Optimizing vortex-induced vibration suppression in π-shaped girders using wind tunnel testing and CFD analysis

Abstract

This investigation meticulously explores the vortex-induced vibration (VIV) characteristics in Π-shaped girders within long-span cable-stayed bridges, presenting novel VIV mitigation techniques. Employing detailed wind tunnel evaluations of a 1:50 scale model alongside computational fluid dynamics (CFD) analyses to model the two-dimensional flow around the girder, this study reveals the formation and shedding of vortices behind the railings and main steel girder, which significantly contribute to VIV in such structures. The introduction of horizontal splitter plates, one m in width, in conjunction with two-m-wide V-shaped guide vanes, was found to substantially reduce the VIV amplitude of the Π-shaped girder, minimizing vortex generation on the deck’s sides and dramatically reducing the maximum vertical VIV amplitude from 208.75 mm to only 5.56 mm. CFD simulations confirm the effectiveness of these measures in suppressing Karman vortex street formation, thereby significantly improving downstream airflow characteristics. These findings offer pivotal insights for the advancement of bridge design and the proactive management of VIV, showcasing the potential of integrated aerodynamic modifications to enhance structural resilience and performance.

Keywords

Cable-stayed bridges vortex-induced vibration Π-shaped girders wind tunnel test computational fluid dynamics aerodynamic optimization

Introduction

In recent years, advancements in design theory and construction technology have given rise to the development of modern bridges, with long-span bridges gaining worldwide recognition for their increased flexibility and expanded spans. However, these innovations have also introduced challenges related to wind-induced vibrations attributable to trends toward lower natural frequencies of vibration and decreased torsional stiffness. Π-Shaped girders are commonly used in bridge building due to their low weight, simple construction, and superior load-bearing capabilities. Famous examples include the Millau Viaduct in France; the Hong Kong-Zhuhai-Macao Bridge and the Sutong Yangtze River Bridge in China; and the Pont de Normandie in France. In contrast to closed box girders, the bluff body shape of Π-shaped girders amplifies the effects of flow separation and vortex shedding, making them more pronounced and intricate (Qian et al., 2015).

As fluid flows past bluff bodies like bridges or buildings, it generates a series of vortices in the wake. Vortex shedding occurs when the frequency of vortex formation synchronizes with a bluff body’s natural oscillation, inducing significant structural vibrations (Battista and Pfeil, 2000; Frandsen, 2001; Fujino and Yoshida, 2002; Huergo et al., 2022; Qian et al., 2015; Wu et al., 2022). When the natural frequency of the structure matches the frequency of the airflow, regular vortex shedding occurs in the wake region of the airflow. This alignment leads to self-excited and self-limiting wind-induced vibrations in the main girder. Vortex-induced vibration oscillation, a prevalent fluid-structure interaction, has garnered significant research interest in recent years (An et al., 2023; Chen et al., 2021a, 2021b; Duan et al., 2023; Hernandez et al., 2020; Ma et al., 2023; Nguyen et al., 2022; Sun et al., 2024; Wang et al., 2019; Wu et al., 2022; Yang et al., 2020; Zhang et al., 2019; Zhu et al., 2022).

The Great Belt East Bridge in Denmark (Frandsen, 2001; Larsen et al., 2000), the Tokyo Bay Bridge in Japan (Fujino and Yoshida, 2002), the Rio-Niteroi Bridge in Brazil (Battista and Pfeil, 2000), and the Xihoumen Bridge in China (Li et al., 2014; Yang et al., 2015), have all experienced vortex-induced vibration (VIV). On May 5, 2020, several VIV events were observed on the Humen Bridge in Guangdong, which caused widespread concern. VIV not only affects the comfort of people and vehicles passing through but also induces structural fatigue over time, which seriously affects the service life and safety of the bridge.

Measures to suppress vortex-induced vibrations primarily fall into two categories: structural and aerodynamic measures. Structural measures, such as increasing structural rigidity, damping, and added mass (Liu, 1995; Xian et al., 2009), are foundational yet often face limitations. These limitations arise due to the inability of such measures to directly change the natural frequency of the vortex forces, compounded by economic and maintenance challenges. In contrast, aerodynamic measures provide a more dynamic solution by optimizing the structure’s aerodynamic profile, which effectively mitigates vortex-induced vibrations (Xu et al., 2010). These methods are popular due to their structural simplicity, environmental friendliness, and high reliability. Expanding upon these methods, aerodynamic measures are classified into two-dimensional (2D) and three-dimensional (3D) approaches. The 2D measure focuses on modifying the cross-section shape of the main girder to enhance flow attachment and reduce fluid separation, thereby minimizing the generation and shedding of vortices. On the other hand, the 3D measure employs geometric distortions of the main girder or the addition of aerodynamic appendages, introducing a 3D disturbance to the wake. Aerodynamic measures currently applied in practical engineering are mainly 2D methods, including guide vanes, splitter plates, and wind noses (Fujino, 2013; Xin et al., 2021).

