Numerical investigation of wind pressure coefficients on different
scallop dome configurations
CAMILA C. GUERRA, MARCO D. DE 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: The effects of the action of wind on scallop domes were numerically investigated using Ansys
software, as well as the interference of the neighborhood on the external pressure coefficient and the
streamlines between geometrically identical domes. The influence of the proportion on the neighborhood
interference in scallop domes and the variations in the dimensions of the structures on the pressure coefficients
and streamlines were also investigated. Five simulations were analysed involving six-grooved domes and
geometric height variations for validation. The numerically obtained coefficients were compared with values in
the literature. Other applications investigated the influence of grooves on the external pressure coefficient and
the effect of wind on the grooved domes. Another application analysed the interference of the neighborhood on
the external pressure coefficients and streamlines between three geometrically identical domes and, finally, the
influence of the proportion in the study of the interference of the neighborhood. Here, the variations in the
dimensions of the structure affected the pressure coefficients, and the streamlines were analysed. It was
possible to verify the versatility and efficiency of the computational method used in the analysis of the action of
wind.
Key-Words: Wind action, pressure coefficients, scallop domes, neighborhood effect, Ansys,
computational method.
Received: July 23, 2021. Revised: April 17, 2022. Accepted: May 13, 2022. Published: June 1, 2022.
1 Introduction
Domes are complex in structural design due to their
unique shape and efficiency in weakening elements
such as wind [1]. In general, a dome is a curved roof
structure that spans an area on a circular base,
producing an equal thrust in all directions. They
have a convex surface with double curvature,
making them suitable for roofing, and can be built
directly on the ground or on cylindrical walls. The
wind loads considerably influence lightweight
spatial structures with, for example, scallop domes
with their various configurations and forms. The
wind impact on a scallop dome is more complex due
to its additional curvature.
Few studies approach the numerical simulation
of wind in domes. Among the recent ones, Sadeghi,
Heristchian, Aziminejad, and Nooshin [2] studied
the effect of wind on grooved scallop domes and
initially investigated the effect of wind on scallop
domes to compare the consequence of grooves
against the similar spherical dome. They concluded
that the insertion of a slot into a spherical dome
caused an abrupt change in its wind pressure
coefficient in the vicinity of this slot. Sadeghi,
Heristchian, Aziminejad, and Nooshin [3] compared
the numerical results with those obtained from the
wind tunnel available in the literature. Then,
numerically, the effect of structural flexibility and
the neighborhood of the objects on the wind
pressure distribution coefficients are studied. In
another recent work, Fernandes and Campos [4]
determined, via numerical simulation, the external
pressure coefficients in vaulted buildings and
analysed the action of the winds on a scallop dome
located in a region where accidents due to wind
occur. Sha, Zheng and Yue [5] investigated the
interference effect on the wind load on two adjacent
hemispherical dome structures. They concluded that
the interference effect on the wind load on the two
adjacent domes cannot be neglected and that a
significant discrepancy exists under different
incident wind directions when considering the
influent of the adjacent dome. This influence is
mainly the shielding effect by the upstream dome
and the blocking effect by the downstream dome.
Rezaeinamdar, Sefid, and Nooshin [6]
investigated the scallop dome and compared the
results obtained from CFD with the corresponding
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wind tunnel empirical data. They concluded that
RANS models and the LES method could
reasonably predict the front pressure coefficients for
the range [0, ±90]. In the literature, dome
arrangements have also been explored. For example,
Tavakol, Yaghoubi, and Ahmadi [7] experimentally
and numerically studied the flow around a series of
domes, structures that, despite being widely used in
the hot arid regions of the Middle East because of
their ventilation advantages, have been little
explored. They used wind tunnels for the
experimental approach and simulation of large
scales in the numerical implementation, exploring
Reynolds numbers of 43,000 and 430,000. The
results indicated that the separation points moved
further downstream for the second and third domes
compared with the first dome. Additionally, the
peak suction pressure occurred near the apex of the
first dome. Now, the maximum pressure occurred
on the windward side of the third dome.
This work first compares and validates the results
of the numerical CFD analysis with the literature.
Then, using the CFD method, this paper investigates
the effect of the neighborhood on the distribution of
the external pressure coefficient. The streamlines
between geometrically identical domes were also
analysed.
2 Methodology
Numerical tests were performed using Ansys
Workbench software, fluid flow module (CFX). The
geometries were modelled with AutoCAD software
and were composed of the structure to be analysed
surrounded by the control volume, whose
dimensions were adopted according to [2]: length of
4 m, width of 24 m and height of 2,6 m, with the
dome centered inside it (Fig. 1). The wind direction
considered was 0° concerning the domes, and the
wind speed adopted was 38 m/s.
