Numerical Investigation Into The Flow-induced Vibrations Of Elastically Mounted Circular Cylinders

Flow-induced vibration(FIV)of circular cylinders exists in many engineering,such as marine engineering,aerospace engineering,mechanical engineering,and so on.Great progress has been made in the problems on vortex-induced vibration of an isolated cylinder over the past decades.In comparison,multi-cylinder system is more widely applied in practical engineering.However,its response mechanism of flow-induced vibration is not well understood in academic circles.The interference between wakes of different cylinders is likely to cause the vortex patterns more complex and the vibration of the structures more violent,developing greater engineering risks.In the face of such a complex flow environment,one of the biggest challenges for researchers is to understand the physical mechanism of flow-induced vibration.Scientific and accurate analysis of the flow field morphology and its mechanism of coupling between cylinders is an important approach to explain the physical mechanism of flow-induced vibration of cylinder cluster.Two-degree-of-freedom(2DOF)flow-induced vibrations(FIV)for a pair of elastically mounted circular cylinders were numerically studied.The Reynolds number range Re=1470–10320 belongs to the subcritical flow regime.The cylinders with mass ratio of m~~*=2.6 and mass-damping parameter of(m~~*+C_a)ζ=0.013 were considered in the simulation.The FIV of the circular cylinders was numerically simulated by solving the 2D unsteady incompressible Reynolds-Averaged Navier-Stokes(RANS)equations on overset grids.The FIV responses,hydrodynamic characteristics and wake patterns of the two cylinders in tandem,side-by-side and staggered anrrangement were presented and analysed successively.The effects of different spacings,angles and reduced velocities on the response characteristics and wake patterns of the cylinder pair were explored.The new FIV phenomena and the physical mechanisms behind them were revealed.Based upon the numerical results,the following conclusions could be drawn:(1)In the tandem arrangement,four spacing ratios S_x/D=3.0,4.0,5.0 and 8.0(S_xis the center-to-center separation distance,D is the cylinder diameter)were employed.For the upstream cylinder,the amplitude responses with respect to V_r in both the in-line and cross-flow directions agree well with those of a single cylinder except for the smallest spacing ratio considered in the present study,i.e.,S_x/D=3.0.It indicates that when S_x/D=4.0,5.0 and 8.0,the downstream cylinder has limited effect on the responses of the upstream one.While for Sx∕D=3.0,the peak amplitudes decrease slightly and shift to a lower V_r.The FIV responses and hydrodynamic characteristics of the downstream cylinder are influenced by the combination of the shielding effect and vortex buffeting of the upstream cylinder.V_r corresponding to the maximum amplitude of is delayed to a higher value as the downstream cylinder undergoes the wake-induced vibrations(WIV).As the upstream cylinder in the present simulation is free to oscillate in 2DOF,the associated vortex shedding is more complicated and the wake stiffness experiences larger variations,which results in the disappearance of the build-up of the response amplitudes.(2)In the side-by-side arrangement,four transverse spacing ratios S_y/D=4.0,6.0,8.0 and 10.0 were considered.When S_y/D=4.0,6.0 and 10.0,the response characteristics of the two cylinders are similar,and the most outstanding vibration feature is that there is no super upper branch existing in above cases.When S_y/D=8.0,the response curves of the cylinder pair coincides that of the single cylinder.However,Discrepancies in response amplitudes are observed between the cylinders for V_r=8.0.Although S_y/D was increased to 10.0,there is still strong mutual interference between the two side-by-side cylinders,but the effect of low frequency components on the downstream responses of the cylinders is attenuated.Four new wake pattens are observed in the FIV process of two side-by-side cylinders.With the increase of V_r,they are the asymmetric shear layer pattern(ASL),asymmetric long-period flip-flopping pattern(ALFF),biased in-phase-synchronized pattern(BIS)and asymmetric-shedding pattern(A-shed),respectively,which account for the asymmetric vibration modes between the two cylinders.(3)In the staggered arrangement,the center-to-center spacing ratio of two cylinders was fixed as P/D=6.0.For small incident anglesα=0°and 30°,the response amplitudes and fluid loads with respect to V_r of the upstream cylinder follow well with those of the single cylinder,while the FIV characteristics of the downstream cylinder have more significant dependency on the variation of the incident angle.At large V_rregion,higher response amplitudes appear for the downstream cylinder compared with the case of the single one.Meanwhile,a phenomenon simiar to the wake-flutter occurs for the downstream cylinder with the in-line dominant frequency approximating to that in cross-flow direction,resulting in an elliptical motion trajectory.For large incident anglesα=60°and 90°,the downstream cylinder ocsillates similarly with the upstream counterpart but not the single cylinder.It should be noticed that the hydrodynamic characteristics between the two cylinders tend to be consistent as the incident angle enlarged.Forα=30°,although the downstream cylinder is oscillating beyond the wake boundary of the upstream counterpart,the vortices shed from the upstream one will still induce the shear layers development and the vortex-shedding process of the downstream cylinder.The wake flutter phenomenon for downstream cylinder is probably attributed to the stable vortex-coupling generated by the synchronous movements between the upstream vortices and the downstream cylinder.FIV responses and wake patterns of the double-cylinder system are systematically analyzed with different configurations.The above conclusions reveal the physical essence behind the phenomenon of flow-induced vibration.In addition,they make up for the deficiency of previous numerical studies on the mechanisms of the wake field at subcritical Reynolds numbers,which further improves the corresponding hydrodynamic theoretical system.The research work in this paper is of momentous significance to theoretical knowledge and engineering application.