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Weak Ex·tinction Limits of Turbulen'
�
Heterogeneous Fuel/ Air Mixtures
-1. .:·:N. 1979
D.R.BALLAL
Vis1t1ng Associate Professor
A.H. LEFEBVRE
Professor and Head
School of Mechanical Engineering,
Purdue University ,
West Lafayette, Ind.
Experimental and theoretical studies are made of the factors governing the weak extinction
limits of stabilized flames supplied with flowing mixtures of liquid fuel drops and air. The test
program includes wide variations in inlet air pressure, velocity and turbulence level, and also
covers wide ranges of fuel volatility and mean drop size. The influence of flameholder size
and blockage 1s also examined. An equation is derived for predicting weak extinction limits
which shows good agreement with the corresponding experimental values.
Contributed by the Gas Turbine Oivision of The American Society of Mechanical 1-�ngineers for
presentation at the Gas Turhine Conference & Exhibit & Solar Energy Conference, San Diego, Calif.,
March 12-15, 1979. Manuscript receivcd at ASME Headquarters January 4, 1979.
Copies will he a�ailable unlil December 1, 1979.
�
�
THI Mii.RiCAN SOCIETY OF MECHANICAL ENOINEERlt UNITED ENGINEERIN
G CENTER, 345 EAST 47tl'I STREET, NEW YORK, N.Y. 10017
,
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Weak Extinction Limits of Turbulent
Heterogeneous Fuel/ Air Mixtures
D.R.BALLAL
A.H. LEFEBVRE
ABSTRACT
Subscripts
Experimental and theoretical studies are made of
the factors governing the weak extinction limits of
stabilized flames supplied with flowing mixtures of
liquid fuel drops and air. The test program includes
wide variations in inlet air pressure, velocity and
turbulence level, and also covers wide ranges of fuel
volatility and mean drop size. The influence of
flameholder size and blockage is also examined. An
equation is derived for predicting weak extinction
limits which shows good agreement with the corre­
sponding experimental values.
a
f
g
INTRODUCTIOt:
An essential feature of most gas turbine combus­
tors is the toroidal flow reversal which is created
and maintained in the primary combustion zone by air
entering through swirl vanes located round the fuel
nozzle, supplemented by air jets injected through one
or more rows of holes in the walls of the liner. In
addition to its main role as the major heat release
zone of the chamber, the other important function of
the primary zone is to recirculate combustion pro­
ducts to mix and burn with the incoming air and fuel.
By this means a mechanism of continuous ignition is
established, and combustion can be sustained over wide
ranges of pressure, velocity and fuel/air ratio.
An alternative method of stabilizing a flame in a
high velocity stream of combustible mixture is by means
of a bluff body, such as a rod, cone or "vee"-gutter,
which produces in its wake a low-velocity recirculatory
flow in which combustion can be initiated and main­
tained. The propagation of flame to other regions of
the flow is rendered possible by the transport of heat
from the boundaries of the recirculation zone to the
adjacent fresh mixture. This method of flame stabili­
zation has been widely used in the �fterburner systems
of turbojet engines.
With both types of stabilization, a parameter of
considerable importance is the weak extinction limit,
i.e., the minimum fuel/air ratio below which the flame
is extinguished. The precise determination of weak
extinction limits is assuming increasing importance at
the present time due to the incentive to operate com­
bustion systems at weak mixture strengths in order to
minimize the emissions of smoke and nitric oxides.
In a recent publication (1), Ballal and Lefebvre
derived an equation for predicting the weak extinction
limits of stabilized flames supplied with turbulent
flowing mixtures of uniform, gaseous composition.
Predictions of weak extinction equivalence ratio based
on this equation were found to be in close agreement
with the corresponding experimental values, measured
over wide ranges of pressure, temperature, velocity and
turbulence level .
