Vorte-Induced Vibration Studies of Arch Bridge Hanger by CFD numerical simulation Hao Zhan 1,Tao Fang 2,Zhiguo Zhang 3 1 China Railway Major Bridge Reconnaissance & Design Institute Co., Ltd.,China poetryzhanhao@163.com 2 Huazhong University of Science and Technology,China 3 University of Shanghai for Science & Technology,China Abstract By secondary development of software FLUENT,this paper establishes two-dimensional bending fluid-structure interaction numerical model to study vorte-induced vibration of steel bo hanger of one arch bridge under different wind attack angle.the numerical result shows: When the wind is blowing along the bridge,the maimum amplitude and lock-in wind speed domains are biggest.it is the most unfavorable direction for vorte induce vibration. When the wind is blowing perpendicular to the bridge,vorte-induced vibrated does not happen. When the wind is blowing along oblique direction.vorte-induced vibrated may along -ais direction or along y-ais direction. It depends on wind speed.this article also study the phase of lift force, vertical displacements and acceleration when vorte vibration happens, reveals the inherent reasons of structural damping effecting on vorte-induced vibration. 1 Introduction Nanjing Dashengguan Yangtze River bridge is a continuous steel truss arch bridge with a span arrangement of 19m+192m+336m+336m+192m+19m.The 336 meters main span is the longest of similar bridges in the world.it is first si line high-speed railway bridge with the largest railway loading in the world. Chamfered rectangle steel bo hanger is used in the bridge. The longest hanger is above 5m. Vorte-induced vibration is easy to happen. An etensive research have been done on vorte-induced vibration.but major research is focus on circular and rectangle section and seldom connect with the actual engineering, especially vorte-induced vibration under oblique wind direction(m.matsumoto et al., 1998; S.Pastò,28; Xavier Amandolèse et al.,21).by secondary development of commercial computational fluid dynamics software FLUENT, this paper establishes two-dimensional bending fluid-structure interaction numerical model to study vorte-induced vibration of the steel truss arch bridge hanger. The maimum amplitude and lock-in wind speed domains were calculated at different wind attack angular in the paper. Bridge pictures are shown in Figure 1.
Rendered picture Bridge hanger Cross-section of hanger(mm) Figure1: Bridge picture 2 Numerical simulation 2.1 Numerical simulation model Properties of the hanger is shown in Table1.It is the longest hanger of bridge which is about 56m.Wind direction in the numerical simulation is shown in Figure 2. Numerical simulation model is according to prototype of the structure.the 1/1 scale model is used in section wind tunnel test. y Table1: Properties of prototype hanger Mass (kg/m) 614.6 Vibration frequency in y-ais direction(hz) 2.81 Vibration frequency in -ais direction (Hz) 2.14 y' y wind wind 27 ' wind y -ais direction oblique direction y-ais direction Figure 2: Wind direction 2.2 Numerical simulation principle The structure is regarded as mass, spring and damping system.the schematic diagram of numerical simulation is shown in Figure 3.The governing structural equation for the one-degree-of -freedom heaving mode is shown as equation (1) and equation (2). Figure 3: Schematic diagram of numerical simulation + + = (1) my + cyy + k yy = Fy my c y k y F (2)
where m is the mass per unit length of the body, k is the translational spring stiffness, c is the structural damping coefficients. F is the fluid forces. y denotes the transverse location. The governing equations of the incompressible flow is the continuity equation and the Navier-Stokes equations as equation (3) and equation (4). V = (3) V 1 + 2 ( V ) V = p + μ V (4) t ρ where ρ is the density of fluid. V, p, tdenote the velocity vector,pressure and time. Solve equation (3),(4),obtain pressure and velocity around object,calculate aerodynamic force acting on the object. This can be done by FLUENT. Then etract lift and moment into vibration equation (1) (2) and solve the vibration equation by Newmark method.the velocity is assigned to the object and simulate object move by FLUENT dynamic mesh technique. This can be done by secondary development of FLUENT which program code is embedded to the FLUENT by user defined function(udf). Computational grid is shown in Figure 4. Whole mesh Local mesh Figure 4: Computational grid As shown in Figure 4,Numerical grid consists of two parts: Boundary layer surrounding subject is composed of structure mesh and outside is composed of structure mesh.a fine grid is created near the body and the grid becomes gradually coarser in the wake and in the far field. Wind direction is from left to right.left side is set speed entrance and right side is set free flow. Upper and lower boundary are no-slip boundary. Navier-Stokes equations are solved by using finite volume method,second-order upwind difference form and SMPLEC algorithm.rng k-e turbulence model is used in numerical simulation. 3 Numerical simulation results 3.1 St and critical wind velocity of vorte-induced vibration When the wind blow along the bridge, the static flow results are shown in Table 2.Critical wind speed of vorte-induced vibration is Vcrit = fd/ St (1), where D is the cross-wind dimension of the body; f is natural frequency of the structure. St is Strouhal number. It can be obtained by FLUENT. Table 2: St and critical wind velocity ( Southwest Jiao Tong University,26) Wind St Critical wind speed (m/s) Direction Simulation Test Simulation Test -ais.175.185 22.5 21.2 Oblique.21 / Vibrationin-ais: 2.9 / Vibrationiny-ais: 15.9 y-ais.17.176 13 12.5 As shown in Table 2. St and critical wind velocity are in agreement with the wind tunnel test.
