Influence of turbulence integral length scale on aerostatic coefficients of bridge sections

Abstract

This study investigates the influence of turbulence on the aerostatic coefficients of typical bridges by obtaining force measurements via the simulation of turbulence in wind tunnels. The traditional simulation method for turbulence based on spires and grilles cannot be employed for the accurate simulation of the large integral scale of turbulence in an actual wind field. Thus, in this study, the turbulence integral length scale was effectively increased using an active control grid. The wind fields of different turbulence integral scales were generated by controlling the vibration frequency of the active control grid. The aerostatic coefficients of five typical bridge sections (single-box girder, twin-box girder, truss girder, edge girder, and edge-box girder) were measured under turbulent and uniform flow. The test results were compared and analyzed, which revealed that the drag coefficients increased in accordance with a decrease in the reduced turbulence integral length scale, and they were lower under turbulent flow than under uniform flow.

Keywords

active control grid aerostatic coefficients turbulence turbulence integral length scale wind field

Introduction

In recent decades, with the development of design concepts and construction technology, a significant number of long-span bridges have been constructed (Ge and Xiang, 2011; Yi et al., 2013; Zhu, 2005), as shown in Table 1. However, with an increase in the bridge span, the flexibility of the structure increases, which enhances the wind load effects on the bridge structure. Wind-resistant stability has been considered as critical to the design of long-span bridges since the collapse of the Tacoma Narrows Bridge. Static wind load can be described using aerostatic coefficients, which are a set of dimensionless parameters that serve as a basis for the evaluation of aerodynamic problems in bridges (Chen, 2005). The aerostatic coefficients of bridge decks are critical parameters for the characterization of their aerostatic characteristics and the estimation of the structural buffeting, galloping, and flutter. Costa (2007) and Hatanaka and Tanaka (2002) used the step function and Theodorsen function to establish a relationship between the flutter derivative and aerostatic coefficients. Fung (2008) assumed that the wing exhibits a simple harmonic movement, and then used a Theodorsen function to derive the relationship between the modified flutter derivative and the aerostatic coefficients. In addition, Simiu (2012) determined the relationship between the aerostatic coefficients and the flutter derivative based on Scanlan estimation. Acampora et al. (2014), Lin et al. (2019), and Nikitas et al. (2011) investigated aeroelastic parameters using full-scale ambient vibration measurements and wind tunnel tests. Thus, it is necessary to accurately determine the aerostatic coefficients and investigate their influence. For thin plates, the aerostatic coefficients vary linearly with respect to the angle of attack before stalling, and theoretical formulations have been proposed accordingly. However, for abstract bridge-deck sections, there is no theoretical formulation for the quantification of the aerostatic coefficients (Ying et al., 2018). Thus, wind-tunnel tests and computational fluid dynamics (CFD) numerical simulations are two methods employed for the determination of the aerostatic coefficients (Bruno et al., 2003). Wind-tunnel tests are more extensively used for the investigation of three-dimensional (3D) and complex wind-induced phenomena. In China’s Wind-Resistant Design Specification, the aerostatic coefficients are obtained under uniform flow based on wind tunnel tests (JTG/T D60-01– 2004). Moreover, a significant number of wind-tunnel tests were conducted to determine the aerostatic coefficients of section models with respect to various angles of attack (Boonyapinyo et al., 2006; Diana et al., 2013; Hui et al., 2008).

Table 1.

Recently constructed bridges with main spans of over 1000 m.

