Numerical Investigation of Forces and Pressure Characteristics on Rivulet Attached Cables

Transcription

1 Numerical Investigation of Forces and Characteristics on Rivulet Attached Cables P. Xie and C. Y. hou Abstract Upper rivulet plays an important role when Rain-wind induced vibration (RWIV) happens. In present work an arch attachment on cylinder face will be modeled to simulate the rivulet. Fluid field around the cylinder is computed using Finite Volume Method (FVM). Large Eddy Simulation (LES) method is introduced for turbulence modeling here because of the Reynolds Number (Re) reaches to at which the flow is turbulent. And self-excited motion of the cylinder is achieved via dynamic mesh. For further understanding of the oscillating manner of the cylinder, aerodynamic force acting on the cylinder and surface pressure are fully studied. The result shows that both statistic forces and Strouhal Numbers change a lot when the rivulet attachment is at different positions and the cylinder oscillating or not also have remarkable affection on these properties. It appears that the max value of average drag force can be doubled from the minimum, and the lift force fluctuations are far more than that. Existence of the rivulet attachment also changes the pressure distribution on the cylinder face, and the attachment at certain position greatly improves the pressure level at the leading edge of the cylinder.. Keywords dynamic mesh, rain wind induced vibration, fluid structure interaction, large eddy simulation, finite volume method. R I. INTRODUCTION ain-wind induced vibration (RWIV) appearing on cable stayed bridge causing many damages, under rainy weather even with low wind speed, was first reported in [1]. For decades studying, people agree that this is a kind of instability causing by the combined influences of rain and wind, in another word fluid induced vibration (FIV), but the mechanism of this coupled fluid-structure interaction is unsure. In [, 3], the author tried to classify RWIV into three types, galloping type, vortex shedding type and their mixed type, which they believed the headmost one was caused by upper water rivulet and/or axial flow. Bosdogianni [] placed two bars on the surface of circular cylinder to implement the affection of rivulets, and they observed strong increase in amplitude of the cylinder oscillation. It was found in [5] that vortex-shedding-induced cable vibration occurred at very low wind speed and the Strouhal number of inclined cable was different from that of the horizontal cable. Galloping occurred when the cable artificial rivulet at certain position. They also reproduced wind-rain-induced vibration, and discovered that the amplitude of this kind vibration depends P. Xie is with the Harbin Institute of Technology Shenzhen Graduate School, Shenzhen China ( xiepeng@hitsz.edu.cn). C. Y. hou is with the Harbin Institute of Technology Shenzhen Graduate School, Shenzhen China (corresponding author to provide phone: ; fax: ; cyzhou@ hit.edu.cn). on rainfall intensity, cable damping ratio, cable inclination, and wind yaw angle. To analyze the modal responses of cables under aerodynamic force, many authors established kinds of models. Xu & Wang [6] established steady-state RWIV model, and applied it to some test cable models. They claimed that the model was able to capture main vibration features of inclined cylinder with moving rivulet. Some researchers [7] presented a possible fluid mechanical interpretation of rain wind induced vibrations, based on the phenomena of the Prandtl trip wire under consideration of the rivulets as a movable disturbance; Using their model, the authors approved good correspondence to the wind tunnel tests and measurements at real structures. In [8], the author showed how the interaction between the wind flow, the movement of the cable and the rainwater rivulets led to self-induced vibration. In Matsumoto et al.[9], the axial flow effects was considered via applying aerodynamics of inclined cable into qusi-steady theory. Others [1, 11] introduced an oscillator to approach the RWIV. In the oscillator, time-varying mass was modeled by a time harmonic function to simulate the raindrops hitting the cable. In most of above references, although the authors considered the interactions between rivulets and cable structures, but as inputs of most models the forces on the cables was drawn just using testing of steady cables, which the coupled effect as known in RWIV between aero flow and vibrating cables were not well accounted. FIV s are common phenomena in engineering. Flows past moveable cylinders both forced and self-excited are investigated of laboratory in respect of these engineering issues. In one way, forced vibration of a cylinder is a favorite issue of many researchers to study the flow field alteration when the cable structure moves. In