Mechanism of transient force augmentation varying with two distinct timescales for interacting vortex rings

Abstract

The dynamics of dual vortex ring flows is studied experimentally and numerically in a model system that consists of a piston-cylinder apparatus. The flows are generated by double identical strokes which have the velocity profile characterized by the sinusoidal function of half the period. By calculating the total wake impulse in two strokes in the experiments, it is found that the average propulsive force increases by 50% in the second stroke for the sufficiently small stroke length, compared with the first stroke. In the numerical simulations, two types of transient force augmentation are revealed, there being the transient force augmentation for the small stroke lengths and the absolute transient force augmentation for the large stroke lengths. The relative transient force augmentation increases to 78% for L/D = 1, while the absolute transient force augmentation for L/D = 4 is twice as much as that for L/D = 1. Further investigation demonstrates that the force augmentation is attributed to the interaction between vortex rings, which induces transport of vortex impulse and more evident fluid entrainment. The critical situation of vortex ring separation is defined and indicated, with vortex spacing falling in a narrow gap when the stroke lengths vary. A new model is proposed concerning the limiting process of impulse, further suggesting that apart from vortex formation timescale, vortex spacing should be interpreted as an independent timescale to reflect the dynamics of vortex interaction.

Transient force augmentation due to counter-rotating vortex ring pairs

“…The overall effect is that the vortices increase in their radii and impulses, resulting in force augmentation. It is also reported by Fu et al (2014) that the interacting vortex rings embody another time scale, independent of vortex ring formation, related to thrust enhancement due to multiple vortex rings.…”

“…As indicated in figure 10(a,b), the shape of the PoVR remains We also calculate the rightmost expression of (2.7) in every cell in the domain. Similar approaches to find the sources of force have been taken by Lee et al (2012) and Fu et al (2014). Between two adjacent time frames, the rate of the impulse change in each grid cell is then regarded as the contribution of force from each fluid element.…”

“…The force augmentation has been found to increase significantly for sufficiently small vortex spacing (Fu et al 2014). In the following case we consider a 'special' configuration, illustrated in figure 12, where the vortex spacing is very small.…”

“…It can be found that the interacting vortical structure induces an area of force source located at x/D < 0.2 and 0.5 < r/D < 0.8. As the negative vorticity is kept sufficiently close to the PoVR, the configuration allows stronger interaction (Fu et al 2014).…”

“…Based on the computational results showing vorticity contours, the boundary of a vortex is empirically determined as the closed curve inside which the magnitude of the vorticity is not smaller than 3 % of the local maximum (Rosenfeld et al 1998(Rosenfeld et al , 2009Fu et al 2014). The area enclosed by the boundary is referred to as the core of a vortex ring.…”