Name	Main span (m)	Construction time (year)
Xihoumen suspension bridge	1650	2007
Gwangyang suspension bridge	1545	2012
Hong Kong Stonecutters cable-stayed bridge	1018	2009
Yangsigang Yangtze river bridge	1700	2019

Previous research on the influencing factors of aerostatic coefficients is mainly focused on the bridge shape, the Reynolds number, and aerodynamic interference. Xu et al. (2014) analyzed the influence of the bridge shape on the aerostatic coefficients based on a significant number of wind tunnel tests and numerical simulations. Moreover, the influence of the Reynolds number on the aerostatic coefficients has received significant research attention (Hearst and Lavoie, 2012; Zhou and Ma, 2010). Irwin (2005) and Kimura (2008) investigated the influence of aerodynamic interference on the aerostatic coefficients based on wind tunnel tests. However, several studies were conducted on the influence of turbulence on the aerostatic coefficients. This is because the current methods employed for the accurate simulation of near-Earth turbulence based on wind tunnel tests and CFD are limited.

Until now, no comprehensive or in-depth fluid motion model has been established due to its complexity, especially with respect to turbulent motion. Moreover, due to the complexity of the Navier–Stokes equations, it is difficult to develop an accurate model based on theoretical analysis or numerical simulation. Therefore, wind tunnel tests are generally conducted for the investigation of turbulence. At present, the simulation of turbulence is mainly dependent on traditional methods, such as spires and grilles, with respect to the average wind speed, turbulence intensity, and pulsating wind spectrum, among other parameters (Li et al., 2020; Ma et al., 2019; Ozono et al., 2007). The turbulence integral length scale represents the measurement of the average size of the turbulence vortices in the air flow (Wang et al., 2019). The influence of the fluctuating wind effect on the bridge is significantly dependent on the size of the turbulence integral length scale. However, the turbulence integral length scales of the traditional simulation methods are very small, with sizes of approximately 5–20 cm in wind tunnels. In addition, the integral turbulence length scales in actual bridges are generally within several tens or hundreds of meters (Ma et al., 2019). The results of the studies conducted by Larose (1999) and Li et al. (2020) on aerodynamic admittance under turbulence reveal that turbulent flow field simulations in the wind tunnels typically do not generate large-scale vortices, thus yielding low aerodynamic admittances in the low-frequency band. Larose compared the flutter derivatives of the large-band East Bridge under passive grid turbulence and boundary layer turbulence, and found that the flutter derivatives of the two wind fields at the same turbulence intensities were significantly different, thus indicating that the turbulence integral length scale has a significant influence on the flutter derivatives. The results reveal that the turbulence integral length scale has a relatively significantly influence on the aerodynamic characteristics of bridges. The turbulence integral length scale has received significant research attention; however, it is difficult to simulate large turbulence integral length scales in experiments. To overcome this limitation, a frequency conversion fan array and rotating grid are generally employed. Fan wind tunnels were set up at the University of Miyazaki in Japan, and rotating grids were constructed at Hunan University in China for use in typical cases (Han, 2007). Current research on active control grids is mainly focused on changing and controlling the turbulence flow conditions and flow field characteristics, especially with respect to the turbulence intensity, and turbulence integral length scale (Hearst and Lavoie, 2012; Hideharu, 1991; Poorte and Biesheuvel, 2002). However, due to the limitations of fan wind tunnels, which include high costs and complex technology, active control grids have recently received significant research attention. In this study, an active control grid system was developed to increase the size of the turbulence integral length scale in wind tunnel tests.

To investigate the influence of the turbulence integral length scale on the aerostatic coefficients of bridge sections, this paper presents a low-cost method for the generation of a large turbulence integral length scale. The aerostatic coefficients of five typical bridge sections under uniform flow and turbulence were measured with respect to different turbulence integral length scales, which were generated by the different vibration frequencies of the grid. The five typical bridge sections are as follows: single-box girder section, twin-box girder section, truss-girder section, edge-girder section, and edge-box girder section. The findings of this study can serve as the basis for research on the influence of the turbulence integral length scale on bridge flutter and buffeting, in addition to future research based on wind-tunnel tests. The remainder of the paper is organized as follows. Section 2 presents the active control grid and wind field test, followed by details of the aerostatic coefficient test in Section 3. In Section 4, a discussion on the aerostatic coefficient results is presented, followed by the conclusions in Section 5.