3.2 Vertical displacements versus velocity and lock -in wind speed domains maimum amplitude(cm) 12 1 8 6 4 2 2 22 24 26 28 3 32 wind speed( m/s) vorte-shedding frequency(hz) 4 3.5 3 2.5 2 22 24 26 28 3 32 wind speed( m/s) Wind is along -ais direction and vibration is in y-ais direction. maimum amplitude(cm) 5 4 3 2 1 2 2.5 21 21.5 22 22.5 23 wind speed(m/s) vorte-shedding frequency(hz) 3.1 3 2.9 2.8 2.7 2.6 2 2.5 21 21.5 22 22.5 23 wind speed(m/s) maimum amplitude(cm) 2 15 1 5 Wind is along oblique direction and vibration is in y-ais direction. 15 15.5 16 16.5 17 17.5 18 wind speed(m/s) vorte-shedding frequency(hz) 2.4 2.3 2.2 2.1 2 15 15.5 16 16.5 17 17.5 18 wind speed(m/s) Wind is along oblique direction and vibration is in -ais direction. Figure 5:Vertical displacements versus velocity Figure 6: Vorte-shedding frequency versus velocity As shown in Figure 5 and Figure 6, the amplitude of hanger increases with the wind in the beginning. Access to the locking wind region resonance happen, amplitude increases rapidly. When the wind speed increases again, amplitude decreases.in a certain range of wind speeds, vorte shedding frequency is no longer the linear function of the speed.it is captured by natural frequency of structure. 1.5 1.5 1 1.5.5 -.5 -.5-1 -1-1.5 5 1 15 2 y-ais direction vibration V=28m/s (Wind is along -ais ) -1.5.1.2.3 (m) 196s~2s
.4.2 -.2.5.4.3.2.1 -.1 -.2 -.4 2 4 6 8 1 12 14.2 -.3 -.4 -.5 -.1.1.2.3 (m) y-ais direction vibration 132s~135s V=22m/s (Wind is along oblique direction ).1.1 (m) -.1.5 -.5 -.2 5 1 15 2 -.1 -.2 -.1.1.2 (m) -ais direction vibration 175s~18s V=16.5m/s (Wind is along oblique direction ) Figure 7:Time histories of vertical displacements Figure 8: Time histories of displacements As shown in Figure 7 and Figure 8, the amplitude of vorte-induced vibration is growing gradually, finally stabilize at a constant value.the vibration orbit is ellipse and usually the displacement along the wind direction is very small. Table 3: Results by numerical simulation Wind direction Maimum amplitude(cm) Lock-in wind speed domains(m/s) -ais y-ais 18 22~29 y-ais -ais 1 / Oblique -ais 41 21~22.2 y-ais 19 16~16.5 As shown in Table 2,When the wind is blowing along the bridge (-ais direction), The maimum amplitude and lock-in wind speed domains are biggest. When the wind is blowing perpendicular to the bridge (y-ais direction),vorte-induced vibrated does not happen. When the wind is blowing along oblique direction.vorte-induced vibration may be in -ais direction or y-ais direction. It depends on wind speed.rms amplitude is shown in Table 4. Table 4: Maimal rms amplitude(southwest Jiao Tong University,26) Wind direction Maimal rms amplitude(cm) Wind tunnel test Numerical simulation -ais 7 78 y-ais <2 1 Although there is difference between numerical simulation and the wind tunnel test in properties of hanger, it is an useful reference. Contours of vorticity magnitude is shown in Figure 9. The maimum amplitude is about 1m.Vorte shedding is very strong.
