Transition in vortex breakdown modes in a coaxial isothermal unconfined swirling jet

Abstract

This paper reports first observations of transition in recirculation pattern from an open-bubble type axisymmetric vortex breakdown to partially open bubble mode through an intermediate, critical regime of conical sheet formation in an unconfined, co-axial isothermal swirling flow. This time-mean transition is studied for two distinct flow modes which are characterized based on the modified Rossby number (Rom), i.e., Rom ≤ 1 and Rom > 1. Flow modes with Rom ≤ 1 are observed to first undergo cone-type breakdown and then to partially open bubble state as the geometric swirl number (SG) is increased by ∼20% and ∼40%, respectively, from the baseline open-bubble state. However, the flow modes with Rom > 1 fail to undergo such sequential transition. This distinct behavior is explained based on the physical significance associated with Rom and the swirl momentum factor (ξ). In essence, ξ represents the ratio of angular momentum distributed across the flow structure to that distributed from central axis to the edge of the vortex core. It is observed that ξ increases by ∼100% in the critical swirl number band where conical breakdown occurs as compared to its magnitude in the SG regime where open bubble state is seen. This results from the fact that flow modes with Rom ≤ 1 are dominated by radial pressure gradient due to swirl/rotational effect when compared to radial pressure deficit arising from entrainment (due to the presence of co-stream). Consequently, the imparted swirl tends to penetrate easily towards the central axis causing it to spread laterally and finally undergo conical sheet breakdown. However, the flow modes with Rom > 1 are dominated by pressure deficit due to entrainment effect. This blocks the radial inward penetration of imparted angular momentum thus preventing the lateral spread of these flow modes. As such these structures fail to undergo cone mode of vortex breakdown which is substantiated by a mere 30%–40% rise in ξ in the critical swirl number range.