Numerical studies of vortex-induced extinction/reignition relevant
to the near-field of high-Reynolds number jets
Rishikesh Venugopal and John Abraham
a͒
School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
͑Received 25 July 2008; accepted 2 April 2009; published online 27 May 2009͒
This work is motivated by the need to understand physical mechanisms governing near-field
phenomena, such as flame lift-off, in high-Reynolds number jet flames. Numerical studies of
vortex-induced flame extinction/reignition are performed for conditions representative of the near
field of high-Reynolds number ͑ϳ100 000͒ jets under high pressure and temperature conditions.
The governing equations for compressible, viscous, and reacting flows are solved along with a
single-step irreversible chemical kinetic model for gaseous n-heptane oxidation. Extinction/
reignition phenomena, influenced by unsteady and curvature effects, are observed. Unsteady
flamelet/progress variable models are shown to accurately describe the flame response during
extinction/reignition observed in the flame-vortex studies. Furthermore, while unsteady effects on
extinction/reignition are found to diminish with weaker vortices and relatively strong flames,
curvature effects are found to increase with relatively thicker flames. The observed flame-vortex
interaction regimes are summarized on an outcome diagram, which is useful to understand the
nature of localized flame dynamics in the near field of jet flames. © 2009 American Institute of
Physics. ͓DOI: 10.1063/1.3139308͔
I. INTRODUCTION
Recent experiments
1,2
in diesel jet flames have shown
that flame lift-off has a significant influence on pollutant for-
mation through fuel/air premixing in the jet near field.
Hence, understanding lift-off, and the development of pre-
dictive computational tools for diesel jet flames are impor-
tant. Recent attempts in literature
3
to numerically predict die-
sel flame lift-off with conventional Reynolds-averaged
Navier–Stokes ͑RANS͒-based modeling approaches, such as
steady diffusion flamelets
4
and perfectly stirred reactors
5
have met with only limited success. RANS models are also
inadequate in reproducing the mixing and entrainment char-
acteristics in the jet-near-field region where lift-off occurs.
6
In addition, jet near-field phenomena contributing to lift-off
could result from a combination of physical processes, such
as autoignition,
7
partially premixed flame propagation,
8,9
and
local extinction/reignition,
8
and a detailed understanding of
these phenomena through fundamental studies is required.
In the present work, we focus attention on the simulation
of local flame extinction/reignition through flame-vortex in-
teraction studies. We consider an initially flat diffusion flame
that interacts with a counter-rotating vortex pair and under-
goes extinction/reignition. We note that this is one of the
possible scenarios for the local flame dynamics at the lift-off
height of a jet flame. Other canonical configurations, such as
triple-flame-vortex interactions, which are relevant to under-
standing lift-off, have been studied in prior works.
10
The
pressure and temperature chosen are representative of diesel
engine combustion chambers. The range of length and veloc-
ity scales of the simulated vortices, and the scalar dissipation
rates characterizing the diffusion layers are relevant to the
near field of high-Reynolds number ͑ϳ100 000͒ jets. In spite
of its configurational simplicity, the flame-vortex setup is
useful to study detailed effects due to unsteadiness and cur-
vature, and to assess the accuracy of turbulent combustion
models, such as flamelet models. Here, we evaluate the ca-
pability of steady-flamelet and unsteady flamelet/progress
variable models to predict flame extinction/reignition. Now,
we will briefly review prior works on flame-vortex interac-
tions relevant to nonpremixed flame extinction/reignition.
In steady diffusion flames, it is well known that extinc-
tion can be characterized by the steady extinction limit
e
,
which is essentially the scalar dissipation rate beyond which
a steadily strained flame cannot be sustained.
9,11
However,
recent studies on vortex-perturbed flames
12–15
have shown
that unsteady extinction limits could be higher than steady
values. For instance, in the recent studies of Venugopal and
Abraham
15
under typical diesel engine conditions, unsteady
limits about ten times higher than
e
were observed due to
characteristic chemical-to-vortex time scale ratios much
greater than unity. In other words, if the characteristic re-
sponse time scale of the flame is slower than the imposed
flow time scale, then large deviations from steady behavior
may be observed due to delayed flame response. Moreover,
prior studies on flame-vortex interactions
14,15
suggest that
unsteady extinction limits are flow dependent, and increase
with increase in the vortex velocity scale. In the present
work, we will corroborate some of these findings on un-
steady flames, and discuss an extinction criterion that is ap-
plicable in unsteady flow fields.
In addition to unsteady effects on extinction, reignition
has received attention through experiments on vortex-
perturbed flames,
16,17
and numerical studies in reacting iso-
a͒
Author to whom correspondence should be addressed. Electronic mail:
jabraham@ecn.purdue.edu.
PHYSICS OF FLUIDS 21, 055106 ͑2009͒
1070-6631/2009/21͑5͒/055106/11/$25.00 © 2009 American Institute of Physics21, 055106-1