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Wind and Structures, Vol. 23, No. 5 (2016) 465-483
DOI: http://dx.doi.org/10.12989/was.2016.23.5.465 465
Copyright © 2016 Techno-Press, Ltd.
http://www.techno-press.org/?journal=was&subpage=8 ISSN: 1226-6116 (Print), 1598-6225 (Online)
Pressure distribution on rectangular buildings with changes in
aspect ratio and wind direction
Young Tae Lee1, Soo Ii Boo1, Hee Chang Lim1 and Kunio Misutani2
1School of Mechanical Engineering, Pusan National University, San 30, Jangjeon-Dong, Geumjeong-Gu,
Busan, 609-735, South Korea
2Department of Architecture, Tokyo Polytechnic University, Atsugi, Kanagawa, 243-0297, Japan
(Received May 21, 2014, Revised May 28, 2016, Accepted September 20, 2016)
Abstract. This study aims to enhance the understanding of the surface pressure distribution around
rectangular bodies, by considering aspects such as the suction pressure at the leading edge on the top and
side faces when the body aspect ratio and wind direction are changed. We carried out wind tunnel
measurements and numerical simulations of flow around a series of rectangular bodies (a cube and two
rectangular bodies) that were placed in a deep turbulent boundary layer. Based on a modern numerical
platform, the Navier–Stokes equations with the typical two-equation model (i.e., the standard k-ε model)
were solved, and the results were compared with the wind tunnel measurement data. Regarding the
turbulence model, the results of the k-ε model are in overall agreement with the experimental results,
including the existing data. However, because of the blockage effects in the computational domain, the
pressure recovery region is underpredicted compared to the experimental data. In addition, the k-ε model
sometimes will fail to capture the exact flow features. The primary emphasis in this study is on the flow
characteristics around rectangular bodies with various aspect ratios and approaching wind directions. The
aspect ratio and wind direction influence the type of wake that is generated and ultimately the structural
loading and pressure, and in particular, the structural excitation. The results show that the surface pressure
variation is highly dependent upon the approaching wind direction, especially on the top and side faces of
the cube. In addition, the transverse width has a substantial effect on the variations in surface pressure
around the bodies, while the longitudinal length has less influence compared to the transverse width.
Keywords: rectangular bodies; wind direction; aspect ratio; surface pressure distribution; wind-tunnel
measurement; k-ε model; Computational Fluid Dynamics
1. Introduction
The study of flow characteristics around a bluff body immersed in a turbulent boundary layer
flow has long been of significant interest to researchers. Such investigations are crucial in the
design and development of practical objects such as vehicles, buildings, and bridges. Over the last
several decades, construction companies have employed high Reynolds number flow as a typical
design parameter. Above all, the study of flow characteristics around a bluff body is now generally
considered an important topic in academic circles as well as in engineering applications, and many
Corresponding author, Professor, E-mail: hclim@pusan.ac.kr
Young Tae Lee, Soo Ii Boo, Hee Chang Lim and Kunio Misutani
related issues remain to be studied.
As regards flow around various types of buildings, a considerable amount of data has been
generated and comparisons have been made between experimental and numerical data. One
often-cited paper in this field is the wind tunnel study by Castro and Robins (1977) (hereafter
denoted by CR), in which the flow around surface-mounted cubes was measured. Their paper
presented the flow characteristics such as surface pressures, and mean and fluctuating velocities
within a body's wake. It was the first study to demonstrate the crucial importance of modelling the
appropriate atmospheric boundary layer. In addition, this paper addressed the influence of
Reynolds number (Re), and found that the effects of Re existed for smooth upstream flow
conditions (i.e., the thickness of the approaching boundary layer was much smaller than the cube
height), whereas for the flow under a fully developed turbulent boundary layer, no effects of Re
were found for Re > 4000.
As regards experimental studies, a number of papers have presented the interaction between the
oncoming turbulent flow and rectangular bodies. Tieleman and Akins (1996) reported that the
variations in the surface pressures at the base and sides of surface-mounted rectangular prisms
were determined by the interaction between the incident turbulence and the separated shear layers.
