A wind tunnel study on control methods for cable dry-galloping

Abstract

The common vibration of cable caused by rain-wind combination has been known as most typical type and a lot kind of its countermeasures has been proposed for suppressing this phenomenon. Recently, stayed-cables were also proved that they could be excited in dry state (without rain), which is called dry-galloping. Recently, its mechanisms have been explained by axial flow, Reynolds number and so on. To clarify the characteristics of this galloping, wind tunnel test of a cable model with various kinds of wind angle was conducted. Then, three types of countermeasure were examined to suppress dry- galloping of bridge cable. The tests confirmed that the occurrence of dry-galloping depends on relative wind attacked angles and onset reduced wind speed. Furthermore, single spiral wire, double spiral wire and circular ring were found to have high effectiveness in mitigating this galloping when those are installed properly.

Keywords

dry-galloping / wind-relative angle / single spiral wire / double spiral wire / circular rings

Introduction

With the development of modern structural materials and the advancement of construction technologies, it is possible to build bridges, which have longer span and taller height. In that expansion, cable-supported bridge type has become more and more popular since recent several decades because of its ease of construction, aestheticism and economic issue. This type of bridge is usually flexible and very sensitive to effects of wind and earthquake. In long span bridges, cable has been widely used in various types of vital component. In the past, during construction or once the bridge is completed and in service stage, stay cable had known to vibrate due to rain wind combination. Recently, it also proved that cable could be excited even though in the condition without rain, which called dry-galloping. In common, cable vibrations can be divided into two main categories: Wind-induced vibration type and non-wind-induced vibration type. Wind-induced vibrations includes rain-wind induced vibration, high-speed vortex-excited vibration, motion caused by cable tensions fluctuation; motions caused by wind turbulence buffeting, wet or dry galloping etc.…; whereas non-wind-induced vibrations are parametric excitation and external excitation. Divergent motion type induced by wind for a dry inclined cable was observed in wind tunnel tests by Saito et al. [ 1], Honda et al. [ 2] and Matsumoto et al. [ 3] in the subcritical Reynolds number regime, and by Miyata et al. [ 4], Cheng et al. [ 5], Arash Raeesi et al. [ 6, 7] and Jackobsen et al. [ 8] in the transition and critical Reynolds number regime.

Matsumoto et al. [ 3] explained the differences between the Saito criterion and FHWA criterion by classifying galloping into divergent-type galloping and unsteady galloping. Furthermore, they also shed light on the role of axial flow for galloping instability by conducting wind tunnel test with and without artificial axial flow along the wake of cable. Beside of that, Matsumoto et al. [ 9] also had pointed out that the axial flow also was visualized in the field by using the light strings for the proto-type stayed cable with relative angle around 40°–50°. In the experiments of Cheng et al. [ 5], both divergent type of motion and limited-amplitude vibration at high reduced wind speed were observed. However, the characteristics and excitation conditions of these two phenomena are different. The former has similar response as galloping while the latter occurs only in certain narrow high reduced wind speed ranges and has different onset conditions. Apart from that, Katsuchi et al. [ 10] conducted wind tunnel experiments for investigating the characteristics of dry-galloping for normal and indented cable surface with different Scruton number. They found that increase of Scruton number decreases the non-dimensional vibration amplitude but not thoroughly. Recently, Jakobsen et al. [ 8] concluded that the most vigorous dry-vibrations were observed at 60° of inclination with damping ratios below 0.2% and significant “lock-in” between the lift force and the violent sway cable response was identified in terms of the transfer function between the two during the large vibration events. Generally, dry-galloping is classified as one of the wind-induced large amplitude vibration phenomena in dry weather, usually occurs at relatively high-reduced wind speed, it also showed some characteristics of limited amplitude vibration, however. Some studies showed the existence of dry-galloping, in both wind tunnel test and the site observation as mentioned above. Nevertheless, its characteristics do not fully understand, as well as control methods for this phenomenon are under developing. In this paper, dry galloping of a round-shape cable will be investigated in different attitudes with smooth cable surface and smooth wind flow. Besides that, single spiral wire, double spiral wire and circular rings were proposed and developed for suppressing dry galloping.