Figure 9: Contours of vorticity magnitude (Wind is along -ais direction, V=26m/s) 3.3 Damping ratio influence on vorte-induced vibration Time histories of some parameters are shown in Figure 1.The phase of lift force,vertical displacements and acceleration have been studied in the following.it reveals the inherent reason of structural damping effect on the amplitude of the vorte-induced vibration. 1 5 F(N) -5-1 256 256.2 256.4 256.6 256.8 257 257.2 257.4 257.6 257.8 258 2 1 Time histories of lift force -1-2 256 256.2 256.4 256.6 256.8 257 257.2 257.4 257.6 257.8 258 4 2 Time histories of vertical displacements a(m/s 2 ) -2-4 256 256.2 256.4 256.6 256.8 257 257.2 257.4 257.6 257.8 258 Time histories of acceleration Figure 1: Time histories of parameters(wind is along -ais direction, V=27m/s) As shown in Figure 1,When time is 257 seconds, Vertical force reach the maimum value. Vertical displacement is very small and almost zero. Displacement is behind the load 1/4 cycles. The acceleration is very small and almost zero. So restoring force and inertia force is very small, the load is mainly balanced by damping force.as shown in Figure 11. When damping ratio is.5,the maimum amplitude is about 2cm, which is 2% of that when damping ratio is.1.before the bridge open to public. The hanger vibrate with amplitudes reported to be above 8cm at the wind speed about 14m/s. After the dampers were installed inside hanger, It has not shown any ecessive vibrations.
maimum amplitude( cm).4.3.2.1 2 21 22 23 24 25 wind speed( m/s) Figure 11: Vertical displacements versus velocity(wind is along -ais direction ( ζ =.5 )) 3.4 Lock-in process of vorte-induced vibration Time histories of lift coefficient are shown in Figure 12.From power spectral density of time histories of lift coefficient at different time,we know the change of vorte shedding frequency. Figure 12: Time histories of lift coefficient(v=27m/s,wind is along -ais) ~8s 8s~12s 12s~26s Figure 13: Time histories of lift coefficient Figure 14: Power spectral density
As shown in Figure 13 and Figure 14,~8 seconds, vorte shedding frequency is 3.3Hz which is equivalent to static flow condition.8~12s,there are two frequencies that are 3.3Hz and 2.8Hz.Vorte shedding frequency and the natural frequency of object appear alternately.12 ~ 26 seconds,vorte shedding frequency is 2.8Hz which is captured by inherent frequency of the object. 3.5 Phase plane We can see the phase points etend outward with the time in Figure 15, gradually reached a stable limit cycle.vorte-induced vibration is limiting vibration. 2 15 1 5 v(m/s) -5-1 -15-2 -1.5-1 -.5.5 1 1.5 Figure 15: Phase plane (V=27m/s,wind is along -ais direction ) 4 Conclusions The major results obtained in this study are summarized as follows: 1.Vorte-induced vibration shows different characteristics at different wind attack angle.when the wind is blowing along the bridge, The maimum amplitude and lock-in wind speed domains are biggest.as to the bridge it is the most unfavorable direction for vorte induced vibration. 2.Structural damping ratio has great influence on the amplitude of vorte-induced vibration.it is an efficient way to install damping device to mitigate the vorte-induced vibration. 3.Lock-in process is a gradual process that vorte shedding frequency is gradually captured by inherent frequency of the structure. Vorte-induced vibration is a limiting vibration by phase plane analysis. References M.Matsumoto,H.Ishizaki,C.Matsuoka,etc.Aerodynamic effect of the angle of attack on rectangular prism.journal of Wind Engineering and Industrial Aerodynamic,77&78(1998) 531-542. S.Pastò.Vorte-induced vibrations of a circular cylinder in laminar an turbulent flows.journal of Fluids and Structures,24(28) 977-993. Xavier Amandolèse,Pascal Hémon.Vorte-induced vibration of a square cylinder in wind tunnel.comptes Rendus Mecanique,338(21)12-17. Wind tunnel test study report of aerodynamic measures to mitigate hanger oscillation of Nanjin Dashenguan Bridge.Southwest Jiao Tong University,26.