Journal of Power and Energy Engineering, 2013, 1, 45-50 Published Online December 2013 (
Copyright © 2013 SciRes. JPEE
Cold-State Investiga ti on on a Flame Holder
Yiqing Du
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, China.
Received October 2013
Slitty bluff body is w idely used as a high-perfor mance flame holder in power industry. To understand the flame stability
mechanism, the evolution of the n ear wake over a slitty bluff body in cold state was numerically investigated using the
renormalization group (RNG) k-ε model at Reynolds number of 470,000. The coherent structure of the near wake was
identified by the vortex shedding simulation. To explain the vortex shedding, a mechanism that single vortex of large
size suddenly immerses two shear layers was proposed. To quantitatively compare the near wakes at different gap ratio,
a vortex shedding character dimension was first proposed. This character dimension has positive correlation with flame
stability. Particle-image velocimetry (PIV) measurements in a close wind tunnel were also carried out to confirm the
observation from the numerical study. The evidence shows that the numerical results are of good agreement with the
cold-state experiments.
Keywords: Flame Holder; Bluff Body; Flame Stability; Coherent Structure; Vortex Shedding
1. Introduction
Bluff body flame holders are widely used to make flames
stable in industry, especially for combustors with high
velocity flows. Many research conducted during the past
five decades indicates that the wake flow structure be-
hind the bluff body is directly related to the flame-hold-
ing performance. The wake contains the complexities of
separation and recirculation, mass and momentum trans-
port across the shear layers, and vortex shedding dynam-
ics. However, the study of the flow structure has not been
thoroughly explored. Yang and Tsai (1993) have expe-
rimentally investigated the effects of the width of gap on
the recirculation zone and the drag in the near wake of a
slitty bluff body in a confined tunnel at Re = 120,000 [1].
According to their experimental evidence, an asymmetric
wake structure is developed behind the symmetric slit
(G/D = 0.2 and 0.4). Compared with traditional bluff
body the slitty bluff body has better flame holding ability
and less pressure loss because the gap flow induces great
reverse flow and greater back pressure in the near wake.
Their investigations also indicate that the gap flow pro-
vokes more extensive transport across the shear layers
and reduces both the turbulent intensity and the Reynolds
shear stress of the wake, but no more data with different
gap ratios and detailed analysis on the wake structure has
been reported.
The understanding of flame holding mechanism of a
slitty bluff body is incomplete without an understanding
of the coherent structure in its near wake. Flow characte-
ristics and vortical motion within the near wake are the
major interest of the present work. The simulation on
flows of engineering and industr ial interest, char acterized
by high Reynolds numbers and complex geometry in con-
fined tunnel, generally requires proper turbulence mod-
eling. The analyses on different models, e.g. the standard
k-ε, the RNG k-ε and the large eddy simulation (LES),
were provided. The flow structure behind the slitty bluff
body was investigated nu merically by using the RNG k-ε.
Experimental results using PIV measurements in a close
wind tunnel were also provided to confirm the observa-
tion from the related numerical cold-state study.
2. Numerical Simulation
2.1. Calculation Model and Condition
Figure 1 shows the geometrical parameters and the co-
ordinate system used for the 2D case considered. The
slitty bluff body of triangle cross-section with side di-
mension D and gap dimension G, is immersed in a uni-
form velocity stream U. The resulting characteristic Rey-
nolds number (Re = ULi/γ) is fixed to 470,000. The di-
mensions of the computational domain are Li, Lx, Ly (250
mm, 450 mm, 200 mm). The slitty bluff body is in the
middle of a confined tunnel with its axis normal to the
inlet side.
