2.1 VIV wind tunnel tests

A bridge across the Yangtze River is used as background framework, which is a highway and railway leveling and dividing cable-stayed bridge with a length of 980 m. The decks for the railway and highway have diverse sectional shapes, and the twin decks are spaced apart by 11.9 m. Figure 1 graphically depicts the span deck cross section. As shown in Figure 2, using an independently constructed twin decks model elastic suspension device, the VIV measurement tests were carried out at the Wind Engineering Test and Research Center of Changsha University of Science and Technology. Laser displacement sensors with 500 Hz sampling rate and 30 s sampling time were used to measure the vibration response. Vertical and torsional vibration could occur freely in the highway and railway model. The test model was chosen with a scale ratio of 50:1 under the condition that the geometric shape, elastic parameters, inertia parameters, and damping parameters were equivalent. This was done in accordance with the aforementioned main beam size, test section size, and test-related requirements. The 1.5 m-long models for railway and highway decks both include an internal steel structure and an outside structure made of acrylonitrile butadiene styrene (ABS) or wood. To assure the two-dimensional airflow characteristics, the ends were each fitted with wooden end plates. The auxiliary facilities were shrunk down and built of ABS board. The highway model is 0.76 m wide and 0.07 m tall, while the railway model is 0.472 m wide and 0.09 m tall. The dynamic features and scale ratio of the highway and railway bridges are shown in Table 1.

Figure 1全屏查看

Cross section at mid-span position

Figure 2全屏查看

Vortex-induced vibration wind tunnel tests: (a) Support system; (b) Model with splitter plates

For investigating the VIV displacements of decks with the original section, wind tunnel tests with various wind incidence angles were carried out in two opposite wind directions, which was shown in Figure 3. The cases of wind directions contain the wind blows from the upstream railway (UR) to the downstream highway (DH) and the wind blows from the upstream highway (UH) to the downstream railway (DR). The test parameters are shown in Table 2. Seven different widths of splitter plates were made from ABS plates and fixed to each side of the twin decks in turn in order to study the VIV-suppress effect of the splitter plates. Wind tunnel experiments were then conducted with α=3° to test the VIV amplitude under various wind directions. The test conditions are shown in Table 3.

Figure 3全屏查看

Schematic illustration of wind directions: (a) Wind blows from UR to DH; (b)Wind blows from UH to DR

2.2 Aerostatic forces tests

In the force-measurement tests, a wind speed of 10 m/s was used, with 25 various wind incidence angles that ranged from -12° to 12° with a region of 1°. The aerodynamic force coefficients of the highway and railway decks with various splitter plates for two opposite wind directions were measured. The cases of different widths are shown in Table 4. Different widths of splitter plate for highway and railway decks were tested with the same basic parameter to methodically study the impact of varying splitter plates on aerostatic performance. As illustrated in Figure 4, the high-frequency balances that were positioned at the bottom of the deck were attached vertically to the sectional model.

Figure 4全屏查看

Examples of wind tunnel tests for measuring aerostatic forces: (a) Without splitter plates; (b) With splitter plates (L = 50 mm)

The aerostatic coefficients of the deck are defined as [36]:

(1)

(2)

(3)

where H is the height of model; B is the width of the model; D is the length of the model; L is the width of the splitter plate. F_l, F_d and F_m are the lift, drag force and lifting moment, respectively. C_l, C_d and C_m are the lift force coefficient, drag force coefficient and lifting moment coefficient, respectively; ρ=1.225 kg/m³; and U is the mean wind velocity.

