Abstract
With global climate and environment deterioration, the desertification is getting worse and the phenomenon of windsand flow frequently occurs in many areas. Hangers of suspension bridges may suffer the impact from windsand flow and be damaged. In this study, the ridingtype hangers with four strands which are the commonly used hanger of longspan suspension bridges are taken as an example to investigate the influence of windsand flow on the hangers. The aerodynamic interference effect can occur among the four strands under the action of windsand flow. In order to explore the influence of windsand flow on the hangers, the windsand flow field around the ridingtype hangers of a longspan suspension bridge is simulated within the FLUENT software on the basis of the numerical simulation of computational fluid dynamics. The pressure and velocity contour, aerostatic coefficients and forces produced by the windsand flow under different wind attack angle and volume fractions of sand phase are analyzed from the simulation. Results indicate that the forces exerted by the windsand flow on ridingtype hangers are greater than the forces exerted only by wind. In the wind and windsand flow field, the drag and lift coefficients of the front two strands of hangers exhibit minor changes with increasing wind attack angle, whereas those of the back two strands increase first and then decrease to a small value. The volume fraction of the sand phase has an insignificant effect on the drag and lift coefficients, but has a significant effect on the force exerted on the hanger, and the force exerted on the hangers multiplies when the volume fraction of the sand phase multiplies. The results lay a theoretical foundation for the corrosion fatigue analysis of ridingtype hangers for largespan suspension bridges under the action of windsand flow.
1. Introduction
With global climate and environment deterioration, desertification has become one of the most prominent environmental problems in the world [1, 2]. The Chinese desertification situation is very serious, and China has become one of the most severely desertification countries in the world, with up to 3.3 million km^{2} desertification lands [35]. Land desertification provides the source material for windsand flow. And the windsand flow occurred in Midwest China has become more and more frequent and serious, and causes huge losses to the country every year. As for the research of desertification, it mainly focused on the prevention and control of desertification itself. For example, Sun et al. [6] inspected the relationship between spatial and temporal distribution of vegetation and climate, and studied the ecological restoration in the Loess Plateau of China. Cheng et al. [7] presented an alternative way to prevent water loss and soil erosion and for prevention and revitalization by using microbial biopolymers. Yang et al. [8] studied the changes of soil organic carbon in soil aggregates associated with different stages of desertification process in the ordos sand land of Inner Mongolia and analyzed the distribution and aggregate changes of soil combined humus. The study of Rocio et al. [9] presented a way that integrated a set of indices on behalf of four desertification factors (vegetation, soil, climate and anthropic disruptors) to analyze desertification risk in the semiarid highlands of central Mexico. Xie et al. [10] studied the formation mechanism and the proper control methods of sand hazards at Honglianghe River section of QinghaiTibet Railway. However, very few studies have been reported on the influence of windsand flow produced by desertification on bridges, especially on the longspan suspension bridges.
Given the rapid economic development and increasing road traffic in Midwest China, the number of longspan bridges across rivers or canyons has been increasing day by day. A suspension bridge as a major bridge type to overcome great distances is required to against external and high intensity loads [11]. The hangers of cable system bridges are one of the members that have important effects on structural safety and are also damageable during the operation period of the bridges [12]. The limiting life of a suspension bridge can be mainly controlled by the aging of the cables and hangers [13, 14]. The ridingtype hangers are the main sling form for suspension bridges. The juxtaposition of four strands shows not only the aerodynamic interference effect by the wind but also the effect of windblown sand on hangers in the desert area, which cannot be disregarded. For a long time, blown sand engineering has always been treated as the main study content of desertification and its governance. However, the current research level of blown sand physics is still far from meeting the various needs of engineering practice. The effect of blown sand on the ridingtype hangers of a suspension bridge is unclear. The basic theory knowledge for the effect of windsand flow on hangers is insufficient, and the experiment research is complex. Therefore, numerical simulation has become one of the effective methods to research sandstorms.