Strømmen and Hjorth (1995) introduced the idea of Vortex-Induced Vibration suppression by incorporating spoilers into the lower wedge angle of cross-sections. Hui et al. (2009a, 2009b) demonstrated through wind tunnel tests on the Stonecutters Bridge that placing guide vanes at the bottom of the girder could compress airflow, thereby disrupting the formation of large-scale vortices between the bridge boxes. Li (2008) established that the effectiveness of guide vanes in suppressing vortex generation significantly depends on their height, width, angle, and slot width. Qian et al. (2015) explored VIV control measures for Π-shaped bridge decks, finding that more acutely angled fairings could reduce vortex excitation. Li et al. (2018) observed that refining the fairing’s sharpness, without modifying the railing distance, enhances VIV mitigation. Larsen et al. (2008) concluded that the measure placement and sizing of guide vanes can lead to more uniform airflow around the girder corners, thereby improving the suppression of vortex-induced vibrations. Matsumoto (2008) suppressed vortex shedding by adding a flow splitter at the tail, thereby inhibiting vortex-induced vibrations. He and Li (2015) explored the impact of various aerodynamic measures on the vortex-induced vibration of box girders through wind tunnel experiments.

Previous studies have extensively explored various aerodynamic measures for mitigating vortex-induced vibrations in Π-shaped girder bridges. However, there is a lack of systematic comparative analysis between different measures of Π-shaped girder. Given this, our study conducted a comprehensive comparison of these measures and proposed a new type of combined vibration suppression method. Utilizing a 1:50 scale section model in wind tunnel experiments, we compared the effectiveness of different aerodynamic measures in reducing the amplitude of vortex-induced vibrations. Further, through Computational Fluid Dynamics (CFD) analysis, we investigated Π-shaped composite girder bridge sections equipped with various suppression measures, revealing the impact and mechanisms of these suppression measures on the surrounding flow field.

Vortex-induced vibration wind tunnel test

Engineering background

The section model used in this study is based on a cable-stayed bridge with two single-column bridge towers, spanning a total length of 714 m. The main span is 360 m, while the side spans are each 177 m. The stay cables are arranged in a spatial double-plane configuration and anchored on both sides of the main girder, as shown in Figure 1.

Figure 1.

Arrangement of bridge spans (unit: m).

The main girder has a composite structure consisting of a steel I-shaped girder and a concrete girder, with a width of 26 m and a height of 2.85 m (at the center of the steel I-shaped girder). The middle span of the main girder features a steel I-shaped girder section, which serves as the model for this study, as shown in Figure 2.

Figure 2.

Standard cross-section of the main girder (unit: cm).

Wind tunnel test setup

The wind tunnel tests were conducted in the second test section of the XNJD-1 Wind Tunnel at Southwest Jiaotong University. This test section has a maximum airflow velocity of 45 m/s and a minimum of 0.5 m/s, with the inflow turbulence intensity being less than 0.5% in an empty wind tunnel state. The section was equipped with a dynamic testing apparatus for bridge section models, consisting of eight springs suspended from a frame, forming a two-degree-of-freedom vibration system capable of vertical movement and rotation, as shown in Figure 3. The test frame was positioned outside the tunnel wall to avoid disturbing the airflow field, thus ensuring the accuracy of the experiments by preventing any wall interference with the airflow. The laser displacement sensors are installed on both sides of the model to measure the vibration displacements, with a sampling frequency of 256 Hz and a sampling duration of 16 s each. The wind speeds were meticulously measured using the TFI Cobra Probe, as shown in Figure 4. This instrument enables accurate determination of all three velocity components and static pressure.

Figure 3.

Schematic of freedom vibration system. (a) Suspension and measurement system of the section model, (b) Motion coordinate system of the section model.

Figure 4.

TFI cobra probe for measuring wind speed.