2.3 Numerical simulation

The flow and vortex volume around the decks can visualize the characteristics and patterns of the blunt body winding flow. The flow visualization surrounding the decks can be obtained through numerical simulation, which may help to shed light on the potential mechanisms of the aerodynamic effects. Therefore, 2D models of highway and railway decks were chosen for numerical simulation to examine the influence of splitter plates on the flow visualization. On the basic of the wind tunnel tests parameters, the computational domain settings in the simulations made in this paper are shown in Figure 5. When the wind flows from the railway deck upstream to the highway deck downstream, taking the L=50 mm splitter plates as an example, the numerical simulation results are compared with and without the splitter plates on both sides of twin decks to analyze the effect of the splitter plates. Among them, the grid near the wall of the decks in the calculation domain is highly encrypted. The remaining region is treated with a sparse grid in order to minimize the number of grids and increase calculation efficiency while still accurately capturing the flow field information in the near-wall region, particularly the development of the free shear layer and the vortex shedding and reattachment phenomena. The shear stress transport (SST) k-omega turbulence model is used to resolve the two-dimensional RANS equations. The pressure-velocity coupling problem was solved using the SIMPLEC method, and second-order interpolation was employed to calculate the pressure. The numerical model underwent grid-independent and time-independent tests before the formal simulation, respectively. The computational domain was finally spatially discretized using around 564000 cells, with the initial layer of cells surrounding the deck having a non-dimensional height of less than y+=1 and the time step of Δt=0.00001 s, and the solution satisfies the Courant number Co<1 at any time. The velocity inlet boundary condition is used at the entrance of the computational domain, the velocity is set to 10 m/s with a turbulence intensity of 1.0%. At the end of the computational domain, the free pressure outlet boundary condition is employed, and the symmetric wall condition is used at the boundary of the upper and lower computational domains; the non-slip wall condition is used at the wall of the main deck of the twin decks. Finally, the reliability of the CFD simulation was validated by comparing wind tunnel tests and CFD results of aerodynamic coefficients [53]. Taking the case of α=0° and the wind flows from the UR to the DH without splitter plates for both girders, three different mesh sizes and three different time step schemes were selected to verify the independence of results. Additionally, these results were compared with wind tunnel experiment data to validate the accuracy of our simulations. The detailed comparison can be found in Table 5.

Figure 5全屏查看

Layout of computation domain discretization and mesh scheme

3.1 Vortex-induced vibration performance of original section

VIV performance of the highway and railway decks without splitter plates was preliminarily studied. Vertical and torsional VIV displacements with two opposite incoming directions were obtained and shown in Figures 6 and 7. Even though both decks experience VIV, the VIV exhibits different traits. Based on the Chinese bridge wind-resistant design specification, the railway and highway decks’ respective permissible vertical VIV amplitudes are 118.7 and 88.8 mm, respectively, and that of torsional VIV amplitudes are 0.2° and 0.12°, respectively.

Figure 6全屏查看

Vortex-induced vibration performance of twin decks for wind blows from UH to DR: (a) Vertical VIV displacement; (b) Torsional VIV displacement

Figure 7全屏查看

Vortex-induced vibration performance of twin decks for wind blows from UR to DH: (a) Vertical VIV displacement; (b) Torsional VIV displacement

When the wind blows from UH to DR, the vertical and torsional VIV displacements are shown in Figure 6. For α=3°, a large vertical VIV occurs on the UH deck, and there are two vertical regions of V1 and V2 and three torsional VIV regions of T1, T2 and T3. With the increase of wind velocity, the UH deck first exhibits vertical VIV in V1 region. At U=12.96 m/s, the initial maximum vertical amplitude of 90 mm was attained. The initial maximum torsional amplitude of 0.21 was attained at U=14.02 m/s, and a tiny torsional VIV follows in the region of T1. Then a large vertical VIV occurred in the region of V2, respectively, and at U=26.88 m/s, the second highest vertical amplitude of 525 mm was attained. While, torsional vortex-induced vibration occurs in the T2 region, whose maximum torsional amplitude of 0.62° was attained at U=14.02 m/s. The third greatest torsional amplitude of 1.32° was attained at U=36.42 m/s, and the high torsional VIV occurs in the T3 region. Due to the shield of the UH deck, the DR deck is not subject to VIV. For α=0°, although the vertical VIV of the UH deck occurs, the vertical VIV region of the highway is still V1 and V2, but the maximum VIV amplitude changes greatly. The maximum vertical amplitude is 380 mm, which is reduced by 30%. There are still three torsional vortex vibration regions, and the maximum amplitude does not decrease significantly. There is still no VIV phenomenon on the DR deck. For α=-3°, there is just one vertical VIV region (V1) on the UH deck, the V2 VIV region is eliminated, and the maximum vertical VIV amplitude is reduced by 65% to 185 mm. There are still three torsional vortex vibration regions (T1, T2 and T3), but the peak torsional amplitude appears in the T2 region. There is still no VIV phenomenon on the DR deck. In a comprehensive comparison, the VIV of the 3° wind incidence angle is more unfavorable, when the wind blows from the UH to the DR.

