Steady-Suction-Based Flow Control of Flutter of Long-Span Bridge

Featured Application: In this work, the e ﬀ ect of steady-suction-based ﬂow control method on ﬂutter performance of long-span bridges was studied by wind tunnel tests. This work can assist the application of this method in practical engineering. Abstract: The present wind tunnel study focuses on the e ﬀ ects of the steady-suction-based ﬂow control method on the ﬂutter performance of a 2DOF bridge deck section model. The suction applied to the bridge model was released from slots located at the girder bottom. The suction rates of all slots along the span were equal and constant. A series of test cases with di ﬀ erent combinations of suction slot positions, suction intervals, and suction rates were studied in detail for the bridge deck model. The experimental results showed that the steady-suction-based ﬂow control method could improve the ﬂutter characteristics of the bridge deck with a maximal increase in the critical ﬂutter speed of up to 10.5%. In addition, the ﬂutter derivatives (FDs) of the bridge deck with or without control were compared to investigate the fundamental mechanisms of the steady-suction-based control method. According to the results, installing a suction control device helps to strengthen aerodynamic damping, which is the primary cause for enhanced ﬂutter performance of bridge decks.


Introduction
Bridge flutter is a catastrophic dynamic aeroelastic phenomenon that occurs due to interactions between wind and the vibrating bridge deck and can induce a total structural collapse. When the inflowing wind is faster than the critical flutter speed, the bridge girder structure extracts energy from the free stream flow for a divergent response. Therefore, flutter is one of the most important factors in the design of a long-span bridge and must not occur during its life cycle. Owing to the increasing bridge span, the flutter problem has become increasingly prominent, and new wind-resisting strategies and techniques are necessary.
Alternative approaches have been presented for cases where the parameters of the structure itself cannot meet the design requirements (i.e., the critical flutter wind speed) of the structure. These are classified into mechanical strategies and flow control strategies. Regarding the mechanical methods, passive approaches with tuned mass dampers (TMDs) have been widely studied. Nobuto et al. [1] studied the control effectiveness of a TMD to suppress the coupled flutter of a bridge deck. The result was a maximal critical flutter wind speed increment of approximately 14%. Pourzeynali and Datta [2] introduced an effective TMD control system with two degrees of freedom for a suspension bridge. considered three experimental variables: the suction slot position, suction interval, and suction rate. The critical flutter speeds of the bridge model with or without a control system were compared to examine the effectiveness and applicability of the self-designed control system. In addition, the measured flutter derivatives (FDs), which are essential for flutter analysis, were compared and analyzed for all test cases to thoroughly examine the control mechanism of the steady-suction flow control.

Models
A simplified bridge deck section model of the Great Belt East Bridge without deck-related facilities was manufactured (1:80 scale, 0.7 m length, 0.3875 m width, and 0.05 m girder depth; Figure 1). The model surface was made of acrylonitrile-butadiene-styrene Plexiglas, and stiffening ribs were rigidly installed inside the model for an adequate vertical stiffness. The mass and mass moment inertia of the deck section, including the contribution from the suction pipes, were 3.701 kg/m and 0.061 kg·m 2 /m, respectively. The end plates were placed on both sides of the bridge section model to ensure the two-dimensional characteristics of the oncoming wind flow. According to the geometrical size of the model, the wind tunnel blockage ratio was approximately 1.7%. Hence, its influence was considered to be negligible. Furthermore, three rows of suction slots were introduced to the low surface of the bridge deck. One row had 11 suction slots, and the distance between two adjacent slots was 0.05 m, which was equal to the section model depth. The detailed layout of the suction slots is shown in Figure 2.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 17 equal. We considered three experimental variables: the suction slot position, suction interval, and suction rate. The critical flutter speeds of the bridge model with or without a control system were compared to examine the effectiveness and applicability of the self-designed control system. In addition, the measured flutter derivatives (FDs), which are essential for flutter analysis, were compared and analyzed for all test cases to thoroughly examine the control mechanism of the steadysuction flow control.

