SSP - JOURNAL OF CIVIL ENGINEERING Vol.
17, Issue 1, 2022
DOI: 10.2478/sspjce-2022-0013
Experimental Measurements of Drag and Lift Coefficient on
Building with an Elliptical Cross-section
Michal Franek1*, Marek Macák2, Oľga Hubová3
Slovak University of Technology in Bratislava, Slovakia
1
Faculty of Civil Engineering, Department of Building Structures
2
Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry
3
Faculty of Civil Engineering, Department of Structural Mechanics
*e-mail: michal.franek@stuba.sk
Abstract
The characteristics of aerodynamic forces acting on an elliptic cylinder with an aspect ratio of 0.5 with a wind
attack angle from 0 to 90° and subjected to the boundary layer wind tunnel were investigated. The model was
initially calibrated and compared with the existing work. The aspect ratio of the investigated model was 0.5, and
the model was emerging in a turbulent flow. The mean and fluctuating drag and lift coefficients were investigated.
The minimum drag coefficient occurred in the wind direction of 0° and the maximum at 90°. The lift coefficient
was the largest in the 30° wind direction and the smallest at 0°. Fluctuating coefficients were similar profiles as
the mean coefficients. Around the 30° wind direction, an inappropriate phenomenon occurred, caused by the
generation of asymmetrical vortices structures and wake instabilities.
Keywords: boundary layer wind tunnel, force sensor, drag coefficient, lift coefficient, elliptical cylinder
1 Introduction
Wind load on unconventional buildings has become more unpredictable. Our article is focused
on the bluff body, especially the building with an elliptical cross-section. In engineering practice
in Slovakia, no specific procedure for evaluating wind pressure or overall wind loads is
mentioned in the code [1]. Therefore, it is necessary to analyze each case individually. Our goal
was to treat isolated elliptical buildings in the overall wind loads, which are crucial for designing
the support system and foundations.
The first studies of the two-dimensional stationary model with an elliptical cross-section were
published by Modi and Wiland [2]. The elliptical cylinder had an eccentricity of 0.8 and 0.6.
With a detailed analysis, they experimentally verified the pressure distribution during the
organized wake condition. Other work [3] analyzed the wakes behind the elliptical cylinder,
which developed shear layer instabilities and unequal wake instabilities. Other researchers [4,5]
investigated the wake and streamline pattern for low Reynolds numbers. Zhao and He [6]
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Franek M., Macák M, and Hubová O.
investigated the effect of the aspect ratio of elliptical buildings on the pressure distribution. The
aspect relationship is the ratio between the major and minor axes, but also the height of the
model. Shi, Alam, and Bai analyzed three flow regimes in the unsteady laminar flow, and they
found three patterns of wakes [7].
The wind load on the elliptical cylinder is very sensitive to the value of the Reynolds number,
which is the ratio of inertial forces to viscous forces within a fluid that is subjected to relative
internal movement due to different fluid velocities. The articles only examined the wind loading
and flow regime for steady or unstable laminar flow. The buildings in engineering practice are
subjected to a turbulent flow. For that purpose, it is necessary to evaluate buildings in
Atmospheric Boundary Layer (ABL), which is fully turbulent. Our goal was to measure drag
and lift forces in Boundary Layer Wind Tunnel (BLWT).
2 Description of the Boundary Layer Wind Tunnel and Instrumentation
Equipment
The experimental investigations were carried out in BLWT Bratislava, where the atmospheric
circulation can be reproduced. This is necessary to correctly reproduce the roughness of the
Earth's surface that covers different terrain categories according to [1]. Particular devices such
as grids, membrane elements, and walls or Counihan vortex generators can be inserted along
wind tunnels [8]. These devices simulate the properties of the atmospheric boundary layer as
the mean wind velocity and the turbulence intensity. BLWT in Bratislava was designed with an
open circuit scheme and two test sections. It is a 26.2 m long low-speed wind tunnel with a
working cross-section of 2.6 × 1.6 m. Tunnel wind velocity was monitored by a static two-pitot
tube mounted on the wall behind the inlet part and in front of the measuring area. The 2.4 m
diameter turntable helps to investigate many directions of incoming wind. The approaching
flow corresponded to the wind flow through the urban terrain with aerodynamic roughness
length z0 = 0.7 m on a full scale. The fully turbulent flow was generated using the barrier as a
plane wall and a long fetch of roughness elements, simulated by the dimpled membrane. The
height of the membrane elements was 20 mm. The mean wind velocity and turbulence intensity
profiles are shown in Figure 1. According to the boundary layer characterization, the mean wind
velocity at the model roof height was 8.6 m/s, and the turbulence intensity was 18.3 %. The
scaling factor of ABL was calculated deterministically from the integral length scale [9], which
was 1/390. The velocity scale was 1/5, which means that the target Mean wind velocity was
30.53 m/s at the roof height in full scale. The Reynolds number was set, considering its critical
value [10]. The Reynolds number of an experiment ranged from 4.4 × 104 to 8.9 × 104,
depending on the direction of the wind, thus a characteristic dimension of the model.
