Two-degree-of-freedom Vortex-induced Vibrations Of Two Square Cylinders In Tandem Arrangement At Low Reynolds Numbers

Fluid-structure interaction is a complex phenomenon which has great practical importance in many engineering disciplines.In past few decades this phenomenon has been investigated theoretically,experimentally,and numerically.Many previous studies show that the change in the cylinder cross-section may change some fundamental aspects of the vortex-induced vibration（VIV）.Square cross-section has been one of the most popular structural cross-sections in the engineering design due to its simple geometry.Nevertheless,multiple degree-of-freedom VIV responses regarding two or more square cylinders have not been studied to date.It is therefore,important to emphasize on the 2-DOF VIV of multiple square cylinders.The goal of this study is to numerically explore the VIV responses of two square cylinders arranged in tandem.Both cylinders are vibrating in the inline and cross-flow directions with the low mass ratio（M_r=2）and zero damping.The inline center-to-center distance between cylinders is kept fixed to five times of the cylinder side length（D）.The governing equations are solved by using the finite element method based characteristics-based-split algorithm.To explore the VIV characteristics at different Reynolds numbers（Re）lying in the laminar flow regime,the Re is varied from 40 to 200 with an interval of 40.For each Re,the reduced velocity（U_r）is varied systematically from 3 to 13.Different VIV characteristics such as frequency characteristics,force and displacement responses,cylinder displacement trajectories,forces and displacements time history and the corresponding fast Fourier transform（FFT）analysis,and the wake patterns are studied.Results show that the effect of the Re and U_r on the dynamic responses are qualitatively similar for both cylinders.However,effects on the downstream cylinder are stronger due to the upstream wake.When Re reaches 120 and higher,the inline low-frequency characteristic in the upstream cylinder becomes obvious for few higher values of U_r,whereas that in the downstream cylinder exists over a wide range of U_r.For Re up to 120,cylinders show steady behavior at U_r=5.However,at the same U_r,cylinders vibrate with the peak vibration amplitudes and show complex wake flow for higher Reynolds numbers.Then,we investigate the effect of the natural frequency ratios(inline to transverse,f_nr=f_nx/f_ny)at a constant Re=100.Three f_nr=1,1.5 and 2 are considered.Results of the frequency ratios 1 and 1.5 are overlapping to each other,indicating no effect of the frequency ratio.The effect of the frequency ratio is observed only when the f_nrincreases to 2.It is to be noted that the effect is sensitive only in the lock-in region.A comparison of the change in cylinders’vibration amplitudes due to the change of natural frequency ratio and due to the cylinders’wake interference at each natural frequency ratio show that the effect of the wake interference in the downstream cylinder is dominating over the effect of the frequency ratio.The comparison of results between the upstream square cylinder of the current study and an isolated cylinder from the previous studies having similar conditions shows that the upstream cylinder could be affected by the wake interference.Nevertheless,in the previous studies of two circular cylinders,results of the upstream cylinder were found to be similar to those of an isolated cylinder.Comparison of the downstream cylinder results between the current study and different previous studies of tandem arrangement of two cylinders’cases demonstrates that both degree-of-freedom and the change in cylinder cross-section（from circular to square）of the upstream cylinder have significant effects on the inline responses of the downstream cylinder.Results of this thesis shed some light on the VIV of two elastically mounted square cylinders in the inline arrangement.Additionally,the comparison of the current simulation results with the existing results of the circular cylinders provides some significant conclusions which could be the fundamental basis for analyzing the stable structure cross-section in engineering design.