Initiation of parallel twin-starting jets with temporal or spatial differences

The interactions between two identical starting jets (twin-starting jets) are numerically investigated, focusing on the influence of initiation with temporal differences (the dimensionless time difference normal upper Delta t overtilde greater than 0 Δ t ~ > 0 $\\Delta \\widetilde {t}\\gt 0$ ) and spatial differences (the dimensionless axial distance normal upper Delta upper X overtilde greater than 0 Δ X ~ > 0 $\\Delta \\widetilde {X}\\gt 0$ ). Temporal differences mainly weaken the mutual interaction between the two leading vortex rings, while spatial differences weaken both the vortex-ring interactions and the influence of mutually induced pressure. In both cases, two leading vortex rings become non-coplanar, increasing their spatial distance along the jet direction and thereby weakening their mutual interaction. For propulsive characteristics, both temporal and spatial differences mitigate the reduction in average thrust caused by jet interactions, whereas only spatial differences significantly suppress the overall thrust fluctuations. In addition, both types of difference induce a net lateral force on the nozzle outer walls. The combined effects of normal upper Delta upper X overtilde Δ X ~ $\\Delta \\widetilde {X}$ and the dimensionless nozzle spacing upper S divided by upper D S / D $S/D$ , where upper S S $S$ is the distance between the axes of the two nozzles, and is the nozzle diameter. are incorporated into the mutually induced pressure model. Finally, the influence distance upper S 3 divided by upper D S 3 / D $S_3/D$ is introduced to quantify the weakening of vortex-ring interactions by temporal and spatial differences. This parameter also unifies the effects of normal upper Delta t overtilde Δ