Wind tunnel test

Experimental parameters

Wind tunnel test (WTT) was carried out in a wind tunnel circuit of the Yokohama National University, Japan. The sizes of the working section are 1.3 m width and 1.8 m height. The maximum wind speed is around 18 m/s. Cable model was supported by 1-DOF spring system in the vertical direction, as shown in Fig. 1. It was tested to observe the characteristics of cylinder oscillation as well as to determine the critical wind angle range for dry-state galloping. To arrange a wide range of wind directions, the experiments were conducted by changing yawed/inclined angles or yawed angles only. Table 1 shows the test conditions in which the cable model diameter was 75 mm in considering the blockage ratio of less than 5%. In addition, damping ratio is kept unchanged throughout whole tests at 0.127%. The experiments were carried out with normal smooth surface and smooth flow.

In Table 1, Scruton number is a non-dimensional parameter that characterizes the mass and damping properties of a flexible body. In this study, Scruton number was defined as follow:

(1) S_{\mathrm{c}}={\displaystyle \frac{2m\delta }{\rho D^{\mathrm{2}}}},

where, δ = logarithmic decrement of cable model; ρ = air density (kg/m³).

Definition of angle

The setting position of model can be defined as vertical angle α and horizontal yawed angle β, see as Fig. 2. Then, wind relative angle β^*, which defines angle between wind direction and cable axis, can be simply calculated by the following formulation:

(2) {\beta }^{*}={\sin }^{-\mathrm{1}}(\cos \alpha \times \sin \beta ).

Results and discussion

Effect of yawed angle

Various wind yawed angles, which ranged from 20° to 70°, are selected to check the effect of this factors to the vibration of cable (see as Fig. 3). In these kind of WTTs, it is clear that inclined angle is equal to 0 (α = 0), therefore it is easy to derive that wind relative angle is coincide with yawed angle (β = β^*).

The effect of wind yawed angle to galloping can be seen in Fig. 4. Obviously, large amplitude vibration occurred in a range of yawed angle from 30° to 60°. Moreover, the divergent galloping took place at reduced wind speed of 110 to 130 in these tests. In case of yawed angle 50°, vibration seems to be the most extreme. In detail, large amplitude vibration started from 90 of reduced wind speed and reach the amplitude 0.7D (D is cable diameter) at reduced wind speed 120. Furthermore, it also showed the sharpest gradient. On the contrary, there is no considerable large amplitude at cases of 20° and 70° respectively, maximum vibration is less than 0.2D in the cases. To summarize, the critical range of yawed angle can be shown as Fig. 5.

According to the WTT results of Saito et al. [ 1], Honda et al. [ 2] and Matsumoto [ 3], unstable response of cable can be find in the subcritical Reynolds number range. Whereas, current test also found the large-amplitude vibration in subcritical Reynolds number range (around 6×10⁴ − 7×10⁴), so this totally agreed with three above WTTs. Besides that, the experimental outcomes of Matsumoto et al. [ 3], Kleissl and Georgakis [ 11] proved that there was an existence of axial flow in near wake of cable, which can excite galloping of cable, and its velocity increased with yawed angle. For this reason, it seems to be that changing of yawed angles may affect to axial flow near the wake of cable. Hence, dry-galloping can be occurred in that range of relative wind angle.

Effect of inclination

These series of these experiments are conducted with inclined angles changing gradually from 25° to 70° in considering the effect of attitudes to cable galloping, whereas yawed angle was unchanged at 45°, which is in yawed angle critical region as Fig. 5. Additionally, other parameters of the WTT were same as Table 1. The detail of yawed angles, inclined angles and relative angles are described as Table 2.

From the Fig. 6, dry-galloping occurred in a relative angle range from 24° to 40°. The case 30° of wind relative angle tends to exhibit the most critical responses. When reduced wind speed increased from 0 to 120, cable vibration was inconsiderable under around 0.2D but then it galloped dramatically with significant amplitudes and reached 0.6D at around 140 of reduced wind speed. Additionally, in the range of wind relative angle (β^*) from 24° to 40°, dry-galloping was taken place at around 120 to 140 of reduced wind speed, compared to 110 to 130 of yawed angle case. This can be caused by the cable model end attitudes, which are different between yawed angle cases and yawed/inclined angle cases.

Effect of cable attitude

To clarify the effect of cable attitudes to vibration and also to compare the responses between yawed angle case and yawed/inclined angle case, which have same wind relative angles, three wind relative angle cases (40°, 30° and 20°) were investigated. The detailed comparison cases are presented as Table 3.