another way, free cylinder is settled in a flow field, periodical forces acting on it will excite the cylinder to oscillate. Vortex induced vibration (VIV) is belong to the later one. Review work in [1, 13] gave a full aspect of VIV research since 198s to early 1s. RWIV is a typical kind of FIV, not only the vortex behind the cable but also the formation of rivulets on the cable surface plays a significant role in this phenomenon. The interactions among cable, rivulet and flow formations behind cable are hard to predict in wind tunnel experiment or field tested. Visualizations using CFD method is a better option to do so. RWIV simulation of cables could help improve understanding the complex coupled behaviors. In the simulation, unsteady flow field will be calculated by fluid governing equations at each time step, and aerodynamic forces

2 Considering that the cable structure has a nature frequency of fn, Formula (1) will be written as: FD x f n x f n x M () y f y f y FL n n M At the end of each time step, once the aerodynamic forces are calculated, then it is imported into Eq.(), and the displacement of the cylinder is obtained with th order Runge-Kutta method. When the cylinder moves, the connecting grids change with it. Dynamic mesh method is absorbed to achieve the grid changing. on the cable structure are obtained. Then these forces make the cable movable, the dynamical mesh will help realize the cable oscillation. The vibrating affection to flow field will be accounted by fluid simulations in the following time step. These circle procedures will finally make couple interactions between fluid and structures realizable. II. PHYSICS AND NUMERICAL METHODOLOGIES A. Physics Model of RWIV In RWIV, the cable oscillates in large amplitude, and two rivulets, upper and lower ones respecting to cable center axis, appear on cable face. Restricting to computational resources, it s hard to take full scale simulation of the cable structure. Aiming to reveal the interaction of cable vibration, rivulets and vortex behind the cable, in present work a cable section is selected. Also, many experiments ([1,, 9] ) indicated that the upper rivulet play a key role in RWIV, and the lower one is negligible, so the later one is omitted for computational convenience. The computational model is shown as in Fig. 1. The diameter of cylinder is D. An elliptical arch attachment at certain position of a vertical cylinder surface is modeled to represent the rivulet. Scale of the attachment is governed by two parameters, the width L (=D/) and the height h (=D/). Position of the attachment is described by an angle θ, originating from the front stagnation point (marked as S in Fig.1). U is the uniform incident flow. When forces act on structures, oscillations may occur. Here in this paper the cable-rivulet structure is model as a vertical cylinder-attachment system, and the spring-damper model in Fig. represents the kinetics of this system. ξ is modal damper ratio of cable, and k is its stiffness. Here we assume the structure has the same damper ratio and stiffness in wind wise and cross wise. FD and FL are drag and lift forces. From D Alembert principle the following kinetic equations can be given: Mx CM x kx FD (1) My CM y ky FL where M is the mass of the cylinder. B. Numerical Method Finite Volume Method is introduced for spatial discretion in these simulations. As the Reynolds number (Re=UD/ν, where U and D referring above definition, ν is kinetic viscosity of air) is about 6.8 1, which means the flow is subcritical; the turbulent model must be involved. Considering a better property in capturing small scale flow structures, the LES method is chosen for turbulence calculation. The filtered incompressible N-S equations in dimensionless form are: ui xi (3) ui uiu j 1 p 1 ui ij t x j xi ReD x j x j x j where ui are the filtered dimensionless velocity components in Cartesian coordinates along the i-th direction (i=1,, 3 corresponding to x, y, z direction), p is the filtered pressure, and are the density and kinematic viscosity of the fluid respectively, and ij is the SGS stress that can be modeled as: 1 () 3 where kk is the isotropic part of SGS stress term treated as a part ij kk ij t Sij of filtered pressure, ij is the Kronecker function, t is the SGS kinematic viscosity. Sij is the strain rate tensor of large scale and is expressed by: 1 u u j Sij i (5) x j xi As seen from Eq.(3), Eq.() and Eq.(5), the filtered quantities of fluid can be obtained only if t is known, and Smagorinsky-Lilly (S-L) model is introduced to calculated it: (6 ) t =ls Sij h X Y L U D S Fig.1 Physical model of single rivulet and cable system where Sij Sij Sij and l s is the mixing length of sub-grid-scale FL U obtained by: (7) ls min(kd, Cs 1 3 ) where k is the von Kármán constant that equals to., d represents the distance to the nearest wall, Cs is the Smagorinsky constant and is the volume of the computational cell. Cs is not a universal constant but usually given between FD Fig. Kinetic model of cable. 1

