Exp Fluids (2017) 58:36
Investigation of the vortex ring transition using scanning Tomo-
· Christoph Brücker
Received: 21 October 2016 / Revised: 22 February 2017 / Accepted: 23 February 2017 / Published online: 27 March 2017
© The Author(s) 2017. This article is an open access publication
vortex ring formation through a piston-cylinder mecha-
nism has been investigated in detail by Gharib et al. (1998).
The ﬂow ﬁeld of a vortex ring was found to be determined
by the formation number (stroke length to piston diam-
eter ratio). A threshold formation number was suggested.
A trailing jet is attached to the leading vortex ring when
produced at a formation number larger than the threshold.
However, the vortex ring detaches from the trailing jet
under a formation number smaller than the threshold value.
Apart from the topic on formation, the evolution of vortex
ring oﬀers an opportunity to study the fundamental aspect
of laminar–turbulent transition process. More recently, due
to the increasing attention paid on the jet noise produced by
airliners, the vortex ring is chosen as a conceptual model
to analyze the noise generation (Ran and Colonius 2009),
because it isolates the ring transition from the pairing pro-
cedure and provides insight on the noise associated solely
with laminar–turbulent transition. In the present paper,
focus is going to be paid on the transition behavior of a sin-
gle vortex ring.
One early experimental study on the evolution of vor-
tex ring was reported by Krutzsch (2011) in the 1930s. In
that experiment, observations on the vortex ring transition
were made with the then novel dye visualization technique,
which is in use even nowadays in vortex ring studies (New
et al. 2016). The laminar circular ring was observed to
exhibit wavy undulations along the core through instabil-
ity mechanism. Moreover, secondary structures associated
with this ﬂow instability were identiﬁed, too. Although
this early work only provided qualitative observation, it did
pave the foundation for the topic of vortex ring transition
and guided research eﬀorts towards the instability phenom-
enon in the vortex ring transition.
Development of the PIV technique in the last three dec-
ades makes quantitative examination on the vortex ring
Abstract The transition of a vortex ring at Re
= 5030 is
studied by time-resolved scanning tomographic PIV tech-
nique. The transition process is ﬁrst analyzed through ﬂow
quantities such as circulation and vorticity components.
Using the volumetric measurement technique, vortical
organization of the vortex ring at early and late transition
stages is visualized, respectively. Focus is paid to the insta-
bility phenomenon associated with transition. The present
4D ﬂow data allows analysis of the temporal evolution
of the wavenumber spectra. The dominant wavenumbers
in transition are identiﬁed and the growth of their ampli-
tude is revealed. The vortex ring transition is ﬁnally stud-
ied through the particle trajectories. A phase diﬀerence
between the axial velocity and radial velocity is found at
the beginning of transition; however, it is subject to change
following the progression of transition. Statistical analysis
on the velocity components helps to identify the aft portion
of the inner ring as the one that is ﬁrst to lose the original
phase relation in velocity, which is caused by the secondary
vortical activity during transition.
Vortex ring is of fascinating nature in ﬂuid dynamics. Both
its formation and evolution have attracted numerous experi-
mental (Maxworthy 1972; Widnall and Sullivan 1973;
Gharib et al. 1998) and numerical studies (Bergdore et al.
2007; Archer et al. 2008; Ran and Colonius 2009). The
* Zhengzhong Sun
Department of Mechanical Engineering and Aeronautics,
City, University of London, London EC1V 0HB, UK