At present, there has been much research on the bridge hangers. For example, in Qiu’s study [15], the influences of sudden breakage of hangers on the bridge due to corrosion are researched and analyzed in detail by using nonlinear dynamic analysis method and setting up the threedimensional finite element model. Shao et al. [16] pointed out a regression equation which is helpful to calculate the hanger's dynamic stresses, and the regression equation is deduced from finite element method. Zeng et al. [17] took the hangers of Jiangyin Bridge as the research example, and pointed out an evaluation method based on SN curve of suspenders fatigue damage, and the research results show that the fatigue life of long hangers is longer than the shorter ones, so the shorter hangers are the focus of maintenance. Gjelstrup et al. [18] analyzed aerostatic coefficients though the static wind tunnel tests on a bridge hanger represented by a circular cylinder with simulated thin ice accretions, while mean and fluctuating responses through the dynamic tests. Demartino et al. [19] also studied the influence of ice accretion on bridge hangers, and measured the aerodynamic force coefficients under different yaw Angle, different wind attack angles and wind speed through wind tunnel test. Zhan et al. [20] studied vortexinduced vibration of steel box hanger with varying wind attack angle by establishing twodimensional bending fluidstructure interaction numerical model within secondary development of software FLUENT. Bai et al. [21] studied the vortexinduced vibration behavior of steel arch bridge hanger by developing a fluidstructure interaction numerical simulation technique which is based on CFD numerical simulation. However, the study of the effect of windsand flow on the damage of hangers has not attracted the attention of experts and scholars.
The current work focuses on the law of aerodynamic interference effect of four strands on a rectangular arrangement and the force of the windblown sand exerted on the four strands. To achieve this goal, we adopted computational fluid dynamics (CFD) on the basis of a previous research that refers to the ridingtype hangers of a longspan suspension bridge. The windsand flow field around the hangers of a longspan suspension bridge is simulated within the FLUENT software. To start with, the drag and lift coefficients of a column section and a rectangular section are calculated to verify the reasonability and validity of the method. Thereafter, the same method is used to simulate the wind flow and windsand flow around the hangers of a suspension bridge, analyzed the influence of different wind attack angle and different sand phase volume fraction on the ridingtype hangers are analyzed respectively. Finally, the influence mechanism of windsand flow on the ridingtype hangers is analyzed. These studies can lay the foundation of the fatigue analysis of ridingtype hangers for largespan suspension bridges.
2. The effect of sand volume fractions on the aerodynamic force on ridingtype hangers
2.1. Numerical simulation method of the aerodynamic coefficients for four cylinders in a rectangular arrangement
Drag and lift coefficients are the dimensionless form of drag and lift forces. The components of applied force for the bluff body downstream and cross flow are called drag and lift forces, respectively. Fig. 1 shows the diagram of the bluff body submerged in fluid. The drag and lift coefficients can be defined as follows [22]:
where ${F}_{D}$ and ${F}_{L}$ are the drag and lift force of the hangers section in the body axis coordinates, respectively; $\rho $ is the density of fluid; $U$ is the average velocity of fluid; $B$ is a characteristic length of the bluff body cross section along the wind dimension [23].
Fig. 1Lift and drag force on any bluff body
The mathematical model of incompressible Reynoldsaveraged NavierStokes equations and the standard $k$$\epsilon $ twoequation turbulence model are adopted. The wind is treated as a 2D unsteady incompressible flow because of the high velocity of crosswind airflow, and the effect of temperature changes is not considered. The finite volume method is combined with the wall function method and use the secondorder upwind scheme. The CFD software FLUENT is used to simulate the flow field around the model and the convection and diffusion terms are used to calculate singleprecision data. The problem of the speed component in momentum equation coupling with the pressure is solved by the default SIMPLE algorithm.
The correctness of the model for numerical wind tunnel test has been verified by Lam et al. [24]. On the basis of the experimental data provided in literature, the data of the spacing ratio $L/D=$ 3.83 is simulated in this paper ($L$ is the centertocenter cylinder spacing and $D$ is their diameter) [24]. Fig. 2 shows the results of the CFD numerical simulation that are almost the same as those of related literature. However, a difference exists between the simulated results and experimental results mainly because of the assumption of that a planar flow field is a 3D flow field in nature. Furthermore, the similar ratio, unit number, and computational domain also have a certain influence to the result. The small difference indicates that the numerical simulation method is reasonable and valid. By contrast, the singlecolumn model of wind flow is simulated with the same method by using a Reynolds number of 8×10^{4}. Table 1 show that the drag coefficient of the column is 1.215, which is almost the same as that in the related literature. Therefore, the numerical simulation method for the wind flow is reasonable and valid.