3 zero and.3. It was suggested that C =.1~.1 may yield good results for turbulent wake simulation([1, 15]). C s =.1 is used in the present work. The SIMPLEC algorithm is introduced to solve pressurevelocity coupling equations. QUICK scheme and second order upwind scheme are used for velocity and pressure spatial discretization respectively. The temporal part is discretized using second order implicit scheme. The computational domain is shown as in Fig. 3. A semi-cylinder zone with radius of 1 is modeled as an upper flow section. is taken between the cable center and the outlet in the flow direction. The scale in the axial (spanwise) direction of the cable is about -. To maintain a good spatial grid when dynamic mesh is used, the computational field is cut into three sub-zones. A kernel zone which is very close to cylinder and shown in red color in Fig. 3 (b) moves with cylinder synchronously and keeps its grid topology all the time. The out zone with green color in Fig. 3 (b) is a grid stable zone, and the grid in it keeps steady during the simulation. In the middle zone seen as blue in Fig. 3 (b), the grid displacements transit from synchronizing with cylinder inside to steady state outside using linear interpolation method. By this way, structural grid could be drawn into the computational zone, as well as the grid resolution could be kept at a high level from beginning to end. The first layer of the grid in the normal direction of the cable cylinder is located around wall y + 1, where y + is a dimensionless length scale based on wall shear stress and flow viscosity. In the simulation circumferential grids are more than 16 at most near, and axial grids vary from 6 to 8. The total grid number change from about one million to more than two millions. A general wind velocity (1m/s) at which RWIV occurs is assumed at the inlet boundary, so Dirichlet boundary condition is taken, which u=1m/s and v=w= (where u, v and w are velocity in x, y and z direction); Neumann boundary conditions are drawn at other boundaries, where the normal gradients of all variables are assumed to be zero. No-slip condition, which means u=v=w=, is used at the cylinder wall. inlet 1 cylinder D side1 side C. Test and Validation outlet Fig.3 Computational domain Validation is carried on firstly using circular cylinder. This step is focus on the efficiency of the numerical methods and grid resolution independency. Four different types of grid are involved in grid X independency testing, Test-A, B, C, D in Table 1. Cases of Test-A, B and C have the same circumferential (Refer to column named Circ in Table 1) grids, but their axial s grids vary from small to lager. Test-D has medium axial grids and less circumferential grids. The resulted force statistics are listed in Table and other authors results ([1, 16-18]) are also introduced for comparison. C D, C Df and C Lf represent average drag force coefficients, drag and lift force coefficients fluctuations (root mean square values). These forces statistics especially C D shows differences comparing with those in reference papers, this is basically because as a subcritical flow the boundary layer on the cylinder undergoes a transition to turbulence and is extremely sensitive to the free-stream disturbances and surface roughness. When considering the axial grid resolution, more grids results lower C Lf that can be conclude, all these C Lf have a correspondence in former papers. Coarse grid (Test-D) testing gives a higher C D than the fine one (Test-B) that has equal spanwise grid distribution. St represents the Strouhal Number, which calculated from time varying lift force using FFT. St of testing cases are slight higher than the exit ones, this is because here we have a lager Re. These results verify the feasibility for further studies. Also considering calculation expense and accuracy, fine grid in XY plain and moderate grid in direction just similar to Test-B are adopt for next step s simulations. Test-E in Table 1 is used to verify the code of dynamic mesh. The time history and Strouhal Number are shown in Fig.. Larger forces fluctuations and smaller St comparing with those of Test-B, D could be found. Table1. DETAILS OF TESTING GRIDS Cases Axial Wall Grids scale y + Axial Circ Planar Total Test-A D y Test-B D y Test-C D y Test-D y Test-E 1D y Table. COMPARISON OF VALIDATION RESULTS WITH EXISTING ONES Cases Re CD CDf CLf St Alam et al. (3) Lam et al. (1995,3) Lin ou et al.(8) Test-A Test-B Present Test-C Test-D Test-E Test-B Test-D Test-E Force Coefficient Dimentionless time:u*t/d Power Spectral Density St= St= St= f*d/u Fig. Time varying force coefficients of cylinder and FFT results of lift force of Test-B, D, E.