The purpose of the present investigation is to ex­
tend the scope of the previous study to include heterc­
geneous mixtures, i.e., to derive an equation for weak
extinction equivalence ratio, �WE, that is valid for
fuel/air mixtures in which the fuel is present in the
NOMENCLATURE
w
u
u'
Tu
To
p
v
\J
k
Cp
Pr
D
Re0
D32
D10
Dzo
D30
c
C1
Cz
C3
Reo
32
p
q
0
0wE
v
A
B
d
dp
Bg
n
f
E
air
fuel
gas
mass flow rate, kg/s
mainstream velocity, m/s
r.m.s. value of fluctuating velocity, m/s
percentage turbulence intensity, (100 u'/U)
initial air temperature, OK
density, kg/m3
kinematic viscosity, kg/ms
dynamic viscosity, kg/ms
thermal conductivity, W/mOk
specific heat at constant pressure, J/kg, °K
Prandtl number
(cpµ/k)
drop size
Reynolds number (u'D/v)
Sauter mean diameter, m
mean diameter, m
mean surface diameter, m
mean volume diameter, m
experimental constant
D20/D3z
=
D10/D3z
D30/D3z
u'D3z/v
air pressure, N/m2
fuel/air ratio, by weight
equivalence ratio
weak extinction value of equivalence ratio
volume of combustion zone, m 3
c.s.a. of combustion zone, m 2
fuel mass transfer number
baffle diameter, m
pipe diameter, m
flameholder blockage (d/dp)2
number of drops in spray
fraction of fuel in vapor state
fraction of total air entrained in wake
region
1
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form of mu1titudinous 1iquid drops of varying size.
Most practica1 combustion devices, burning 1iquid
hydrocarbon fue1s, employ mixtures of this latter
type.
EXPERIMENTAL
The apparatus employed is shown schematically
in Fig. 1. Essentially, it comprises a circular
pipe, 25 cm in diameter, throug h which metered air
flows into a larg e settling chamber housing a number
of flow-smoothing g rids. To the downstream flange of
the sett1ing chamber is connected the working section,
which is a1so a circular pipe of 2 5 cm in diameter,
fitted with sma11 quartz windows to facilitate obser­
vation of the flame. The flameho1der is in the form
of a hollow cone of 450 included angle, which is
mounted on three thin stays at the center of the pipe
with its apex poitning upstream. Four g eometrically
similar cones were manufactured to g ive the following
val ues of blockage ratio, Bg . [Note: Bg
(cone
dia/pipe dia) 2 ]
using a series of Fischer-Porter flowmeters.
The fuel nozzle fs mounted inside the hollow cone
flameholder with its discharg e orifice just protruding
beyond the base of the cone, as illustrated in Fig. 1.
Ten different simplex atomizers, varying in flow number
from 0.15 to 0.80 US g allons hr(ps1)D.5, (note that flow
0.0456 x flow number in
number in liters/hr N/m2)0.
US g allons/hr(psi)O. ) are used in order to cover wide
ranges of air velocity, air pressure and mean drop size
(SMD). D rop sizes are measured using the lightscattering technique in the form developed by Lorenzetto(2).
All measurements are carried out by spraying the fuel
downwards into still air at norma1 atmospheric pressure
and temperature. The influence of variation in air
pressure on mean drop size is accomodated by employing
the relationship, SMO
Pa -0. l (l).
�
�
=
�
=
Blockage ratio, Bg
Cone dia
5.0
8. 3
12.5
14. 6
0.04
0.11
0. 2 5
0.34
cm
cm
cm
cm
Ig nition is accomplished by means of an elec�
tric spark. After each ig nition the spark plug is
withdrawn to avoid disturbance to the flowing stream.
Flame ionization probes are mounted at the down­
stream end of the working section to assist flame
detection at low combustion pressures. The combus­
tion products discharg e into a lar g e circular exhaust
duct which is connected to an air-ejector facility to
permit studies at subatmospheric pressures. Liquid
nitrogen is sprayed into the combustion products at
entry to the exhaust duct in order to reduce their
temperature to an acceptable level for satisfactory
and reliable operation of the ejector rig.
Perforated plates located 20 cm upstream from
the base of the cone provide near-isotropic turbu­
lence in the flow entering the recirculation zone
varying between 5 and 15 percent in intensity.
