Dynamics and bifurcations of laminar annular swirling and non-swirling jets

Abstract

This paper presents bifurcation analyses characterising the nonlinear dynamics of fully developed laminar annular jets with respect to the centrebody diameter ${ {d}}$ , Reynolds number ${ {Re}}$ , and swirl ratio ${ {S}}$ . Similar flows appear in numerous applications and feature a vibrant range of topological and dynamical characteristics associated with phenomena including shear layer separation and vortex breakdown. Our results begin by describing the non-monotonic evolution of the axisymmetric jet's steady topology under varying ${ {S}}$ . In accord with earlier reports, the jet progresses through a sequence of wake, breakdown and wall jet regimes in a qualitatively similar manner across a wide span of ${ {d}}$ and ${ {Re}}$ values. In the wake regime, the non-swirling jet bifurcates to a plane-symmetric, but not axisymmetric, steady flow pattern beyond a ${ {d}}$ -dependent critical ${ {Re}}$ value. With further increase in ${ {Re}}$ , the steady non-swirling jet destabilises subsequently via multiple distinct Hopf bifurcations. Introducing ${ {S}}>0$ to the jet also induces unsteadiness by twisting the singly azimuthally periodic ( $|m|=1$ ) asymmetric wake structure and causing it to precess periodically in time about the central axis. Intermediate swirl stabilises this unsteady dynamics and restores the jet's axisymmetry. This stabilising effect is then reversed in the breakdown regime at higher ${ {S}}$ , where a variety of different $|m|=1$ and $|m|=2$ instabilities bifurcate from the steady flow as ${ {S}}$ is increased. Several instances of hysteresis and subcritical behaviour are reported and discussed, including one that manifests precessing vortex core oscillations.

Confinement effects in laminar swirling jets

“…In a recent pair of studies led by the first author, bifurcation analysis was used to investigate the steady and time-periodic dynamics of radially unconfined laminar swirling jets issuing from rotating pipes mounted flush against a semi-infinite axial wall (Douglas, Emerson & Lieuwen 2021, 2022). Those studies demonstrated that in the steady regime, an axisymmetric CRZ emerges gradually in the quasi-columnar jet due to vortex breakdown as the swirl ratio is increased.…”