4 III. RESULTS DISCUSSION In present work, rivulets attachments at four different positions are investigated for both steady and oscillating cylinders, which are θ=, 3, 5, 6. Details of modeling of grids are shown in Table 3 where cases with are corresponding the cylinders are steady means the cylinders are oscillating. Vibrating properties of cylinder systems and flow fields around them are obtained via simulation. To get a full view of flow pattern when the cylinder vibrates, several points at certain locations behind the cylinder are monitored. Detailed discussions will be given in the following sections. Table3. DETAILS OF COMPUTATIONAL GRIDS Cases Axial Wall y + Grids scale Axial Circ* Planar Total y y y y D y D y y D y A. Forces and Strouhal Numbers Aerodynamic forces acting on the cylinder are calculated at each time step during simulation. Forces mentioned as lift and drag is corresponding to flow-wise and trans-flow directions respectively. Time varying force coefficients are shown in Fig. 5, where (a) exhibits cases that cylinders are steady, and (b) exhibits oscillating ones. Generally from (a) and (b) larger forces fluctuations of oscillating cases can be seen comparing with those of steady ones. The right column of each case in Fig. 5 is the frequency spectrum of lift force via FFT calculation, and the peak frequency corresponds to the Strouhal Number. St of steady case gradually increases when θ below 5 from.185 to.39 and suddenly drops to.165 when θ=6. While St of oscillating cases changing with attachment positions are more complicated, beginning with.1811 at θ=, a slight decrease at θ=3, at θ=5 up to., then dramatic drop happens like that of steady case at θ=6. When θ=5 in vibrating case a second peak corresponding to a very low frequency also appears. Totally, St of oscillating cases is smaller separately comparing with steady ones. Force statistics of different cases are listed in Table, and Fig. 6 gives a direct prospect of them. Average drag force coefficient C D of steady cases begins with.917 at θ=, which is similar with that of steady cylinder without rivulet attachment, it then decreases with θ before 5, and the minimum value is.75. But in oscillating cases, C D at θ= is much higher than that of steady case, which is instead, then it goes slightly up to 1.5 at θ=3, after that dramatically drops down to.9895 at θ=5. C D of both steady and oscillating cases have large increasing when θ=6, and the two values are nearly the same of about 1.6. The drag force fluctuations C Df of steady cases are much smaller than those of oscillating ones respectively, except when θ=6, and same result appears in C Lf. At θ=6, C Lf of steady is.838 exceeding that of oscillating case which is Table. FORCES STATISTICS AND STROUHAL NUMBERS Cases CD CDf CLf St (a) Force Coefficient Dimentionless time:u*t/d Force Coefficient Power Spectral Density St= St= St= St= f*d/u (b) Fig.5 Time varying force coefficients of cylinder and FFT results of lift force: (a) steady cylinders, (b) oscillating cylinders Force Coefficients: lift-fluctuation( C Lf ), average-drag( C D ), drag-fluctuation( C Df ) Dimentionless time:u*t/d C D -S C Df -S C Lf -S C D -O C Df -O C Lf -O Power Spectral Density St=.185 St= St= St= f*d/u Rivulet Position: () Fig.6 Statistics of forces varing with rivulets attachments.(dot and dash lines represent the color-corresponding forces statistics of cylinder without attachment. Dot and dash-dot are used to separate the steady and oscillation cases. Suffix -S in legend means steady cases, and -O represents oscillating cases.) 3

5 CLf vary with θ much milder in steady circumstances comparing in oscillating ones. So it seems that vibration induced by fluid suppress the force fluctuations causing by the rivulet. B. s Distributions In this section the average pressures on the cylinder faces are studied. For the convenience of description, the three dimensional cylindrical surface in Cartesian coordinate is converted into two dimensional rectangle with circumferential (Φ) direction and axial (Ζ) direction. The circumferential coordinate origin form the front stagnation point (marked as S in Fig. 1) with Φ=, along the clockwise direction, and end at the same point with Φ=. (a) Steady Oscillating / / 3/ 3/ D (b) Fig. 7. s on surface of cylinder without rivulet: (a) contours; (b) s varing with Φ (or Ζ) at different Ζ (or Φ) Surface pressures of cylinder without rivulet both steady and oscillating cases are given in Fig. 7. The pressures get max at the stagnation lines in the front of the cylinder, where it is nearly. of steady case and lower of of oscillating case. When the cylinder is steady, it goes down symmetrically along the two sides of the cylinder to the minimum at about Φ=/ and Φ=3/, then goes up to a medium level. Because of separation of