Models
A simplified bridge deck section model of the Great Belt East Bridge without deck-related facilities was manufactured (1:80 scale, 0.7 m length, 0.3875 m width, and 0.05 m girder depth; Figure  1). The model surface was made of acrylonitrile-butadiene-styrene Plexiglas, and stiffening ribs were rigidly installed inside the model for an adequate vertical stiffness. The mass and mass moment inertia of the deck section, including the contribution from the suction pipes, were 3.701 kg/m and 0.061 kg·m 2 /m, respectively. The end plates were placed on both sides of the bridge section model to ensure the two-dimensional characteristics of the oncoming wind flow. According to the geometrical size of the model, the wind tunnel blockage ratio was approximately 1.7%. Hence, its influence was considered to be negligible. Furthermore, three rows of suction slots were introduced to the low surface of the bridge deck. One row had 11 suction slots, and the distance between two adjacent slots was 0.05 m, which was equal to the section model depth. The detailed layout of the suction slots is shown in Figure 2.

Wind Tunnel Set-Up and Test Measurements
The experiments were conducted in a closed-circuit wind tunnel located in the Department of Civil Engineering at the Harbin Institute of Technology. The test section of the wind tunnel was 3.0 m in height, 4.0 m in width, and 25 m in length; the available wind velocity range was 2-45 m/s. Moreover, the maximal free-stream turbulence intensity was 0.46%, and the maximal free-stream nonuniformity was 1%. In this study, the oncoming flow was uniform and smooth. A very fine scan of the wind speed range of interest was conducted for each test case. During the tests, the bridge model was mounted inside the wind tunnel with a suspension system consisting of eight coil springs  Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 17 equal. We considered three experimental variables: the suction slot position, suction interval, and suction rate. The critical flutter speeds of the bridge model with or without a control system were compared to examine the effectiveness and applicability of the self-designed control system. In addition, the measured flutter derivatives (FDs), which are essential for flutter analysis, were compared and analyzed for all test cases to thoroughly examine the control mechanism of the steadysuction flow control.

Models
A simplified bridge deck section model of the Great Belt East Bridge without deck-related facilities was manufactured (1:80 scale, 0.7 m length, 0.3875 m width, and 0.05 m girder depth; Figure  1). The model surface was made of acrylonitrile-butadiene-styrene Plexiglas, and stiffening ribs were rigidly installed inside the model for an adequate vertical stiffness. The mass and mass moment inertia of the deck section, including the contribution from the suction pipes, were 3.701 kg/m and 0.061 kg·m 2 /m, respectively. The end plates were placed on both sides of the bridge section model to ensure the two-dimensional characteristics of the oncoming wind flow. According to the geometrical size of the model, the wind tunnel blockage ratio was approximately 1.7%. Hence, its influence was considered to be negligible. Furthermore, three rows of suction slots were introduced to the low surface of the bridge deck. One row had 11 suction slots, and the distance between two adjacent slots was 0.05 m, which was equal to the section model depth. The detailed layout of the suction slots is shown in Figure 2.

Wind Tunnel Set-Up and Test Measurements
The experiments were conducted in a closed-circuit wind tunnel located in the Department of Civil Engineering at the Harbin Institute of Technology. The test section of the wind tunnel was 3.0 m in height, 4.0 m in width, and 25 m in length; the available wind velocity range was 2-45 m/s. Moreover, the maximal free-stream turbulence intensity was 0.46%, and the maximal free-stream nonuniformity was 1%. In this study, the oncoming flow was uniform and smooth. A very fine scan of the wind speed range of interest was conducted for each test case. During the tests, the bridge model was mounted inside the wind tunnel with a suspension system consisting of eight coil springs