Details of plate g eometry and corresponding turbu­
lence levels are listed in Table 1.
Table 1.
Details of Turbu1ence-Promoting Grids
Grid
Mesh
-�Size, cm
2
3
4
1. 45
1. 70
2. 00
2.20
Hole
l. 27
1. 27
1. 27
1. 27
Intensity
u'/U%
Scale
L, cm
5.5
7.8
12. 2
14. 7
0. 40
0.58
0. 73
0.90
Turbulence intensities and scales are measured
with a DISA 55001 constant temperature, hot-wire
anemometer at a plane just upstream of the base of
the cone. For test runs with minimum turbulence,
the perforated plates are replaced by a fine mesh
wire g auge. With this arrang ement the turbulence
1evel in the air stream approaching the cone is less
than 2 percent.
Air metering is provided by fitting a venturi
section in the pipe, the static depression at the
throat being measured by means of a \1ater (or alcohol)
manometer. The fuel flow is metered and controlled
Fig. 1.
Arrang ement of the test rig (1 - air flow;
2 - reg ulating va1ve; 3 - settling chamber;
4 - flow smoothing g rids; 5 - turbu1ence
g r ids; 6 - stay; 7 - conical baffle with
spray nozzle; 8 - spark plug ; 9 - f1ame
detector; 10 - nitrogen spray ring; 11 - air
ejector connection).
In a series of tests carried out on a similar
ho11ow cone plus pressure atomizer configuration, Plee
and Mellor (4) observed that, under certain conditions,
the fuel spray penetrated rig ht through the recircul a­
tion zone to produce a tongue of flame downstream.
This problem of loss of fuel drops from the wake region
is much 1ess serious in the present experiments since
spray penetration is relatively low at the low fuel-flow
rates associated with weak extinction limits. Moreover,
by comparing the time required for a fuel drop to
traverse the wake reg ion (using the values of drop dis­
charge velocity from a pressure swir1 atomizer as
measured by York and Stubbs (5)) with the calculated
evaporation lifetime of the same drop, it can be shown
that, except for the combination of the smallest flame­
holder with drop sizes in excess of 150 microns, the
fuel spray is fully confined to the recirculation zone.
The test program includes several different hydro­
carbon fue1s, representing a wide rang e of transfer
number as indicated by the transfer number, B (6). The
main properties of interest for these fuels are-listed
in Table 2. The values of B quoted in this table are
calculated for conditions of stoichiometric combustion
in air at normal room pressure and temperature.
2
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Ti1t1l
Stoi chi 01cctr i c.;
Fuel/Air Ratio
Carbon/
Hydrogen
Ratio
- ----·�· -� -
..., ..
Specific
Gn1 vi
at
f'.
l'.i nc:r,c:t ic
Spaldin')
Viscosity
rr ?/scc· lQ-G
Transfer
fiudwr
293"
0.06(,
�.
t'.
J. j _)
0. 59;·
0.71
6 .1 [)
t'.erosine
(AVTUR)
0. 06�
6.10
0. 77'S
l.3Q
3.75
Gas Qil
0. 06(;
6.40
0.637
S.00
3 .10
Diesel Oil
0.070
7. 00
0.900
14.5
2.80
Light Fur-l
0.072
7.40
0.930
165.0
2.50
Heavy Fu c-1
0.07"
7. 7L•
0. 97 :·
f,(,Q. 0
l . 'i'l
Iso-octanl
Oi 1
Oi1
The heavy fuel oil is too viscous to be pumped
at normal room temperature.
However, by heating it
to a temperature of 350°K, it is possible to achieve
fine atomization without resorting to excessively
high fuel injection pressures.
The test procedure, for any given flameholder/fuel
nozzle combination, is first to establish the desired
flow conditions of air pressure, velocity and turbu­
lence, and then to gradually increase the fuel flow
Having stabilized th�
until the onset of ignition.
flame on the conical baffle, the spark plug is with­
drawn to lie flush with the duct wall, and the supply
of fuel is slowly reduced until flame extinction occur:.-..