the flow the pressure keeps at the medium level at the trailing edge of the cylinder. The pressure shows certain symmetry about Φ= on the Φ-Ζ plain in steady case, on contrary this property doesn t appear in oscillating case but lower at one side (basically Φ<) higher at the other side. In general the varying D 1D / / 3/ 3/ D D 1D amplitude of pressure on the cylinder face of steady cases is much higher than that of oscillating one. Considering the pressure varying with Ζ at different Φ (right column in Fig. 7 (b)), in the steady case the periodical fluctuations appears when Φ are at / and 3/, on the other hand a larger fluctuations exist in the interval from about Φ=/ until about Φ=3/, nevertheless these fluctuations seldom have periodical properties. Fig. 8 shows the face pressure distributions of cylinders with upper rivulet attachments. From contours scene of Fig. 8 (a), (b), it apparently displays distinctions among cases varying with rivulet positions. Comparing cases (a) and (b) with the same rivulet attach angle but the cylinder is steady or not, they are also quite different. Their common points are that in all cases max pressure exists at the leading edge of the cylinder, and each case except θ= pressure suddenly drops at attachment position. Circumferential pressure distributions at different axial position are given in Fig. 8 (c), (d). At θ=, the oscillating case shows similarity with case of oscillating cylinder without rivulet that have discussed above, but the steady cases are much different, the symmetry appearing in bare cylinder case becomes obscure here in this case. In steady cases (shown in Fig. 8 (c)), when θ=3, after sudden drop at Φ=/6, the pressure quickly rises, then drops later rises again, and keeps at a medium level at the trailing edge. When θ=5, the rivulet attachment makes medium level zone appear early before Φ=/3. In the case which θ=6, the pressure at the front of cylinder is much higher than other cases, which is up to.1 while in other cases it is about. In this case the pressure along the circumferential direction is totally asymmetric, which after sudden drop at Φ=/3 it keeps on decreasing until Φ=, then fluctuations happened between Φ= and Φ=3/. When talking about oscillating cases in Fig. 8 (d), pressure curves varying with circumference at different Ζ position show various tendencies even in the same case, fluctuations exists between rivulets position and Φ=3/. Oscillating case at θ=3 the leading edge of.1 is higher than any other oscillating case of about. Axial pressure distributions at different Φ in Fig. 8 (e) indicate that in steady cases when the attach angle (θ) below 5 the large alteration appear near Φ=/ and Φ=3/, while in the case θ=6 at the whole back area of cylinder, where /<Φ<3/, pressure along axial direction vary significantly, especially near Φ= where the amplitude is about.1. Fig. 8 (f) shows that when the cylinder oscillates the pressure distributions along Ζ direction is polytropic, and remarkable fluctuations exist at large area of the cylinder surface. In oscillating case that θ=6 big valleys turn up when <Φ<3/ at the middle of Ζ position, the extreme values are about In general, upper rivulet attachment on cylinder face makes pressure drop suddenly at the attachment position. Also attachment existing at certain position, like θ=6 of steady cases and θ=3 of oscillating cases, let pressure at the leading edge higher than other cases. In another way, the pressure being made unstable by the cylinder oscillation that can be concluded.

6 (b) = 3/ -.15 / / / (c) 3/ / / 3/ = -.1 = / 3/ -.5 = 3/ / 3/.5 = / 1D / /.5 3/ -.5 1D.5 / 3/ D = -.5 = 3/ = (d) -.15 / / = / / / = /.5 = 3/ 1D -.5 1D / / 3/ = 1D -. / 3/ (a) (e) (f) Fig.8 on surface of cylinder with rivulets: (a), (b) contours; (c), (d) circumferential pressure distributions at different Ζ; (e), (f) axial pressure distributions at different Φ. cylinder face are studied comparatively. Average drag force coefficient CD of steady cases at θ= is similar with that of steady cylinder without rivulet attachment; it decreases with θ before 5, and the minimum value is.75. But in oscillating cases, CD at θ= is much higher than that of steady case, which is instead of.917; then it goes up slightly at θ=3 ; after that dramatically drops down to.9895 at θ=5. CD of both steady and oscillating cases have large increasing when IV. CONCLUSIONS In present work, simulations for unsteady flow field around cylinder with rivulet attachment are carried out using Finite Volume Method with LES to make a closure of turbulence model. Both steady cylinder and oscillating cylinder cases are investigated. Statistic forces and pressure distributions on 5