In other words, the surface pressure is a function of the small-scale turbulence that could be
quantified by a modified parameter S, which is defined as the normalised spectral density of the
streamwise velocity fluctuations. Furthermore, not only the value of S, but also the prism
geometry (i.e., its longitudinal length-to-width (L/W) ratio) has an effect on the variations in the
surface pressures at the base and sides. These results can also be seen in the study by Schofield and
Logan (1990), which analysed the turbulent shear flow over surface-mounted obstacles. Their
analysis concentrated on the manner in which the major features of the flow are influenced by the
body geometry and the condition of incident turbulent flow. In addition, Martinuzzi and Tropea
(1993) focused on the flow around surface-mounted prismatic obstacles with different spanwise
dimensions, with the aim of investigating the effects of aspect ratio (i.e., width-to-height (W/H)
ratio). According to the pressure measurements and vortex visualization results, the body width
has a major influence on the flow characteristics in the separation, pressure recovery, and wake
regions. In addition to the research on the effects of changes in aspect ratios, the effects of wind
direction have also been studied by many researchers. The most notable example of studies on
bodies placed at an angle to the approaching flow was the study conducted by Richards et al.
(2007), who investigated the pressure distribution on the roof of a building for a range of wind
directions (0°, 15°, 30°, and 45°). According to their results, both the mean and peak pressures are
highly sensitive to the wind direction. For example, a change of wind direction by 30° can alter the
mean static pressure coefficient from a negative value to a positive value.
As regards the computational fluid dynamics (CFD) techniques, there have been substantial
changes in numerical modelling as well as hardware development, and this field continues to
develop rapidly. One of the strongest merits of using a simulation is that it can provide a quick
view of the full range of flow characteristics around target objects that have complex shapes at
each time step and in the full domain simultaneously. For this reason, many attempts have been
made to simulate the precise flow around a variety of bodies by solving the governing Navier–
Stokes equations. In the early years of such research, many turbulence models were developed to
solve the complicated turbulent flow around a body, some of which were compared to each other
to determine their different degrees of systematic efficiency (i.e., Murakami 1993, Meroney, Leitl
et al. 1999). It was found that the accuracy of the numerical calculation was highly dependent on
the choice of the turbulence model. Most previous studies have focused on the Reynolds-averaged
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Pressure distribution on rectangular buildings with changes in aspect ratio and wind direction
Navier–Stokes (RANS) method, especially the k-ε model (e.g., Tominaga and Stathopoulos 2009).
However, more comparisons and discussions are needed to judge the accuracy of the k-ε model.
Section 2, which follows, outlines the experimental techniques used, and Section 3 describes
the computational techniques used. Section 4 presents an analysis of the surface pressure
characteristics, as well as some findings, and discussion of the major results obtained when the
aspect ratio of the bodies and the wind direction were changed. Finally, Section 5 presents the
major conclusions.
2. Experimental techniques
2.1 Artificial generation of a thick turbulent boundary layer
Fig. 1 illustrates the detailed set-up inside the boundary layer wind tunnel, showing a grid, a
tripping fence, roughness, and a cube model. The experiment was conducted in a closed-circuit
subsonic atmospheric boundary layer wind tunnel of the Pohang University of Science and
Technology in South Korea, whose working section is 0.72 m height × 0.6 m width × 6 m length, with a
maximum wind speed of approximately 40 m/s. The wind tunnel is suitable for generating an
artificial boundary layer, and is also equipped with a modern hot-wire anemometer (IFA100), a
multi-channel pressure scanning system, and a PIV system for optical measurement of the airflow.
Thick boundary layers were generated using a technique that is often employed by
wind-engineering practitioners; this technique was first devised by Cook (1978). Toothed barriers
spanning the floor of the working section near its entry, followed by a square section, bi-planar
mesh across the entire working section, and an appropriate rough surface after this region can be
designed to yield mean-velocity profiles that are closely logarithmic over a significant portion of
the working-section height, with turbulence stresses and spectra similar to those found in neutrally
stable atmospheric boundary layers. There are other ways also to simulate atmospheric boundary
layers (e.g., Hunt and Fernholz 1975 for an old, but still appropriate review). This particular
method has the advantage of maximising the depth of the logarithmic region, but has the
disadvantage of not simulating the largest-scale eddies in the upper part of the atmospheric
boundary layer.
Fig. 1 The 0.6 mwidth × 0.72 mheight × 6 mlong wind tunnel test section
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Young Tae Lee, Soo Ii Boo, Hee Chang Lim and Kunio Misutani
As our intention was to make comparisons with the existing data such as wind tunnel and field
data (e.g., for a 6 m-height cube in Silsoe, UK (Richards, Hoxey et al. 2001), the use of less than
one-tenth of the height of the logarithmic region, thus maximising the depth of this region, was
deemed the most important factor for the purposes of this study. It was also considered crucial to
design the barrier wall and mix the grid geometries in tandem with the intended roughness, since
any mismatch would yield unacceptably long fetches before reasonably well-developed flows are
made (Lim 2009). In this case, commercially available plastic artificial grass was used to provide
the surface roughness. This gave a roughness length z0 of 0.17 mm, where z0 is defined in the
usual way via the mean velocity log law, which is expressed as
(1)
where is the friction velocity ( ) and is the zero plane displacement.