2.0 �-------.
P=IO� Nlm2
T0=300°K
•
'
SMD=60µ.m
1.6
The fuel flow at this condition is recorded.
Thi�
procedure is repeated for all fuels over the entir8
range of test conditions in order to study the separate
effects on weak extinction limits of variations in
pressure, velocity, turbulence intensity, flameholder
size, flameholder blockage, fuel volatility and fuel
drop size.
Tu=2%
Bg=0.04
- EQ23
Heavy Fuel
Oil
1.2
•
P= 105 Nim� ; T0 300°K
SMD= 100 µ.m
•
cf>W.E.
Tu=2%
� W.E.
0.8
•
89=0.34
'
EQ 23
0.6
0.4
Heavy Fuel
A
Oil"
Diesel"- ,,...•
�-J-_-•·--·
�
..
40
0
�
Influence of mainstream velocity on weak
�
0.2
extinction equivalence ratio for a
conical baffle of low blockage ratio.
The test conditions are listed below:
15 to 75 m/sec
0.2 to 1.0 105 N/m2
290°1'.
Mainstream velocity
Air pressure
Air temperature
Turbulence intensity
Blockage ratio
Fuel transfer number, B
Fuel drop diameter (SMD)
=
.
80
U, mis
Fig. 2.
..
./.��clone
2 to 14.7 percent
0.04, 0.11, 0.25 and 0.34
1. 5 to 6 .1
40 to 160 microns
40
80
U, mis
Fig. 3.
Influence of mainstream velocity on weak
extinction limits for the case of high
blockage ratio.
The results obtained are shown plotted in Figs.
2 to 10.
They demonstrate that weak extinction limits
are improved, i.e., extended to lower values of equiv­
alence ratio, by increases in flameholder size, fuel
volatility and air pressure, and by reductions in
3
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:nainstream velocity and mean drop size.
The influence of turbulence intensity on 0wE is
For highly volatile fuels 0WE always
complex.
increases with Increase in turbulence, due to the
Jdditional air that is entrained into the wake region,
'»<hich reduces the time available for combustion.
,Jowever, for less volatile fuels, such as heavy fuel
oil, the beneficial effect of turbulence in accel­
erating fuel evaporation rate can often outweigh
this effect and lead to a reduction in 0�E with
increase in turbulence intensity, as illustrated for
10.
heavy fuel oil in Fig.
where C is a mixing factor which depends on the
stabilizer configuration and the turbulence level of
the fresh mixture, and must be determined experimentally
for each individual combustor.
Equation (2) is satisfactory for premixed gaseous
fuel-air mixtures and also for premixed/prevaporlzed
1iquid fuel-air mixtures. However, it cannot be used
for heterogeneous liquid fuel-air mixtures unless the
rate of fuel evaporation is sufficiently high to ensure
that all the fuel is fully vaporized within the com­
If the fuel does not fully vaporize,
bustion zone.
then clearly the "effective• equivalence ratio will be
However, if the fraction
lower than the no111inal value.
of fuel that is vaporized is known, or can be calculated,
it can then be combined with equation (2) to yield the
weak extinction value of equivalence ratio, i.e.,
P=l05N/m2•' T0 =300°K
!
�
0
U=l5 mis
Tu=2%
Bg= 0.04
wE(heterogeneous)
=
0
WE{ premixed)
x
f -1
( ,3)
where f is the fraction of fuel that is vaporized in
the combustion zone.
-EQ23
Now, for a single drop in stagnant gas the
average rate of fuel evaporation during the lifetime
of the drop is given by
1.
(§.)
(4)
k/c ) log(l+B)
p g
where D is the initial drop diameter
Since the fuel drops are usually quite small, when
injected into a flowing air stream they tend to remain
airborne, and their velocity relative to that of the
air stream is insufficient to enhance appreciably the
rate of fuel evaporation.
However, if the flow is
turbulent, the fuel drops are subjected ful
to the
ZOO
100
SMD, µ.m
Fi�. 4.