Wind field test

Active control grid

An active control grid mainly consists of five independent airfoils, a connecting rod, and a servo motor. Compared with a blunt body, the airfoil does not generate flow separation, thus resulting in 3D turbulence in the downstream wind field. The connecting rod connects the airfoils to the motor, and the motor results in reciprocal movement of the airfoils in up-and-down rotation. The airfoils have a length of 2 m and the chord has a length of 0.35 m, as shown in Figure 1. By inputting commands into the console, the servo motor can be used to drive the connecting rod for operation according to the set frequency. The driving airfoils of the connecting rod then vibrate at a fixed frequency, thus generating turbulent wind. The vibration frequency of the active control grid is determined by the motor rotation frequency. Assuming that the motor completes one rotation each second, the active control grid has a vibration frequency of 1 Hz, where “vibration frequency” refers to the oscillations of the airfoils in this paper. The range of the vibration frequency is 0.3–1.8 Hz.

Figure 1.

Image of active control grid: (a) service stage, (b) overall design diagram, (c) close-up airfoil view, and (d) airfoil schematic.

Wind field test

For the investigation of the wind field generated by the active control grid, a series of wind field experiments was conducted. These wind tunnel tests were conducted in the second test section of the XNJD-1 wind tunnel (see Figure 2), which is a closed-circuit low-speed wind tunnel located at Southwest Jiaotong University, China. The test section has a width and height of 2.4 m and 2 m, respectively. The wind speed can be adjusted from 1 m/s to 45 m/s. The quality of the flow field is very stable, and the longitudinal and transversal turbulence intensity of the empty wind tunnel is less than 0.5%, on average, according to its performance report (Wu et al., 2020).

Figure 2.

Partial view of XNJD-1 wind tunnel: (a) floor plan, (b) image, and (c) schematic of active control grid.

The flow velocities were measured using a Cobra Probe (TFI, Australia) located at the leading-edge of the model. The probe employed was a multi-hole pressure probe that can resolve three components of the flow velocity, with a frequency response of 0–2 kHz. Moreover, the probe can be used to conduct multiple-channel synchronous measurements and output wind speed time history data. The built-in probe software then generated statistical data with respect to the measured mean wind speed and fluctuating velocities. To obtain accurate measurements of the simulated turbulence flow field, three probes of the same type were employed. The layout of the test is shown in Figure 3, where the model placement point shown in Figure 3(c). The distance between the model and the active control grid is 2.4 m, and the specific ground distance of the wind tunnel is 1.2 m. An image of the test setup is shown in Figure 4.

Figure 3.

Sketch of wind field test layout: (a) horizontal measurement point, (b) vertical measurement point, and (c) longitudinal measuring point and model placement point.

Figure 4.

(a, b) Image of the wind field test setup, and (c) probe equipment.

Results and analysis

Turbulent flow characterization

The time history and turbulence spectrum of the wind speed generated by the active control grid for simple harmonic motion are shown in Figure 5. The vibration frequency of the active control grid is 1 Hz, and similar results were obtained for different vibration frequency levels. The incident wind velocity does not change during the entire test, and at the same time guarantees the stability of the power supply. The mean horizontal wind speed is 6.5 m/s, as shown in Figure 5(a). The vertical turbulence component primarily consists of one harmonic component, as shown in Figure 5(c). The energy in the vertical wind direction is concentrated at 1 Hz, as shown in Figure 5(d).

Figure 5.

Characteristics of wind field at 1 Hz: (a) mean horizontal wind speed, (b) transverse component of the wind velocity vector, (c) vertical component of the wind velocity vector, and (d) Fourier transform amplitude spectrum of pulsating component.

Turbulence intensity

The turbulence intensity with respect to different wind speeds, heights, and airfoil frequencies were measured in this test to fully determine the turbulence characteristics.

I_{α} = \frac{σ_{α}}{U}

(1)

where $I_{α}$ is the turbulence intensity, α is the direction of fluctuating wind, $σ_{α}$ is the variance of the pulsating wind speed, and $U$ is the mean wind speed of the directional wind component.

