The excessive and unanticipated vibrations of stay cables in cable-stayed bridges aroundthe world have been often observed with the occurrence of wind and wind-rain. Thesevibrations with low frequency and high amplitude are important for the safety andserviceability of cable-stayed bridges. There has been extensive research involving windtunnel experimentation and field observations that is devoted to investigating the mainfactors contributing to the cable vibration and that propose potential mechanisms. Acomprehensive understanding is, however, still not available. Moreover, there have beenfew studies involving in-depth investigation of the fluid flow around a stationary cable,which is fundamental to understanding the aerodynamic instability associated with thecable vibration.In order to investigate the fundamental characteristics of aerodynamic forces on acable oblique to wind in this work, the 3-D DES (Detached Eddy Simulation) approachwas applied to flow around a yawed and inclined circular cylinder in this study. DESenables simulation of unsteady three-dimensional flow at high Reynolds number whilemaintaining reasonable computational requirements.First, simulations of flow normal to a circular cylinder using 2-D RANS(Reynolds-averaged Navier-Stokes equation) were conducted for verification ofnumerical schemes/conditions and for validation of the simulated flow. In DES, the flowregion near a wall is treated in the RANS mode whose solution becomes converged withgrid refinement. Therefore, 2-D RANS could be used to examine the numerical effects ofspatial/temporal discretizations and computational schemes on the simulated flow. Theverification associated with three-dimensional effects, such as spanwise grid sizes,cylinder lengths and spanwise boundary conditions, was performed in flows normal toand oblique to a cylinder using 3-D DES and comparison to experimental data.The verified and validated 3-D DES was used to investigate characteristics of theflow and the associated aerodynamic forces on a yawed and inclined circular cylinder.The study shows that the flow around the cylinder is inherently three-dimensional.According to the proposed mechanism to explain the flow-induced forces, an importantfactor is a swirling flow, which has an axial velocity component as well as rotational one.The swirling flow is developed by the rolled-up shear layer flowing past the obliquecylinder, generating relatively large forces on the cylinder. Multiple forces with peaks offinite length occur at spatial intervals along the cylinder axis, alternating on both sides ofthe cylinder while moving at a fixed speed. The speed of these force peaks isapproximately 90% of the velocity component of the oncoming upstream flow parallel tothe cylinder axis.Three-dimensional characteristics of the aerodynamic forces on the cylinder arediscussed in local coordinates as well as in global coordinates. While a few highfrequencies are observed in the force coefficient (Cy) of the local y axis, the forcecoefficient (Cx) in the local x axis has a significant low-frequency component. It is muchlower than that of Karman vortex-induced vibration in the same flow environment. Thebehaviors of Cx and Cy result from the periodic moving forces due to traveling swirlingflows in equi-spaced intervals. This regular pattern of the multiple moving loads is apotential source for low-frequency and high-amplitude aerodynamic instability of a longcircular cylinder oblique to the flow.Since the forces move along the cylinder, they were investigated in a Lagrangianreference frame as well as in an Eulerian frame. The moving force coefficients (Cmx andCmy) have one dominant frequency for the fluctuations in the x and y axes, respectivelywhen they travel along the cylinder. The dominant frequency of Cmx is twice as high asfor Cmy, which implies that the moving forces are related to classical Karman vortices.The effects of the angle of the cylinder to the flow on characteristics of the flowand the associated forces were also examined in this study. As yaw angle increases, thepeak frequency of Cy deviates from the prediction by the Cosine Rule. The dominantfrequency of Cx has a relatively low-frequency component and increases with yaw angle,but it cannot be predicted by the Cosine Rule. The comparison results indicate that thethree-dimensional characteristics of the forces cannot be precisely explained by a quasitwo-dimensional approximation, such as the Cosine Rule.While there have been many efforts to investigate the characteristics of cylinderflow and related forces, this is, to the author???s knowledge, the first numerical study tofocus on the three-dimensional characteristics of the fully-developed flow at highReynolds number and associated forces on a yawed and inclined circular cylinder. Thisstudy is a significant contribution for improved understanding of the complex threedimensionalcharacteristics of the flow and flow-induced forces. The low frequencycomponents of the forces provide insights into the fundamental mechanism of cablevibrations with low frequency and high amplitude. This study also can be applied notonly to circular cylindrical structures under oblique flow such as electrical transmissionlines under oblique wind and marine structures under inclined currents but also to anyelongated bluff bodies under flow in three-dimensional environments.
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