( 5)
Effects of spray drop size (SMD) on weak
extinction limits for
ratio.
condiUnder
fluctuating components of velocity.
tions, the average rate of fuel evaporation is given by
a
low blockage
\vhere
(u'
�'.:EORY
'.n a previous publication Bal lal and L•:febvre ( 1J
. nowed that 1veak extinction limits for flames sup�' i�d with premixed gases could be expressed in
·:�rms of thf' combustion volume, pressure, initial
D/;)
Thus, for a flame zone of volume,
drops of diameter,
V,
containing n fuel
0, equation (5) becomes
° 5
· )
l.33rnD(k/c ) log(lt-B)(l+0.25Re
0
p g
":1;;peniture and mass flow rate, by the·relationship
(6)
For a fuel/air ratio in the flame zone, q, we have
(l)
c n(rr/6
f ------
'l
i11 •:1ilich the val11es for the constants a, b �nd c ure
l�termined, respectively,
�.he collis ion factor
1:F, the activati0n enerqy,
, ,ind the qlobal reac'=i1rn 1;rcJer, n.
Fro111 �nalysi; of available reilCtion rate ciuta
from well-stirred reactors, it was concluded that
tne weak extinction equivalence ratio for hydro­
•:irrion-dir •:i><:t1irPc; is Jiven by
c
· a
h•:nce
( 7)
(8)
Substitution of n from
(8)
into (6) yields
(' ,/, f) ( k/cP) 91 o g (1 •B) (VI o2)
( l HJ.
0.5)
�))
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ie'..I to thr co:d•u'..tir,r:
fut·�
Of tllfc tote,
Vir:
zone� the� fra c t i c n ) f, tf1£11 is vaporized with1
zone is 9iven by
w f/q\(d
Substitu': ing
Wf
( l (J)
fro1:1
' O(·'g I
f
e q u a t i on
(9)
into
U=l5m/s
Tu= 2%,
) 100(l+C)(V/� n2)
·.)(k/c
T
a
pg
from equations
(l l )
(2), (3)
(11)
and
have
we
T = 300°K
0
,... B1t 0.34
EQ23
"
(1+0.2:, Reno. 5 )
Hence,
P=:iO� l�/rr.";
(10) 1 eads tc
06'
Heavy Fuel
Oil
BwE(heterogeneuus)
\
-
_
11 ___.J.--E
•
'
Fig.
·�'i-Octane
Fffects of spray d rop size (SMD) on weak
extinction limits for a high blockag�
ratio.
atomizing devices, some modifications are needed to
T =3 00 " K ;
0
account for the distribution of drop sizes in the
system. Thus, equations (6) and (8) become
p
(l+0.25c 2°·5Re
(where
0 32
U=l5rn/ s
89 =004
1.2
x
0.5
)
-EQ 23
SMD=60 µ.rn
respectively
wf
200
100
SMD, µrn
5.
In the above equations, it is assumed that all
For a poly­
the fuel drops are of uniform size.
disperse spray of the type produced by most practical
o 32( k/c ) glog (l +B )
.L�__.
-Diesel
(12)
1.
,,,..
::,_.. ----1
--.--- � �
�
It should be noted that equation (11) allows F
However, when this occurs, it simply
to exceed unity.
means that fuel evaporation is not limiting to per­
formance, i.e., f
1.0 and 0wE(heterogeneous
) ;
8wE ( premixed)·
·
�
II
'-
Oil
•
(13)
u' o32 ;v )
g
Heavy Fuel
•
¢WE
Diesel
and
n
where
(6/1f)(t. /r;f)IV/(C �/D�2)3Jc
.J
.J
g
(14)
•
0.8
Sauter mean diameter
D3z
C1
0 20ID32
010ID32
D3 0ID32
Following the same procedure as before leads to
3
0.5
2
)( pg/ Df )(k/ cp )g log( l+B)(V/Ha 0�2 )
.
J
Fig.
6.
P, N/rn2
I
x10�
Influence of pressure on weak extinction
limits for a low blockage ratio.