The flame holder problems involve very complicated
flow behaviors that cannot be accurately simulated using
improper computational methods. In addition, the physi-
Cold-State Investigation on a Flame Holder
Copyright © 2013 SciRes. JPEE
Figure 1. Definition of the co-ordinate and the geometrical
parameters for the flow past a slitty bluff body.
cal geometries are generally bluff body and require spe-
cial attention when attempting to predict the associated
flow. In most problems, the flow is unsteady and turbu-
lent with vortex shedding. It is theoretically possible to
directly resolve the whole spectrum of turbulent scales
using an approach known as direct numerical simulation
(DNS) to capture the fluctuations. DNS is not feasible for
practical engineering problem, as DNS approaches are
too computationally inten se. An alternative f or numerical
simulation of complex turbulent flows is the large eddy
simulation (LES). It should, however, be stressed that the
application of LES to engineering simulations is in its
infancy. Evidence shows that LES is improper to calcu-
late the 2D bluff body flow.
Traditionally, numerical si mulations of these flows are
performed using the Reynolds-averaged Navier-Stokes
(RANS) equations and using phenomenological model to
fully represent the turbulence. The available turbulence
models vary extensively in complexity, in particular, from
simple algebraic eddy viscosity relationships to complex
formulations involving several additional differential equa-
tions. In each model, values for the empirical constants
are obtained from turbulent flows that are fundamentally
The RANS equations represent transport equations for
the mean flow quantities only, with all the scales of the
turbulence being modelled. A computational advantage is
seen in transient situations, since the time step will be
determined by the global unsteadiness in the mean flow
rather than by the turbulence. The Reynolds-averaged ap-
proach is generally adopted for practical engineering cal-
The RNG k-ε model is one of the k-ε variants of
RANS derived using a rigorous statistical technique
called renormalization group theory. It is similar in form
to the standard k-ε model, but includes the following
The RNG model has an additional term in its ε equa-
tion that significantly improves the accuracy for ra-
pidly strained flows.
The effect of swirl on turbulence is included in the
RNG model, enhancing accuracy for swirling flows.
These features make the RNG more accurate and reli-
able for a wider class of flows than the standard k-ε
model. Thus RNG k-ε model in FLUENT 6.0 is used in
the present investigation using.
The computational meshes employed are non-uniform
grids. The number of grid cells is about 140,000 (slightly
varied with different gap ratio), these quadrilateral cells
are obtained with interval size 1mm using the Quad/
Tri-Pave meshing Scheme in GAMBIT, which creates a
paved mesh that consists primarily of quadrilateral ele-
ments but employs triangular mesh elements in any cor-
ners, the edges of which form a very small angle with
respect to each other.
Velocity Inlet boundary conditions include the flow
velocity, and all relevant scalar properties of the flow.
The total properties of the f low are not fixed, so they will
rise to whatever value necessary to provide the pre-
scribed velocity dis tribution. Figure 1 defined the inf low
velocity Re = 470,000 (nor mal to the boundary).
Pressure Outlet boundary conditions specify the static
pressure at flow outlets (and also other scalar variables,
in case of backflow). The use of a pressure outlet boun-
dary condition instead of an outflow condition often re-
sults in a higher rate of convergence when backflow oc-
curs during iteration. The outlet boundary is far enough
from the bluff body (x = Lx) with constant static pressure
which can be measured experimentally.
In order to model the natural perturbations in any real
flow, many numerical simulation s usually use an explicit
perturbation at the onset of the trans ient calculation. This
numerical disturbance exists in the form of a deranged
initial flow field often formed by applying slip velocity.
This explicit perturbation is said to be necessary in order
to disturb the Navier-Stokes equations and provoke or
kick-startthe vortex shedding process by Anderson
(1993) [2]. D.G.E. Grigoriadis et al. (2003) investigated
incompressible turbulent flow past a long square cylinder
using LES [3]. They used a uniform stream U superim-
posed with Gaussian random divergence-free perturba-
tions of intensity 2% - 5% w.r.t. the local value. After a
transient time the flow rejects the initiate unrealistic co n-
dition and the shear layers at the cylinders’ faces initiated
vortex shedding.