When the wind blows from UR to DH, as shown in Figure 7, highway and railway decks show completely different VIV performances. For α=3°, the vertical VIV of the UR deck occurs during the region V1, and the highest vertical VIV displacement of 300 mm was attained at U= 12.96 m/s. Although the shade reaction of the UR deck remains, the DH’s VIV phenomena have not vanished. Vertical VIV occurs in highway deck in the region of V2. There are still three torsional VIV regions (T1, T2 and T3) for DH deck. However, the VIV amplitude and the VIV range are significantly affected. The peak vertical amplitude of 300 mm was attained at U=15.60 m/s, while the peak torsional amplitude of 1.9° was reached at U= 32.00 m/s. The torsional amplitudes in the T3 region of the highway deck greatly reduce for α=0°, and the vertical VIV displacements of the UR deck and the DH deck also decrease. The UR deck has essentially negligible vertical VIV. The torsional VIV amplitude, torsional VIV range, and vertical VIV amplitude of the DH deck all continue to decline. So, the VIV of the 3° wind incidence angle is the more unfavorable angle, when the wind blows from the UR to the DH.

3.2 Vortex-induced vibration performance of twin decks with various splitter plates

To suppress the appearance of VIV, this study adopted the measure of adding splitter plates on both sides of twin decks to suppress the VIV. From the analysis in Section 3.1, it is clear that the phenomenon of VIV of the twin decks is relatively obvious, and the results under different directions under incoming flow are completely different, and the 3° wind incidence angle is the most unfavorable. To systematically investigate the influence of various splitter plates on VIV performance for twin parallel decks, we tested seven different widths of splitter plates (20, 30, 40, 50, 60, 70 and 80 mm) deck under two opposite incoming flow directions, as shown in Figures 8 and 9. The VIV-suppress effect of the 0-80 mm splitter plates on the twin decks was compared under 3° wind incidence angle for two opposite inflow directions.

Figure 8全屏查看

Vortex-induced vibration performance of twin decks with splitter plate for wind blows from UH to DR: (a) Vertical VIV displacement; (b) Torsional VIV displacement

Figure 9全屏查看

Vortex-induced vibration performance of twin decks with splitter plate for wind blows from UR to DH: (a) The vertical VIV displacement; (b) The torsional VIV displacement

As shown in Figure 8(a), when the wind blows from UH to DR, the vertical VIV displacement of the UH deck gradually decreases with the width of the splitter plate. When the splitter plate width is L=50 mm, one of the VIV regions even disappears directly, the vertical VIV region becomes only one, and the maximum VIV amplitude is 82 mm, which meets specification limits. When the width increases to L=80 mm, the vertical VIV of the UH deck does not occur at all. As shown in Figure 8(b), for the torsional VIV, the VIV response gradually becomes weaker as the splitter plate’s width increases. When the width is L=20 mm, the torsional VIV region is changed from three to one, and the maximum torsional amplitude is reduced by 20%. As the width of the splitter plates keeping increasing, the amplitude of the torsional VIV continues to decrease, and the speed range continues to decrease. When the width is L=50 mm, the torsional VIV for the UH deck completely disappears. And if the width of the splitter plate continues to increase, there is also no torsional VIV. It demonstrates that the thin-walled splitter plate can successfully reduce the torsional VIV.

In addition, peak VIV amplitudes of different widths of splitter plates are shown in Figure 10(a). Through comprehensive comparison, it is evident that when the splitter plate’s width is L=50 mm, the VIV amplitude meets the requirements of the specification, and the larger the width of the splitter plate, the smaller the amplitude.

Figure 10全屏查看

Peak VIV amplitude of twin decks with different splitter plates: (a) Wind blows from UH to DR; (b) Wind blows from UR to DH

As shown in Figure 9(a), when the wind blows from UR to DH, the vertical VIV displacements and VIV region of the UR deck and the DH deck also gradually decrease with the splitter plate’s width. When the width is L=20 mm, the DH deck’s maximum vertical VIV displacement is decreased to 82 mm, which is reduced by 73%, which also meets the requirements of the specification. When the width increases to L=50 mm, the VIV of the UR even disappears directly. The DH deck’s vertical VIV amplitude is sensitive to the splitter plate’s width. But for the DH decks, as the width of the splitter plate keeps increasing, although the amplitude of the vertical VIV continues to decrease, the amplitude is obviously smaller, but the vertical VIV does not completely disappear until the width is L=80 mm. As shown in Figure 9(b), for the torsional VIV, with the increase of the splitter plate’s width, there is no new torsional VIV phenomenon in the DR deck. The highway deck’s maximum torsional VIV amplitude is also reduced dramatically, but the torsional VIV does not completely disappear. Figure 10(b) shows the variation of the peak vertical and torsional VIV displacements of the DH deck and the UR deck with different splitter plates, through comprehensive comparison, when the width is L=50 mm, the VIV performance of the twin decks can meet the specification requirements, but the wider width of the splitter does not mean the better VIV performance. There is an increasing trend for the VIV amplitude as the width increases. When the width is L>50 mm, the torsional VIV’s displacement of the DH deck increases with the width of the splitter plate, and there is a rising tendency in the torsional VIV’s displacement of the DH with the splitter plate.