Wind Tunnel Set-Up and Test Measurements
The experiments were conducted in a closed-circuit wind tunnel located in the Department of Civil Engineering at the Harbin Institute of Technology. The test section of the wind tunnel was 3.0 m in height, 4.0 m in width, and 25 m in length; the available wind velocity range was 2-45 m/s. Moreover, the maximal free-stream turbulence intensity was 0.46%, and the maximal free-stream nonuniformity was 1%. In this study, the oncoming flow was uniform and smooth. A very fine scan of the wind speed range of interest was conducted for each test case. During the tests, the bridge model was mounted inside the wind tunnel with a suspension system consisting of eight coil springs and two supporting frames, which established the heave and pitch stiffness of the bridge section model. The natural vertical and torsional frequencies of the overall test model in still air were 2.586 and 6.8 Hz, respectively, with an acceptable deviation within 5% compared to the design values of 2.548 and 7.092 Hz, respectively. The vertical and torsional damping ratio of the overall test model were 0.44% and 0.74%, respectively. It should be mentioned that, whether or not suction control was applied, the bridge model was connected to the suction control device throughout the test process, including the measurement stage of frequencies and damping ratios. Two laser reflection sensors set in pairs were installed underneath one side of the test section and aimed at the reflected target set on the lever arm. They were used to measure the vertical and torsional responses of the model. The signals from the reflection gauges were sampled at 1000 Hz. Furthermore, steady suction was realized by installing a self-designed suction control system. Figure 3a depicts details of the control system. The suction pump pumped the air out of the vacuum tank to generate differential pressure. This provided suction power at the bottom of the bridge deck. The digital readout flowmeter used to monitor the flow rate and the pneumatic junction throttle employed to adjust the suction flow were installed in the control system to ensure a precise control device. Moreover, the suction control device was connected to the test model through air suction pipes. The overall model configuration of the wind tunnel is shown in Figure 3a,b.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 17 and two supporting frames, which established the heave and pitch stiffness of the bridge section model. The natural vertical and torsional frequencies of the overall test model in still air were 2.586 and 6.8 Hz, respectively, with an acceptable deviation within 5% compared to the design values of 2.548 and 7.092 Hz, respectively. The vertical and torsional damping ratio of the overall test model were 0.44% and 0.74%, respectively. It should be mentioned that, whether or not suction control was applied, the bridge model was connected to the suction control device throughout the test process, including the measurement stage of frequencies and damping ratios. Two laser reflection sensors set in pairs were installed underneath one side of the test section and aimed at the reflected target set on the lever arm. They were used to measure the vertical and torsional responses of the model. The signals from the reflection gauges were sampled at 1000 Hz. Furthermore, steady suction was realized by installing a self-designed suction control system. Figure 3a depicts details of the control system. The suction pump pumped the air out of the vacuum tank to generate differential pressure. This provided suction power at the bottom of the bridge deck. The digital readout flowmeter used to monitor the flow rate and the pneumatic junction throttle employed to adjust the suction flow were installed in the control system to ensure a precise control device. Moreover, the suction control device was connected to the test model through air suction pipes. The overall model configuration of the wind tunnel is shown in Figure 3a,b.
(a) (b) In this study, the effects of the test variables, including the suction slot position, suction interval, and suction rate, on the control were studied in detail. To distinguish between the positions of the suction slots, positions on the windward side were denoted by l, positions in the middle were denoted by m, and positions on the leeward side were denoted by b. The suction interval was expressed in a nondimensional form as   / dH , where  is the relative suction interval, d is the distance between two adjacent slots, and H is the model section height. The suction rate was also described in a nondimensional form as  max / q C Q U LH , where q C is the relative single-slot suction flow rate, Q the single-slot suction flow rate, max U the maximal upcoming wind velocity, and L the model length. Three test cases with three different locations of suction slot rows (i.e., on the windward side, in the middle, and on the leeward side) were investigated to determine the best suction position. In addition, to systematically investigate the influence of different suction intervals and suction flow rates on the flutter instability of the bridge, four representative relative suction intervals (  ) (i.e.,  = 1, 2, 3, 4) and three relative suction flow rates (i.e., q C = 0.00174, 0.0244, and 0.00348 corresponding to Q = 5, 7, and 10 L/min, respectively) were selected for the specified suction positions. In total, nine test cases (Table 1) were adopted with a naming standard. For example, l-2d-10 implies that the suction position was on the windward side, the relative suction interval (  ) was 2, and the single-  In this study, the effects of the test variables, including the suction slot position, suction interval, and suction rate, on the control were studied in detail. To distinguish between the positions of the suction slots, positions on the windward side were denoted by l, positions in the middle were denoted by m, and positions on the leeward side were denoted by b. The suction interval was expressed in a nondimensional form as λ = d/H, where λ is the relative suction interval, d is the distance between two adjacent slots, and H is the model section height. The suction rate was also described in a nondimensional form as C q = Q/U max LH, where C q is the relative single-slot suction flow rate, Q the single-slot suction flow rate, U max the maximal upcoming wind velocity, and L the model length.
Three test cases with three different locations of suction slot rows (i.e., on the windward side, in the middle, and on the leeward side) were investigated to determine the best suction position. In addition, to systematically investigate the influence of different suction intervals and suction flow rates on the flutter instability of the bridge, four representative relative suction intervals (λ) (i.e., λ = 1, 2, 3, 4) and three relative suction flow rates (i.e., C q = 0.00174, 0.0244, and 0.00348 corresponding to Q = 5, 7, and 10 L/min, respectively) were selected for the specified suction positions. In total, nine test cases (Table 1) were adopted with a naming standard. For example, l-2d-10 implies that the suction position was on the windward side, the relative suction interval (λ) was 2, and the single-slot suction flow rate was 10 L/min. Moreover, s00 denotes the single-deck case without steady-suction control.