In our investigation all flow fields were firstly calcu-
lated with a “stable” solver on the assumption that the
flow field can be time-independent. This assumption is of
signality, although it is undoubted that the real flow past
a bluff body is a ti me-dependent problem. To investigate
the intrinsic mechanism in the w ake flow of a slitty bluff
body, the inflow perturbation is unwanted. The perturba-
tion can be reduced to a certain level, but it can never be
removed completely or be diminished to very small level
in a real flow. However the simulation can initiate the
inflow perturbation to zero. All further time-dependent
simulations are on the basis of the stable results.
Cold-State Investigation on a Flame Holder
Copyright © 2013 SciRes. JPEE
2.2. Numerical Result
The present investigation concentrates on the near wake,
that is, the region at x < 200 mm. Development of the
wakes further downstream will not be considered in the
present study.
The stable simulation reveals tha t the canonical biased
gap flow patterns can be identified at gap ratios 0.22 -
0.48. Corresponding example vector field at G/D = 0.22
is given in Figure 2.
Figure 2 shows that the gap flow divides the near
wake into two recirculation zones, the big one is called
the main rec ircu lation zone ( MRZ), the sma ll one is called
the secondary recirculation zone (SRZ). Generally the
recirculation zone in the near wake consists of a vortex
pair closed in a zero streamline.
In most situations, the near wake flow at high Rey-
nolds nu mber is time-dependent and very turbulent. This
unstable character depends on the perturbation and the
flow structure itself. Coherent structures in the near wake
are related to fluctuation amplitudes of drag and lift and
also to the mean flow quantities. All these evidence in-
dicates that the stabilities of the wake and the perturba-
tion itself intimately depend on the coherent structure of
the wake.
Despite of the complexity of disturbance and the tur-
bulent transition regime, we f ocused our investigation on
the flow structure and how the structure influences the
instability. All time-dependent computations begin with
the stable converged results by setting the solver to un-
stable. The unstab le numerical resu lts reveal that gap flow
shows obvious asymmetric in the wake flow field. The
gap flow penetrating the leading open slit of the bluff
body turns toward either the upper or the lower wing and
then stays relativ ely stable owing to the bi-stable status
of th e flow field at G/D = 0.22 - 0.48. The gap flow does
not diffuse symmetrically in the near wake region.
The concepts of absolute and convective instabilities
have provided new physical insights into wake control
since 1985. The difference between absolute instability
and convective instability is that th e impulse response of
a fluid system can propagate in both upstream and down-
stream direction in an absolutely unstable flow, whereas
it can only propagate in the downstream direction in a
convectively unstable flow region. Therefore, a flow sys-
Figure 2. Coherent structure in flow over a slitty bluff body.
tem that contains a sufficiently large region of absolute
instability will respond to externa l forcing by developing
time-amplifying global oscillations, a response that is
fundamentally different from that of a system that is co n-
vectively unstable everywhere. In wake flow, both types
of instability exist. The near wake is governed by abso-
lutely instability, the wake then changes to convective
instability at short distance from the solid boundary due
to the rapid filling of the velocity deficit. In the abso-
lutely unstable region, wake flow acts as a resonator
where all unstable disturbances are self-excited or time-
amplified. In the convectively unstable region, wake flow
is similar to a spatial amplifier in that all unstable fre-
quencies (for small-amplitude perturbations) will grow
exponentially along the downstream direction. Therefore,
the disturbances will first resonate in the absolutely un-
stable region and then serve as an initial perturbation in
the convectively unstable region. MRZ sheds a large
vortex street, whereas SRZ has a small vortex pair, the
vortex shedding cannot be seen behind SRZ. As MRZ
and SRZ are in the near wake and governed by abso-
lutely stability, the unstable disturbance of MRZ or SRZ
has an impact on each other through the gap flow. This
results in fluctuation in the SRZ and the swing of the gap
There are three main factors that will play important
role in the interference between MRZ and SRZ. One is
the distance G between two recirculation zones. The nu-
merical study reveals the distance nearly equals to the
gap width, a smaller distance G can make it easier to
transfer the interference. The second is the proportion
between MRZ and SRZ, the bigger the deflection angle
of the gap flow is, the bigger the proportion is. The third
factor is the gap flow strength.
