Nonlinear dynamics of fully developed swirling jets

Abstract

This paper characterises the steady and time-periodic behaviour of swirling jets using numerical bifurcation analysis. Its objective is to elucidate the dynamics of fully developed, unconfined, laminar swirling jets under variations in the Reynolds number $\textit {Re}$ and swirl ratio $S$ . Within the $(0,0)\leq (\textit {Re},S)\leq (300,3)$ range, the steady, axisymmetric flow exhibits several distinct patterns ranging from a quasi-columnar jet along the central axis at low $S$ to a radial jet attached to the containing wall at high $S$ with various forms of vortex breakdown in between. A cusp bifurcation appears in the steady solution manifold which triggers bistable behaviour due to a competition between inner and outer low pressure regions associated with vortex breakdown and entrainment of the ambient fluid, respectively. Instability of the steady flow is linked to eigenmodes which are singly ( $|m|=1$ ) or doubly ( $|m|=2$ ) azimuthally periodic, although additional instabilities with other azimuthal wavenumbers occur at $(\textit {Re},S)$ -values beyond the leading neutral curves. The various branches of limit cycle solutions stemming from these neutral curves are associated with both super- and sub-critical Hopf bifurcations. The resulting unsteady flow fields exhibit a wide array of rotating, three-dimensional flow structures, and comparisons between the time-averaged and steady flow patterns highlight the role of these unsteady nonlinear interactions on the overall behaviour of swirling jets. Similarities and differences between this laterally unconfined jet and broader classes of swirling flows, including confined swirling jets and unconfined vortex models, are also discussed.