To obtain the three unknowns (, , and ) from the mean velocity profile alone, in the
present study, was deduced by extrapolation of the measured turbulence shear stress (
)
to the surface (see Lim, Castro et al. 2007), and then and were obtained from the best fit of
the mean velocity data to Eq. (1). In the tunnel, the barrier wall had a height of 50 mm, with
triangular cut-outs at the top; a pitch of 50 mm; and a depth of 50 mm, and the mixing grid
consisted of a bi-planar grid of 10 mm bars at a pitch of 50 mm.
2.2 Building models and measurements system
Rectangular bodies with a height of 80 mm and having a smooth surface were used in the
tunnel, and were equipped with 0.8 mm pressure taps at numerous salient points on the top surface,
as well as on the front and side faces (see Fig. 2). Table 1 lists the rectangular models used in the
study. The models were made of plexiglass and consisted of three bodies: a cube (80 mm height × 80
mm width × 80 mm length with 1:1:1 ratio) for comparing with the existing results from a reference
(Lim, Thomas et al. 2009), and two rectangular bodies (80 mm height × 40 mm width × 80 mm length
with 1:0.5:1 ratio and 80 mm height × 160 mm width × 80 mm length with 1:2:1 ratio) having
dimensions in such a way that two more aspect ratios could be created for flow around the
rectangular bodies by rotating them by 90° (e.g. 80 mm height × 80 mm width × 40 mm length with
1:1:0.5 ratio and 80 mm height × 80 mm width × 160 mm length with 1:1:2 ratio). Standard tube
connections to a micromanometer (Furness, FC-012) allowed the measurement of mean surface
pressures. Mean velocity and turbulence stress data within the boundary layers at the (subsequent)
model locations and around the bodies themselves were obtained using a hot-wire anemometer
(HWA). For HWA measurements, the errors caused by inadequate yaw response were minimised
by using crossed-wire probes along with the standard ±45° wires (Dantec 55P61, Miniature
cross-wire) and employing the effective cosine-law method to calibrate for yaw sensitivities. The
probes had 1.25 mm-long platinum-plated tungsten wires with a diameter of approximately 5 μm
and were driven by IFA100 (TSI) CTA bridges, with the outputs filtered to avoid aliasing. In
addition, they were modified by an appropriate gain and offset to allow the best use of the
analogue–digital converters (NI PCI-MIO-16E-1). Calibrations were performed against a standard
pitot-static tube using the same micromanometer as was used for the (static) pressure
measurements, and all analogue signals were digitized and transmitted to a desktop computer. The
difference between the surface pressure p around the surface of the body and the reference
pressure pr was normalized by the dynamic pressure with free-stream velocity Uh and air density ρ
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Pressure distribution on rectangular buildings with changes in aspect ratio and wind direction
to give the surface pressure coefficient , which is expressed by .
Specialized software ('Virtual instruments', written in National Instruments‟ LabVIEW) allowed
online calibration and measurement of all the desired quantities. The probes were supported on
traverse systems driven by the same computer. The sampling rate was typically between 2 kHz and
10 kHz, depending on the quantities being measured, with a sampling time of 60–120 s.
3. Computational techniques
3.1 Numerical methods
A schematic diagram of the computational domain with a wall-mounted bluff body is shown in
Fig. 3. To make an appropriate calculation, the proper domain size is a prerequisite in the
beginning state so that the cube (i.e., 80 mm height × 80 mm width × 80 mm length) has a computational
domain size of 4h height × 7h width × 14h length in the Cartesian coordinate system, where h is the cube
height. The origin of the domain was set at the windward foot of the cube.