Fig. 3 shows the layout of the ridingtype hangers of a largespan suspension bridge. The ridingtype hangers include the general sling, short sling, and long sling near the tower. The general sling is taken as the research object because it is mostly used in the hangers of a suspension bridge. The slings are in a rectangular arrangement, and the spacing is 600 mm across the bridge and 300 mm along the bridge. Fig. 4 shows the constructed diagram of a general ridingtype hanger. Given that the length of the sling is larger than its diameter, the calculation problem of the flow field is approximated into a plane problem, i.e., the flow is calculated around four cylinders that are in rectangular arrangement.
Fig. 2Results of the numerical simulation and related literature [24]
a) Drag coefficients
b) Lift coefficients
Table 1Force calculation results compared with experimental results
Author  Re  Drag coefficients 
Simiu et al. [22]  10×10^{4}  Approximately 1.22 
Lam et al. [24]  6×10^{4}  1.217 
This study  8×10^{4}  1.215 
Fig. 3Layout of the ridingtype hangers of a largespan suspension bridge
Fig. 4A photo of the ridingtype hangers
Fig. 5Diagram of the wind field around the hangers
In Fig. 5, $U$ is the wind speed and $\alpha $ is the wind attack angle. Four slings are named No. 1, No. 2, No. 3, and No. 4, respectively. The distance between No. 1 and No. 2 correspond to the distance of the sling along the bridge, whereas the distance between No. 2 and No. 3 correspond to the distance of the sling across the bridge. The sling diameter is 60 mm. Referring to the simulation results of the bluff body with a rectangular section. Fig. 6 shows the distance of the center to the upstream boundary (5 B1), downstream boundary (10 B1), and top and bottom boundaries (both 5 B1). B1 is the width of the circumscribed rectangle section of the four slings. By adopting the massive grids, Fig. 7 shows that the minimum size of the grid is 0.0036 B1, and the total number of the grid is 181,500.
Fig. 6Computational domain for windsand flow around the ridingtype hangers
Fig. 7Mesh of the windsand flow on the ridingtype hangers
a) Mesh of the windsand flow field used in the calculation
b) The detailed figure of Fig. 7(a)
2.2. Aerodynamic performance comparative analysis of the ridingtype hangers in wind and windsand flow field
According to the wind resistance design specification for highway bridges (JTG/T D60012004) on the basis of the effect of the maximum wind speeds and wind forces of different reproduced periods on highway traffic meteorological condition grades, the entrance windsand flow speed is 20 m/s [25]. The outlet boundary is outflow. The threshold boundary is outflow. The surface of the hanger section is treated as noslip wall boundary conditions, and the top and bottom boundary conditions are symmetry boundary.
On the basis of the numerical simulation of the singlephase wind field of the hanger section, we introduce the second phase, i.e., the sand phase. The density of the sand is 2000 kg/m^{3}, and the diameter is 5×10^{6}^{ }m. The speed of the windsand flow is 20 m/s. The mixture model is used as a multiphase flow model because of the simplicity and stability of the simulation result of the mixture model [26]. By adding only 2 % of the particle phase volume fraction, FLUENT is used to numerically simulate the wind flow and the windblown sand flow field under different wind attack angles.
Fig. 8 and Fig. 9 show the pressure contour and velocity contour of the four cylinders under 0° wind attack angle, respectively. It can be found that the shapes of pressure contour and velocity contour in the numerical simulation of windsand two phase flow are almost the same, but the maximum pressure in windsand flow field is about 30 times of wind field, so the effect of windsand flow on cables is exerted considerable. From the velocity contour, we can see that the velocity of mixture, air phase and sand phase are almost the same. Compared with the velocity contour in wind flow field, the velocity contour affected by the cable cross section area is larger, but the maximum velocity is smaller. The magnitude of pressure contour in windsand flow field is greater than it in wind flow field, because the density of sand is much largest than the density of air. Since the numerical simulation of windsand two phase flow is mixture model, and without considering the coupling effect between each phase.