7 θ=6, and the two values are nearly the same of about 1.6, which is more than twice of the value of steady case at θ=5. The drag force fluctuations C Df of steady cases are much smaller than those of oscillating ones respectively, except when θ=6, and same result appears in C Lf. At θ=6, both C Df and C Lf of steady case surpass these of oscillating case. C Lf vary with θ much milder in steady circumstances comparing in oscillating ones. So it seems that vibration induced by fluid suppress the force fluctuations causing by the rivulet. St of steady case gradually increases when θ below 5 from.185 to.39 and suddenly drops to.165 when θ=6. While St of oscillating cases changing with attachment positions are more complicated, beginning with.1811 at θ=, a slight decrease at θ=3, at θ=5 up to., then dramatic drop happens like that of steady case at θ=6. When θ=5 in oscillating case a second peak corresponding to a very low frequency also appears. Totally, St of oscillating cases is smaller separately comparing with steady ones. When talking about pressure, upper rivulet attachment on cylinder face makes pressure drop suddenly at the attachment position that can be first drawn. At steady case of θ=6 and oscillating case of θ=3, pressure at the leading edge are.1 rather than in other cases, which means flow on the most front of cylinder is not stall any more. In another way, the pressure being made unstable by the cylinder oscillation that can be concluded. application to aerodynamics," Wind and Structures, vol. 8, pp. 17-1, 5. [1] A. H. P. van der Burgh and Hartono, "Rain-wind-induced vibrations of a simple oscillator," International Journal of Non-Linear Mechanics, vol. 39, pp. 93-1,. [11] A. H. P. van der Burgh, Hartono and A. K. Abramian, "A new model for the study of rain-wind-induced vibrations of a simple oscillator," International Journal of Non-Linear Mechanics, vol. 1, pp , 6. [1] C. H. K. Williamson and R. Govardhan, "A brief review of recent results in vortex-induced vibrations," Journal of Wind Engineering and Industrial Aerodynamics, vol. 96, pp , 8. [13] C. H. K. Williamson and R. Govardhan, "Vortex-induced vibrations," Annual Review of Fluid Mechanics, vol. 36, pp ,. [1] L. OU, Y. LIN and K. LAM, "Large-eddy simulation of flow around cylinder arrays at a subcritical reynolds number," Journal of Hydrodynamics, Ser. B, vol., pp. 3-13, 8. [15] W. HAO and A. Huhe, "Large-Eddy simulation of three-dimensional turbulent flow around a circular pier," Journal of Hydrodynamics, vol. 18, pp , 6. [16] K. Lam, J. Y. Li and R. M. C. So, "Force coefficients and Strouhal numbers of four cylinders in cross flow," Journal of Fluids and Structures, vol. 18, pp. 35-3, 3. [17] M. M. Alam, H. Sakamoto and M. Moriya, "Reduction of fluid forces acting on a single circular cylinder and two circular cylinders by using tripping rods," Journal of Fluids and Structures, vol. 18, pp , 3. [18] K. Lam and X. Fang, "The Effect of Interference of Four Equispaced Cylinders in Cross Flow on and Force Coefficients," Journal of Fluids and Structures, vol. 9, pp , [19] ACKNOWLEDGMENT The work described in this paper was supported by a grant from National Natural Science Foundation of China (Project number No ). The financial support is gratefully acknowledged. REFERENCES [1] Y. Hikami and N. Shiraishi, "Rain-wind induced vibrations of cables stayed bridges," Journal of Wind Engineering and Industrial Aerodynamics, vol. 9, pp. 9-18, [] M. Matsumoto, T. Yagi, M. Goto, and S. Sakai, "Rain-wind-induced vibration of inclined cables at limited high reduced wind velocity region," Journal of Wind Engineering and Industrial Aerodynamics, vol. 91, pp. 1-1, 3. [3] M. Matsumoto, T. Saitoh, M. Kitazawa, H. Shirato, and T. Nishizaki, "Response characteristics of rain-wind induced vibration of stay-cables of cable-stayed bridges," Journal of Wind Engineering and Industrial Aerodynamics, vol. 57, pp , [] A. Bosdogianni and D. Olivari, "Wind- and rain-induced oscillations of cables of stayed bridges," Journal of Wind Engineering and Industrial Aerodynamics, vol. 6, pp , [5] S. han, Y. L. Xu, H. J. hou, and K. M. Shum, "Experimental study of wind-rain-induced cable vibration using a new model setup scheme," Journal of Wind Engineering and Industrial Aerodynamics, vol. 96, pp , 8. [6] Y. L. Xu and L. Y. Wang, "Analytical study of wind-rain-induced cable vibration: SDOF model," Journal of Wind Engineering and Industrial Aerodynamics, vol. 91, pp. 7-, 3. [7] C. Seidel and D. Dinkler, "Rain-wind induced vibrations - phenomenology, mechanical modelling and numerical analysis," Computers & Structures, vol. 8, pp , 6. [8] U. Peil and O. Dreyer, "Rain-wind induced vibrations of cables in laminar and turbulent flow," Wind and Structures, An International Journal, vol. 1, pp , 7. [9] M. Matsumoto, T. Yagi, S. Sakai, J. Ohya, and T. Okada, "Steady wind, force coefficients of inclined stay cables with water rivulet and their 6