( 5)
x
From inspection of this equation, it is clear
that some simplification is possible for the two
important practical cases of low and high Re
03 2
5
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where Z
=
sprays.
When Re
0
f
=
<<
32
1.0, equation
(15)
reduces to
f
'
2
8.0(c ;c3�)(a /r ) k/c ) log(l+ B)(V/W D32 )
a
p g
1
9 f
=
3
0
(C1/Cz ·5 ;c3 )
1.46 for most practical
Substituting this value of Z into (13) gives
(2.9/Pr)(r to )log(l+B)V[(Tu/100)
f
9
•
lJ /\l
- aDJ 2
9
(16)
This is the appropriate expression for esti­
mating the fraction of fuel that is vaporized within
the combustion volume under conditions of low pressure
and low turbulence.
Ideally, the values of C1 and C3 should be
1etermined from analysis of the drop-size distribu­
3
Al
0.5
(19)
This expression is most relevant to conditions of
high pressure and high turbulence, such as exist, for
example, in the primary zones of modern gas turbine
combus tors.
tion for each individual spray. This could be a
�edious and time-consuming process, but fortunately,
•ls
demonstrated by Simmons
(ZJ,
the sprays produced
by well-designed atomizers of various types have
2
P= 105 N/rn ; T0=300°K
�everal important features in common.
B ased on their
Jnalysis of drop-size data, the present authors conuded that, for simplex and airblast atomizers,
0.31 and Cz
0.21.
Inserting these values
1
i nto ( 16) y ields
SMD = 100 µ. rn
U=l5 m/s
Tu= 2 %
=
Heavy F. 0.
•
f
Light F. 0.
x
0.8
¢W.E.
�
rpW.E.
=300°K; -EQ 23
SMD=IOO µ. m
U =30 m/s
89 =0.34
•
••
•
Fiq. 7.
N/m2
04
I
.
I
xJ05
Fig.
lnflueni.:e of pressure on 1·1eak extinction
1 irnits
Kerosine
i-Octane
EQ 23
for a high blockage ratio.
B
g
x
0.04
I
�\J
&
P,
'V
0
9
0.6
- . �.
-----­
�
.
i-Octane .----�
·•
-----0.5
Diesel Oil
Gas Oil
--
Heavy
��el Oil
�el j---__ •
0.6
..
· �·
·-
3
B
5
7
Influence of fuel transfer number B on
weak extinction limits.
The 1"1eak extinction equivalence ratio for any
combustion zone supplied with a heterogeneous liquid
fuel-air mixture is obtained by substituting into
equation (3) the corresponding value for a homogeneous
When
(15) for u'
(c p,Jk)g
Pr,
=
f
·�
1.0, by substituting in equation
(Tu/!OO)U
�
(Tu/100)\� hril, and
a
.J
it n�·Juces to
2.0(Z/Pr)(" /c )log(lHl)I/ (Tu/100)
g f
:, D 32 3A
'"J / ,·•,11
I
.
o 5
mixture, along with an appropriate value of f from
equations (15) to (19). For example, the "�eaK extinc­
tion limit for a gas turbine combustor under normal
op eration in obtained from equations (2), (3) and (l'.J)
:is
l l:l)
6
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0. 16
.
0"
'
�ps :: ]
�,,,::0.,1] [1�::ho�.s·'
c
,
(T 11s01
,
·
(20)
It should be noted that equations (15} to (20) embody
the assumption that the fuel spray comprises a
multi-droplet mist whose overall evaporation charac­
teristics are identical to those of a single evap­
orating drop. Thus, droplet interaction is ignored,
and this could appreciably affect the overall rate of
fuel evaporation. Another potential source of error
is the combustion volume, V. Due to the physical
space occupied by air jets and recirculating burned
products, the actual reaction zone is normally
appreciably less than that indicated by the liner
dimensions. Thus, the constant, C, should be deter­
mined experimentally for each particular liner/nozzle
combination.