Fig. 8Pressure contour under 0° wind attack angle
a) In wind flow field
b) In windsand flow field
Fig. 9Velocity contour around the cable under 0° wind attack
a) Velocity contour in windsand flow field
b) Velocity contour of air phase in windsand flow field
c) Velocity contour of sand phase in windsand flow field
d) Velocity contour in wind flow field
Fig. 10 and Fig. 11 show that the drag and lift coefficients of the four cylinders in the wind flow and windblown sand flow field that vary with the wind attack angle. From these diagrams, we can get the results as follows:
(1) The wind attack angle has a small effect on the drag and lift coefficients of No. 1 and No. 2, whereas the effect on No. 3 and No. 4 is larger. The lift coefficients of No. 1 and No. 2 decrease with increasing wind attack angle in the range of a small particle size. On the contrary, a fluctuation arises when the wind attack angle greatly increases. The absolute values of the lift coefficients of No. 3 and No. 4 firstly increase and then decrease at a small wind attack angle, but the fluctuation is not obvious when the wind attack angle becomes large.
(2) The drag coefficients in the windblown sand flows are approximately 1.2 times to 1.3 times higher than those in the wind flow. The lift coefficients in the windblown sand flow are also higher than those in the wind flow. Thus, the effect of sand is significant.
(3) Difference of the drag and lift coefficients between the front and back columns is large under the action of the sand flow. In the model of ridingtype hangers, the forces of the back two columns in the wind and windsand flow field are approximately 0.5 times to 0.7 times of that of the front two columns when the wind attack angle is from 0° to ±9°. The difference of the force on four cylinders becomes small with increasing wind attack angle (±15° to ±45°).
Fig. 10Drag coefficients of hangers under different wind attack angles in the 20 m/s wind field and 20 m/s windblown sand field
a) No. 1
b) No. 2
c) No. 3
d) No. 4
Fig. 12 shows the drag force on the hangers. The results indicate that the force on the hangers in windblown sand flow with a 2 % volume fraction of sand phase is considerably larger than that in the wind flow. The reason is that the introduction of sand increases the force on the columns. The former is approximately 40 times of the latter. Therefore, the effect of sand in the windblown sand flow on the force of the hanger cannot be disregarded.
Fig. 11Lift coefficients of hangers under different wind attack angles in the 20 m/s wind field and 20 m/s windblown sand field
a) No. 1
b) No. 2
c) No. 3
d) No. 4
Fig. 12Forces on No. 1 and No. 2 under different wind attack angles in the 20 m/s wind field and 20 m/s windblown sand field
a) No. 1
b) No. 2
2.3. The effect of the different volume fractions of sand phase on the aerodynamic force on ridingtype hangers
On the basis of previous analysis, the effect of the different volume fractions of the sand phase on the force exerted on four cylinders in a rectangular arrangement is simulated and analyzed under two different wind attack angles. The computational model of the 0° and −45° wind attack angle is calculated by changing the volume fractions of the sand phase only (0 %, 2 %, 4 %, 6 %, 8 %, and 10 %).
Fig. 13 and Fig. 14 show that the sand phase volume fraction has no effect on the shape of pressure contour and velocity contour, but has effect on the magnitude of pressure contour. With the increase of the sand phase volume fraction, the magnitude of pressure contour is also increased. Different wind attack angle has little impact on the magnitude of pressure contour.