The section model of the main girder is geometrically scaled down to a 1:50 ratio, measuring 2.095 m in length, 0.520 m in width, and 0.057 m in height. According to the Wind-Resistant Design Specification for Highway Bridges (JTG/T 3360-01-2018), the damping ratio for steel-concrete composite bridges is set at 1%. To control the mass and moment of inertia of the model, ensuring sufficient rigidity, the main longitudinal girder of the model was made from aluminum strips, while the rest was constructed from high-quality wood and fiber-reinforced plastic sheets. Auxiliary components such as bridge guardrails, paving stones, and handrails were produced using engineering plastics and CNC milling machines. Boundary plates are installed at both ends of the section model to ensure uniform airflow, and the section model suspended in the wind tunnel is shown in Figure 5, with the wind tunnel test parameters parameters of the section model detailed in Table 1.

Figure 5.

Section model in the wind tunnel.

Table 1.

Wind Tunnel Test Parameters.

Parameter	Unit	Scaling	Prototype	Required value	Achieved value
Height	m	1/50	2.85	0.057	0.057
Width	m	1/50	26	0.52	0.52
Mass per unit length	kg/m	1/50²	38154	15.26	15.30
Mass moment of inertia	kg⋅m²/m	1/50⁴	3683728	0.5894	0.5908
Radius of rotation	m	1/50	9.8259	0.1965	0.1965
Vertical bending frequency	Hz	√50	0.3705	2.705	2.705
Vertical damping ratio	%	1	1	1	0.94
Torsional frequency	Hz	√50	0.625	4.548	4.548
Torsional damping ratio	%	1	1	1	0.90

The vortex-induced vibration tests were conducted in a smooth flow. Considering the wind environment characteristics at the bridge location, experiments were performed under five different angles of attack: α = −5°, −3°, 0°, +3°, and +5°. The test wind speed range was set from 0 to 6 m/s to ensure coverage of potential vortex-induced vibration lock-in wind speed range, with a wind speed increment controlled at 0.2 m/s. During the tests, two laser displacement sensors were used to measure the vertical and torsional vibration displacement responses of the section model under different test conditions. The test results were then scaled to the full-scale bridge structure according to the model scaling ratio, providing the displacement responses of the actual bridge under different wind attack angles and wind speeds.

Test result

According to Article 8.5.1 of the Wind-Resistant Design Specification for Highway Bridges (JTG/T 3360-01-2018), the peak vertical acceleration due to vortex-induced vibration for bridges with pedestrian access should not exceed 1.1 m/s². Therefore, the allowable vertical vibration amplitude of the main girder is calculated as follows:

[h] = 1.1 / {(2 \times π \times f_{h})}^{2} = 1.1 / {(2 \times π \times 0.3705)}^{2} = 0.2030 m

(1)

where

[h]

is the vertical vortex-induced resonance amplitude, and

f_{h}

is the vertical vibration frequency.

The calculated maximum allowable vortex-induced vibration (VIV) amplitude for the actual bridge is 203 mm, and the VIV amplitudes converted to the actual bridge from wind tunnel tests are shown in Figure 6. There is no significant torsional VIV observed at various angles of attack (angles of attack α = −5°, −3°, 0°, +3°, and +5°), but there is a noticeable vertical VIV. The vertical VIV amplitudes are presented in Figure 6, with the maximum amplitudes of vertical VIV at angles of attack α = −5°, −3°, 0°, +3°, and +5° being 201.25 mm, 210.13 mm, 220.00 mm, 223.25 mm, and 182.25 mm, respectively.

Figure 6.

Vertical vortex-induced vibration response.

The amplitude of vortex-induced vibration at angles of attack α = −3°, 0°, and +3° exceeds the allowable limit specified in the Wind-resistant Design Specification for Highway Bridges (JTG/T 3360-01-2018). Therefore, effective aerodynamic measures must be proposed to improve the vortex-induced vibration performance of the Π-shaped girder.

Vortex-induced vibration suppression measures

To ensure the stable operation and comfort of cable-stayed bridge users, adopting aerodynamic measures to reduce or control vortex-induced vibrations is crucial. This study conducted a wind tunnel test on a 1:50 scale bridge model to assess the effectiveness of various aerodynamic measures in mitigating vortex-induced vibrations. Fujino and Siringoringo (2013) and Xin et al. (2021) analyzed the impact of railing design, bottom support, and cross-section shape on the vertical displacement caused by vortex-induced vibrations. Nakamura and Nakashima (1986), along with Matsumoto et al. (1993) focused on installing separation plates in the wake to suppress the detachment of Karman vortex street. This paper, after reviewing these previous studies, compares the vertical amplitude of vortex-induced vibrations measured in models with various measures to that of the original bridge model without any measures (Figure 2, Case 0) to determine the effectiveness of these vibration suppression measures. During the wind tunnel tests, these aerodynamic measures were fabricated using PVC plastic sheets and primarily attached to the main girder section model using strong adhesive. However, in actual bridge structures, these aerodynamic measures are typically made of steel and are connected to the railing posts, Π-shaped girder deck, or I-girder through bolting or welding.