Table 1 Scale-down models used in the wind tunnel study
Case
H (height)
[mm]
W (width)
[mm]
L (length)
[mm]
W/L
H:W:L
1
80
80
80
1
1:1:1
2
80
40
80
0.5
1:0.5:1
3
80
160
80
2
1:2:1
4
80
80
40
2
1:1:0.5
5
80
80
160
0.5
1:1:2
Fig. 2 A cube model (80 mm height × 80 mm width × 80 mm length) and pressure taps
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Young Tae Lee, Soo Ii Boo, Hee Chang Lim and Kunio Misutani
Although a gap of 3 both to the sides and to the roof is quite small, this computational
domain is suitable for generating an appropriate turbulence boundary layer to match the real wind
conditions; however, there may still be some blockage effect. In addition, the boundary conditions
were set to velocity inlet (inlet condition), outflow (mass flow conservation for outlet conditions),
symmetry (mirror condition for the top roof of the domain), and periodic boundary conditions
(infinite perfect tiling condition on the opposite face at the same velocity), as shown in Fig. 3. To
generate a practical turbulent boundary layer in the computational domain, the periodic boundary
conditions would be applied in the inlet and the outlet, so that the turbulence would be developed
by flow recycling, as in the Lund method (Lund, Xiaohua et al. 1998). When the calculation of the
channel flow without any model in the computational domain is completed, the averaged mean
and turbulence quantities were implanted on the inlet boundary plane of the channel flow with the
rectangular body. In the case when the wind direction was changed (symbolized as , which had
values of 0°, 10°, 20°, 30°, and 45°), a schematic model obtained by computational techniques was
used, as shown in Fig. 4. Even though the geometry of the flow configuration is simple, the flow
characteristics are essentially unpredictable, as they display multiple separations and both large-
and small-scale vortex regions.
The commercial code of FLUENT was used in this calculation. In terms of the mesh size used
to resolve the small-scale turbulent flow, 73, 115, and 178 nodes were used for the height, width,
and length directions respectively. The first grid spacing near the wall was 0.025h and the spacing
ratio was 1.1 to ensure that the value of was acceptable. Here, was defined as
,
where is the distance from the wall, and is the kinematic viscosity. In this study, was
approximately 45 in the standard k-ε model, and it was within the required range of 30 to 60, as
suggested by Salim and Cheah (2009). For example, the inlet surface grid mesh is as shown in Fig.
5, since it requires a fine mesh resolution near the (model) wall. When the aspect ratio of the
model varies, the computational domain and the number of grids must be reconstructed, as listed
in Table 2. Especially, to avoid blockage effects, with increase in the angle of the wind direction,
the calculation domain will also increase in proportion. For example, when the wind direction is at
45°, the calculation domain will become 4h height × 11h width × 14h length.
Fig. 3 Computational domain and boundary conditions
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Pressure distribution on rectangular buildings with changes in aspect ratio and wind direction
Fig. 4 Top view of a bluff body model with different wind direction angles (0°, 10°, 20°, 30°, and 45°)
Fig. 5 Frontal view of grid mesh in the inlet condition
Table 2 Computational domains and grid nodes
Case
H:W:L
Domain
Grid nodes
1
1:1:1
4h×7h×14h
73×115×178
2
1:0.5:1
4h×6.5h×14h
73×100×178
3
1:2:1
4h×8h×14h
73×145×178
4
1:1:0.5
4h×7h×13.5h
73×115×163
5
1:1:2
4h×7h×15h
73×115×208
3.2 Governing equations and turbulence models
To describe the precise motion of fluid flow, the Navier–Stokes equations with various
turbulence models must be solved, and all the boundary conditions are required to solve the
equation. The RANS model was employed to render the Navier–Stokes equations tractable in
order to avoid the need to directly simulate the small-scale fluctuations in turbulence.
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Young Tae Lee, Soo Ii Boo, Hee Chang Lim and Kunio Misutani
This study implements the standard k-ε model, which is the simplest complete model of
turbulence. It is a semi-empirical model, and the derivation of the model‟s equations relies upon
empirical considerations. It is based on two separate transport equations for the turbulence kinetic
energy (k) and its dissipation rate (ε). The equations are as follows
(2)
(3)
In these equations, represents the generation of turbulence kinetic energy due to the mean
velocity gradients; is the generation of turbulence kinetic energy due to buoyancy;
represents the contribution of the fluctuating dilatation in compressible turbulence to the overall
dissipation rate; and and are user-defined source terms.
In addition, is the turbulent viscosity, and is computed by combining and as follows.
(4)
In the above equations, the values of the model constants are, =0.09, = 1.44, = 1.92,
= 1.0, and = 1.3. In addition, is not specified, but is calculated according to the
following relation.
(5)
where is the component of the flow velocity parallel to the gravitational vector and is the
component perpendicular to the gravitational vector.