3. Vortex Shedding Mechanism
The investigation over the vortex shedding mechanism
over a slitty bluff body is very important not only in en-
gineering applications but also in understanding the basic
nature of turbulent flows.
Generally, all the above evidences indicate that the
circular cylinder vortex shedding physics is very com-
plex because of its separated shear layers and the interac-
tion between the second eddies and the Strouhal vortices.
Other factors, like the disturbance from free stream or
even three-dimensional contributions make experimental
investigation almost impossible to understand the real
physics of vortex shedding. Our slitty bluff body model
is simpler than the circular cylinder, for the reason that
there is no separate shear layer on the surface. Further
more the gap flow can be easily measured by experiment,
which can be used as index to evaluate the numerical
results and theory analysis.
Cold-State Investigation on a Flame Holder
Copyright © 2013 SciRes. JPEE
A pair of vortices with different direction between the
shear layers, see in PRZ, can be stable in the near wake
at certain condition. For example, at low Reynolds num-
ber. There are a stable vortex pair in the near wake be-
hind a bluff body, see in Figure 3(a). A single vortex
with a scale of 2D between two shear layers gains stream-
wise velocity from the shear layers so it will detach from
the near wake, see in Figure 3(b). Vortex shedding
process was simulated by our unstable numerical com-
putations. It should be noted that unlike some previous
work the vortex shedding was not artificiall y initiated by
numerically inducing slight twist to cylinder. For the pre-
sent simulation, shedding of Strouhal vortices occurs natu-
rally through time evolution of an unstable wake. The
vortex shedding mechanism over the slitty bluff body can
be explained as following according to our numerical
This vortex shedding process can be divided into two
stages, the growing stage and the detaching stage. At
the “growing stage, the small vortex becomes bigger
and bigger slowly. At “detaching stage, the single vortex
suddenly detaches downstream. The first stage spends
mor e time (Δτ1) while the detaching stage spends less
time (Δτ2). The ratio Δτ1/Δτ2 is about 3 by our cal-
The instantaneous character of vortex detachment in
near wake is depicted in Figure 4. Yet the vortex shed-
ding phenomena in PRZ over a slitty bluff body is
largely the same as the near wake of a cylinder known as
Von Karman vortex street. A single vortex confronts
with the two shear layers, exchanging momentum and
Figure 3. Vortex pair and single vortex between the two
shear layers.
Figure 4. Instantaneous character of the near wake (a) stat-
ic pressure (b) tur bulent kineti c energy.
energy with the mean flow. At the same time, the vortex
gets a speed of X component which makes the vortex
shedding, and initiates sudden change of pressure and
kinetic energy. Figure 5 depicts the disperse distribution
of P and k at the detachment moment. The kinetic energy
gathers near the saddle point and low pressure at the
center of the vortex collapses, leads to the disturbance.
The pressure disturbance can propagate in all direction at
sound speed and the average velocity is low in the near
wake with back flows, so the disturbance can propagate
upstream. That is the reason why the near wake is abso-
lute instable.
To compare the time-dependent flow over the slitty
bluff body new character dimension is needed. Accord-
ing to the above model of the single vortex between two
shear layers, we first define the vortex shedding character
dimension Ls as the streamwise distance between the
centre of the single vortex and the rear edge of bluff body.
The single vortex gets momentum from the shear layers
and detaches from the near wake rapidly, the detached
vortex does not contribute to the flame instability, so the
definition of Ls is of great signality in quantitively com-
Cold-State Investigation on a Flame Holder
Copyright © 2013 SciRes. JPEE
Figure 5. Instantaneous vectors of (a) (G/D = 0) and (b)
(G/D = 0.22) by PIV.
paring the time-dependent wake flow over slitty bluff
bodys and predicting flame stability.