Experiment Validation
To verify the positive effect of the steady-suction control on the bridge flutter performance, two types of information should be collected: (1) the geometric information of the model and (2) important aerodynamic parameters, including the FDs and critical flutter speed obtained through the FDs. Table 2 lists the structural information of the actual bridge and bridge section model, including the geometric dimensions, mass characteristics, and vertical and torsional frequencies. Flutter derivatives are important aerodynamic parameters for the evaluation of the vibration tendency of a bluff body under flow action, and they provide a better insight into the flutter sensitivity of bridge decks. Therefore, FD identification is an indispensable step. Scanlan and Tomo [17] proposed the application of FDs to define a linear aeroelastic system. The FDs are identified in experiments and used to estimate the self-excited forces acting on the vibrating body, which can be expressed as linear combinations of the body motions: where F se represents the motion-related self-excited forces, including the aeroelastic lift and pitching moment forces; B denotes the section width, ρ is the air density, U is the far-field wind speed, K is the reduced frequency defined as K = 2π f B/U with f as vibration frequency of the model; H * i and A * i (i = 1 − 4) are the FDs; and h and α are the vertical and torsional displacements, respectively. Numerous theories have been developed to determine the FDs in wind tunnel tests [18][19][20]. In this study, the iterative least-squares (ILS) theory proposed by Chowdhury and Sarkar [20] was adopted to determine the FDs. Specifically, the experiments were conducted with the free-vibration technique, and the initial forced displacements were applied to the bridge model in the vertical and rotational directions. Then, the free-decay oscillations under different wind speeds were measured (inlet wind speeds of 2, 4, 6, 8, 10, 12, and 14 m/s were considered). After obtaining the time history response, the FDs were determined using the ILS method. Finally, based on the determined FDs, the flutter motion equation was solved to obtain the critical flutter velocity with the conventional method (omitted for brevity).
To validate the reported results, the FDs and critical flutter speed of the bridge section model without a control system were compared with previous results of a similar bridge deck section investigated by Poulsen et al. [21] and Xiang [22]. Figure 4 compares the results of eight FDs. In order to clearly compare the trends of FDs, the data were fitted into a smooth curve using a quadratic polynomial with one variable. The values and trends of the FDs A * 1 , A * 2 , A * 4 , H * 2 , and H * 4 agreed well with those of previous studies. However, some deviations at isolated points, as shown in Figure 4c,e,g, existed, which belonged to A * 3 , H * 1 , and H * 3 . Nevertheless, the overall trends were consistent. Two possible reasons exist for the previously mentioned discrepancy. The first one might be the minor differences in the design of the tested bridge deck section; the second reason is that the ILS method used for extracting the FDs is dependent on the actual situation. In general, the extraction results of the FDs were acceptable for subsequent analysis. The obtained FDs were used to deduce the critical flutter speed, which was 76.65 m/s and approximately the results of other researchers (73 and 74 m/s in Poulsen et al. [21] and Xiang [22], respectively). The comparison implies that the experimental results are credible.