3.3 Boundary conditions
The present numerical simulation was carried out as per the conditions in the experimental
study. The Reynolds number based on (model height) and (mean inlet velocity at ) was
4.6 × 104. After completing the calculation of the channel flow without any model, the averaged
mean and turbulent quantities were implanted on the inlet boundary plane of the channel flow with
the rectangular body. Fig. 6 compares the profiles of the inlet mean-velocity (a) and turbulence
intensity (b) in the streamwise components. The results of the wind-tunnel experiment (EXP) and
the numerical simulation (k-ε) were also compared with the existing results from other papers (e.g.,
Castro and Robins 1977 and Lim, Castro et al. 2007, hereafter denoted by CR and LCH). As can
be seen in the vertical wind profiles, a fully developed shear flow was produced in the wind tunnel
as well as in the numerical wind tunnel, which were specifically designed to be similar to the (rural)
atmospheric boundary layer.
The entire domain containing the cube models, internal working section, and surface wall are
shown in each figure (see Fig. 3), along with the boundary conditions for the flow. Five different
boundary conditions were used in the numerical domain: inlet and outlet flow conditions for the
inlet/outlet domain, periodicity for the side, symmetry for the upper wall, and wall conditions for
the rest of the surface wall. The boundary layer in the domain is continuously regenerated in the
channel flow, which is possible because it uses the periodicity boundary condition that combines
the inlet with the outlet layer and repeatedly recirculates the flow. There are essentially two
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Pressure distribution on rectangular buildings with changes in aspect ratio and wind direction
methods for generating the necessary inflow. The first is a statistical method wherein a sequence of
random numbers is generated and then filtered to yield appropriate statistical properties and spatial
correlations (see Xie and Castro 2013). The second involves performing a separate „precursor‟
simulation of a wind environment and sampling the inflow data directly from this simulation (see
Lim, Castro et al. 2009). The second method has the desirable feature that the generated inflow
should naturally contain physically realistic coherent structures without these having to be
produced artificially; hence, this method was adopted in the present work. A similar method was
used by Nozawa and Tamura (2002) in their computations of flow over a half-cube.
The velocity profile was also fitted to the power law profile, in which the exponent α was 0.14,
which was dependent on the terrain roughness. The mean velocity at the cube height was
approximately 8 m/s. From the turbulence intensity profiles, it can also be seen that the high
turbulence intensity (14%) was induced at a certain height (i.e., near the wall surface), and it
gradually decreased in the region far away from the wall. For example, at the cube height, the
turbulent intensity decreased to approximately 10.7%.
4. Results and discussion
4.1 Surface pressure distribution - cubical model (H: W: L=1:1:1)
The surface static pressure distributions along the centreline around the 1:1:1 model are shown
in Fig. 7. The figure compares the numerical and experimental results for the variations in the
mean static pressure coefficient , where is the mean static pressure
in the upstream flow along the axial centreline of the cube. Fig. 7 also presents the existing results,
i.e., the wind tunnel (WT) and field scale (FS) measurements, as a function of the measurement
location x/h. Here, x = 0 corresponds to the foot of the front face of the model body, which
actually depends upon the wind direction (e.g., see the solid arrowed line in the right-hand figure).
It may be noted that the rest of the figures are arranged in a manner similar to the arrangement in
Fig. 7, i.e., the profile at the mid-height.
Fig. 6 (a) Mean velocity profile and (b) Turbulence intensity profile
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Young Tae Lee, Soo Ii Boo, Hee Chang Lim and Kunio Misutani
Fig. 7 Mean surface static pressure coefficient along the central section with wind normal to the face
The profiles in Fig. 7 have the expected shape in that the largest negative pressures occur just
beyond the separation at the leading edge, and are followed by substantial pressure recovery on the
top surface, as has been shown in numerous previous studies. It may also be noted that the
experimental data agree well with the earlier field data of LCH (Lim, Castro et al. 2007), but are
significantly different from the wind-tunnel data of CR (Castro and Robins 1977). The latter are
similar to those of Murakami and Mochida (1988); they are in agreement with CR's discussion,
and are undoubtedly a result of turbulence levels that are very much higher upstream, which leads
to much earlier reattachment and pressure recovery on the top surface. In addition, the k-ε model
data are nearly similar, except for the region just within the right-hand corner of the position x/h =
1, which has a negative peak. This seems to have been caused by the turbulence model itself.
However, regardless of this peak region, there are still some variations between the experimental
data and the k-ε model data. For example, in the k-ε model data, the pressure recovery is
consistently underpredicted, which may be because of the blockage effects in the small-size
computational domain. It is well known that the flow will be artificially accelerated by the
blockage effects.
