The influence of background co-flow on the propulsive characteristics of starting jets

The influence of uniform background co-flow on the propulsive characteristics of starting jets with stroke ratios (length to diameter ratio, L/D) from 1 to 5 and velocity ratios (ratio of co-flow velocity to maximum jet velocity, R_v) from 0 to 0.6 has been investigated numerically. The total impulse generated increases with increasing R_v for L/D<1.5, but increases initially and then decreases for 1.5≤L/D≤3.5. Furthermore, it decreases with increasing R_v for L/D>3.5. The co-flow affects the generation of total impulse mainly by modifying the development of pressure thrust F_P(t). The influence on F_P(t) can be divided into three stages. During the initial and final stages, F_P(t) decreases with increasing R_v, and increases during the middle stage. These three stages are explained by the influence of co-flow on wake vortex ring, leading vortex ring and stopping vortex ring, respectively. Transition between stages can also be related to the instantaneous velocity ratio R_v(t), which is the ratio of co-flow velocity to instantaneous jet velocity. The negative influence of co-flow on the generation of impulse can be mitigated by the velocity program with faster acceleration and shorter deceleration duration, which is equivalent to reducing the average value of R_v(t).