Fig 1.
Geometric details of vortex ring and ring generator.
(A) Piston-nozzle arrangement for generating vortex ring. Dashed line shows the outline of piston after it has moved by ΔX. Grey shaded region is the length of fluid that emerges from the nozzle, called here as slug length (L). (B) Variation of piston velocity/slug velocity with time. D and Up are diameter and velocity of piston, respectively, D0 and Us are exit diameter and velocity at the exit of the nozzle, respectively. Tp is the total time for which piston moves. (C) Side view, (D) isometric view and (E) line diagram of side view of the ring. Black circle denotes the core of the vortex ring, in which the vorticity is concentrated. Dr, Dvb and e denote diameter of the ring (distance between the cores), diameter of the vortex bubble including entrained air, and eccentricity of the ellipsoid, respectively.
Fig 2.
The input signal to the DAQ (top) is a trapezoidal wave with voltage amplitude V, rising time t1, constant duration t2-t1 and fall time t3-t2-t1. This signal is converted into analog form, amplified and fed to the speaker for vortex ring generation. Fog particles were injected into nozzle through fog injection port (FIP), and a high speed camera was placed horizontal to record the lateral view of the vortex ring as it propagates. In experiments with flies, we used two high-speed cameras to capture the 3D trajectories for the flies. All dimensions are in cm.
Fig 3.
Flow visualization and characterization of vortex ring.
(A) White and red circles denote leading edge (LE) and extreme end of the ring, respectively. These were tracked to calculate its axial position and diameter respectively. (B) Flow visualization at different time instances for Uavg = 1.9 m/s. The ring propagates from left to right. Tn = 0 indicates the time instance when ring just starts forming. (C) Effect of gust (Uavg = 6.4 m/s) on a freely hanging Styrofoam bead. Position of bead (i) when there is no gust, (ii) just before the gust, (iii) during gust, and (iv) after gust. The bead moves with the gust (iii) until the thread is taut. Black circle in (iii) shows the position of the bead when it is at the centre of the vortex ring.
Fig 4.
Flow characteristics of vortex ring.
(A) Average propagation velocity of the ring as a function of input voltage to the speaker. Velocity of the ring obtained using fog visualization (circles) and bead method (triangles) are in good agreement for different input voltages. Dashed line is Uavg = 0.2745 Vin, R2 = 0.99. (B-D) Non-dimensional flow properties of vortex ring with Uavg = 6.4 m/s and vortex bubble diameter 8.6 cm measured using flow visualization and bead method. (B) Xn is the axial distance from the nozzle exit, non-dimensionalized reative to the exit diameter D0 and given by Xn = X/D0. Xn = 0 indicates the centre of nozzle exit. (C) Dn = Dvb/D0, is the dimensionless diameter of the ring, where Dvb is the instantaneous diameter of vortex bubble. (D) Un = Uvb/Uavg is the dimensionless velocity of the ring, where Uvb is instantaneous velocity of the vortex bubble. Values are mean ± SD.
Fig 5.
Changes in body kinematics of soldier flies (Hermetia illucens) due to the gust induced by the vortex ring in 4 different trials.
(A) Trajectory in Y-Z plane normalized by the average body length (Lavg) of flies. The mean axial distance where the gust hits the insects is X0 = 3.7±0.38D0. Black circle indicates the front view of the vortex ring, and the intersection of vertical and horizontal dashed lines is the centre of the vortex ring. Coloured lines are the trajectories of flies for each trial represented by 1–4, and open circles on each curve denote the position of the flies just before they were hit by the ring. (B) Normalized speed versus non-dimensional time (in wing beats). Forward speed is normalized with the average speed of the flies before being hit by the ring, and time is non-dimensionalized by multiplying with the wing beat frequency. T = 0 indicates the time instance just before flies were just hit by the ring. Time period of gust is indicated in vertical grey strip. (C) Oblique top and the corresponding side views of flight sequences for trial 4 at different time instances showing distinct change in body roll angle. Number on the top row indicates the time instance of fly with respect to gust in terms of wing beats. (D) Change in body roll angle plotted against the wingbeat. Filled circles on black curve (trial 4) denote the time instances of the fly in (C).