Fig. 8 shows the mean surface static pressure distribution along the mid-height of the cube. As
shown in Fig. 8, the experiment data agrees well with the field measurement data of RHS (2001)
(i.e., Richards, Hoxey et al. 2001), except for the results of CR. The k-ε model data are similar to
the experiment data, but still show a significant difference just inside the right-hand corner of the
position x/h = 1. The numerical data, however, show a relatively low value in the pressure
recovery region (x/h = 1.4 to 3) compared to other existing works. One explanation for this might
be that because of the blockage effects, the flow is artificially accelerated, so the reattachment and
pressure recovery are delayed.
The reported comparison of experimental and numerical data can serve to validate a developed
computational approach, which is therefore applied to analyze pressure distribution on rectangular
buildings, as reported in the remaining part of this study. Therefore, the results in the current
section could be seen as a precursor to the rest of the pressure profiles, as the next section
discusses the pressure profiles around rectangular obstacles having the same boundary layers.
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Pressure distribution on rectangular buildings with changes in aspect ratio and wind direction
Fig. 8 Mean surface static pressure coefficient at the mid-height of the cube
4.2 Surface pressure distribution - models with different aspect ratios
The mean surface static pressure profiles along the centreline of the models using three
different aspect ratios are plotted in Fig. 9. The figure shows how the surface static pressure on the
top as well as on the front and rear faces varies with changes in the body width. It may be noted
that several subsequent figures, i.e., Figs. 10-17, are arranged in the same manner as in Fig. 9; i.e.,
the pressure profiles obtained from the experiment are shown in Fig. 9(a), and those from CFD
(k-ε model) are shown in Fig. 9 (b). In addition, the schematic view of the models are shown
underneath the profiles, which make it easy to visualize the measurement locations around the
body. In these profiles, the reason for the high suction pressure on the top surface along the
centreline is obvious: the wider the shape of the body, the stronger the surface suction pressure on
the top surface. It is also interesting that the front and rear faces of the body have relatively less
surface pressure variations.
Another interesting phenomenon is that around the position x/h = 2, there is a small dip in the
cases of 1:0.5:1 and 1:2:1; however, there is lack of data for these regions in the experimental
measurements. It should also be noted that these surface pressure profiles reflect the flow features,
with different aspect ratios discernible in the surface profiles of the body. The immediate
implication of the data in Fig. 9 is that the variations in width, while the length and height are
maintained, cause the surface pressure on the top surface to become more negative, while the front
and rear faces change relatively less in response to variations in width. The solid arrow in Fig. 9
shows the direction of the pressure drop as the width changes.
Fig. 10 presents the mean surface static pressure distribution along the side face at the
mid-height of the three different boxes for different transverse widths. The abscissa in Fig. 10 is
normalised with the body height. Consistent with the previous figure, i.e., Fig. 9, a pressure drop
with increasing width is noticeable in the negative direction. These results demonstrate that with
an increase in the horizontal width, i.e., with an increase in the aspect ratio, there is a concurrent
suction pressure drop on the side face. By comparison, it can be seen that the pressure difference
between the cases of 1:0.5:1 and 1:1:1 was not significant in the experimental measurements.
These pressure differences can be regarded as the effect of wind tunnel blockage, based on the
ratio of areas of the model and the tunnel section.
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Young Tae Lee, Soo Ii Boo, Hee Chang Lim and Kunio Misutani
Fig. 9 Mean surface static pressure coefficient along the centreline for different transverse widths – (a)
experimental results and (b) k-ε model results
Fig. 10 Mean surface static pressure coefficient at the mid-height for different transverse widths – (a)
experimental results and (b) k-ε model results
Figs. 11 and 12 show the mean surface static pressure profiles along the centreline and the
mid-height of the models for different longitudinal lengths (i.e., length l). The different size of the
longitudinal length is considered while maintaining the front face area, and the aspect ratios were
1:2:4, respectively. The flows around wall-mounted sharp-edged models usually display separation
and reattachment around the body, so the pressure profiles in Figs. 11 and 12 have a similar shape
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Pressure distribution on rectangular buildings with changes in aspect ratio and wind direction
as shown in the above results. In Figs. 11 and 12, the pressure profiles seem to show a similar
trend, and it may be noted that the overall distributions of the surface pressure are in good
agreement. However, there are still some variations between each case. We may thus draw the
conclusion that compared to the significant transverse width effects seen in Figs. 9 and 10, the
longitudinal length of the body has less influence (but it exists) on the surface pressure around
rectangular bodies.