Enclosed railings

Firstly, the railings, as the prominent structures on the bridge deck, are the components of primary focus and research. The investigation into the effect of closing different railings on the suppression of vertical vortex-induced vibrations is conducted. The specific configurations are as shown in Figure 7, where Figure 7(a) illustrates the arrangement of closed pedestrian railings, and Figure 7(b) shows the layout of closed divider railings. Since the bridge deck is symmetric about its center, a symmetric arrangement is used when closing the railings, and the figure displays the layout on one side only.

Figure 7.

Schematic diagram of enclosed railings (unit: mm). (a) Case 1 (b) Case 2.

The data obtained from wind tunnel tests converted to the actual bridge are shown in Figure 8. The maximum vertical vortex-induced vibration amplitudes for the bridges with closed pedestrian railings and divider railings at a 0° wind attack angle are 205.66 mm and 203.18 mm, respectively. Although these values are somewhat lower compared to the original bridge measurement of 220 mm, the suppression effect is not significant and still exceeds the regulatory requirement of 203 mm. Closing the bridge railings has limited effectiveness in reducing fluid separation and consequently has limited impact on reducing vertical vortex-induced vibration amplitudes. Therefore, other aerodynamic measures to reduce fluid separation should still be considered.

Figure 8.

Vertical vortex-induced vibration response.

Splitter plates

This section attempts to install splitter plates on the railings to reduce fluid separation from the railings and thus achieve a reduction in the amplitude of vertical vortex-induced vibrations. The specific configurations are illustrated in Figure 9, where Figure 9(a) demonstrates the installation of splitter plates on pedestrian railings, and Figure 9(b) shows the installation of splitter plates on crash railings.

Figure 9.

Schematic diagram of splitter plates installation (unit: mm). (a) Case 3 (b) Case 4.

The data obtained from wind tunnel tests converted to the actual bridge are shown in Figure 10. The maximum vertical vortex-induced vibration amplitudes for the bridges with splitter plates installed on the pedestrian railings and divider railings at a 0° wind attack angle are 182.08 mm and 116.75 mm, respectively. These measures exhibit a noticeable suppression effect on vertical vortex-induced vibrations compared to the original bridge measurement of 220 mm, especially when splitter plates are added to the divider railings. Although these measures reduced the vortex shedding-induced amplitudes below the specification limit of 203 mm, the maximum vertical vortex-induced vibration amplitudes of 182.08 mm and 116.75 mm still do not reach the “very good” level of pedestrian comfort. Therefore, adopting other similar structures, such as deflectors, to reduce vertical vortex-induced vibration amplitudes while minimizing fluid separation has become a new attempt in aerodynamic measures.

Figure 10.

Vertical vortex-induced vibration response.

Splitter plate and guide vane

The installation of guide vanes can facilitate smooth airflow around the corners of the bridge deck, and its effectiveness is closely related to the location and size of the installation (Larsen et al., 2008). The mitigation of vortex-induced vibrations on the Great Belt East bridge can be effectively achieved by installing guide vanes at the connection between the horizontal bottom plate and the lower side plate of the box girder, which can prevent the formation of vortices by introducing high-velocity airflow in the wake area of the upwind box (Larsen et al., 2000).

Splitter plates can effectively reduce fluid separation, thereby lowering the amplitude of vertical vortex-induced vibrations. Installing splitter plates on the railings can reduce the amplitude of vertical vortex-induced vibrations to some extent, but the effect is limited. Therefore, an attempt was made to install splitter plates on the bridge deck to test their suppression effect. Based on previous research indicating that guide vanes can effectively suppress vortex-induced vibrations, this experiment also tested the suppression effect of guide vanes. The suppression effects of installing both suppression measures were tested simultaneously.

The size information and installation methods for the installed measures are shown in Table 2. Case 5 involves the installation of a one-m-long horizontal splitter plate, Case 6 involves the installation of a one-m-long splitter plate inclined at a 30° angle, and Case 7 involves the installation of a guide vane at the bottom of the main girder. To test the combined suppression effect of these two different suppression measures, Case 5 and Case 7 were installed together, creating Case 8.

Table 2.

Suppression measures of splitter plate and guide vane (unit: mm).

