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, 𝑅𝑣 ) from 0 to 0.6 has been investigated numerically. The total impulse generated increases with increasing 𝑅𝑣 for 𝐿∕𝐷 < 1.5, but increases initially and then decreases for 1.5 ≤ 𝐿∕𝐷 ≤ 3.5. Furthermore, it decreases with increasing 𝑅𝑣 for 𝐿∕𝐷 > 3.5. The co-flow affects the generation of total impulse mainly by modifying the development of pressure thrust 𝐹𝑃 (𝑡). The influence on 𝐹𝑃 (𝑡) can be divided into three stages. During the initial and final stages, 𝐹𝑃 (𝑡) decreases with increasing 𝑅𝑣 , 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 𝑅𝑣 (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 𝑅𝑣 (𝑡).