Fig. 11 Mean surface static pressure coefficient along the centreline for different longitudinal lengths – (a)
experimental results and (b) k-ε model results
Fig. 12 Mean surface static pressure coefficients at the mid-height for different longitudinal lengths – (a)
experimental results and (b) k-ε model results
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Young Tae Lee, Soo Ii Boo, Hee Chang Lim and Kunio Misutani
Fig. 13 Mean surface static pressure coefficient along the centreline with change in width and length at the
same time, but with the ratio W/L = 0.5 unchanged – (a) experimental results and (b) k-ε model results
Fig. 14 Mean surface static pressure coefficient along the centreline with change in width and length at the
same time, but with the ratio W/L = 2 unchanged – (a) experimental results and (b) k-ε model results
Figs. 13 and 14 present the pressure coefficient comparisons for the cases when both the length
and width of the body are changed, but the ratio of width over length (i.e., W/L) is the same. Fig.
13 shows the pressure distribution on the top surface when the W/L ratio is 0.5, whereas Fig. 14
shows the distribution when the W/L ratio is 2. In Figs 13 and 14, although there is an obvious gap
478
Pressure distribution on rectangular buildings with changes in aspect ratio and wind direction
between the cases 1:0.5:1 and 1:1:2, and between the cases 1:1:0.5 and 1:2:1, the trend of the
variation is generally similar. Even though the length and width of the rectangular body have
changed, with the width over length ratio unchanged, the characteristics of the static surface
pressure profiles, at least along the centreline, remain unchanged. If there is any change in the
profiles, it is because of a little scatter. We might regard this scatter of pressure differences as the
wind tunnel blockage effect. Furthermore, a larger body is far more prone to the blockage effect.
4.3 Surface pressure distribution – models with different wind directions
Richards, Hoxey et al. (2007) have created a 1:40 scale wind tunnel model of the Silsoe 6 m
Cube. In their research, the effects of wind direction are shown by altering the angle in 15° steps
(0°, 15°, 30°, and 45°). Their results are presented in Figs. 15(a) and 16(a), and can be compared
with the CFD data in Figs. 15(b) and 16(b). In the present study, to observe the effect of wind
direction on the pressure variations around the cube (80 mm height × 80 mm width × 80 mm length, a
1:75 scale-down model), it is rotated by 0°, 10°, 20°, 30°, and 45°, which represent the salient
wind directions in the tunnel measurements. The results are given below.
The mean surface static pressure profiles along the centreline of the models with different wind
directions are plotted in Fig. 15. Fig. 15 shows how the surface pressure along the centreline varies
with change in the wind direction. It may be noted that Fig. 16, which follows, is arranged in a
manner similar to Fig. 15; i.e., the experimental results of Richards, Hoxey et al. (2007) are shown
on the left, and the CFD results (k-e) on the right. Even when the wind direction is changed, the
static pressure coefficient is still a function of the measurement location x/h. By comparing the
two figures, i.e., Figs 15 and 16, it can be seen that the data from CFD results are generally in
good agreement with the earlier wind tunnel data of Richards, Hoxey et al. (2007). It can also be
seen that these surface pressure profiles reflect the flow features with different wind directions. As
shown in Fig. 15, the profiles have the same expected shape as before, in spite of different wind
directions, in that the largest negative pressures still occur just beyond the separation at the leading
edge, and are followed by substantial pressure recovery on the top surface.
Fig. 15 Mean surface static pressure coefficient along the centreline for different wind directions – (a)
experimental results of Richards, Hoxey et al. (2007) and (b) k-ε model results
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Young Tae Lee, Soo Ii Boo, Hee Chang Lim and Kunio Misutani
Fig. 16 Mean surface static pressure coefficient at the mid-height for different wind directions – (a)
experimental results of Richards, Hoxey et al. (2007) and (b) k-ε model results
Although effects of changes in the angle of wind direction in Richard‟s experiment differ from
the results of this study‟s numerical simulation, the same trend can be seen, in that the greater the
angle of the wind direction, the weaker the surface suction pressure on the top face. The surface
suction pressure on the rear face, however, shows the opposite trend. In addition, the positive
pressure on the front face also becomes weaker as the angle of the wind direction increases. In
addition, the amplitude of the surface pressure variation on the rear face is less than that on the
front and top faces.
Fig. 16 shows the mean surface static pressure at the mid-height of the cube for different wind
directions. Compared to the results in Fig. 15, the surface static pressure coefficient profiles in Fig.