The data obtained from wind tunnel tests converted to the actual bridge are shown in Figure 11. The maximum vertical vortex-induced vibration amplitudes for the bridges with one-m-wide horizontal splitter plates and splitter plates inclined at a 30° angle at a 0° wind attack angle are 85.56 mm and 149.75 mm, respectively. This indicates that installing splitter plates on the bridge deck effectively reduces fluid separation, thereby lowering vertical vortex-induced vibration amplitudes. Furthermore, horizontal splitter plates demonstrate superior suppression effects compared to those inclined at a 30° angle, indicating greater effectiveness. Additionally, aligning splitter plates parallel to the direction of incoming flow further enhances their suppression capabilities.

Figure 11.

Vertical vortex vibration responses.

In the case of the individual guide vane, the maximum vertical vortex-induced vibration amplitude at a 0° wind attack angle is 143.25 mm, which is below the specification limit of 203 mm. Furthermore, when two effective measures (Case 5 and Case 7) are installed together, the maximum vertical vortex-induced vibration amplitude at a 0° wind attack angle is only 5.56 mm, far below the 203 mm limit, demonstrating significantly superior suppression performance. This suggests that when splitter plates and guide vanes are installed simultaneously, they reduce fluid separation on the upper side of the bridge deck, minimize vortex generation, and reduce vortex generation on the lower side of the bridge deck. When both aerodynamic suppression measures are installed simultaneously, they optimize different parts of the bridge.

CFD analysis

Wind tunnel testing of bridge girder models remains the primary method of investigating vibration suppression measures, although its results may be limited and non-universal due to increased variance in Vortex-Induced Vibration suppression measures required for different sections of the main girder. With the introduction of advanced CFD and modern computer technology, a new approach called the “numerical wind tunnel” is emerging as an alternative to these traditional wind tunnel experiments. By utilizing CFD methods, researchers can analyze the velocity and pressure fields surrounding bluff bodies, such as bridge decks and building structures, resulting in a visual representation of external flow characteristics and patterns that can reveal important data about the VIV phenomena (Hu et al., 2023; Townsend et al., 2022).

Numerical setup

In this study, a numerical analysis of the transient 2D flow field around the main girder section of a bridge under crosswind influence was conducted using Fluent, a commercial CFD software. The model, corresponding to Case 0 in our research (representing the original bridge section model without vibration suppression measures), was scaled at a 1:50 ratio. The specifics of the computational domain are illustrated in Figure 12. To meet the requirement of a 5% blockage ratio, the calculation domain employed an unstructured mesh with dimensions of 14 B × 22 B, where B (26m) represents the width of the bridge deck. This setup included ancillary elements such as pedestrian railings, divider railings, and the bridge deck itself. The SST k-ω turbulence model, proposed by Menter in 1994 (Menter, 1994), was selected for turbulence modeling, using the SIMPLE algorithm for calculations.

Figure 12.

CFD computing domain and mesh generation.

Tables 3 and 4 Before proceeding with the simulations, we conducted grid independence verification and time step independence verification to ensure the accuracy and efficiency of the numerical results. The grid independence verification results are summarized below:

Table 3.

Calculation Results of Grid Independence Verification.

Grid number	Lift coefficient	Drag coefficient	Moment coefficient
52284	−0.3034	1.6144	−0.0175
105754	−0.3332	1.6197	−0.0182
223090	−0.3354	1.6203	−0.0183

Table 4.

Calculation Results of Time Step Independence Verification.

Time step/s	Lift coefficient	Drag coefficient	Moment coefficient
0.002	−0.2954	1.5979	−0.0191
0.001	−0.3332	1.6197	−0.0182
0.0005	−0.3398	1.6211	−0.0182

Based on these results, a grid number of 105754 was selected as it balanced both accuracy and computational efficiency. In addition, the time step independence verification was performed, with the results as follows:

We ultimately selected a time step of 0.001s for the simulations, which provided a good balance between accuracy and computational cost. The numerical simulations were focused solely on a 0° wind angle of attack and the airflow was modeled from the left boundary to the right boundary. The computational results of the velocity field at different time instants were extracted to display the flow trajectories. This analysis of the vortex shedding patterns helps identify the causes of vortex-induced vibrations and determine the key areas of the main girder responsible for VIV. This information is crucial for the targeted development of vibration suppression measures.

Vortex generation mechanism

In this section, we present a comprehensive analysis of the airflow patterns depicted in Figure 13, with a focus on highlighting the key phenomena in fluid dynamics. As depicted in Figure 13, the airflow undergoes a distinct partition upon encountering the Π-shaped bridge section. It separates into two distinct regions: one flows over the upper surface, while the other passes beneath it. Notably, these regions exhibit contrasting flow characteristics due to variations in the 2D structural features.

