低雷诺数下四圆柱涡激振动特性研究

Numerical Investigation on Characteristics of Vortex-Induced Vibration of Four Circular Cylinders at Low Reynolds Numbers

该文运用单元型光滑有限元法和分区强耦合算法数值研究了低雷诺数下,四圆柱两自由度涡激振动特性与尾涡脱落模式。来流条件为不可压黏性均匀流动;柱阵采用方形布列,圆心间距s=5,质量比m^(*)=10。为调查折合速度和雷诺数对柱群涡激振动的影响,考虑了两种工况:①工况一,雷诺数Re=100时,折合流速U_(r)=1~14;②工况二,U_(r)=7.3时,Re=40~300。数值研究发现:①在工况一中,上游两圆柱横向振幅及流体力系数均方根值随Ur变化趋势均与单圆柱情形一致;观察到下游两圆柱横向振幅不相等,将其归类为两种情况:其一,上游两圆柱出现横向振幅不相等现象,下游两圆柱横向振幅受前者影响产生差异;其二,下游两圆柱尾涡脱落模式不一致引起横向振幅不同;②在工况二中,上游圆柱振动响应于Re=130时发生转换且响应分支对应不同尾涡脱落模式;响应分支转换后,四圆柱耦合机制发生变化,下游圆柱流向振幅和升力均方根值剧增;同时观察到“2P+2S”尾涡脱落模式,涡对脱落周期随雷诺数增大而减小;特别是Re=140时,下游两圆柱每隔4~5个周期脱落一对涡对;250≤Re≤300时,下游两圆柱后尾迹均形成两排旋涡,仅隔1~2个周期脱落一对涡对。

Numerical results are presented for the simulation of vortex-induced vibration(VIV)of four elastically mounted circular cylinders at low Reynolds numbers(Re)by using the cell-based smoothed finite element method and partitioned strong coupling algorithm.Uniform flows of an incompressible viscous Newtonian fluid are taken into account.The four circular cylinders in a square arrangement are free to vibrate in both in-line and transverse directions.The spacing between the centers of two cylinders is s=5 and the mass ratio of each cylinder to the fluid is m^(*)=10.To investigate the impact of the reduced velocity and Reynolds number,two cases are considered,namely①various reduced velocities(U_(r)=1-14)for Re=100,and②40≤Re≤300 for U_(r)=7.3.It is found in the first scenario that the variation of the amplitude and force coefficients of the upstream cylinders at various Ur is consistent with that of the single cylinder.Different transverse amplitudes of the downstream cylinders are detected thanks to transverse amplitudes of the upstream cylinders affecting the former’s motion.In the other scenario,the vortices shedding from the downstream cylinders also lead to unequal transverse amplitudes.In the second situation,two response branches of the upstream cylinders are found at Re=130,corresponding to distinct vortex-shedding patterns.After the branch conversion,the streamwise amplitude and lift coefficient of the downstream cylinders increase dramatically.The coupling mechanism of the four cylinders is changed accordingly.Meanwhile,the"2P+2S"vortex-shedding mode is observed.The vortex-shedding frequency of the downstream cylinders continues to rise as Re grows.In particular,a pair of vortices shed from the downstream cylinders every 4-5 cycles at Re=140.By contrast,the vortex pair sheds from the downstream cylinders every 1-2 cycles for 250≤Re≤300.