| Rain-wind induced vibration(RWIV) is a large amplitude and low frequency vibration of cables of cable-stayed bridges under wind and rain, which may cause the fatigue failure of stay cable and reduce its service life and threat to the safety of pedestrians and vehicles. The study of many scholars in the past three decades suggests that the RWIV makes a big difference with the formation and oscillation of the water-film on the surface of cables.In this paper, based on gas-liquid two-phase flow theory and Volume of fluid method(VOF method), the effects of different wind speeds on cable stayed water film are researched, and the effects of the motions of water-film on the cable vibration are also taken into consideration.And then 2D coupled equations of water film evolution and cable vibration with two degrees of freedom are presented based on the combination of lubrication theory, thus bidirectional coupling of water film evolution and cable vibration are achieved.Finally, 3D equations of water film evolution on cable-stayed rigid segments are presented based on the combination of lubrication theory and computational fluid dynamics(CFD) method. From three angles-depth study of the RWIV, The water film evolution has been solved under different conditions. The main research contents are as follows:Based on gas-liquid two-phase flow theory and VOF method, 2D water film evolution on the cables are calculated at different speeds, and the formation and evolution of upper and lower rivulets are obtained at different moments.The Schedule of aerodynamic lift and frequency value obtained by post-treatment is applied to a single degree of freedom model of stay cable to calculate cable vibration response at different speeds. The analysis suggests that the periodic oscillation of the upper rivulet is the main cause of RWIV;Considering about the downwind vibration of cables, 2D theory of RWIV with two degrees is built based on lubrication theory. The wind pressure coefficient Cp and the wind friction coefficient Cf obtained by CFD are applied to equations for iterative solution, which achieves the bidirectional coupling of water film evolution and cable vibration.The vibration regulation of the upper and lower rivulets and cables in crosswind and downwind directions obtained by calculation are compared with the results of 2D RWIV with a single degree. The results showed that there is obvious oscillation phenomenon of both upper and lower rivulets, and the oscillation frequency of the upper rivulet is very close to the natural frequency of cables, which explains resonance between rivulets and cable leads to RWIV from another perspective.Considering about the impact of axial flow, the equations with fourth order of water film on 3D rigid segments of cables are built established on lubrication theory. The equations are solved by alternating direction implicit difference scheme(ADI difference scheme), where the wind pressure coefficients and wind friction coefficient is calculated by 3D model of rigid segments of dry cables in CFX.The accuracy of this method is proved by calculating the rivulet motion on the surface of both horizontal and vertical cables under the action of gravity. This method can well simulate water film movement in three-dimensional variation of the surface of the cables, at different speeds. Upper rivulets appear only when the wind speed increases to a certain extent, and the change of its location is affected by wind speed and gravity, which is much larger than lower rivulets. |
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