Figure 13.

The original bridge section vortex streamline diagram.

Figure 13 illustrates the trajectories of airflow as it traverses the Π-shaped bridge section. At a distance from the bridge’s structural components, the streamlines remain predominantly parallel to the bridge’s axis, indicating relatively laminar flow and minimal disturbance in this region. However, as the airflow approaches the geometric features of the bridge section, the streamlines start to deform and curve, signifying the onset of flow separation and the emergence of a complex flow field.

Flow separation prominently occurs at the protruding structures, such as railings, and at the leading and trailing edges of the cross-section. This results in the formation of vortices. Notably, significant flow separation is observed at the sharp edges of the bridge, especially at the upstream leading edge and downstream acute angles. This separation arises from variations in velocity gradients within the boundary layer and the pressure changes associated with abrupt geometric transitions.

The closed loops within the streamlines represent vortices, which are local rotating regions within the airflow. Vortices are particularly prevalent at the upper surface of the bridge, primarily generated by protruding structures like railings. Conversely, in the lower region, vortices originate near the I-girders, which also serve as protruding structures. Due to the larger cross-section area at the bottom of the Π-shaped main girder, a larger vortex is formed at this location. These vortices play a crucial role in aerodynamic forces and the potential for vortex-induced vibration (VIV), which impacts the bridge’s dynamic response.

Downstream of the flow separation regions, shear layers develop, characterized by sharp velocity gradients. These shear layers induce fluid mixing and kinetic energy transfer, contributing to vortex generation and flow separation. In certain instances, shear layers may experience instability, leading to the formation of additional vortices. At the I-girders, a recirculation zone forms, where airflow reverses direction downstream of the bridge cross-section. This region exhibits inherent instability, which can impact the aerodynamic stability of the bridge.

The vortex shedding period of the original bridge section obtained through CFD calculations is illustrated in Figure 14. “nT” represents non-dimensional time, where T is the period of alternating vortex shedding from the surface of the main girder. Figure 14(a) to (d) respectively show the velocity contours around the main girder at the beginning of the (n + 1)th vortex shedding cycle (nT + 0), one-quarter of the cycle (nT + 1/4T), half of the cycle (nT + 2/4T), and three-quarters of the cycle (nT + 3/4T). These figures illustrate the changes in the velocity contours around the cross-section of the main girder during one vortex shedding cycle. It is observed that when obstructed airflow reaches the upper side of the bridge deck, it encounters obstacles such as railings, leading to the formation of vortices. These vortices predominantly accumulate around the obstacles, playing a significant role in the fluid-structure interaction that causes VIV on the bridge deck. The diagram shows that both upper and lower layers of airflow form vortices, with their length reaching twice the width of the bridge deck within one cycle. The prominent railings on the bridge deck are identified as the primary cause for the generation of large vortices. Additionally, large vortices are formed near the Π-shaped main girder, with the vortex length and amplitude increasing continuously. The instability caused by these vortices leads to the breaking of symmetrical vortex shedding, forming a periodic alternation of vortex streets and fluid separation. The airflow periodically sheds at the tail end of the bridge, forming the classic von Karman vortex street. This phenomenon is one of the primary causes of VIV on the bridge deck.

Figure 14.

Vortex shedding period diagram of the original bridge section. (a) Time = nT + 0, (b) Time = nT + 1/4T, (c) Time = nT + 2/4T, (d) Time = nT + 3/4T.

Flow characteristics in different cases

In section 4.1, a numerical simulation analysis method was employed to evaluate the effectiveness of various vibration reduction measures in suppressing vortex-induced vibrations (VIV). The analysis identified the locations and reasons for the differential effectiveness of these measures, providing insight into how the bridge design impacts flow fields leading to VIV.

Case 0 (Original Model): Figure 15(a) shows that airflow obstruction by the left bridge deck panel and the steel I-girder creates significant vortices on both the upper and lower sides. These vortices interact at the tail of the bridge deck, forming a Karman vortex street. The vector diagram indicates that the majority of the airflow diverts around the cross-section, converging at the left railing and forming additional vortices.

Figure 15.

Vorticity and vector diagrams with different cases. (a) Case 0, (b) Case 1, (c) Case 2, (d) Case 3, (e) Case 4, (f) Case 5, (g) Case 6, (h) Case 7, (i) Case 8.