To sum up, the installation of splitter plates on each side of the twin decks affects the vertical and torsional VIV. It is more appropriate to comprehensively select the width of splitter plates for L=50 mm.

3.3 Aerostatic coefficients of twin decks with various splitter plates

To prevent the adverse effects of the excessively wide splitter plates on the static wind stability of the twin decks, an analysis was conducted on the aerostatic coefficients of the twin decks with the splitter plate at different angles. When the wind blows from UH to DR, the comparison of aerodynamic coefficients of twin decks under different widths of splitter plates is shown in Figure 11. C_l-h, C_d-h and C_m-h are the lift force coefficient, drag force coefficient and lifting moment coefficient of the highway bridge. While, C_l-r, C_d-r and C_m-r are the lift force coefficient, drag force coefficient and lifting moment coefficient of the railway bridge.

Figure 11全屏查看

Aerostatic coefficient of twin decks with splitter plate for wind flows from UH to DR: (a) C_l; (b) C_d; (c) C_m

As seen in Figure 11(a), when α changes from -12° to 12°, both the change patterns of C_l-h and C_l-r transfer from the smaller negative values to the positive values. The splitter plates installed on both sides of the twin decks do not change the trend of lift coefficient with wind incidence angle. However, when the splitter plate’s width has increased, the influence on the upstream and downstream decks is different. For the UH deck, C_l-h is not greatly affected by the splitter plate’s width in the range of -12°-0°, and the curves almost coincide. In the range of 0°-12°, the curvature of dC_l-h/dα gradually increases with the increase of splitter plate width, which is obvious. For the DR deck, in the range of -12°-12°, the curvature of dC_l-r/dα gradually decreases with the increase of width. As shown in Figure 11(b), when the wind incidence angle is negative (from -12° to 0°), C_d-h and C_d-r both decrease; however, the relationship is reversed when the attack angle is greater than 0°. When the splitter plate’s width has increased, there were no significant concerns about the value and curvature of the drag coefficients. As shown in Figure 11(c), both the change trends of C_m-h and C_m-r transfer from the smaller negative values to the large positive values when α shifts from -8° to 12°. The splitter plates installed on both sides of the twin decks do not change the trend of moment coefficient with wind incidence angle. However, with the increase in the width of the splitter plate, the influence on the upstream and downstream decks is different. For the UH deck, C_m-h is mostly independent of the splitter plate’s width in the range of -12°--4°, and the curves almost coincide. In the range of 4°-12°, the curvature of dC_m-h/dα gradually increases with the increase of splitter plate width, which is obvious. For the DR deck, in the range of -12°-0°, the curvature of dC_m-r/dα gradually decreases with the increase of width. In the range of 0°-12°, the width has less influence on the curvature of dC_m-r/dα.

The critical wind speed of the static wind transverse instability is inversely proportional to the curvature of the lift coefficient, and the critical wind velocity of the static wind torsional divergence is inversely proportional to the curvature of the moment coefficient. Therefore, the wider the width of the splitter plate, the larger the curvature of the lift coefficient and the moment coefficient of the UH deck, and the smaller the critical wind speed for static wind stability, which is unfavorable for the wind resistance performance of the bridge. For the DR deck, the width of the diverter plate has little effect on the critical wind velocity of static wind stability of the downstream deck, and it is even reasonable to increase the critical wind velocity of static wind stability.