Fig. 1 Volume control
3 Numerical applications
Case 1: Here, to validate the methodology, the
scallop domes were adopted with 6 grooves with
variations in the height of the geometry, adopting
the aspect ratio given by k=h/D and the relationship
between height (h) and diameter (D) fixed at 50 cm.
Considering the two decimal place precision, for
k=0,1, the greatest difference (24%) occurred
between the first boundary, starting from the outer
edge to the inner line of the dome. The same
occurred for the domes with k=0,2. In the scallops
domes with six grooves and k=0,3;...; 0,5, the values
for the Cpe contours were similar (Tab. 1) when
compared to those presented by [2]. However, for
k=0,4 and k=0,5, at the top of the geometry crest, an
area of the larger contour can be observed, which
has a high aspect ratio and, consequently, presents
the highest Cpe values. Compared with [2],
differences of 17% and 13% were obtained for the
maximum and minimum pressure coefficients,
respectively. According to [2], with the increase in
the aspect ratio of the dome, the lengths of its
grooved parts decrease, especially in the grooves at
90° concerning the wind direction, due to the type of
cutout of this dome. In this way, with the increase in
the aspect ratio, the suction effect of the critical
groove was increased; for example, Cpemin=- 0,88
for k=0,3 and Cpemin=-1,31 for k=0,5 were obtained.
Case 2: In this case, wind pressure coefficients in
three distinct dome scenarios with various aspect
ratios are studied. All domes have the same
diameter, varying their elevation, denoted by h,
from 0,1D to 0,5D, with D being its diameter. The
three situations analysed, different by the number of
grooves in each geometry (10, 14, and 25), aim to
investigate the influence of the grooves on the wind
behavior and, consequently, on the pressure
coefficients. Initially, the wind action was simulated
in domes with 10 grooves, with a 0° wind direction.
The pressure coefficients obtained, as well as the
pressure contour lines, can be seen in Fig. 2(a). It
was found that as the aspect ratio was increased,
there was an increase in the external pressure
coefficient. A significant suction area to leeward
was also noted, especially in the domes with k =
0,3;...;0,5, and for these, it was noted that the
module higher values of the pressure coefficient,
they are directed to the grooved sections between
36° and 108° concerning the wind direction and,
similarly, in the grooves between 252° and 324°,
thus evidencing the increase in the indentations
represented by the contour lines. Additionally,
Cpemin for k=0,4 and k = 0,5 occurred in the groove
at 72° and 288° for the wind, and this suction was
relieved at the top and lee side of the geometries. To
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Table 1. External pressure coefficients of the scallop dome with six grooves considering k = 0.1;...; 0.5
k = 0,1
Sadeghi et al. [2]
+0,25
+0,00
-0,25
Present work
+0,19
-0,02
-0,24
Difference
0,06
0,02
0,01
k = 0,2
Sadeghi et al. [2]
+0,50
+0,25
+0,00
-0,25
-0,50
-0,75
Present work
+0,40
+0,19
-0,02
-0,24
-0,45
-0,67
Difference
0,10
0,06
0,02
0,01
0,05
0,08
k = 0,3
Sadeghi et al. [2]
+0,75
+0,50
+0,25
+0,00
-0,25
-0,50
-0,75
-1,00
Present work
+0,62
+0,40
+0,19
-0,02
-0,24
-0,45
-0,67
-0,88
Difference
0,13
0,10
0,06
0,02
0,01
0,05
0,08
0,12
k = 0,4
Sadeghi et al. [2]
+0,75
+0,50
+0,25
+0,00
-0,25
-0,50
-0,75
-1,00
-1,24
Present work
+0,62
+0,40
+0,19
-0,02
-0,24
-0,45
-0,67
-0,88
-1,09
Difference
0,13
0,10
0,06
0,02
0,01
0,05
0,08
0,12
0,15
k = 0,5
Sadeghi et al. [2]
+0,75
+0,50
+0,25
+0,00
-0,25
-0,50
-0,75
-1,00
-1,24
Present work
+0,62
+0,40
+0,19
-0,02
-0,24
-0,45
-0,67
-0,88
-1,09
Difference
0,13
0,10
0,06
0,02
0,01
0,05
0,08
0,12
0,15
the windward side, it was observed that Cpemax
occurred in the frontal part of the domes configured
with an aspect ratio greater than 0,3. For the domes
with 14 grooves, the same geometric parameters
previously adopted were maintained. Figure 2(b)
shows the pressure coefficients and isobaric lines as
well as the pressure distribution on the external
surface of the domes. It was noted that the isobaric
lines behaved similarly to the previous case, in
which the domes had 10 grooves; however, with the
increase in grooves and, consequently, in the
number of geometry sections, there was an increase
in indentations, and these, in turn, were
predominantly located at 51° and 77°.
