Computational Simulation of Wind Loads on Three Curved Eave Models
with Different Height-Width Relationships
GUILHERME S. TEIXEIRA, LEONARDO G. TEODORO JÚNIOR, MARCO D. CAMPOS
Institute of Exact and Earth Sciences,
Federal University of Mato Grosso,
Av. Valdon Varjão, 6390, Barra do Garças, 78605-091, Mato Grosso,
BRAZIL
Abstract: - This work deals with the effects of wind loads on two industrial shed models with curved eaves
aspect of different height-to-width ratios. Using Ansys Workbench software, the external pressure coefficients
for the entire roof by applying refinement levels were determined. Also were studied the quality of the
unstructured and tetrahedral grid according to recommendations to ensure greater efficiency in the simulation
results. The results generated provided evidence that the wind in the transverse direction is more damaging in
the windward region: for a wind at 45º the most critical region appeared both windward and leeward in the
model with a ratio of h/b=0.5 (Model 1) and to windward in the models with a ratio of h/b=1 (Model 2) and
h/b=1.5 (Model 3). The leeward suctions increased due to the reduction in the height-width ratio considering a
wind direction of 45º. The increase in this ratio intensified the values of the external pressure coefficients in the
windward region for the 90º wind direction.
Key-Words: - Wind action, industrial shed, eaves, Ansys, pressure coefficient, height-width ratios, wind
directions.
1 Introduction
The use of CFD tools in the study of wind effects
has proven to be a viable alternative in recent
decades for obtaining data regarding the pressure
distribution on the roof in low-rise buildings,
allowing the analysis of the various geometric
parameters that influence wind loads in this type of
building. Some aspects, for instance, height, width,
and wind direction, can significantly alter the
magnitude of pressure on the roof of a low-rise
building, [1]. However, the number of studies of
wind loads on curved free roofs is relatively limited,
[2], [3].
Recently, some studies have explored the effects
generated using the curved eave aspect and, despite
the difficulties in making these models, measured
wind pressure in wind tunnel experiments, [3], [4].
In this way, [5], reviewed the information
available in the open literature about the wind loads
on cladded buildings with vaulted roofs, including
some significant studies written in Portuguese that
are not readily accessible, with the CIRSOC 102
treatment then compared with state-of-the-art
results. The authors listed the need to update the
code and suggested possible criteria and values for
future research.
Using wind tunnel experiments, [6], examined
wind pressure characteristics at the rounded edges
and, for flat roofs with rounded leading edges,
suctions induced by separation bubble and conical
vortices increased near the chamfer, decreased
beneath the vortices, and invariant far from the
principal edge.
Using a wind tunnel experiment and a
computational fluid dynamics (CFD) analysis, [7],
investigated the fundamental characteristics of wind
loading on curved roofs and discussed the effects of
rise-to-span ratio, length-to-span ratio, and wind
direction on the wind pressure and force coefficients
on the roof. The results indicated that the rise-to-
span ratio affects the flow and the resulting wind
pressures on the roof, and the effect of the length-to-
span ratio is relatively small.
Therefore, this work aims to produce data
regarding the behavior of pressure coefficients for
wind incidents at 45° and 90° in three curved eave
models with different height-width relationships.
2 Methodology
In this work, for geometries and simulations, the
Autodesk AutoCAD and Ansys Workbench 2023 R2
Received: February 24, 2023. Revised: December 13, 2023. Accepted: February 16, 2024. Published: March 12, 2024.
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DOI: 10.37394/232013.2024.19.12
Guilherme S. Teixeira,
Leonardo G. Teodoro Júnior, Marco D. Campos
E-ISSN: 2224-347X
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software were used, respectively. The solver used to
solve the equations was the CFX code.
Fig. 1: Geometric configuration
Table 1. Geometric parameters of the models.