respectively.
Numerous theories have been developed to determine the FDs in wind tunnel tests [18][19][20]. In this study, the iterative least-squares (ILS) theory proposed by Chowdhury and Sarkar [20] was adopted to determine the FDs. Specifically, the experiments were conducted with the free-vibration technique, and the initial forced displacements were applied to the bridge model in the vertical and rotational directions. Then, the free-decay oscillations under different wind speeds were measured (inlet wind speeds of 2, 4, 6, 8, 10, 12, and 14 m/s were considered). After obtaining the time history response, the FDs were determined using the ILS method. Finally, based on the determined FDs, the flutter motion equation was solved to obtain the critical flutter velocity with the conventional method (omitted for brevity).
To validate the reported results, the FDs and critical flutter speed of the bridge section model without a control system were compared with previous results of a similar bridge deck section investigated by Poulsen et al. [21] and Xiang [22]. Figure 4 compares the results of eight FDs. In order to clearly compare the trends of FDs, the data were fitted into a smooth curve using a quadratic polynomial with one variable. The values and trends of the FDs H agreed well with those of previous studies. However, some deviations at isolated points, as shown in Figure 4c,e,g, existed, which belonged to H . Nevertheless, the overall trends were consistent. Two possible reasons exist for the previously mentioned discrepancy. The first one might be the minor differences in the design of the tested bridge deck section; the second reason is that the ILS method used for extracting the FDs is dependent on the actual situation. In general, the extraction results of the FDs were acceptable for subsequent analysis. The obtained FDs were used to deduce the critical flutter speed, which was 76.65 m/s and approximately the results of other researchers (73 and 74 m/s in Poulsen et al. [21] and Xiang [22], respectively). The comparison implies that the experimental results are credible.

Effects of Steady-Suction-Based Flow Control on Flutter Derivatives
Based on Equation (1), the FDs are transfer functions of bridge displacements to self-excited forces that might lead to flutter. They are regarded as indicators of the bridge deck flutter susceptibility. Therefore, they are often employed to assess the aerodynamic stability of structures. The purpose of this part is to discuss the effects of steady-suction flow control on FDs to theoretically analyze the control mechanism.

