有限长圆管内刚体旋转流的直接数值模拟

Numerical Study of Dynamics of Solid-body Rotation Flow in Finite-length Pipe

通过对三维不可压缩粘性流体的直接数值模拟,研究了有限长圆管内刚体旋转流在初始扰动下,扰动的增长和动力学演化过程。首先,通过改变流动的Reynolds数和旋转角速度ω,分析了轴对称流动中Reynolds数和ω对流动失稳的影响。对于高Reynolds数轴对称流动,利用数值模拟得到的不稳定结果与无粘线性稳定性理论预测的结果一致。最后,为进一步研究流动不稳定发展的三维效应,又进行了完全三维流动的模拟。数值结果表明,三维流动中不稳定的主导模态为螺旋模态,模态在线性段指数增长,导致流动产生螺旋型的漩涡破裂,之后经过非线性段的增长后达到饱和,流动最终发展为轴对称泡型旋涡破裂的稳定状态。

Three- dimensional direct numerical simulations of a base solid- body rotation flow with a uni- form axial velocity in a rotating, finite- length, straight circular pipe are presented. First, the axisymmetric flow are simulated to investigate the effect of Re number and swirl ratios on the dynamics of flow. We find that the instability result of high- Re axisymmetric viscous swirling flow agrees well with the prediction of the inviscid linear stability theory. Then,it is found that there exists a dominant spiral type of an instabili- ty mode when the full three- dimensional flow are simulated. This three- dimensional mode leads to a spi- ral type of flow roll-up that subsequently stabilizes on a steady axisymmetric bubble type of vortex breakdown.