Investigations Of Vortex-induced Characteristics Of Bridge Decks Based On Numerical Simulations

Modern long-span bridges may be subjected to vortex-induced vibrations(VIV)at medium wind speeds due to their low stiffness and damping ratio.The VIVs of bridges not only threaten the safety of the structures and vehicles,but also lead to huge economic losses and negative social influences.The VIV is usually triggered by the regular vortex shedding in the flows around a bridge deck,which gives rise to a periodical aerodynamic force acting on the deck.Before studying the VIV characteristics and exploring effective aerodynamic suppression measures,it is essential to first get a deep understanding of the vortex shedding behavior and mechanisms in the flows around bridge decks.Nevertheless,the flows around bridge decks are highly turbulent due to the large width-to-depth ratios,complex aerodynamic configurations,and the high Reynolds numbers,making it very difficult to explore the flow mechanisms through wind tunnel tests.In the present study,the numerical simulation method based on the computational fluid dynamics and the dynamic mode decomposition method are adopted to address some critical problems,including the windless-air-induced added mass and damping effects on the vibrating bridge decks,the elaborate simulation method for the unsteady flows around bridge decks,the vortex shedding mechanisms in the flows around large-aspect-ratio rectangular cylinders and flat box girders,and the vortex shedding mechanisms during VIV.Main contents and conclusions of this paper are as follows:(1)To determine the requirement of the spanwise length and mesh resolution for 3D simulations,their influences on the flow properties,including the aerodynamic force coefficients,Strouhal number,pressure distributions along the lateral faces,separation bubble size,3D vortical structures,and spanwise correlation functions,are thoroughly investigated based on a 5:1 rectangular cylinder.Four types of spanwise length and four types of spanwise grid size are considered.It is found that the flow properties are more sensitive to the spanwise grid size than the spanwise length.Based on the comparisons,the reasonable spanwise length and grid size which take account of both efficiency and accuracy are determined.(2)3D LES simulations are carried out for a series of rectangular cylinders with the width-to-depth ratio varies from 3 to 12.The flow instability modes corresponding to the global vortex shedding processes are extracted through the dynamic mode decomposition.Based on the instability modes,the interaction between the leading-and trailing-edge vortices,the mechanisms for the stepwise propagation of the Strouhal number with the width-to-depth ratio,and the pressure feedback-loop maintaining the self-sustained flow oscillations are revealed.Further,the leading-and trailing-edge vortices are separated by two special geometric configurations,and their shedding mechanism are discussed separately.The preferred frequency range for the trailing-edge vortex shedding and its modulation effects on the frequency of the global instability are analyzed.(3)3D LES simulations are carried out for a flat box girder.The dynamic mode decomposition is applied to both the spanwise-averaged velocity field and the original 3D velocity field.Two dominant vortex shedding modes are identified in both fields and are characterized by the large-scale leading-edge vortex shedding,the trailing-edge vortex shedding,and their interactions.The frequencies of the two vortex shedding modes are different and related to the leading-edge vortex numbers within the deck width.As a result,the VIV corresponding to a particular vibration mode of the structure may be triggered twice at two different wind speed ranges.A super-low-frequency flow mode,which has a frequency of 1/8-1/9.5 of the global vortex shedding frequency,is also identified in the 3D field and is found to be related to the periodical enlargement and shrinkage of the separation bubble.(4)To quantify and omit the aerodynamic components in the vibrating frequencies and damping ratios of the bridge deck models in the windless air,a linear expression for the nonwind-induced aerodynamic forces is established based on the added mass and damping coefficients.The added mass and damping coefficients for six typical deck sections are identified based on free vibration numerical simulations.Then,the influences of the added mass and damping on the vibration frequencies and damping ratios are quantified for each section.Results show that the influences of added mass on the vibration frequencies are negligible,while the influences of added damping on the vibration damping ratios are significant,especially at larger vibration amplitudes.If the aerodynamic damping ratios are not eliminated from the vibration damping ratios,the mechanical damping ratios of the deck models will be significantly over-estimated,which will further deteriorate the accuracy of the VIV and post-flutter analysis.Thus,three effective approaches for identifying the mechanical frequencies and damping ratios before wind tunnel tests are proposed.(5)The VIV responses of a 5:1 rectangular cylinder within the lock-in wind speed range are simulated based on LES simulations.The vortex shedding mode during VIV are extracted based on the dynamic mode decomposition method,and the cooperative shedding mechanism of the leading-edge motion-induced vortices,the impinging leading-edge vortices caused by the shear-layer instability,and the Karmon-type vortices at the trailing edge are analyzed.It is found that the cooperative variations of the vibration amplitude and vortex size with the wind speed is the basic reason for the locking of the vibrating frequency and vortex shedding frequency within a wide range of wind speed.Finally,the absent of VIV outside the lock-in wind speed range is explained from the perspective of vortex interactions.