In order to apply equation (20) to baffle­
stabilized flames, it must be modified to allow for
the fact that only a small fraction of the flowing
air stream is entrained into the wake region. Thus
equation (20} becomes
Ew
a
J
c[
1
25
lvP exp(T/ 15o}J
0wE
[(
·
P
f
p Vlog(l+B)
g
l(
) ]
EW D�2 A
{Tuf100)µ
9
�ubstituting for E from (22} into (21), and also for
W
pAU leads to
a
=
C
[(
4
�
U(1+O.l2Tu)
�
0 2
p · 5d(l-B )T exp(T /150)
p
f
d log{l+B)
g
l(
0
0
0. 16
LID�z{lt0.12Tu)
x
) ]
P p { Tu/lOO}B {l-B )
g
g
g g
0 5
'
{23)
In the present study a value for c4 of 0.005
was found to give a good fit to all the experimental
data.
D ISCUSSION
The validity of the proposed model for deter­
mining the weak extinction limits of flames supplied
with flowing heterogeneous fuel-air mixtures may be
tested by comparing measured values of weak extinction
��� : �� ;�
P=I05 N/m
o
U=30 mis
Tu =2%
-EQ 23
•
Diesel
0.6
Heavy Fuel
011
-
i-Octone
•
0. 5
{ 21)
.&.
r/>WE.
OA
(22)
0WE
\
·
O . Hi
where E represents the fraction of the total air flow,
Wa, that is entrained into the recirculation zone.
From analysis of the fluid dynamics of this
region, and examination of the experimental data
obtained on the weak extinction limits of premixed
flames, Ballal and Lefebvre (1) concluded that the
entrainment factor, E, could be expressed as
=
equivalence ratio with th� corresponding predicted
valur,;. froo1 equation (23). T his is done in Fi g s . 2
to 10, in which the full linrs represent theoretical
values detern1ined from equation (23). It is observed
that the level of agreement between theory and experi
ment is generally very satisfactory, thus confimins
the basic premise of the proposed model.
:::-- ---'------,...,__
0
d,
Fig. 9.
10
---'-- ---'
__
20
ems
Effects of the flameholder dimensions on
weak extinction limits.
Of special interest are the results obtained on
the influence of turbulence on 0WE • as illustrated in
Fig. 10. According to equation (23), for fuels that
vaporize rapidly, the first term on the right-hand
side is equal to unity, and 0wE increases with turbu­
lence intensity according to the relationship,
0wE (1+0.12T u)0 . 16 . In this situation, where the
fuel-air mixture is effectively homogeneous, the
effect of an increase in turbulence intensity is to
raise 0wE by increasing the amount of air entrained
in the recirculation zone, thereby reducing the time
available for combustion. Thus, for fuels of relatively
high volatility such as isoctane, equation (23) pre­
dicts that 0 wE should increase continuously with
increase in turbulence intensity, and this is borne out
by the experimental data for iso-octane, shown plotted
in Fig. 10.
For less volatile fuels, there are many operating
conditions at which the rate of heat release within
the wake region is limited, not only by reaction
kinetics, but also by rates of fuel evaporation. In
this situation, we have, from equation (23)
�
And thus, 0wE diminishes with increase in turbulence,
as shown in Fig. 10 for heavy fuel oil. For diesel
oil, at the conditions tested, the beneficial effect
of an increase in turbulence in promoting fuel evapor­
ation is outweighed by the accompanying adverse effect
of a reduced residence time for combustion. This is
evident from Fig. 10 which shows that, for diesel oil,
7
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['�
[
is sensibly independent of Tu.