Case 1 (Closed Pedestrian Railings): Figure 15(b) illustrates that closing the pedestrian railings does not improve the flow characteristics of the structure. The separated upper and lower side airflow in Case 1 has a higher velocity compared to Case 0 due to the closed pedestrian railings, which increases the height of the produced vortex. Additionally, closing the pedestrian railings makes the structure more blunt and increases the circulating airflow inside the semi-enclosed structure, which not only fails to reduce the vortex but also exacerbates its production.

Case 2 (Closed Divider Railings): As shown in Figure 15(c), the numerical results indicate that the closed divider railings cannot improve the flow characteristics of the structure either. Due to the presence of the closed divider railings, the upper-side vortex produced in Case 2 is hindered and moves backward relative to those produced in Cases 0 and 1. Additionally, vortices are formed between the pedestrian railings and the divider railings, contributing to an increase in the extent of circulating airflow inside the semi-enclosed structure, which further exacerbates the production of vortices.

Case 3 (Splitter Plates on Pedestrian Railings): Figure 15(d) indicates that adding splitter plates to the pedestrian railings increases vortex intensity at the junctions and brings the vortices closer to the bridge deck. This configuration fails to suppress vortex formation and instead enhances turbulence.

Case 4 (Splitter Plates on Divider Railings): In Figure 15(e), splitter plates on the divider railings are shown to similarly fail in suppressing vortices. The setup generates three large vortices above the bridge deck, increasing overall turbulence.

Case 5 (Horizontal Splitter Plates): Figure 15(f) demonstrates that horizontal splitter plates installed on both sides of the bridge deck significantly reduce vortex generation by 30%. The vector diagram shows that the installation of horizontal splitter plates causes the airflow to pass over the upper side of the bridge deck and the aft side to become smoother, effectively reducing VIV.

Case 6 (Inclined Splitter Plates): In Figure 15(g), inclined splitter plates reduce the vortex intensity by 15%, but disrupt the smoothness of the airflow more than horizontal plates, making them less effective in mitigating VIV. The vector diagram shows that the installation of inclined splitter plates causes the airflow passing over the upper side of the bridge deck and the aft side to become less smooth than in Case 5. Additionally, a new vortex is formed at the end of the flow barriers on the right side of the bridge deck, indicating that this arrangement of splitter plates is less effective in suppressing vortex formation than the horizontal splitter plates in Case 5.

Case 7 (Guide Vane under I-girder): Figure 15(h) shows that the V-shaped guide vane with angles of 135° installed under the I-girder significantly reduces vortex intensity and amount in the semi-enclosed space of the Π-shaped girder section. The vector diagram indicates that after the airflow passes over the left-side I-girder and the installed guide vane, some of the airflow changes direction due to the guide vane, while the other part flows more smoothly, not participating in the airflow circulation inside the semi-enclosed space of the Π-shaped girder section. This reduces the formation of larger vortices in the semi-enclosed space.

Case 8 (Combined Measures): As illustrated in Figure 15(i), combining horizontal splitter plates on both sides of the bridge deck with guide vanes under the I-girder optimizes the flow characteristics. This combined measure reduces vortex intensity and height by 30%, preventing the formation of Karman vortex streets. The airflow above and below the girder becomes stable and laminar, effectively mitigating VIV. The vortex diagram and the vector diagram demonstrate that after adding this vibration control measure, no obvious Karman vortex street phenomenon is formed at the tail.

Effectiveness of suppression methods

This paper investigates the mechanism of VIV on a Π-shaped girder bridge section and analyzes the effectiveness of various vibration suppression measures using wind tunnel experiments and CFD simulations. The experiment results suggest that Case 8 is the most effective solution among the series of tested vibration reduction measures. Therefore, further analysis is necessary to determine the specific vibration suppression mechanism of this measure.

Figure 16 elucidates the alteration in airflow behavior around the Π-shaped main girder with the implementation of effective aerodynamic mitigation measures for VIV in Case 8. These measures are designed to optimize airflow to minimize aerodynamic disturbances and the resulting VIV, in contrast with the scenario depicted in Figure 13, which represents the original truncated model of the bridge without any suppression measures (Case 0).

Figure 16.

Streamline diagram for Case 8.

On the upper side of the bridge deck, as the airflow crosses over the upper protrusion, no discernible vortices are formed, nor is there any significant disturbance observed in the airflow. This suggests that the laminar airflow passing over the upper protrusion does not induce significant disturbances or prominent vortices. Furthermore, a portion of the airflow bypasses the left I-girder, exhibiting laminar characteristics upon encountering the guide vanes at the bottom of the I-girder. This diminished participation of airflow within the Π-shaped structure results in a reduction in the size of the vortices on the lower side. Additionally, on the left side of the right main girder, no recirculation zone is formed, leading to the absence of noticeable vortices.