Compared with the 10-groove geometries, a
decrease in the external pressure coefficients was
noted. For cases with 14 grooves, the increase in the
number of grooved sections influenced the result of
the coefficients. Finally, five situations were
simulated with the same aspect ratio variations for
the domes with 25 grooves (Fig. 1(c)), and a
significant difference was observed in the results
obtained for the external pressure coefficients when
compared to the cases with 10 and 14 grooves. A
23% reduction in Cpemin was noted with the 14-
slotted geometry and 26% with the 10-slotted
domes. An increase in indentations was noted for
the case with 25 grooves (Fig. 1(c)), demonstrating
the tendency of the module highest coefficients to
be directed towards the sections delimited by the
grooves. For k=0,5, Cpemin was concentrated on
sections between 58° and 86° for the wind direction
and, similarly, on grooves between 302° and 331°,
in addition to converging to the crest of this
geometry. When comparing the cases with 10, 14,
and 25 grooves, it was noted that the wind behaved
similarly, and the maximum and minimum
coefficients were concentrated in the same regions,
with the maximum in the windward sections and the
minimum at the top and sides of geometries. As the
number of grooves was increased, a decrease in
pressure coefficients was noticed, showing the
influence of the grooves. Therefore, the dome with
25 grooves presented a better performance regarding
the minimum external pressure coefficient and was
chosen for Case 3.
Case 3: The distribution of wind pressure
distribution on an object is not only a function of its
shape but is also a function of the effect of the
nearby objects, according to [3]. Thus, this effect
was studied, as well as the Venturi effect and the
blowing effect on the external pressure coefficient
between the cups. The domes were named A, B, and
C, with A and B being the source of interference and
dome C referred to as the reference dome (Fig.
3(a)). All have 25 grooves and ratio k=0,5 and were
positioned at a distance L, which varies in the range
[0;2D], measured from their outer edge, where D is
the diameter of the dome. To calculate the wind
speed along the control volume, 38 m/s was adopted
for the basic speed. The neighborhood effect tends
to decrease with increasing distance between them.
Thus, for L=0,25D and L=0,5D, a smaller influence
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k = 0,1
k = 0,2
k = 0,3
k = 0,4
k = 0,5
(a)
k = 0,1
k = 0,2
k = 0,3
k = 0,4
k = 0,5
(b)
k = 0,1
k = 0,2
k = 0,3
k = 0,4
k = 0,5
(c)
Fig. 2 Variation of external pressure coefficients on scallop domes with (a) 10 grooves, (b) 14 grooves, (c) 25 grooves and
different aspect ratios
of the interference domes A and B on the reference
dome C was noticed. In addition, there was an
increase in the flow velocity caused by the
bottleneck in flow between geometries A and B,
making the external pressure coefficients higher on
the surfaces where the taper occurred (Fig. 3(b-c)).
Vortex shedding became more evident from the
set L=0,25D, and consequently, the blowing effect
caused by the interference domes became more
active. This dynamic effect generated by wind
turbulence from structures A and B caused changes
in pressure, causing the Cpe of reference dome C to
increase. For the last two simulations, L=D and
L=2D were adopted, there was a small interference
from the neighborhood, and the values of the
external pressure coefficients were similar to those
found in the previous case. In the L=D
configuration, domes A and B had no interference
from the neighborhood, while dome C had a small
decrease in the Cpemax region. Furthermore, there
was no change in the values of the pressure
coefficients, and the wind taper started to decrease
and, consequently, the interference of the effects on
the structures (Fig. 3(e)). As the value of L
increases, the areas of overpressure in the reference
domes also increase. Furthermore, the critical
suction range tends to increase in these domes, and
for L=2D, a wider area is reached with the highest
suction, different from those with low values of L,
which suffer from the shielding effect of the domes
of interference A and B (Fig. 3(f)). It was noted that
for the distance L=2D, the external pressure
coefficients remained the same as in the previous
case considering 25 grooves and the ratio k=0,5,
unlike the domes spaced at L < D, which suffered
directly from the effects caused by the presence of
the neighborhood. Concerning the wind speed in the
simulations, a percentage increase of approximately
21% was observed for the basic speed, especially in
areas where the bottleneck in the wind caused by the
proximity of the structures occurred, reaching
approximately 46 m/s, making the external pressure
coefficients larger on these surfaces.