0
wE
0
SUMMARY AND CONCLUSIONS
0.005p
wE
From analysis of the processes governing the
rates of fuel evaporation and chemical reaction in a
combustion zone supplied with heterogeneous liquid
fuel-air mixtures, it is concluded that the weak
extinction equivalence ratio is given by
0
0
wE(heterogeneous)
wE (premixed)
x
f
O .S
f
3
=
3
•
8.0(C ;c 3 )(p /p )(k/c ) log(l+B)(V/W o3 )
a 2
p g
1
9 f
0 5
(l+o.2sc, · Re
�
D3
2
Re
D3
2
f
=
<<
UD3
2
1.0, (low pressure, low turbulence)
3
(l+o.12T u)
]
)]
0.5
p p (Tu/lOO)B (l-B )
g
g
g g
U(l+0.12Tu)
�
f
O.l6
x
__ ___ ____
------P- N / m 2 · T3
= 00 0 K__,
=lO ' _
' 0
SMD =100 µ.m
U=l5 mis
B0=0.34
05
· i
For the important practical cases of low and
nigh droplet Reynolds number the above expression
simplifies to
(a)
)(
0 25
p · d(l -B )T exp(T l50)
g 0
0
-l
·11here
f
log(l+B)
<PW.E.
•. � •
�
0.6
�
-EQ 23
Heavy Fuel
·�Oil
•
•
3
2
8.0(c ;c3 )(p /p )(k/c ) log(l+B)(V/Wa D32 l
p g
1
g f
and
(b)
Re
f
0
32
>>
1.0, (high pressure, high turbulence)
3
° 5
(2.0 /Pr)(C c · ;c3 )(p /p )log(l+B)V
1 2
g f
.
[( T u/ 100)µ /W o3
9 a 2
3
A]
o.5
x
Recommended values of C1, C 2 and C3 for prac­
tical atomizers of the simplex and airblast type
are 0.3 1, 0.21 and 0.46, respectively. (For mon-
1isperse sprays, C1 = c2 = C3
1.0, by definition).
For the highly turbulent primary zones of gas
turbine combustion chambers, the weak extinction
equivalence ratio is given by
Fig. 10.
Tu,
%
20
Influence of mainstream turbulence
intensity on weak extinction limits.
The theory predicts, and the experimental data
confirm, that for heterogeneous mixtures of fuel drops
and air, the weak extinction limit may be extended to
lower values of equivalence ratio by increases in
combustor size, fuel volatility, air pressure and
temperature, and by reductions in air mass flow rate
and mean drop size.
REFERENCES
1 Ballal, D.R. and Lefebvre, A.H., "Weak Extinc­
tion Limits of Turbulent
Flowing Mixtures," ASME Gas
Turbine Conference, London, England, Paper No. 78-GT-144,
April, 1978.
2 Lorenzetto, G.E., "Influence of Liquid Proper­
ties on Plain-Jet Airblast Atomization," Ph.D. Thesis,
School of Mechanical Engineering, Cranfield, 1976.
For baffle-stabilized flames the role of turbulence
Is more complex because it affects not only the rate
of fuel evaporation, but also the rate of entrain­
ment of air into the wake region. Either effect
could predominate but, in general, �WE increases
rlith turbulence intensity for fuels of hi�h vola­
tility and decreases with increase in turbulence
intensity for fuels of low volatility.
For this
type of flame 0
is given by
wE
3
Ballal, D.R. and Lefebvre, A.H., "Ignition of
Liquid Fuel Sprays at Subatmospheric Pressures,"
.Combustion and Flame, 31, 1978, pp. 115-126.
4
Plee, S.L. dnd tlellor, A.M., "Flame Stabiliza­
tion in Simplified Prevaporizing, Partially Vaporizing
and Conventional Gas Turbine Combustors, Paper No.
73-103 8, AIAA /SAE 14th Joint Propulsion Conference,
Las Vegas, tlevada, July, 1978.
5 York, J.L. and Stubbs, H.E., 'Photographic
1\nalysis of Sprays," Trans ASME, Vol. 74, pp 1157-1162,
1 'J52.
8
_l\
-------
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li.011,
6
7
Spalding. D.[;., SoM:Funda1nentals of
··-·······
·····Cornbu,­
don;·1�i:;�-:--·-····Gutterworth;;, Lon
Sirrw1ons,
Distribution�
------
· ·--·····
H.C.,
in Fuel
, July,
"The, Correlation rf Drop-Size
Nozzle Spray:," Trans ASME,
------ ··
1977, pp. 309-319.
,
,
'
9
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/84049/ on 06/15/2017 Terms of Use: http://www.asme.org/