Model
Dimensions
Ratios
Width (B) [m]
Length (L)
[m]
Hight (H)
[m]
Eave radius (R)
[mm]
Roof Slope (Degree)
H/B
L/B
1
15.00
30.00
7.50
635
5
0.5
2
2
12.50
30.00
12.50
635
5
1.0
2.4
3
10.00
30.00
15.00
635
5
1.5
3
The geometric model chosen was a rectangular
shed whose dimensions, including height, were
varied (Figure 1). The building also had curved
eaves, with a fixed radius of curvature of 635 mm
(like those evaluated in [2] and [8]). Furthermore,
the building's roof had a fixed slope of 5º in both
models (Table 1). The control volume adopted had
boundaries 5H away from the front and side
facades, the maximum height of the area of interest,
and 15H from the rear facade, [9]. In all directions,
a sub-domain spaced H/2 for local refinement was
adopted.
The unstructured mesh was composed of
tetrahedra and has four refinement levels. The first
was controlling the size of elements in the fluid
domain. The second is control of the sub-domain.
The third refers to the facade elements, and finally,
the fourth level is the refinement of the eaves and
roof elements. The element size adopted was half of
the previous level.
The quality of the meshes was analyzed using
three parameters: the aspect ratio, the skewness, and
the orthogonal quality. For three-dimensional
elements, the aspect ratio is the relationship between
the radius of the circles circumscribed and inscribed
in the base geometry, which, in our specific case,
refers to triangles. The skewness indicates the
proximity of the cells or faces of the mesh to the
ideal geometry, such as a tetrahedron, with
recommended values between 0 and 0.5.
Additionally, the orthogonal quality metric
evaluates the orthogonality of the element, with
recommended values approaching 1.0, [10].
The Power Law approximation was used to
incident wind profile, given by:
where is the wind speed (in meters per second) at
height Z (in meters), and is the pre-established
wind speed at a reference height . The exponent
α is an empirically derived coefficient that varies
depending on the terrain roughness and the time
interval. Also, α=0.16 representing open terrain with
high grass was adopted.
Considering the recommendations of [11]
defined the High-Resolution schemes (including
additional turbulence equations) since high orders of
discretization of the advective terms of the
equations solved in the model can improve the
accuracy of the results.
The RNG K-EPSILON model - widely used in
applications such as those analyzed here - was
employed to simulate the turbulent effects of the
flow. The simulation stopping criterion was the
RMS Residual equal to 10E-4, sufficient for many
engineering cases, [12].
The results were analyzed using external
pressure coefficients (Cpe), a dimensionless
parameter dependent on the difference in external
pressure coefficient (Δp), and dynamic pressure (q)
using the expression Cpe=Δp/q.
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In the Cpe contour maps, the hot colors
represent overpressures (Cpe>0), and cold colors
represent suctions (Cpe<0).
Finally, Table 2 shows the rest of the boundary
conditions adopted.
Table 2. Boundary conditions and non-dimensional
parameters
Condition
Parameters
Method of mesh
Tetrahedron
Capture curvature and
proximity
On
Reference pressure
101325 [Pa]
Air temperature
25º [C]
Turbulence intensity
Medium (5%)
Flow regime
Subsonic
Inlet
U/Uref = (Z/Zref)^α
α
0.16
Zref
40 [m]
(Application 1)
10 [m]
(Application 2)
Uref
33 [m/s]
(Application 1)
30 [m/s]
(Application 2)
Relative pressure of outlet
0 [Pa]
Wall - Ground
Rough wall
Model wall roughness
Smooth wall
Roughness
0.01 [m]
Advection scheme
High resolution
Turbulence numeric
High resolution
Minimum number of iterations
100
Maximum number of
iterations
300
3 Numerical Results
Application 1 (validation): To validate the
methodology, two low-rise building models with a
flat roof and rounded leading edge were evaluated,
[6]. The buildings had dimensions of 120x120x40 m
(BxWxH) and edge rounding radii of 5.00 m and
7.00 m.
Figure 2 shows the representation of the model,
and Table 3 brings together the details of each work.
Here, the naming of the models is the same as in
the original work, FM2 and FM3 models.
