Bistability of bubble and conical forms of vortex breakdown in laminar swirling jets

Hysteresis and turbulent vortex breakdown in transitional swirling jets

“…where , x represents an inner product with respect to x , ' * ' denotes conjugate transpose and λ i is the eigenvalue corresponding to ψ i , representing the relative energy associated with the SPOD mode (see Moise (2020a), pp. 7-8).…”

“…A swirling jet is one such flow which, prior to undergoing VB, is characterized by a core region of rotating jet and negligible coflow. Recent computational studies employing inflow conditions that model a laminar swirling jet have revealed interesting VB features at low Reynolds numbers (for which the entire This hysteresis behaviour is an important feature exhibited by many VB flow states (see Moise (2020a), pp. 3-4).…”

“…Another feature commonly observed in swirling flows is the development of spiral coherent structures. In addition to the SVB (Lambourne & Bryer 1961;Sarpkaya 1971), other VB flow states that contain such structures include the precessing vortex core (PVC) (Syred & Beer 1974;Syred 2006), asymmetric BVB (Billant et al 1998;Moise 2020a), BVB with spiral tail (Sarpkaya 1971;Moise & Mathew 2019) and modes associated with CVB (possibly in Liang & Maxworthy (2005) and Tammisola & Juniper (2016) as discussed in § 6.1.2; also see § 3.3.1). The exact differences between these states remain unclear, although the PVC is usually identified by a displacement of the vortex core of the swirling jet away from the flow axis (Syred 2006;Oberleithner et al 2011;Manoharan et al 2020).…”

“…A swirling jet is one such flow which, prior to undergoing VB, is characterized by a core region of rotating jet and negligible coflow. Recent computational studies employing inflow conditions that model a laminar swirling jet have revealed interesting VB features at low Reynolds numbers (for which the entire flow field remains laminar), including the existence of numerous distinct VB flow states and hysteresis effects (Moise & Mathew 2019; Moise 2020 a ). In the present study, using the same model for inflow conditions, large eddy simulations (LESs) were performed to study unconfined swirling jets undergoing VB at a relatively higher Reynolds number with the objective of examining the effect of the transition to turbulence on VB.…”

“…These forms can be further classified into different ‘types’. For example, the BVB can be categorized as either a one-celled (Escudier 1988; Brücker & Althaus 1992) or two-celled type (Faler & Leibovich 1978; Moise 2020 a ), while the CVB can be differentiated into the regular (Billant et al. 1998) and wide-open types (Mourtazin & Cohen 2007; Moise & Mathew 2019).…”