Case 4: In this case, two 25-grooved scallop domes
were studied to verify the influence of proportion in
the study of neighborhood interference. The same
aspect ratio as in the previous case was adopted,
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(a) Geometric configuration
(b) L=0,01D
(c) L=0,25D
(d) L=0,5D
(e) L=D
(f) L=2D
Fig. 3 Geometric configuration and variation of external pressure coefficients and the streamlines with respect to the
arrangement of three scallop domes with 25 grooves and k=0,5.
varying the diameter, height, and distance of the
domes. According to the previous case, there was a
greater influence of the neighborhood when L≤D,
and consequently, in the first two simulations, the
distance was adopted as L = D and L = 0,5D. The
diameter of the interference domes was fixed at D =
0,5 m, and for the reference dome, the value of
D’=4/5D was assumed in both
applications. The external pressure coefficients and
current lines for these profiles are shown in Fig. 4(a-
b). Adopting these same distances, there was no
discrepancy in the results when compared to the
values obtained in the previous case, and the
isobaric lines and the current lines were distributed
similarly, with a change of 9% in the first simulation
and 3% in the second simulation for the minimum
external pressure coefficient. In the third and fourth
simulations (Fig. 4(c-d)), a diameter of 4/5D was
adopted for the interference domes, and the value of
D was fixed for the reference dome. The distances
used were L=0,5D and L=0,25D, respectively. The
results for the third simulation showed a reduction,
in module, of 11% of the Cpemin when compared to
the case with the same distance between the domes,
demonstrating the tendency of attenuation of the
suction values according to the reduction in the
proportion of the domes of interference. It was also
verified that this same pressure coefficient in the
module increased as the distance between the
structures decreased, as observed in the fourth
simulation (Fig. 4(d)), contrary to what occurred in
the first two simulations, in which Cpemin declined
with the proximity of the domes. The Cpemin, in turn,
increased as the structures approached due to the
“funneling” of the wind caused by the interference
domes. For the last simulation, L=0,25D was
adopted. One of the interference domes was
designed with a diameter equal to D, while the other
interference geometry and the reference dome were
configured with D’=4/5D (Fig. 4(e)). As in other
simulations involving neighborhoods, it was found
that the minimum pressure coefficient of the
interference domes to leeward in the module was
greater than that of the reference domes due to the
mat formed between the geometries. In general, in
the simulations of this case, there were no
significant changes in the pressure coefficients or
the distribution of the streamlines compared to the
previous case. However, in the domes with 4/5D, as
the distance from the other buildings was made, the
pressure coefficient in the module was reduced as a
result of the decrease in the proportions of the
geometry. Nevertheless, the reduction pressure
coefficient was not significant. In turn, the diameter
domes D showed results similar to the previous
case.
4 Conclusions
In the first case, five applications involving scallop
domes with six grooves and with variations in the
height of the geometry, the coefficients obtained
numerically were compared with the literature for
validation. The pressure coefficients presented
differences concerning the literature, on the order of
13% and 17%, for the minimum and maximum
pressure coefficients, respectively. In the second
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(a) L=D; D’=4/5D
(b) L=0,5D; D’=4/5D
(c) L=0,5D; D=4/5D’
(d) L=0,25D; D=4/5D’
(e) L=0,25D; D=4/5D’
Fig. 4 Variation in the external pressure coefficients and streamlines with respect to the arrangement of three
scallop domes with 25 grooves and k=0,5.
case, the influence of the grooves on the external
pressure coefficient and the wind distribution in the
structure was investigated considering domes with
10, 14, and 25 grooves. A decrease in the pressure
coefficients was observed as the number of grooves
was increased, proving the influence of the grooves
on the coefficients. In the third case, the interference
of the neighborhood on the external
pressure coefficient and the current lines between
three domes with identical geometric characteristics,
with 25 grooves, and the ratio k=0,5 was analysed.
The results showed that the wind action caused
changes in pressures and current lines in the vicinity
of the structures, especially when L<D, and they
became almost null from L=2D. For the wind speed,
there was a percentage increase of approximately
21% concerning the adopted basic speed, seen,
above all, in the areas of "tapering" of the wind
caused by the proximity between the structures,
causing an increase in the external pressure
coefficients in these areas. In the last case, the
influence of proportion in the study of neighborhood
interference for domes with 25 slots and ratio k =
0.5 was investigated, as well as the effect of
variations in structure dimensions on pressure
coefficients and streamlines. It can be noted that for
this configuration, compared to the previous case,
the pressure coefficients and the distribution of the
current lines did not show significant changes less
than the 4/5 D domes, which, as the distance of the
buildings, the pressure coefficient in the module was
reduced.
Although some contours presented errors in the
range of 20% to 30% to the literature, Ferziger
(1990) points out that lower accuracies, with errors
above 25%, can be admitted in Wind Engineering.
In future works, other configurations and
arrangements involving scallop domes could be
studied, as well as the calculation of the internal
pressure.
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[1] R. L. C. Canlas, M. T. J. N. Principe, G. S.
Riego and V. E. DyReyes, Finite Element
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E-ISSN: 2732-9984
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Volume 2, 2022
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Contribution of individual authors to
the creation of a scientific article
Camila Guerra was responsible for the methodology
and carried out the simulation and writing. Marco
Campos carried out the conceptualization; writing,
review and editing.
Creative Commons Attribution
License 4.0 (Attribution 4.0
International , CC BY 4.0)
This article is published under the terms of the
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