When the wind blows from UR to DH, the comparison of aerodynamic coefficients of twin decks under different widths of splitter plates is shown in Figure 12. As shown in Figure 12(a), both the change trends of C_l-h and C_l-r were transferred from the smaller negative values to the positive values when α shifts from -12° to 12°. The splitter plates installed on both sides of the twin decks do not change the trend of lift coefficient with wind incidence angle. However, with the increase in the width of the splitter plate, the influence on the upstream and downstream decks is different. For the UR deck, in the range of -4°-12°, the curvature of dC_l-r/dα gradually increases with the increase of splitter plate width, which is obvious. For the DH deck, in the range of -12°-12°, the width of the splitter plate has little influence on C_l-h. As demonstrated in Figure 12(b), both C_d-h and C_d-r drop when the wind incidence angle is negative (from 12° to 0°), but the opposite is true when the attack angle is greater than 0°. When the splitter plate’s width has increased, there were no significant concerns about the value and curvature of the drag coefficients. As shown in Figure 12(c), both the change trends of the moment coefficient of C_m-h and C_m-r transfer the smaller negative values to the large positive values when α shifts from -8° to 12°. The splitter plates installed on both sides of the twin decks do not change the trend of moment coefficient with wind incidence angle. However, when the splitter plate’s width has increased, the influence on the upstream and downstream decks is different. For the UR deck, in the range of -8°-12°, the curvature of dC_m-r/dα gradually increases with the increase of splitter plate width, which is obvious. For the DR deck, in the range of -12°--2°, the curvature of dC_m-h/dα gradually decreases with the increase of width. In the range of 0°-12°, the width of the splitter plate has less effect on the curvature of dC_m-h/dα. The critical velocity of the static wind transverse instability is inversely proportional to the curvature of the lift coefficient, and that of torsional divergence is inversely proportional to the curvature of the moment coefficient. Therefore, the wider the width of the splitter plate, the larger the curvature of the lift coefficient and the moment coefficient of the UR deck, and the smaller the critical wind speed for static wind stability, which is unfavorable for the wind resistance performance of the bridge. For the DH deck, the width of the diverter plate has little effect on the critical velocity of static wind stability of the downstream deck, and it is even reasonable to increase it.

Figure 12全屏查看

Aerostatic coefficient of twin decks with splitter plate for wind flows from UR to DH: (a) C_l; (b) C_d; (c) C_m

To sum up, no matter what the incoming flow direction is, the splitter plates have an adverse effect on the critical velocity of the upstream deck static wind stability, and have little effect on that of the downstream deck.

3.4 Flow and wind pressure coefficients around twin decks

To further discuss the VIV-suppress mechanism, the flow and surface pressure distribution around the twin decks were analyzed. As shown in Figure 13, the static highway and railway decks with and without splitter plates were compared for vortex contour and wind pressure coefficients. When the wind flows from the UR deck to the DH deck, the 16 subplots in Figure 13 represent the vortex flow on the surface of the decks at various time (T/8-8T/8) during a complete cycle with and without splitter plates. As shown in Figure 13(a), distinct vortices periodically shed from the leeward side of the upper and lower surfaces of the UR deck and then impinged on the windward side of the DH deck. The vortex shed from the UR deck’s upper surface flows directly over the upper surface of the DH deck, while the vortex shed from the UR deck’s lower surface impinged the winding nozzle of the DH deck. As shown in Figure 14, this process could lead to significant fluctuations in the fluctuating wind pressure at the gap between the railway and highway decks, which is the primary cause for the presence of VIV in both the UR and the DH decks. And when the splitter plates were installed on each side of the twin deck, the splitter plates make the flow field separate in advance and affect its wake shedding. As shown in Figure 15, it can be observed from comparing the mean wind pressure coefficient of the DH deck that the splitter plates have a greater influence on it, especially at the winding nozzle of the windward side. Besides, as shown in Figure 15(b), the flow around twin decks becomes smooth and no periodic vortices are generated. In other words, once the splitter plates are installed, the highway and railway bridges tend to be streamlined under the airflow. Therefore, as shown in Figure 14, the fluctuating wind pressure coefficient around the static twin decks on the overall surfaces is also severely diminished.

Figure 13全屏查看

Vortex contour without splitter plates (a) and with splitter plates (b)

Figure 14全屏查看

Comparison of the fluctuating wind pressure coefficients: (a) Upper surfaces; (b) Lower surfaces

Figure 15全屏查看

Comparison of the mean wind pressure coefficients: (a) Upper surfaces; (b) Lower surfaces

In summary, when the wind flows from the UR to the DH, the splitter plates can impede the process of vortex generation, shedding and impinging at the gap between twin deck, and significantly reducing the twin decks’ fluctuating wind pressure coefficients, thus effectively suppressing VIV. So that the incoming flow can flow steadily through the UR deck and the DH deck.