The vertical turbulence intensity increased in accordance with an increase in the height within the range of 110–130 cm, as shown in Figure 6(a). The turbulence intensity increased in accordance with an increase in the wind speed in the low-frequency region; whereas in the high-frequency region, the turbulence intensity decreases and then increases in accordance with an increase in the wind speed. Moreover, it should be noted that the turbulence intensity in the low-frequency vibration region rapidly increased in accordance with an increase in the vibration frequency; the turbulence intensity in the high-frequency region gradually decreased in accordance with an increase in the vibration frequency, followed by an increase. In the horizontal direction, the turbulence intensity varied with respect to the vibration frequency; however, the turbulence intensity with respect to different heights was consistent with the variations in the vibration frequency, as shown in Figure 6(b). The turbulent wind field was uniform at different vibration frequencies and heights, as shown in Figure 6.

Figure 6.

Turbulence intensity with respect to vibration frequency of active control grid: (a) vertical measurement point and (b) transverse measurement point.

Turbulence integral length scale

In the traditional passive turbulent wind field, the turbulence integral length scale is based on the frozen turbulence hypothesis, and the calculation method is as follows:

L_{u}^{x} = \frac{1}{σ_{u}^{2}} \int_{0}^{\infty} R_{u_{1} u_{2}} (x) dx

(2)

where $R_{u_{1} u_{2}} (x)$ is the cross-correlation function of $u_{1}$ and $u_{2}$ , and $σ_{u}^{2}$ is the variance of the wind speed.

The flow field simulated by the probe based on the collected pulsating wind speed time history and pulsating wind spectrum curve can be approximated as a sinusoidal pulsating flow field with a single frequency; thus, it cannot be calculated based on the frozen turbulence assumption. For a special flow field, such as the sinusoidal uniform flow field in this study, the size of the vortex can be measured based on the wavelength of the vortex (Hinze, 1959); thus, based on the Hinze’s work, the turbulence integral length scale can be expressed as follows:

\begin{matrix} L_{u}^{x} = U \cdot T \\ T = 1 / f \end{matrix}

(3)

where $L_{u}^{x}$ is the turbulence integral length scale, T is the period, and $f$ is the vibration frequency of the airfoils.

The test results are shown in Figure 7. The size of the turbulence integral length scale of the wind field was larger at high wind speeds. In the low-frequency vibration region, with an increase in the vibration frequency, the size of the turbulence integral length scale of the wind field rapidly decreased. However, in the high-frequency vibration region, with an increase in the vibration frequency, the turbulence integral length scale of the wind field gradually decreased. The values were plotted with respect to the reduced velocity V^*, as shown in Figure 7(a), which is defined as $V^{*} = U / (fB)$ , where U is the mean horizontal velocity magnitude, and B is the model chord length. Moreover, in the absence of a model, B = 1 m. The turbulence integral length scale increased in accordance with an increase in the reduced velocity, as shown in Figure 7(b).

Figure 7.

Turbulence integral length scale with respect to vibration frequency and reduced velocity.

Aerostatic test

An industrial wind tunnel (XNJD-1) was used at Southwest Jiaotong University for the investigation of the static wind loading, lift, drag, and moment, as shown in Figure 8. The test section was equipped with a rig and force balance system for the static wind loading testing of the bridge section. The attack angle of the model installed on the rig was adjustable from −20° to 20°, with a minimum increment of 0.1°.

Figure 8.

Aerostatic test system.

The force balance employed was a strain gauge with three components: lift, drag, and moment, with maximum load ranges of ±50 kg, ±120 kg, and ±12 kg, respectively. In the test results section, we show a 95% confidence interval for the drag coefficients.

The five typical bridge models were all based on actual bridges, and the model scales were 1:40. The model sizes are listed in Table 2, and the models are shown in Figure 9.

Table 2.

Model sizes.