Fig. 13Pressure contour in windsand flow field
a) 4 % volume fraction of sand phase under 0° wind attack angle
b) 6 % volume fraction of sand phase under 0° wind attack angle
c) 4 % volume fraction of sand phase –45° wind attack angle
d) 6 % volume fraction of sand phase –45° wind attack angle
Fig. 14Velocity contour in windsand flow field
a) 4 % volume fraction of sand phase under 0° wind attack angle
b) 6 % volume fraction of sand phase under 0° wind attack angle
c) 4 % volume fraction of sand phase under –45° wind attack angle
d) 6 % volume fraction of sand phase under –45° wind attack angle
Fig. 15 and Fig. 16 show the results. The drag coefficients of the two columns in the front increase with the introduction of the sand phase and decrease gradually with increasing volume fraction of the sand phase. The reason is because the drag coefficient varies with drag force and the density of the flow in our specific model. When introducing the sand phase, the drag force on the column and the density of the flow increases. However, the increase in drag force is larger; thus, the drag coefficient increases as the sand is introduced. With an increase in sand, and the densities increase although the drag coefficient increases at the same time. The densities increase quickly; thus, the drag coefficients decrease slowly. With the increasing volume fraction of the sand phase, the drag coefficients of the back two columns almost remain invariant whether the wind attack angle is 0° or −45°. The absolute values of the lift coefficients of the front columns are larger with the introduction of the sand phase, whereas the lift coefficients almost remain the same or have a tendency to decrease slowly with the increasing volume fraction of the sand phase. The drag and lift coefficients of the back columns are affected not only by the volume fraction of the sand phase but also by the wind attack angle. With the introduction of the sand phase and the increase in volume fraction of the sand phase, the absolute values of the lift coefficients of No. 3 at a 0° wind attack angle and No. 4 at a −45° wind attack angle slowly decrease; by contrast, the lift coefficients of No. 4 at a 0° wind attack angle and No. 3 at a −45° wind attack angle almost remain invariant. The introduction of the sand phase significantly increases the force on the hangers, and the magnitude is greater than that of the densities of the windblown sand flow. With the increasing volume fraction of the sand phase, the densities of the flow increases largely, whereas the drag and lift coefficients have a tendency to decrease.
Fig. 15Drag coefficients of hangers under the different volume fractions of sand phase in the 20 m/s wind field and 20 m/s windblown sand field
a) No. 1
b) No. 2
c) No. 3
d) No. 4
Fig. 16Lift coefficients of hangers under the different volume fractions of sand phase in the 20 m/s wind field and 20 m/s windblown sand field
a) No. 1
b) No. 2
c) No. 3
d) No. 4
3. Discussions
This paper studied the numerical simulation of windsand flow on suspension bridge hangers. Analyze and compare the influence on the sling section forces in windsand flow field with different sand phase volume fraction under different wind attack angle. The force of sling section in the windsand flow field under different wind attack angle is bigger than the force in wind field. The reason is because the hangers can be affected by not only the wind but also the windblown sand. When introducing the sand phase, the drag force on the column and the density of the flow increases. With an increase in sand, and the densities increase although the drag coefficient increases at the same time. The influence of windsand flow on the cables cannot be ignored.
Numerical simulation of windsand flow in this paper treats sand phase as continuous medium, and does not consider the coupling effect between sand and the air. However, in the actual windsand flow, sand phase is discrete medium, and the diameter of sand is unclear. Therefore, Numerical simulation of windsand flow in this paper may be different from effect of the actual windsand flow. The next work of the corrosion fatigue effect of windsand flow on ridingtype hangers is to develop the more reasonable numerical simulation model, in a more realistic reflection of the sand flow of the results, in order to reflect effect of windsand flow more veritably. At the same time, the wind tunnel test and numerical simulation should be conducted on the basis of field observation, in order to understand characteristics of windsand flow more roundly.
4. Conclusions
Fluent is used to simulate the windsand flow field around the hangers of a longspan suspension bridge on the basis of the numerical simulation of computational fluid dynamics and the main conclusions are summarized as follows:
1) The lift and drag coefficients of the hanger section in the windsand flow field are slightly larger than those in the wind flow field, but the force of the hanger section in the windsand flow field is larger than that in the wind flow field. Thus, the effect of sand on the hanger in the windsand flow field is significant.
2) The effect of the different wind attack angles on the ridingtype hanger of a suspension bridge is listed as follows: the wind attack angle has a small effect on the windward hangers but has a large effect on shelter hangers.
3) In the model of ridingtype hangers, the forces of the back two columns in the wind and windsand flow field are approximately 0.5 times to 0.7 times higher than those of the front two columns when the wind attack angle is from 0° to ±9°. The difference between the forces exerted on the four cylinders decreases with increasing wind attack angle (±15° to ±45°).
4) The volume fraction of the sand phase has an insignificant effect on the drag and lift coefficients of the hanger but has a significant effect on the force exerted on the hanger. The force exerted on the hangers multiplies when the volume fraction of the sand phase multiplies.
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About this article
The authors are grateful for the financial support from the National Natural Science Foundation of China (51208471), Natural Science Foundation of Henan Province of China (162300410255), Outstanding Young Talent Research Fund of Zhengzhou University (1421322059) and Science and Technology Planning Project of Transportation in Henan Province (2016Y22).