Figures 7, 8 and 9 demonstrates the comparison of cable vibration in different type of angles. It can be seen that same wind relative angle (β^*) exhibited same vibration trends in all cases, although cable model were fixed in different attitudes. In another expression, inclined cable’s response depends on wind relative angle. This finding can play a significant role for later WTT. Instead of setting up cable model in different attitudes, we can set up the cable model simply at only horizontal plane, which has the same wind relative angle. However, it should investigate other cases as well as study on flow field for further conclusions.

Control methods for cable dry-galloping

It was pointed out that instability level of cable is sensitive to the surface of cable. In the past, some types of cable surface modification had been proposed to suppress rain-wind induced vibration. Flamand [ 12] used helical fillets of 1.5 mm on the cable surface of Normandie Bridge and this countermeasure was proven effectively. Since then, this kind of cable surface modification has come to be used for cable-stayed bridges. Moreover, Gu and Du [ 13] concluded that only proper spacing of the spiral wires could destroy the upper rivulet and further suppress rain−wind-induced vibration of cables. Apart from that, Phelan et al. [ 14] showed some test cases about this kind of countermeasure to suppress rain-wind-induced vibration. Kleissl et al. [ 11] presented the smoke visualizations of the near-wake flow structures of the cable for 45° relative wind angle. In the first WTT with plain cable (normal surface), a strong channel of axial flow was observed clearly along the leeward side of cable. Nevertheless, this type of flow is found to be nearly suppressed in the WTT with the helical fillets. These test findings affirmed that helical wire could eliminate the axial flow but we should note that their WTTs were conducted under static condition. Until now, some types of control method have been given, however, the optimum parameters for installing as well as design code for eliminating dry-galloping is under developing. In this study, single spiral wire, double spiral wires and circular rings are proposed to mitigate dry-galloping by different series of test. The details of three types of countermeasure are displayed as Fig. 10.

Single spiral wire

According to the discussions above, Matsumoto et al. [ 3] proved clearly the role of axial flow near wake in exciting cable galloping. In addition, K. Kleissl et al. [ 11] indicated that helical wire can suppress the axial flow. Therefore, as spiral wire is installed along the cable in proper manner, it can reduce galloping of cable. Indeed, it is necessary to figure out the optimum twined pitches of this countermeasure. In the current test, single spiral wire of diameter D/25 (3 mm), D/15 (5 mm), 2D/15 (10 mm) and D/5 (15 mm) were selected in considering that wire diameter should be large enough to suppress the formation of axial flow near cable wake. These wires were twisted along the cable with different spacing from one time of cable diameter to five times of cable diameter (1D–5D). To verify the mitigation level, cable model was set up in the horizontal plane at 45 degree of yawed angle. The WTT installing is as Fig. 11.

Figures 12 −15 illustrate the effectiveness of spiral wire on mitigating vibration of cable. In these WTTs, different wire diameter and twine spacing were checked. Single spiral wire cases of D/15 and 2D/15 in spacing from 2D to 3D along the cable showed dominant cases. For the case with 2D/15 wire diameter, twined spacing 2D to 4D exhibited the highest mitigation ability. Amplitude less than 0.2D was recorded at 120–130 of reduced wind speed, compared to 0.65D of none-wire case. However, as increasing twined pitch to 5D or decreasing to 1D, effectiveness of the spiral wire decreased moderately as shown in Fig. 12. Additionally, nearly same effectiveness was found for the D/15 case as Fig. 13. On the other hand, the cases with spiral wire of D/25 and D/5 did not perform well in eliminating dry-galloping as presented in Figs. 14 and 15. The similar outcome for case D/25 were found, non-dimensional amplitude around 0.2D and 0.4D were found at reduced wind speed around 120 at twined spacing 2D and 4D, respectively. Nevertheless, the case of wire D/5 (15 mm) was quite ineffective, as Fig. 15. As a result, helical wire diameter in combining with the twined pitches must play very vital role in mitigating dry galloping by a complicated manner. The changing of each factor will lead to different level of efficiency.

Besides that, single spiral wire also showed high efficiency in case of yawed angle 30° when wire was twisted at spacing 2D and 3D respectively as shown in Fig. 16. This confirmation reaffirmed the ability to eliminate the cable galloping of spiral wire in the other wind angle. At present, the cases with diameters from D/15 to 2D/15 at pitches of 2D–3D are the most eligible for suppressing dry-galloping.