	Single-box girder (m)	Twin-box girder (m)	Edge-box girder (m)	Edge girder (m)	Truss girder (m)
Length	2.09	2.09	2.09	2.09	2.09
Width	0.71	0.75	0.66	0.67	0.55
Height	0.058	0.06	0.07	0.068	0.15

Figure 9.

Sketches of the test model sections: (a) single-box girder, (b) twin-box girder, (c) edge-box girder, (d) edge girder, and (e) truss girder.

Each section model was directly installed on the force test system. End plates were set at both ends of the model, and the force measurement system was placed outside the tunnel wall to prevent interference from the flow field. The probe was set at the front of the model to monitor the wind speed at the bridge location.

To investigate the influence of turbulence on the aerostatic coefficients of the bridge sections, five bridge models were employed for force tests under uniform flow and turbulence. In the wind tunnel test, the turbulence integral length scales were 7.3 m, 8 m, 12.4 m, and 17.4 m, respectively. In the aerostatic coefficient tests, two wind speeds were set (6.8 m/s and 8.7 m/s), which were also employed in the uniform flow test. The wind speed was 8.7 m/s in the turbulence flow test, and the frequencies of the active control grid were set at 0.5 Hz, 0.7 Hz, 1.0 Hz, and 1.2 Hz. The attack angles were set at −5°, −3°, 0°, +3°, and +5°. In the uniform flow test, the collection time was set at 30 s, and the turbulent wind speed was random. To obtain the mean wind speed and force from the statistical data, the data sample time under the turbulence condition was set at 100 s, and the wind speed and force under turbulence were measured simultaneously. The selection of 100 s was determined by performing the same experiment at 30 s, 50 s, 80 s, 100 s, 120 s, 150 s, and so on. According to the data coincidence under a 99% confidence interval comparison, as shown in Figure 10, when the experiment lasted longer than 80 s, the data tended to stabilize. Thus, we chose 100 s to ensure the stability of the data, and to save test time and cost. Given that the frequency of the vortex shedding in the model can exceed 20 Hz, the data acquisition frequency of the force test was set at 256 Hz. The data was collected after stabilization of the test conditions. The operating conditions are listed in Table 3, and the test conditions are shown in Figure 11.

Figure 10.

Variation of data coincidence with test time (99% confidence interval).

Table 3.

Test conditions.

No measures	Single-box girder	Twin-box girder	Edge-box girder	Edge girder	Truss girder
	Uniform flow	Uniform flow	Uniform flow	Uniform flow	Uniform flow
Active control grid	0.5 Hz/7.3 m	0.5 Hz/7.3 m	0.5 Hz/7.3 m	0.5 Hz/7.3 m	0.5 Hz/7.3 m
	0.7 Hz/8 m	0.7 Hz/8 m	0.7 Hz/8 m	0.7 Hz/8 m	0.7 Hz/8 m
	1 Hz/12.4 m	1 Hz/12.4 m	1 Hz/12.4 m	1 Hz/12.4 m	1 Hz/12.4 m
	1.2 Hz/17.4 m	1.2 Hz/17.4 m	1.2 Hz/17.4 m	1.2 Hz/17.4 m	1.2 Hz/17.4 m

Figure 11.

Aerostatic coefficient test under uniform flow and turbulence: (a) truss girder under turbulent flow, (b) edge-box girder under uniform flow, (c) twin-box girder with −5° attack angle, and (d) truss girder with +3° attack angle.

The aerostatic force that acts on the section of the girder differs, and is dependent on the coordinate system used. In particular, there are two types of coordinate systems, namely, the body coordinate system and the wind coordinate system, as shown in Figure 12. The aerostatic coefficients for the wind coordinate system are defined as follows:

C_{D} (α) = F_{D} (α) / (\frac{1}{2} ρ U^{2} HL)

C_{L} (α) = F_{L} (α) / (\frac{1}{2} ρ U^{2} BL)

C_{M} (α) = M_{Z} (α) / (\frac{1}{2} ρ U^{2} B^{2} L)

(4)

where $α$ is the angle of attack of the incoming flow; $\frac{1}{2} ρ U^{2}$ is the pressure of the incoming flow; $F_{D} (α)$ , $F_{L} (α)$ , and $M_{Z} (α)$ are the drag, lift, and moment on the deck in the wind coordinate system; and $H$ , $B$ , and $L$ are the height, width, and length of the model, respectively.