16 display greater changes, particularly on the side face for the positions x/h = 1 to 2. Both the
experimental results of Richards in Fig. 16(a) and CFD results in Fig. 16(b) indicate that the
surface pressures on these walls are highly sensitive to the wind direction. For example, for the
side face, a change of wind direction by 30° can cause a considerable change in the pressure
coefficient, and can even change the pressure coefficient from a negative value to a positive value.
Fig. 17 Mean surface static pressure coefficient along the transverse centreline for different wind
directions
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Pressure distribution on rectangular buildings with changes in aspect ratio and wind direction
Fig. 17 presents the mean surface static pressure along the transverse centreline of the cube for
different wind directions, but the data from Richards, Hoxey et al. (2007) is not presented for
comparison. In Fig. 17, it can be seen that when the wind direction is 0°, the profile is symmetrical.
In addition, the largest negative pressures occurs in the middle of the top surface, and is followed
by gradual pressure recovery that is associated with the separation and reattachment range on the
top and side surfaces. However, once the wind direction changes, the profiles show some
asymmetry, and the largest suction pressure position also changes, as shown in Fig. 17. When the
wind direction changes from 10° to 45°, the surface suction pressure becomes gradually weaker. In
particular, at the positions x/h = 2 to 3, the surface pressure even changes from negative pressure
to positive pressure when the wind direction changes, until it reaches 45°.
5. Conclusions
To understand the surface pressure distribution around rectangular bodies with different aspect
ratios and wind directions, we conducted wind tunnel measurements and numerical simulation (in
the case of the turbulence model, we used the standard k-ε model) of flow around a series of
rectangular bodies placed in a deep turbulent boundary layer. According to the results of the
velocity and pressure measurements, substantial changes were observed in the flow and pressure
characteristics around the rectangular bodies. In this study, the results of the mean static pressure
coefficient were compared for various aspect ratios and wind directions. Ultimately, the numerical
k-ε model results were compared with the wind tunnel experimental data and the existing field
data.
We mainly focused on the effects of various aspect ratios and approaching wind directions on
the flow characteristics around rectangular bodies. We summarize our major contribution as
follows. First, for flows and wind loads around rectangular obstacles, the aspect ratio and wind
direction are important, and can be used for the design and deployment of neighbouring buildings
and structures. Second, despite the lack of wind tunnel data, new mean flow data for a variety of
model cases have been generated. Third, this paper includes much more reasonable and improved
flow quantities based on the numerical calculation than earlier ones. Finally, we observed that the
aspect ratio of a rectangular body and the wind direction have a substantial effect on the surface
pressure around the body, a finding that has never before been reported in the existing papers.
Although more comparisons are needed to arrive at more definitive conclusions, this study is
able to contribute with the following findings.
(1) The CFD (k-ε model) results are in overall agreement with the experimental results, including
the existing data. However, because of the blockage effects in the computational domain, the
numerical data underpredicts the pressure recovery as compared to the experimental data. In
addition, the k-ε model sometimes fails to capture the exact flow features in some special regions;
for example, a relatively higher negative sharp peak (strong suction) close to the leading edge
compared to the other existing works.
(2) The turbulent flow around the wall-mounted bluff body separates from the front edge of the
body, and then reattaches on the top and side faces. Regarding the pressure distribution, the
largest negative pressures occur just beyond the separation region, and are followed by
substantial pressure recovery on the top and side faces. In addition, a higher upstream turbulence
level will lead to much earlier reattachment and pressure recovery, as well as higher static
pressure coefficient.
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Young Tae Lee, Soo Ii Boo, Hee Chang Lim and Kunio Misutani
(3) When the wind direction towards a bluff body changes, the variation in the surface pressure on
the body is highly sensitive to the wind direction, especially on the top face and the side face of a
cubical body. Sometimes, a change of wind direction by 30° can even change the pressure
coefficient from a negative value to a positive value.
(4) When the aspect ratio of a rectangular body changes, the transverse width has a substantial
effect on the surface pressure around the body; for example, the wider the geometry of body
becomes, the stronger the surface suction pressure on the top and side faces will be. In addition,
compared to the substantial effects of the body transverse width, the longitudinal length shows
less influence (but it exists) on the surface pressure variation.
Acknowledgments
This work was supported by “Human Resources Program in Energy Technology” of the Korea
Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource
from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20164030201230). In
addition, this work was supported by the National Research Foundation of Korea (NRF) grant
funded by the Korea government (MSIP) (No. 2016R1A2B1013820). This work was also
supported by the China-Korea International Collaborative work (Project ID: SLDRCE15-04).
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