摘要
对低雷诺数旋转振动圆柱绕流问题运用低维Ｇａｌｅｒｋｉｎ方法将Ｎ－Ｓ方程约化为一组非线 性常微分方程组．运用打靶法数值求解了这组方程的周期解，并用 Ｆｌｏｑｕｅｔ理论对周期解的稳 定性进行了分析，研究了流动失稳的机制．
Oscillation of a circular cylinder is a important manner for the active control of its wakes. Understanding the dynamical characteristics of the flows will be helpful for us to explore the mechanism of the control. In present study a low dimensional Galerkin method (LDGM), which has been confirmed to be an ideal tool for investigation on global stability and theoretical analysis of chaos, is applied to reduce the Navier-Stokes equations to a set of nonlinear ordinary differential equations (ODEs). Periodic solutions (stable or unstable) of the equations are obtained by a shooting method for the flows over a rotationally oscillating circular cylinder at low Reynolds number. The bifurcation characteristics of these periodic flows are analyzed with the help of Floquet theorem. Results show that in the unstable periodic flow obtained by the shooting method at supercrit-ical Reynolds number, the two vortices behind the circular cylinder just become strong and weak periodically, rather than shedding alternately, i.e., no Karman vortex street is formed. The Floquet stability analyses describe the complicated transition procedure from the periodic flow to the quasi-periodic flow at a fixed Reynolds number Re = 60 with natural vortex shedding frequency fs. The double periodic bifurcation, Hopf bifurcation, and lock-in phenomenon are observed for different forcing frequencies fe, and the obtained theoretical results agree with the direct numerical integration and fast Fourier transformation (FFT) analyses of the ODE system. When fe = 2.0fs, the largest Floquet multiplier crosses the unit circle from negative real exis, which indicates the occurrence of double periodic bifurcation of the flow. When fe = 2.4fs , a pair of conjugate imaginary Floquet multipliers cross the unit circle, which suggests the onset of Hopf bifurcation. The lock-in phenomenon is observed when fe = 1.2fs, and the corresponding periodic solution obtained from the shooting method is always stable since the vortex shedding frequency is captured by the forcing frequency. An interesting extension of the present work is to determine the stability region of the periodic solutions in the parameter space fe, forcing amplitude, and Reynolds number. It is hard to perform such analyses because of the complexity of the flows leading to huge computation. However, this work is being undertaken.
出处
《力学学报》
EI
CSCD
北大核心
2001年第3期309-318,共10页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(19393100-6A).