Figure 12.

Body coordinate system and wind coordinate system.

Results and discussion

The aerostatic coefficients of five typical bridge models under four vibration frequencies of the active control gird were compared with those under uniform flow. This study presents the aerostatic coefficients using only the wind coordinate system. Moreover, the drag coefficients at an angle of attack of 0° were separately compared. The aerodynamic characteristics of structures under turbulent flow are closely related to the turbulence integral length scale and the width of the structures. The values were plotted as a function of the reduced integral length scale L^*, which is defined as $L^{*} = L_{u}^{x} / B$ , where B is the model chord length, as displayed in Table 2.

Single-box girder

As shown in Figure 13(a), the drag coefficients of the uniform flow were the largest, and the drag coefficients under turbulence increased in accordance with an increase in the reduced turbulence length integral scale. This is because with an increase in the size of the reduced turbulence integral length scale (and decrease in the turbulence intensity), there was an increase in the correlation between the forces acting on the bridge deck, and the forces increased. The lift coefficients and moment coefficients varied slightly with respect to the reduced turbulence integral length scale, and no consistent trend was observed. As shown in Figure 13(d), the drag coefficients increased in accordance with an increase in the reduced turbulence length integral scale at an attack angle of 0°, and the drag coefficients were largest under uniform flow.

Figure 13.

Aerostatic coefficients of single-box girder: (a) drag coefficients, (b) lift coefficients, (c) moment coefficients, and (d) drag coefficients at attack angle of 0°.

Twin-box girder

As shown in Figure 14, the drag coefficients of the twin-box girder under uniform flow were the largest. The variation trend of the resistance coefficient of the twin-box girder under turbulent flow was different from that of the single-box girder, and the drag coefficients did not increase in accordance with an increase in the size of the reduced turbulence length integral scale under turbulence. Due to the central slot of the twin-box girder with respect to the passage of the vortex across the bridge, flow separation and reattachment occurred, which influenced the response of the bridge. Kwok (2012), Ma et al. (2018), and Zhu and Xu (2014) investigated the aerodynamic characteristics of twin-box girder bridges based on wind tunnel tests and particle image velocimetry (PIV) measurements. The test results revealed that the upstream vortex in the twin-box girder has an influence on the downstream deck. The moment coefficients did not exhibit a consistent trend with respect to the changes in the size of the reduced turbulence integral length scale. The lift coefficient of the twin-box girder was significantly larger under a uniform flow than under a turbulence flow. As shown in Figure 14(d), the rate of change of the drag coefficients decreased in accordance with an increase in the size of the reduced turbulence integral length scale from 9.73 to 10.67, and the drag coefficients gradually decreased in accordance with an increase in the size of the reduced turbulence integral length scale from 10.67 to 23.2.

Figure 14.

Aerostatic coefficients of twin-box girder: (a) drag coefficients, (b) lift coefficients, (c) moment coefficients, and (d) drag coefficients at angle of attack of 0°.

Edge-box girder

As shown in Figure 15, the drag coefficients of the uniform flow were the largest, and the drag coefficients under turbulence increased in accordance with an increase in the size of the reduced turbulence integral scale. The lift coefficients and moment coefficients varied slightly in accordance with an increase in the size of the reduced turbulence integral length scale, and no consistency was observed. As shown in Figure 15(d), the drag coefficients increased in accordance with an increase in the size of the reduced turbulence integral length scale at a 0° angle of attack, and the drag coefficient values were largest under uniform flow.