Qualitatively, based on the Cpe contours, it was
possible to note, in both cases, the similarity of the
models with the original work (Figure 3).
Due to the detachment of the flow, the most
intense zones appeared on the windward edges,
although, in the present work, they occupy a larger
region of the coverage. One can also notice a large
central area with uniformly distributed Cpe values.
Quantitatively, the T-test was used to evaluate a
statistically significant difference between the
means of two Cpe samples.
Fig. 2: Representation of the models analyzed in
validation
Thus, were extracted data from 10 points (Table
4) along the line "X" illustrated in Figure 4.
Furthermore, an F-test was applied to define
whether the data variances were supposedly
equivalent or different. For the FM2 model,
considering the null hypothesis (H0) that the means
are not statistically significant, assuming two
samples with equal variances, two-tailed
distribution, and significance α' = 0.05, and using
Microsoft Excel software obtained a p-value =
0.2670.
As p-value > α', we do not reject the null
hypothesis (H0) and consider the difference between
the means in the Cpe values insignificant. Similarly,
for the FM3 model, however, assuming different
variances, we obtain a p-value = 0.0930. Also, as p-
value > α', we do not reject the null hypothesis (H0),
considering insignificant differences between the
means. Therefore, the methodology is appropriate to
produce results accurate to reality.
Application 2 (variation in width, length, and
height of buildings with curved eaves): Table 5
shows the results of the simulations referring to
Models 1, 2, and 3 regarding the variation in width,
length, and height of the buildings. For the three
models, the high suction was more pronounced in
the 90º wind in the region of approximately 0.00%
of the span, as shown in Figure 5(a), Figure 6,
Figure 7 and Figure 8. In addition, there was an
inversion in the pressure distribution from ~60.00%
of the span, in which the magnitude of the pressures
became maximum in the 45º wind configuration. In
Figure 5(d), the velocity contour showed that the
wind accelerated in the leeward region, causing a
higher velocity. This unexpected behavior is
responsible for the higher magnitude of the suctions
in the 45º configuration.
In Models 2 and 3 with the wind at 45º, the
external pressure coefficient values are close,
especially at ~0.00% of the span (Figure 8 (b) and
Figure 8(c)). This behavior was similar for the 90º
wind, nonetheless, only from ~50.00% of the span.
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However, the results showed that the values of the
pressure coefficients in both wind directions were
closer in this model than in model 1.
In all Models with the wind at 45º, it was noted in
the vicinity of the leeward an increase in suction,
intensified with the h/b ratio reduction. Also, with
the increase in the height-to-width ratio, a
considerable growth in suctions at ~0.00% of the
span was noted.
Table 3. Model information summary
Model
Dimensions
Angle of attack
(degree)
Width (B)
[m]
Length
(L)
[m]
Hight (H)
[m]
Edge diameter
(D)
[m]
FM2
(present work)
120.00
120.00
40.00
5.00
45
FM3
(present work)
120.00
120.00
40.00
7.00
45
Mesh data
Model
Nodes
Elements
Aspect ratio
(average)
Skewness
(average)
Orthogonal
quality
(average)
FM2
(present work)
218393
1205800
1.9687
0.27433
0.72459
FM3
(present work)
186367
1020871
1.9575
0.27041
0.72853
(a) (b)
(c) (d)
Fig. 3: Top view of the Cpe contour map on the roofs of models (a) FM2 [4], (b) FM2 (present work),
(c) FM3 [4] and (d) FM3 (present work) (the map does not include the results of the leading edges)
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Table 4. Data for T-test and F-test of FM2 and FM3 models.