Comparing the streamlines between Case 0 and Case 8, the streamlines in Case 8 are notably more parallel, suggesting a reduction in airflow disturbance. The parallelism of the streamlines is typically indicative of laminar flow, characterized by lower kinetic energy losses and more orderly momentum exchange among fluid layers. These alterations signify that the optimized structural shape effectively diminishes fluid separation. Such optimization is commonly achieved by softening sharp edges or protrusions and introducing appropriate curvature to these areas, thus averting abrupt pressure gradients at these geometric features.

Analyzing the rationale, when the airflow traverses the left side of the bridge deck, the presence of a one-m-long flow stabilizer on the left ensures a smooth bifurcation of the airflow into its upper and lower components. This is in stark contrast to the situation depicted in Case 0, as shown in Figure 13, where the bifurcation of airflow is attributed to the geometric shape of the bridge deck, while in Figure 16, this division is facilitated by the addition of the flow stabilizer. The introduction of the flow stabilizer results in a smoother airflow, and the stabilizer’s efficacy in maintaining laminar flow characteristics in the divided airflow surpasses the natural division provided by the bridge deck alone. This demonstrates that structures with sharp fronts can diminish turbulence generation, while those with minimal airflow disturbance help maintain laminar flow characteristics. As the laminar flow traverses protruding bridge structures, it mitigates vortex formation while preserving laminar flow characteristics. Additionally, the installation of guide vanes at the bottom of I-girders curtails the formation of vortex circulation and recirculation zones within the Π-shaped structure.

In conclusion, a comprehensive comparison between Figures 13 and 16 reveals that the incorporation of flow stabilizers and guide vanes substantially improves the stability and laminar characteristics of the airflow, while reducing vortex formation. The role of flow stabilizers can be likened to the introduction of a streamlined geometric feature into the fluid domain, diminishing the likelihood of fluid separation by providing a more uniform pathway for the airflow, thereby reducing turbulence and vortex generation stemming from geometric discontinuities. Simultaneously, guide vanes alter the airflow direction at the base, diminishing airflow engagement in vortical structures and decreasing the formation of vortex circulation and recirculation zones. When both measures are applied concurrently, they enhance the laminar characteristics on both the upper and lower sides, attenuate the vorticity of vortices on the bridge deck’s upper and lower sides, and optimize the flow field characteristics at the trailing end of the airflow.

Conclusions

This study provided a comprehensive evaluation of vortex-induced vibrations (VIV) in a large-span twin-tower cable-stayed bridge through wind tunnel tests and Computational Fluid Dynamics (CFD) simulations. The effectiveness of various aerodynamic suppression measures was assessed, including enclosed deck protrusions, horizontal splitter plates, and angled guide vanes. Key findings are as follows:

(1) Enclosed protrusions such as pedestrian and divider railings demonstrated only modest reductions in VIV amplitude, underscoring their limited utility in significantly mitigating vibrations in large-span cable-stayed bridges.

(2) The installation of one-m-wide horizontal splitter plates on the upper flange of the Π-shaped girder and 135° angled V-shaped guide vanes beneath the I-steel effectively reduced VIV amplitude. When used together, these modifications markedly decreased vortex generation and altered airflow characteristics.

(3) The strategic placement of sharp structures on the upper flange maintained laminar flow over the bridge surface and prevented the formation of vortices. Similarly, guide vanes installed at the bottom of the main girder effectively redirected airflow, minimizing the development of recirculation areas and further suppressing VIV.

(4) The combined implementation of sharp structures and guide vanes not only reduced the formation of vortices on both sides of the bridge but also significantly altered the airflow dynamics, effectively diminishing the formation of Karman vortex streets in the bridge’s wake.

These findings highlight the critical role of targeted aerodynamic modifications in enhancing the structural stability and aerodynamic performance of large-span cable-stayed bridges. Further research should explore the scalability of these interventions and their effectiveness under different environmental conditions.

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 China Scholarship Council (Grant No. CSC202208515006), the Scientific Research Starting Project of SWPU (Grant No. 2019QHZ021), Research on the Characteristics of Regional Debris Flow Disaster and Operation Safety Risk Control in the Jiumian Expressway (The KY2 contract section), and the Open Fund Program of the State Key Laboratory of Geological Disaster Prevention and Geological Environment Protection (Grant No. SKLGP2021K017).

ORCID iD

Jun Liu

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