TRANSITIONS AND INSTABILITIES OF FLOW IN A CHANNEL WITH A SUDDENLY EXPAN DED PART

采用三种不同的方法，即动力学方程的时间推进法、SOR迭代法和稳态方程的有限元法，从理论上研究了具有突然扩张和收缩部分的对称通道中流动的过渡和不稳定性。将线性和弱非线性稳定性理论应用于流动。这些转变通过流动可视化和速度测量得到了实验证实。在低雷诺数下，流动是稳定和对称的，在临界雷诺数下，流动变得不对称，在另一个临界雷诺数下恢复对称，在非常大的雷诺数下，流动变得振荡。在某些情况下，会发现多个稳定的稳态解，从而导致滞后。用数值方法确定了多个稳定稳态解存在的临界条件，并与线性和弱非线性稳定性分析结果进行了比较。发现在流动中振荡不稳定性的模态交换随着展弦比（展开部分的长度与宽度之比）的变化而发生，并讨论了其与冲击自由剪切层不稳定性的关系。本文还研究了一入口两出口通道内流动的过渡，并通过数值计算得到了流场的压力分布。

Transitions and instabilities of flow in a symmetric channel with a suddenly expanded and contracted part are investigated theoretically by three different methods, i.e. the time marching method for dynamical equations, the SOR iterative method and the finite element method for steady-state equations. Linear and weakly nonlinear stability theories are applied to the flow. The transitions are confirmed experimentally by flow visualizations and velocity measurements. It is found that the flow is steady and symmetric at low Reynolds numbers, becomes asymmetric at a critical Reynolds number, gets the symmetry back at another critical Reynolds number and becomes oscillatory at very large Reynolds numbers. Multiple stable steady-state solutions are found in some cases, which lead to a hysteresis. The critical conditions for the existence of the multiple stable steady-state solutions are determined numerically and compared with the results of the linear and weakly nonlinear stability analyses. An exchange of modes for oscillatory instabilities is found to occur in the flow as the aspect ratio, the ratio of the length of the expanded part to its width, is varied, and its relation with the impinging free shear layer instability (IFLSI) is discussed. Transitions of flow in a channel with an inlet and two outlets are also investigated and the pressure distribution in the flow fields is obtained numerically.