摘要:
采用有限体积法联合大涡模拟方法求解三维湍流流场,采用有限元法离散弹性管结构,对Re=1.35×104的湍流流动作用下三维弹性管的涡致振动进行了数值模拟,结构的动力学响应用Newmark算法来求解,管的运动采用基于扩散光顺方法的动网格模型来实现.利用建立的数值模型,分析了升力系数、阻力系数、位移、涡脱频率、相位差随频率比的变化特征,成功扑捉到锁定、相位开关,并联合运动轨迹、相图及Poincaré截面映射,研究了升力系数与横向位移的极限环与分叉等非线性特性.研究结果表明,在阻力系数的最小值处,横向振幅达到最大值,同时,横向响应的“锁定”也始于阻力系数最小值处;在"锁定"范围内,横向振幅随着频率比的增大而逐渐减小;在升力系数的最小值处,升力系数与位移间的相位由反相变为同相;在均匀湍流流动作用下,三维弹性管的升力与横向位移并未出现周期解的分叉.
Abstract:
Numerical simulations of vortex-induced vibration of a three-dimensional flexible tube under uniform turbulent flow were calculated when Reynolds number was 1.35×104. In order to achieve the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model were solved in the finite volume approach, the tube was discretized according to the finite element theory, and its dynamic equilibrium equations were solved by the Newmark method. The fluid-tube interaction was realized by the diffusion-based smooth dynamic mesh method. For a VIV system, the varying trends of lift coefficient, drag coefficient, displacement, vortex shedding frequency, phase difference angle of the tube were analyzed at different frequency ratios. The nonlinear phenomena of lock-in and phase-switch were captured successfully. Meanwhile, the limit cycle and bifurcation of the lift coefficient and displacement were analyzed with trajectory, phase portrait and Poincaré section mapping. The results reveal that: when the drag coefficient reaches its minimum value, the transverse vibration amplitude reaches its maximum and lock-in begins simultaneously. In the range of lock-in, the vibration amplitude decreases gradually with increase of the frequency ratio. When the lift coefficient reaches its minimum value, the phase difference between the lift coefficient and lateral displacement undergoes a sudden change from an out-of-phase to an in-phase mode. There is no bifurcation of the lift coefficient and lateral displacement occurring to the three dimensional flexible tube under uniform turbulent flow.