Abstract:
A complete analysis of the steady flow states of swirling flows in diverging (or converging) pipes was developed. The uniqueness of the steady flow state in a certain swirl range was rigorously proved by using nonlinear functional analysis. The co-existence of multiple steady states of swirling flows in diverging (or converging) pipes for the swirl beyond the uniqueness range were demonstrated numerically. A complete global bifurcation diagram of the flow steady state was also developed by using computational methods. By using the steady flow states obtained by the research described above one may investigate the linear stability of the steady-state flow in various swirl ranges. Due to limited scope of this research, detailed stability analysis will be carried out in future. This research will lead to a deeper understanding of the instability mechanism of the swirling flow in a diverging (or converging) pipe.
