Cold-State Investigation on a Flame Holder

doi:10.4236/jpee.2013.17008

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Journal of Power and Energy Engineering, 2013, 1, 45-50

http://dx.doi.org/10.4236/jpee.2013.17008 Published Online December 2013 (http://www.scirp.org/journal/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.

Email: [email protected]

Received October 2013

ABSTRACT

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

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

simple.

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-

culations.

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

refinements:

• 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-start” the 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

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

flow.

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

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

calculation.

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-

culation.

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

(a)

(b)

Figure 3. Vortex pair and single vortex between the two

shear layers.

(a)

(b)

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

(a)

(b)

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

5(a)).

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.

(a)

(b)

Figure 7. Turbulent kinetic energy contour by PIV (a) G/D

= 0 (b) G/D = 0.22.

497.429

398.541

332.615

266.689

365.578

134.838

35.9489

X mm

Y mm

20 40 60 80

199.213

146.296

66.9203

185.984

80.1495

14.0033

X mm

Y mm

20 40 60 80

Cold-State Investigation on a Flame Holder

(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

stability.

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%.

REFERENCES

[1] J. T. Yang and G. L. Tsai, “Near Wake Flow of a V-

Gutter with Slit Bleed,” Journal of Fluids Engineering,

Vol. 115, No. 1, 1993, pp. 13-20.

http://dx.doi.org/10.1115/1.2910096

[2] C. R. Anderson, “On the Accurate Calculation of Vortex

Shedding,” Physics of Fluids, Vol. 2, No. 6, 1990, pp.

883-885. http://dx.doi.org/10.1063/1.857646

[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.

http://dx.doi.org/10.1002/fld.458