The models were fixed to the 6-axis force and torque sensor Nordbo Robotics NRS-6050-D50
[11]. The force sensor was strongly screwed into the model with 6 screws, so the movement of
the model could be transferred to the sensor. Figure 2 illustrates the position of the force sensor
in the wind tunnel. Various bearing systems of the force sensor were used to turn the table to
ensure accurate results. The results achieved were compared with measurements made by other
authors. The partial goal was to calibrate and find the bearing system method that could partially
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SSP - JOURNAL OF CIVIL ENGINEERING Vol. 17, Issue 1, 2022
dampen the vibration from the wind tunnel and the vortex-induced vibration from the measured
model.
Figure 1: Mean wind velocity (umean) and turbulence intensity (lu) profile
Figure 2: Position of the force sensor and arrangement in the wind tunnel
3 Experimental Model
The experimental model was made from PLA using the 3D printing technique. The dimensions
of the cylinder were 77 × 154 × 180 mm (width × length × height). The model proportions take
into account the existing buildings in our location. Based on the proportions, the aspect ratio
was 0.5 (1/2). The scaling factor of the model had to be chosen equal to the ABL scaling, which
was 1/390. The model was rotated from 0 to 90° to the wind with rotation increments of 10°.
Three configurations were used to obtain correct results and calibrate with other measurements
[12]. The first was the PLA bearing plate, the second was the steel plate, and the third was the
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Franek M., Macák M, and Hubová O.
steel plate with a damper in the model. As a damper, the sand filling integrated into the model
was chosen.
4 Aerodynamics Coefficients
The main goal was to determine the aerodynamic coefficients on the 180 mm high tower with
an elliptical cross-section with an aspect ratio of 0.5. The arrangement and wind direction
scheme is illustrated in Figure 3. The model was rotated by 10° steps. The drag coefficient cd
was given as:
2 ∙ 𝐹𝑑
𝑐𝑑 = 𝜌 2
∙𝑣𝑟𝑒𝑓 ∙ 𝐴𝑟𝑒𝑓
(1)
𝑎𝑖𝑟
where cd is the drag coefficient in [-], Fd is the mean drag force in the wind direction in [N], ρair
is the air density in [kg/m3] at the temperature of 18 °C, vref is the reference wind velocity in the
aerodynamic center at 2/3 of the height of the model and Aref is the projected reference area
perpendicular to the wind direction in [m2].
The lift coefficient cl was also measured and given as:
2∙𝐹
𝑐𝑙 = 𝜌 ∙𝑣2 𝑙 𝐴 (2)
𝑎𝑖𝑟 𝑟𝑒𝑓 𝑟𝑒𝑓
where cl is the lift coefficient in [-], Fl is the mean lift force perpendicular to the wind direction
in [N], ρair is the air density in [kg/m3], vref is the reference wind velocity in the aerodynamic
center at 2/3 of the height of the model and Aref is the projected reference area perpendicular to
the wind direction in [m2].
Figure 3: The footprint of the tested tower and the directions of the drag (cd) and lift (cl) coefficient
4.1 Calibration for Alternative Bearing System
The first step was to compare existing works with our results to ensure the relevant results and
analysis. Our measurements had 3 configurations, as was mentioned in the previous chapter.
For the comparison, the publication by Takeuchi et al. [12] was chosen. Their research evaluated
the cylinder with an elliptical cross-section with the same aspect ratio. The difference was
between the approaching flow. In their research, steady approaching flow with the short-rise-
time gusts in the rear section was used. The comparison in Figure 4 showed adequate similarity
with the steel plate configuration with sand filling. The results were statistically verified. The
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correlation coefficient for the third configuration was 0.991. A minor variation was caused by
the approaching flow and roughness of the model, which is common knowledge. Based on the
comparison, it could be claimed that the steel bearing plate with the sand filling was adequate
for further analysis of the drag and lift coefficient of the elliptical cylinder.