Effects of Steady-Suction-Based Flow Control on Flutter Derivatives
Based on Equation (1), the FDs are transfer functions of bridge displacements to self-excited forces that might lead to flutter. They are regarded as indicators of the bridge deck flutter susceptibility. Therefore, they are often employed to assess the aerodynamic stability of structures. The purpose of this part is to discuss the effects of steady-suction flow control on FDs to theoretically analyze the control mechanism.
All eight FDs, i.e., H * 1 − H * 4 and A * 1 − A * 4 , of the different cases extracted through the ILS method are presented in Figures 5-10      H is positive for negative aerodynamic damping, which indicates a potential dynamic instability of the bridge deck section. To be specific, if the negative aerodynamic damping is stronger than the positive structural damping, the total heave damping (the sum of aerodynamic damping and mechanical damping of a structure) in the heave Figure 9. H is positive for negative aerodynamic damping, which indicates a potential dynamic instability of the bridge deck section. To be specific, if the negative aerodynamic damping is stronger than the positive structural damping, the total heave damping (the sum of aerodynamic damping and mechanical damping of a structure) in the heave generally lower than those of the cases with longer intervals (l-3d-5 and l-4d-5). Thus, a shorter interval is the better choice. Regarding the cases with different suction flow rates (Figure 10a), the growth rate of A * 1 decreased with increasing suction flow rate. Thus, increasing the suction flow rate reduces the negative aerodynamic damping, and flutter can be avoided.
The A * 2 derivative is crucial for studying pitch dynamic stability because it is directly related to the aerodynamic damping in the pitch motion. The critical destabilizing role of A * 2 was reported by Matsumoto et al. [23]. Negative aerodynamic damping in the pitch motion due to positive values of A * 2 can lead to negative total damping and therefore flutter. The suction strengthens the dynamic stability in a torsional motion because the resulting negative slope of A * 2 is greater than that of the single-deck case. According to Figure 8b, case l-2d-10 exhibited the sharpest decrease in A * 2 , followed by the cases m-2d-10 and b-2d-10. Figures 9b and 10b show that a shorter suction interval and higher suction flow rate caused A * 2 to decrease more rapidly. Thus, the net damping increased. This demonstrates the positive influence of the suction control system on the aerodynamic characteristics of the bridge deck from another angle.
Although the A * 3 derivative tended to increase with installed control system for U r > 8 indicating that the total torsional stiffness decreased, flutter is generally not caused by a negative torsional stiffness because of the relatively large structural torsional stiffness. Moreover, A * 4 has proven to be small and sensitive to noises [24]. Although the A * 4 derivative had a relatively unpredictable trend for the entire range of the studied wind velocities, it is reported for the sake of completeness.
In general, the FDs were significantly influenced by the steady-suction-based control method, particularly A * 1 , A * 2 , H * 1 , and H * 2 , which were related to the aerodynamic damping of the structure. According to the results, installing the control device with optimal control parameters reduced the negative aerodynamic damping and therefore the total damping of the structure.

Influence of Steady-Suction-Based Flow Control on Critical Flutter Speed
The objective here was to investigate the influence of different control parameters, including the suction slot position, suction interval, and suction rate, on the critical flutter speed (U c ) of the bridge girder to verify the effectiveness of the steady-suction control regarding the flutter performance. Moreover, the sensitivity of the control effect to various parameters was studied. The critical flutter speeds and the corresponding growth rates β at three slot positions and for four suction intervals and three suction flow rates were compared and analyzed. The growth rates β of U c were calculated with β = (U c − U c0 )/U c0 × 100%, in which U c0 is the value of U c without steady-suction-based control system. All test cases were conducted under a 0 • wind attack angle.

Influence of Suction Slot Position
Three representative test cases with different slot positions (i.e., l-2d-10, m-2d-10, and b-2d-10) were performed to determine the influence of the slot position on the flutter control effect. Figure 11 shows the critical flutter speeds of the three test cases and that of the single-deck case (i.e., s00). The critical flutter speeds (U c ) of cases l-2d-10, m-2d-10, and b-2d-10 were 84.68, 76.84, and 79.45 m/s, respectively, which were higher than that of the single-deck case (U c0 of 76.65 m/s). The corresponding β were 10.5%, 0.25%, and 3.7%, respectively. According to the control results, case l-2d-10 was the best choice. The other two cases had relatively limited positive influence on the flutter characteristics, and case m-2d-10 resulted in the worst outcomes. It can be concluded that disturbing the flow separation directly at the windward edge of the girder is better than disturbing the vortex drift. In conclusion, the steady-suction-based method can improve the flutter performance of the bridge based on critical flutter speed. However, the control effect is sensitive to the suction slot position, and the optimal position is located on the windward side of the low surface.
characteristics, and case m-2d-10 resulted in the worst outcomes. It can be concluded that disturbing the flow separation directly at the windward edge of the girder is better than disturbing the vortex drift. In conclusion, the steady-suction-based method can improve the flutter performance of the bridge based on critical flutter speed. However, the control effect is sensitive to the suction slot position, and the optimal position is located on the windward side of the low surface.

