results over the building and thus can be
regarded as independent of the solution.
5. C
ONCLUSIONS
From the results presented above, it is seen that the
numerical solution obtained from the k-
ε
turbulence
model can be misleading. As the grid is refined, the
solution diverges from the experimental results and
then converges on the correct result. The solution is
grid dependent since the solution does not converge
on a solution as the grid is refined. Any subsequent
refinement may lead to a converging solution but any
application of the grid independent solution would be
too numerically expensive in even the simplest two-

dimensional cases. At present, applying the k-
ε
model to any complicated geometry such as three-
dimensional flow through the urban environment
would be far too computationally expensive and thus
impractical.
The presented work emphasises the strong
dependence of the numerical solution on grid size. If
the grid is not verified over a large range of nodal
refinements, conclusions may be drawn for grid
dependent solutions. This is difficult to verify
especially for three-dimensional problems since the
studied range of grid refinements would be very
computationally expensive. It is seen that convincing
results can be obtained even with a quite coarse mesh
as in the first grid studied. These results suggest that
proposed converged solutions from previous
investigations may be grid dependent.
Recent investigations carried out by Hargreaves and
Wright [13] as well as Blocken et al. [14] have
indicated many of the difficulties with sustaining a
atmospheric boundary layer profile over a uniform
terrain in commercial software. Attempts were made
to minimize these effects in this study by making the
fetch as short as possible in front of the building in
the domain. These effects of the sustainable
boundary layer are currently being investigated on
the previously investigated building configurations.
6. R
ECOMMENDATIONS AND
O
UTLINE FOR
F
UTURE
W
ORK
Two-equation models are an attractive turbulence
model due to their simplicity and relative robustness.
Inconsistent results are obtained when the k-
ε
turbulence model was applied to this simplified case
of flow over a two-dimensional building. The
upwind advection scheme produced an accurate
result but was misleading in the fact that the results
were not verified to be grid independent. Even
though the k-
ε
model is capable of solving the flow
accurately for grid dependent solutions, any
implementation in complex geometries in three-
dimensions would be impractical due the increase in
computational expense when implanted in three
dimensions.
Aside from the k-
ε
turbulence model, alternative
turbulence models should be considered for their
usefulness in this problem. It is suggested that
models that perform more favourably with high
stream-wise strain rates and in anisotropic flow be
investigated such as the Reynolds shear stress
models. Currently, the k-
ω
and the blended k-
ε
and k-
ω
models are being studied with the Reynolds
shear stress model.
Figure 5: Velocity profile around the building for the finest grid with the numerical prediction
of the stagnation point and reattachment location identified.

A
CKNOWLEDGEMENTS
The authors would like to recognize the funding from
the Ontario Centre of Excellence (OCE).
R
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