PLA Steal Steal with sand Takeuchi et al. 2009
2.6
2.4
2.2
2
1.8
1.6
cd [-]
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 10 20 30 40 50 60 70 80 90
a) wind direction [°]
PLA Steal Steal with sand Takeuchi et al. 2009
4.4
4
3.6
3.2
2.8
2.4
cl [-]
2
1.6
1.2
0.8
0.4
0
0 10 20 30 40 50 60 70 80 90
b) wind direction [°]
Figure 4: Comparison of variation of mean force coefficients with Takeuchi et al. [12]: a) drag
coefficient, b) lift coefficient
5 Results and Discussion
5.1 Mean and Fluctuating Drag and Lift Coefficient
The drag and lift coefficients were measured in the time domain, where the sampling frequency
was set to 100 Hz. Each measurement was set to 10 seconds in duration. Coefficients were
treated by the mean and fluctuating values. The mean value of the coefficient was obtained as
a time-averaging value. The fluctuating value of the coefficient was obtained as a root mean
square value. The results were processed into graphs depending on the incident wind, illustrated
in Figures 5 and 6.
The mean value of the drag coefficient varied fundamentally according to the direction of the
wind. From the perspective of the minimum value of the drag force, the ideal wind direction
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Franek M., Macák M, and Hubová O.
was 0 to 15°. It was expected because the area exposed to the wind was the smallest in these
directions. The maximum value of the drag force was expected for the direction of the wind at
90°, where the exposed area was the largest. An interesting phenomenon occurred when the
wind direction was between 30 and 45°. The most significant increase in the drag coefficient cd
occurred from the value of 0.34 to the value of 0.68. A similar phenomenon occurred for
fluctuating values. It could have been caused by flow separation, asymmetrical vortices
structures on the sides of the elliptical building, and wake instabilities. Maximum fluctuations
occurred for wind direction of 90°. It was caused by the maximum drag force occurring in this
direction, generated by the vibrations of the model.
The mean value of the lift coefficient had a different profile than the drag. The minimum value
occurred for wind directions 0 and 90°, where the value approached zero. It could have been
caused by the stable flow structure without asymmetrical vortices. The maximum lift coefficient
occurred around the wind direction of 20 and 30°. Here, we can state that the phenomenon of
the generation of asymmetrical vortices structures and wake instabilities caused it. A similar
profile of the lift coefficient was observed for the fluctuating value. The maximum force made
the vibration go in the same direction.
1.1
1
0.9
0.8
0.7
cd [-]
0.6
0.5
0.4
0.3
0.2
0.1
0
0 10 20 30 40 50 60 70 80 90
a) wind direction [°]
0.16
0.14
0.12
0.1
cd,fluc [-]
0.08
0.06
0.04
0.02
0
0 10 20 30 40 50 60 70 80 90
b) wind direction [°]
Figure 5: Variation of drag coefficients: a) mean, b) fluctuating
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1.4
1.2
1
0.8
cl [-]
0.6
0.4
0.2
0
0 10 20 30 40 50 60 70 80 90
a) wind direction [°]
0.22
0.2
0.18
0.16
0.14
cl,fluc [-]
0.12
0.1
0.08
0.06
0.04
0.02
0
0 10 20 30 40 50 60 70 80 90
b) wind direction [°]
Figure 6: Variation of lift coefficients: a) mean, b) fluctuating
6 Conclusions
This article aimed to find the appropriate method to evaluate and measure the drag and lift
coefficient with the force sensor. The main goal was to analyze the free-standing building with
the elliptical cross-section for various wind directions. Subsequently, find out the
maximum/minimum or optimal/critical value of the drag and lift force.
From the results, the conclusions are as follows:
- the optimal bearing system for the force sensor resulting from the verification with other
work [12] was the steal bearing with the sand filling in the model,
- the value of drag and lift coefficient varied fundamentally according to the wind
direction,
- the maximum drag occurred in the wind direction of 90°,
- minimum drag occurred in the wind direction of 10°,
- maximum lift occurred in the wind direction at 30°,
- minimum lift occurred in the wind direction 0°,
- fluctuating coefficients had similar profiles and copied the maximum and minimum
wind-induced forces,
- taking into account the overall forces, the optimal wind direction was 0°,
- the inappropriate wind directions were around 30°,
- the inappropriate phenomenon was caused by the generation of asymmetrical vortices
structures and wake instabilities.
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Franek M., Macák M, and Hubová O.
For a better understanding of this phenomenon, future research will suggest additional
measuring methods with the help of Computational Fluid Dynamics. To get an overall view of
the wind-induced force on the elliptical cylinder.
Acknowledgments
This work was supported by the Scientific Grant Agency MŠVVŠ SR and SAV under VEGA 1/0113/19.
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