Influence of Suction Interval
To investigate the influence of the suction interval on the control effect, five test cases with different relative suction intervals (i.e.,   1, 2, 3, 4, and  ) were selected. The infinity value  denotes the case without control (i.e., s00). As shown in Figure 12, the flutter onset velocities of cases l-1d-5, l-2d-5, l-3d-5, and l-4d-5 were 82.51, 79.66, 79.36, and 79.05 m/s, respectively, and the corresponding  were 7.6%, 3.9%, 3.5%, and 3.1%, respectively. According to the test results, c U of the model constantly decreased with increasing suction interval. For a relative suction interval of   1, a maximal c U increment of 7.6% was obtained. In general, the control effect highly depended on the suction interval. Moreover, a short suction interval had a significant effect on the surrounding flow field and flutter performance of the structure. Thus, setting a suction interval as narrow as possible within a reasonable range is a recommended flutter countermeasure for a bridge deck.

Influence of Suction Interval
To investigate the influence of the suction interval on the control effect, five test cases with different relative suction intervals (i.e., λ = 1, 2, 3, 4, and ∞) were selected. The infinity value ∞ denotes the case without control (i.e., s00). As shown in Figure 12, the flutter onset velocities of cases l-1d-5, l-2d-5, l-3d-5, and l-4d-5 were 82.51, 79.66, 79.36, and 79.05 m/s, respectively, and the corresponding β were 7.6%, 3.9%, 3.5%, and 3.1%, respectively. According to the test results, U c of the model constantly decreased with increasing suction interval. For a relative suction interval of λ = 1, a maximal U c increment of 7.6% was obtained. In general, the control effect highly depended on the suction interval. Moreover, a short suction interval had a significant effect on the surrounding flow field and flutter performance of the structure. Thus, setting a suction interval as narrow as possible within a reasonable range is a recommended flutter countermeasure for a bridge deck. the flow separation directly at the windward edge of the girder is better than disturbing the vortex drift. In conclusion, the steady-suction-based method can improve the flutter performance of the bridge based on critical flutter speed. However, the control effect is sensitive to the suction slot position, and the optimal position is located on the windward side of the low surface.

Influence of Suction Interval
To investigate the influence of the suction interval on the control effect, five test cases with different relative suction intervals (i.e.,   1, 2, 3, 4, and  ) were selected. The infinity value  denotes the case without control (i.e., s00). As shown in Figure 12, the flutter onset velocities of cases l-1d-5, l-2d-5, l-3d-5, and l-4d-5 were 82.51, 79.66, 79.36, and 79.05 m/s, respectively, and the corresponding  were 7.6%, 3.9%, 3.5%, and 3.1%, respectively. According to the test results, c U of the model constantly decreased with increasing suction interval. For a relative suction interval of   1, a maximal c U increment of 7.6% was obtained. In general, the control effect highly depended on the suction interval. Moreover, a short suction interval had a significant effect on the surrounding flow field and flutter performance of the structure. Thus, setting a suction interval as narrow as possible within a reasonable range is a recommended flutter countermeasure for a bridge deck.

Influence of Suction Flow Rate
Four cases (i.e., l-2d-0, l-2d-5, l-2d-7, and l-2d-10) with the suction rate as a single variable were designed to study their control effects. As shown in Figure 13, the control effect was observable for the relative suction flow rates of C q = 0, 0.00174, 0.0244, and 0.00348 L/min, which corresponded to Q = 0, 5, 7, and 10 L/min, respectively. Further increasing the suction flow rate led to a higher flutter onset velocity with a peak value at the highest relative flow rate of C q = 0.00348 L/min. More specifically, the critical flutter speeds measured for suction flow rates Q = 5, 7, and 10 L/min were 79.66, 80.34, and 84.68 m/s, respectively. The corresponding β were 3.9%, 4.8%, and 10.5%, respectively. These results