Figure 15.

Aerostatic coefficients of edge-box girder: (a) drag coefficients, (b) lift coefficients, (c) moment coefficients, and (d) drag coefficients at angle of attack of 0°.

Edge girder

As shown in Figure 16, the drag coefficients were larger under uniform flow than under turbulence flow, and they increased in accordance with an increase in the size of the reduced turbulence integral length scale. Due to the grooves on the bottom-side of the girder, the aerostatic coefficients were more dependent on the turbulence when there were variations in the attack angle. The lift coefficients and moment coefficients varied slightly with respect to variations in the reduced turbulence integral length scale, and no consistency was observed. As shown in Figure 16(d), the drag coefficients increased in accordance with an increase in the size of the reduced turbulence integral length scale at an attack angle of 0°, and the drag coefficients were larger under uniform flow than turbulent flow.

Figure 16.

Aerostatic coefficients of edge girder: (a) drag coefficients, (b) lift coefficients, (c) moment coefficients, and (d) drag coefficients at angle of attack of 0°.

Truss girder

As shown in Figure 17, the drag coefficients under uniform flow were largest, and the drag coefficients under turbulence increased in accordance with an increase in the size of the reduced turbulence integral length scale. Moreover, no consistent variation trend was observed for the lift coefficients or moment coefficients. Due to the complex structure of the truss girder, the aerostatic coefficients were significantly influenced by turbulence when the angle of attack was varied. As shown in Figure 17(d), the drag coefficients increased in accordance with an increase in the size of the reduced turbulence integral scale at an attack angle of 0°, and they were larger under uniform flow than under turbulent flow.

Figure 17.

Aerostatic coefficients of truss girder: (a) drag coefficients, (b) lift coefficients, (c) moment coefficients, and (d) drag coefficients at angle of attack of 0°.

With respect to different attack angles, the influence of turbulence on the aerodynamic coefficients was different. There are two important reasons for the additive attack angle and the aerodynamic shape change. The turbulence flow was found to have a more significant influence on the drag coefficient at large attack angles with respect to the twin-box and the truss girders. For the case of the edge-box girder, turbulent flow was found to have a more significant effect on the drag coefficient at small attack angles. Moreover, for different girders, with an increase in the size of the reduced turbulence integral length scale, the influence of turbulence on the drag coefficient decreased.

Most of the results revealed that at an angle of attack of 0°, the gradient of the drag coefficient curve varied in accordance with changes in the reduced integral scale. This can be mainly attributed to the force measurement system used in this experiment, which can be used to calculate the average forces, but not the instantaneous forces. Moreover, the additive attack angle should not be ignored.

Conclusion

Under the existing experimental conditions, it was difficult to achieve a large turbulence integral length scale. In this study, large-scale turbulence was generated in the wind tunnel using the developed active control grid. Based on the active control grid, the aerostatic coefficients of typical bridge sections under turbulence flow were investigated. Overall, the aerostatic coefficients were influenced by the turbulent flow. The conclusions can be summarized as follows:

Based on the test results, the aerostatic coefficients under turbulent flow were different from those under uniform flow. The turbulence had an influence on the aerostatic coefficients of the bridge. The drag coefficients were larger under uniform flow than under turbulent flow.

The drag coefficients of the bridges at an angle of attack of 0° were compared in detail. In particular, the drag coefficients were largest under uniform flow, and they decreased in accordance with an increase in the size of the reduced turbulence integral scale. Furthermore, the results revealed the practicability of the determination of aerostatic coefficients under uniform flow.

The turbulence integral length scale was found to have an influence on the magnitude of the static coefficient and the aerodynamic performance of girders, which includes fluttering and buffeting, as verified in numerous studies (Lin et al., 2019; Yang et al., 2019).

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (grant number 51778545) and Science and Technology Projects of Power China (grant number SCMQ-201728-ZB).

ORCID iD

Cunming Ma

Supplemental material

Supplemental material for this article is available online.

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