TRANSITIONS AND INSTABILITIES OF FLOW IN A SYMMETRIC CHANNEL WITH A SUDDENLY EXPANDED AND CONTRACTED PART

Transitions and instabilities of flow in a symmetric channel with a suddenly expanded and contracted part are investigated numerically by three different methods, i.e. the time marching method for dynamical equations, the SOR iterative method and finite element method for steady state equations. Numerical results are analyzed by using the bifurcation theory. Linear and weakly non-linear stability theories are also applied to the flow. It is known that the flow is steady and symmetric at low Reynolds numbers, becomes asymmetric at a critical Reynolds number, gets symmetric again at another critical Reynolds number and becomes oscillatory. Multiple stable steady solutions are found in some cases and the parameter range of existence of the multiple stable solutions is obtained. Impinging free shear layer instabilities are found to cause the flow oscillations, and the mechanism of this instability is clarified.