| dc.description.abstract | The present study focusses on vortex breakdown (VB), which occurs in axially convected
swirling
flows and is characterized by the development of an internal stagnation point
and regions of reverse
flow. VB has been observed or utilized in a variety of situations
including
flow over delta wings, tornadoes, re whirls, turbomachinery, fuel injectors and
combustors. Flows where VB is observed include swirling round jets with non-swirling
and negligible co
flow. The experimental study of Billant et al., (1998) has shown VB
characteristics unique to this family of
flows. In addition to the commonly observed
bubble form of breakdown (BVB) the experiments revealed a new form, referred to as
conical form of breakdown (CVB). Features of these forms (especially the latter) remain
mostly unexplored. This serves as motivation for the present numerical investigation of
VB in swirling jets.
In this study, a survey of different VB states (laminar and turbulent) observed with
varying
flow parameters has been carried out using numerical simulations, along with investigations
on hysteresis effects and bistability phenomenon. Previous theoretical models
for VB have been assessed using these results. Helical instabilities that were observed to
arise in the simulations have been examined using the tools of stability analysis.
Three-dimensional numerical simulations were carried out using the open-source incompressible
flow solver incompact3d in a Cartesian coordinate framework to study a
swirling jet entering an adequately large domain to prevent con nement effects. The
swirling jet was modelled using the axisymmetric and steady `Maxworthy' in
flow pro le
(Ruith et al., 2004), with the main control parameter as the swirl number, S, representing
the relative rate of rotation in comparison to the centreline axial velocity of the jet. The
Reynolds number (Re) was chosen based on the jet radius and centreline axial velocity.
The long-time flow states achieved with varying S and initial conditions are reported
for Re = 200 and 1000. For the latter case, where the
flow transitioned to turbulence,
large eddy simulations were carried out using the explicit fi ltering approach. Both local
and global stability analyses have been performed to examine instabilities. Selective frequency
damping and axisymmetric simulations using ANSYS Fluent have been used to
compute base
flows.
For Re = 200, BVB and CVB were observed and could be clearly distinguished by
the distinct spatial structure of the recirculation zone. These different VB forms could
be further classi ed based on unique characteristics into different types. For BVB, the
following types were identi ed{ steady one-celled BVB, one-celled BVB with spiral tail,
pulsating BVB, two-celled BVB with spiral tail and asymmetric BVB. The categorization
as one-celled and two-celled was based on the number of toroidal structures that could be
identi fied within the bubble, while the pulsating BVB was observed to be an intermediate
state between the two. The term `spiral tail' is used to denote the presence of a helical
mode that developed in the wake of the bubble which had no signifi cant effect on the
axisymmetric upstream portions of the bubble. In contrast, for the asymmetric BVB, a
helical mode was present, which caused asymmetric motion of the entire bubble. Two
types of CVB were identifi ed{ regular and wide-open{ the latter with an approximately
radial expansion of the
flow downstream to the stagnation point. Comparisons with
different experimental results showed strong similarities in features for most
flow states.
Hysteresis studies established the coexistence of different types of BVB with the regular
CVB in overlapping ranges of swirl numbers, confo rming that these are bistable
forms. Remarkable differences in length scales involved for the two forms could be observed
when comparing time-averaged
flow structure. A hysteresis plot is provided based
on the maximum radius achieved by a streamline starting from the in
flow plane at an
arbitrary radius. It was additionally seen that the two-celled BVB with spiral tail and
asymmetric BVB coexist (along with regular CVB) over a small range of swirls.
For Re = 1000, a transition to turbulence was observed, leading to some interesting
differences in the
flow states observed. At low swirls, the stagnation point occurred
only intermittently in time, in contrast to the steady VB observed for equivalent S for
Re = 200. For swirls above this, a two-celled BVB with a turbulent wake was observed for
a large swirl range. The stagnation point at the bubble's nose was lost at swirls just above
those for which BVB was observed. For this range, a spiral coherent structure was seen to
arise intermittently in the bubble's wake, accompanied by streamwise oscillatory motions
in the
flow. At higher swirls, this motion was subdued and the spiral downstream of the
bubble was lost, while the stagnation point at the bubble's nose eventually reappeared.
The streamwise oscillations of the bubble being a common feature to all long-time
flow
states observed, these states are collectively referred to as oscillating BVB.
For even higher swirls, turbulent regular and wide-open types of CVB were observed.
Bistability of oscillating BVB and regular CVB, and additionally, between regular and
wide-open CVB were established using hysteresis studies. The stark differences in length
scales associated with the bistable bubble and conical forms were reduced due to turbulence,
indicating that CVB might be misidenti ed as BVB at high Re. Indeed, it is
speculated that some of the VB states reported in experimental studies of Liang and
Maxworthy, (2005) are likely the CVB. The bistable regular and wide-open types of CVB
were found to have considerable differences in the length scales of respective recirculation
zones.
The two VB states for which helical modes were observed, the BVB with spiral tail and
asymmetric BVB, were examined using stability analysis. A closely related
flow state to
BVB with spiral tail is the spiral vortex breakdown (SVB). In previous studies, SVB was
identi ed to arise due to the instability of a nonlinear steep global mode. Assuming weakly
non-parallel
flow, a local spatio-temporal analysis coupled with a WKBJ framework was
used to show that the global mode associated with BVB with spiral tail differed from
that of the SVB, with the linear frequency selection criterion (Chomaz et al., 1991) better
predicting the global frequency. Using tools of global stability analysis, the asymmetric
type of BVB was shown to arise due to a different unstable mode that has strong energy
content in the bubble region. It was observed in the simulations that the base state was
strongly modifi ed by the instability. The stability analysis using the mean
flow made
better predictions as compared to that based on the base
flow for this type of BVB.
Two theories developed by Benjamin, (1962) and Brown and Lopez, (1990) towards
explaining VB were assessed. It was observed that the prediction from the former theory,
that the
flow becomes subcritical downstream of VB, was confi rmed based on simulation
results. However, other aspects of the theory, which have not been scrutinized in previous
studies displayed a trend opposite to that observed in the present simulations as well as
other available experimental results. That is, the conjugate states predicted by the theory,
modelling the
flow downstream of VB, were found to better resemble the primary state
upstream of VB with increasing swirl. This contradicts the observation that the bubble
increases in size with swirl. Reasons for why the predictions display this trend, based
on analogies to gasdynamic shockwaves, are provided. The theory of Brown and Lopez,
(1990) was found to give qualitatively similar predictions for BVB, but deviated strongly
from the numerical results for CVB.
A major highlight of this study is the signifi cance of the initial conditions in determining
the VB form or type achieved, with results showing the coexistence of three distinct
pairs of long-time
flow states in overlapping parametric ranges for swirling jets. Though
emphasized by Billant et al., (1998), many later studies on swirling jets have generally neglected
this aspect. Similarly, as this study shows, the CVB is a distinct form of VB that
has not been clearly identifi ed in previous studies on swirling jets. These results might
aid in better understanding features of the elementary
flow confi guration of swirling jets
and allow for more informed developments of design and control strategies in practical
applications. | en_US |
