Study On Evolution Of Three-dimensional Unstable Modes In Flow Past Four Square Cylinders

Flow past four square cylinders is a common topic in the field of civil engineering,marine engineering and other disciplines.When the structure is exposed to fluid such as wind or ocean current,it will probably vibrate or even be destroyed under the influences of fluid separation and vortex shedding.Therefore,the subject of flow past four square cylinders has important value and significance.Based on the actual engineering backgrounds,such as oil platforms and building complexes,the threedimensional transition of flow past four square cylinders has been investigated.In this paper,the direct numerical simulation of the three-dimensional problem of flow past four square cylinders in an in-line square configuration is performed by the spectral/hp element method embedded in the open source software Nektar ++.Through the hydrodynamic coefficients,wake flow patterns,drag and lift time-history curves,time series of modal energies,and visualized three-dimensional vortex structures,the whole process of the evolution of flow past four square cylinders over time is analyzed in depth.The three-dimensional development characteristics of the flow past four square cylinders with five different spacing ratios at typical Reynolds numbers of 150 is studied.It is found that in the flow past four square cylinders with low spacing ratio,the gap flow disturbs the upper and lower shear layers,resulting in three-dimensional transition phenomenon.When the spacing ratio further increases,it is found that the three-dimensional effect disappears,and when the spacing ratio increases to 3.5,the threedimensional transition of the wake repeatedly occurs and is dominated by the third basically instability Mode C.The three-dimensionality of the wake gradually disappears at high spacing ratio.The three-dimensional development characteristics of the flow past four square cylinders with five different spacing ratios at typical Reynolds numbers of 200 is studied.The wake of four square cylinders completely developed in the stage of three-dimensional unstable mode at Re=200.It is found that multiple modal interference occurs in three-dimensional unstable development due to the impact of gap flow at low spacing ratios.It is revealed that the development of three-dimensional instability of the wake at spacing ratio L/D=2.5 and 4 are dominated by the basic instability Mode C one more time,while the intermediate L/D=3.5 wake shows chaotic flow regimes with interference of multiple modes.After the spacing becomes large enough,Mode C disappears again,and the wake development shows similar characteristics to that of the flow around single square cylinder.The three-dimensional development characteristics of the flow past four square cylinders with a fixed spacing L/D=2.5 at various Reynolds numbers are studied.It is found that with the development of Re from 150 to 300,the three-dimensionality during the flow regime,from the periodic laminar flow to the wake transition stage,is instability Mode C.The wake flow pattern switched from anti-phase pattern to in-phase pattern.The threedimensional development changes from wave-number 5 mode to wavenumber 4 mode,and both modes belong to the basic instability Mode C.In all,the evolution characteristics of wake and three-dimensional unstable modes under different spacing ratios and Reynolds numbers are revealed in this study,providing academic support for the study of threedimensional transitions of flow past four square cylinders and multi-bluff bodies.