Double spiral wire

According to the test results of single wire case, double spiral wire of diameters D/15 (5 mm) and D/25 (3 mm) were twined clockwise and anti-clockwise along the cable model with spacing of 2D−4D to confirm the effectiveness and compare to the single spiral wire case. Setting up of double spiral wire countermeasure is illustrated as Fig. 17. According to test results as Figs. 18 and 19, vibration amplitude with double spiral wires at spacing of 2D to 4D is quite small. Dry galloping at high-reduced wind speed was reduced efficiently in these cases. For D/25 (3 mm) double spiral wire case, vibration was almost suppressed at twined pitches 2D and 3D. Furthermore, non-dimensional amplitude less than 0.2D can be found at reduced wind speed 140, whereas plain cable (no wire) case reached amplitude 0.65D at same wind speed. As twined spacing was up to 4D, mitigation ability was declined moderately, in which non-dimensional amplitude 0.3D occurred at reduced wind speed of around 125. Consequently, it is undeniable that twined spacing has great effect on vibration mitigation. In comparison, the case with D/15 (5 mm) double spiral wire exhibited more effective than D/25 (3 mm) case. However, both cases showed the good performance in destroying large amplitude vibration. Additionally, this countermeasure also performed well when conducted with yawed angle of 30° as Fig. 20. To summarize, double spiral wire is able to mitigate dry galloping significantly. Nevertheless, it should conduct with the other WTT for further conclusions.

Figure 21 demonstrates the comparison of single and double spiral wires countermeasures in mitigating dry galloping. Overall, almost divergent vibration was suppressed totally, typical amplitude under 0.25D. Among of these, double spiral wire D/15 at the pitch of 2D shows more dominant than others. In detail, vibration amplitude tends to level off at approximately 0.1D even though reduced wind speed increased up to 140 for this case.

Circular ring

To investigate the effectiveness of circular rings, D/10 (7.5 mm) rings were attached at pitches from 2D to 4D. The attachment of circular ring countermeasure is shown as Fig. 22.

According to Fig. 23, it is clear that circular rings were much effective when placed at two times to three times of diameter (2D–3D). It is absolutely agree with single and double spiral case above. No divergent galloping was observed. Among three cases, the case with 2D spacing exhibited the most effectiveness. Non-dimensional amplitude did not exceed 0.2D even at high-reduced wind speed 140. Similarly, twined spacing of 3D almost suppressed large amplitude vibration; however, efficiency is less than the case with pitch at 2D. On the other hand, the pitch at 4D can only mitigate vibration in some extent, approximate 0.4D amplitude occurred from 115 to 130 of reduced wind speed.

This result absolutely agreed with the outcomes of Phelan et al. [ 14] in which the ring countermeasure exhibited effectiveness in suppressing cable vibration. Additionally, effectiveness of circular ring countermeasure was also reconfirmed clearly by different yawed angle (30°) as shown in Fig. 24. In conclusion, single spiral wire, double spiral wire and the circular ring are the adequate countermeasures to versus dry galloping; nevertheless, the selection of twined pitches as well as wires diameter should be considered carefully. The spacing of 2D to 3D showed the most optimal range in almost all cases through all WTT.

Findings and conclusions

In the present work, cable dry-galloping were investigated by WTT with normal smooth surface cable and smooth wind flow. Various experimental cases were considered and discussed. Under each case, responses of cable were different and it depended on wind attack angle as well as cable attitude. More importantly, some types of countermeasure were suggested for mitigating dry-galloping. Cable galloping at high-reduced wind speed and effectiveness of its countermeasures were recorded. Important findings are given as follow:

1) Dry-state-galloping occurred in some range of yawed angles at high reduced wind speed. For the cases of yawed/inclined angle combination, dry-galloping is almost consistent to yawed angle case.

2) The same wind relative angles (β^*), the nearly same responses and vibration’s trend will be exhibited. In other expression, dry-galloping is governed by wind relative angle even for different cable attitudes to wind flow.

3) Among the experimental results, optimum twined pitch range is around 2D to 3D.

4) Wire diameter incorporates with twined pitch by complicated manner and they play a significant role in mitigating dry-galloping. Single spiral wire, double spiral wire and circular ring are much effective in eliminating cable galloping when installed properly. The changing of each factor will lead to different level of efficiency. Therefore, it should be careful when determine the diameter, twined pitch of wire for controlling this phenomenon.

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