Formation of leading vortex ring in the starting jet with background crossflow

The influence of background crossflow on the formation process of leading vortex ring in starting jet has been systematically investigated over the range of 1≤R_v≤6 and 0.7≤L/D≤6, where R_v is the ratio of jet velocity to crossflow velocity and L/D is the ratio of jet column length to diameter. Particular attention is being paid to the unique interaction between the leading vortex ring and the trailing vortex structures. In general, the background crossflow disrupts the normal formation process of leading vortex ring by either stopping its growth prematurely (R_v≥2) or preventing it from formation entirely (R_v<2). For R_v≥2, a new line, denoted as the optimal curve, is proposed with the formation number to illustrate the optimal application characteristics. The formation number diminishes with decreasing R_v. The mechanisms responsible for the clockwise (L/D>L/D_tran) and anticlockwise (L/D<L/D_tran) rotations of leading vortex ring have been further analyzed via kinematics and vortex dynamics. L/D_tran represents the L/D corresponding to the transition of leading vortex ring from anticlockwise rotation to clockwise rotation. As for the inability to produce a complete leading vortex ring at R_v<2, it is largely due to the fact that the crossflow weakens and directly inhibits the roll-up for the shear layer of starting jet on the windward side.