Model
Points
1
2
3
4
5
6
7
8
9
10
FM2 [6]
Cpe
0.729
0.519
0.411
0.378
0.360
0.348
0.338
0.341
0.347
0.345
FM2
(present work)
0.790
0.565
0.410
0.300
0.260
0.200
0.190
0.180
0.175
0.170
FM3 [6]
0.614
0.484
0.419
0.405
0.403
0.395
0.394
0.396
0.379
0.350
FM3
(present work)
0.710
0.560
0.400
0.280
0.225
0.185
0.180
0.175
0.170
0.165
Fig. 4: Data extraction region for T-test and F-test, according to the format originally
proposed and evaluated in [4]
Table 5. Mesh results for models 1, 2, and 3
Mesh data
Model
Wind
direction
(degree)
Nodes
Elements
Aspect ratio
(average)
Skewness
(average)
Orthogonal
quality
(average)
1
45
425854
2334618
1.8950
0.24821
0.75067
90
416230
2287943
1.8917
0.24696
0.75192
2
45
411527
2258825
1.9128
0.25534
0.74348
90
400045
2195354
1.9153
0.25614
0.74267
3
45
401910
2213536
1.9220
0.25780
0.74115
90
388571
2139797
1.9223
0.25798
0.74098
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(a)
(b)
(c)
(d)
Fig. 5: Wind pressure coefficients across the roof at (a) 90º and (b) 45º respectively and the velocity contour
with the wind at (c) 90º and (d) 45º for model 1
(a)
(b)
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(c)
(d)
Fig. 6: Wind pressure coefficients across the roof at (a) 90º and (b) 45º respectively and the velocity contour
with the wind at (c) 90º and (d) 45º for model 2
(a)
(b)
(c)
(d)
Fig. 7: Wind pressure coefficients across the roof at (a) 90º and (b) 45º respectively and the velocity contour
with the wind at (c) 90º and (d) 45º for model 3
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(a)
(b)
(c)
Fig. 8: Pressure coefficients plotted normal to the ridge for (a) Model 1, (b) Model 2, and (b) Model 3,
respectively
4 Conclusions
In this work, the pressure coefficients on the roof of
three models with curved eaves and different height-
to-width ratios were generated for two wind
directions (90º and 45º) using Ansys Workbench
software.
The results showed similar behavior for the
pressure distribution in models when analyzing both
wind directions: the magnitude of the pressures
increased with the wind at 90º up to approximately
60.00% of the span; for the wind at 45º, the
pressures were higher in the remaining region. In
this way, the leeward region with the wind at 90º
configuration can be neglected. For wind at 45º,
attention should be paid to the windward and
leeward regions, since for height-width relations
less than 1.5, the pressures intensify in the leeward
direction for height-width relations less than 1.5.
Furthermore, the increase in the height-width
ratio was more harmful to regions close to the
windward eaves with a 90º wind configuration.
In the results obtained via CFD, the regions with
the most intense winds have the highest pressure
coefficient values, as discussed in Fluid Mechanics,
and the leeward region in 90º configurations is less
damaging than the windward region, according to
[3]. Given the above, the work carried out
contributes to the formation of data in the literature
regarding the analysis of the influence of curved
eaves on wind loads in low-rise buildings. In this
way, future studies will be able to analyze the
behaviour of external pressure coefficients for
different height-width relationships with changes in
the slope and radius of the eaves. In addition, other
types of relationships may be considered, such as
height-length and length-width.
References:
[1] R. P. Hoxey, A. P. Roberstson, B. Basara and
B. Younis, Geometric parameters that affect
wind loads on low-rise buildings: full-scale
and CFD experiments, Journal of Wind
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Vol. 50, 1993, pp. 243-252.
[2] A. P. Robertson, Effect of eaves detail on
wind pressures over an industrial building,
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Journal of Wind Engineering and Industrial
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[3] W. Ding and Y. Uematsu, Discussion of
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[9] J. Franke, A. Hellsten, H. Schlünzen and B.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
Guilherme Teixeira was responsible for the
methodology, carrying out the simulation, and
writing the validation. Leonardo Teodoro wrote the
results and conclusions. Marco Campos carried out
the conceptualization, review, and editing.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
The present work was partially supported by Federal
University of Mato Grosso.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2024.19.12
Guilherme S. Teixeira,
Leonardo G. Teodoro Júnior, Marco D. Campos
E-ISSN: 2224-347X
128
Volume 19, 2024