4. PIV Measurement
The tested bluff body with a slit in a wind tunnel is
shown in Figure 1. The experiments were conducted in a
close-circuit wind tunnel blown by a blower, the speed of
which was controlled by a frequency inverter. The free
stream turbulence was controlled by a turbulence-gener-
ating screen place at the entrance of the test section, 800
mm upstream of the bluff body. The free stream turbu-
lence intensity is lower than 0.5% and the non-uniformity
of the mean flow distribution is less than 0.5%. Figur e 5
gives a typical instantaneous velocity vector field. The
vortex shedding character dimension of slitty bluff body
(Figure 5(b)) is much longer than bluff body (Figure
The velocity vectors by PIV also show the gap flow is
biased. The results are in good agreement with the RNG
simulation. By comparing the instantaneous velocity vec-
tors, the coherent structures are similar except the ampli-
tude of disturbance of near wake by PIV is greater than
the simulations, which is probably attributed to the greater
disturbance in the free stream in experimental flow.
Figure 6 gives the vortex shedding character dimen-
sion Ls at different gap ratio G/D. We get the maximum
Ls at G/D = 20%. The Turbulent kinetic energy contour
in PIV using the global average mean (Figure 7) shows
that maximum k is exactly at the vortex shedding point
Figure 6. Effect of gap ratio on change of vortex shedding
character dimension.
Figure 7. Turbulent kinetic energy contour by PIV (a) G/D
= 0 (b) G/D = 0.22.
X mm
Y mm
20 40 60 80
Cold-State Investigation on a Flame Holder
Copyright © 2013 SciRes. JPEE
(Ls from the bluff body rear edge). This evidence proves
the above vortex shedding dynamics characterised by the
character dimension Ls. The near wake gains a wider k
distribution but less intensity as its vortex shedding char-
acter dimension Ls increases. Our numerical study also
reveals the same trend. These phenomena reveal slitty
bluff body has better flame stability than bluff body.
5. Conclusions
Impetus of the present RNG k-ε simulation was to inves-
tigate the coherent structure of the near wake behind a
triangle slitty bluff body. We computed the flow in the
near wake behind a slitty bluff body at gap ratios from 0
to 0.48 at a Reynolds number of 470,000. Based on this
study, the following concluding remarks are offered:
Detail analysis on the RNG k-ε model shows that this
model is adequate in computing the near wake over
bluff body, especially better than the standard k-ε
model and LES.
The flow in the near wake behind the slitty bluff body
is unstable structure. Without any perturbation initia-
tion (kick-start), we got a time-dependent flow field.
The reason is that there are numerical disturbance
during the iterations.
Based on the computational results, the vortex shed-
ding was analyzed. A single vortex between shear
layers mechanism was proposed. The production of
perturbation and instability mainly depends on this
sudden confrontation between a single vortex of large
size and the two shear layers.
Vortex shedding character dimension was first pro-
posed to compare time-dependent wake according to
vortex shedding dynamics. The vortex shedding char-
acter dimension has positive correlation with flame
The computations were further compared with PIV
measurements. PIV vector field and Turbulent kinetic
energy contour indicates that the simulation can get right
information on th e coherent structure of bluff body flow,
the vortex shedding character dimension over slitty bluff
body is longer than over bluff body, it reaches maximum
at gap ration G/D = 20%.
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Gutter with Slit Bleed,” Journal of Fluids Engineering,
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[2] C. R. Anderson, “On the Accurate Calculation of Vortex
Shedding,” Physics of Fluids, Vol. 2, No. 6, 1990, pp.
[3] D. G. E. Grigoiadis and J. G. Bartzis, “LES of the Flow
Past a Rectangular Cylinder Using the Immersed Boun-
dary Concept,” International Journal for Numerical Me-
thods in Fluids, Vol. 41, No. 6, 2003, pp. 615-632.