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Air Entrainment Rate Calculations using
Baum s Fire Induced Flow-field Formulation
J. P. GoreMaurice J. Zucrow Laboratories
School of Mechanical EngineeringPurdue University
W. Lafayette, IN 47907 - 1003
Acknowledgment: Work Supported by Building and Fire ResearchLaboratory, National Institute of Standards and TechnologyGaithersburg, Maryland, with Dr. Howard Baum serving as NIST ScientificOfficer. The work summarized here is a result of MS and PhD dissertationsby Dr. X. C. Zhou
Institute of Mathematics and Its ApplicationsUniversity of Minnesota
October 11-13, 1999
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1. MOTIVATION
2. SPECIFIC OBJECTIVES
3. THEORETICAL METHOD
4. LDV MEASUREMENTS AND DISCUSSION
5. PIV MEASUREMENTS AND DISCUSSION
6. THERMAL EXPANSION SOURCE TERM
AND VORTICITY DISTRIBUTION
7. SUMMARY AND CONCLUSIONS
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OUTLINE
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1. Air entrainment of accidental fires influences gas
temperatures, radiation properties, fire growth rate andtoxicity of smoke.
2. Existing correlations of air entrainment show a large scatterdue to different measurement techniques and boundaryconditions.
3. In many numerical simulations an entrainment constant isassumed.
4. Recent optical techniques provide an opportunity to measurethe instantaneous and mean entrainment velocity field.
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MOTIVATION
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DEFINITION OF ENTRAINMENT
ri
R
0 xent
uR2
drurdx
d2m i
Local Air Entrainment Rate:
Total Air Entrainment Rate:
0,entx
0 ri
fR0 xent
mdxuR2
mdrur2m i&
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PAST MEASUREMENT TECHNIQUES ( I )
McCaffrey (1979)
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PAST MEASUREMENT TECHNIQUES ( III )
Zukoski and Coworkers (1980)
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Air Entrainment Correlations
Author(s) Year Correlation Formula Dependent
on Burner
size?
Dependent
on Heat
Release
Rate?
Yih 1952f
3/53/1p0
2ent mx)TC/Qg(153.0m && =
No Yes
Thomas et
al.
1963
f3/53/1
p020ent mx)TC/Qg(153.0m && =
No Yes
McCaffrey 1979
f2/1
0ent mxQ055.0m && =No Yes
Cox and
Chitty
1980
f5/4
02/1
ent mQx008.0m && =No Yes
Hasemi 1982
)037.0Q/x(Q043.0m 4.0
0ent =&No Yes
McCaffrey
and Cox
1982
f48.0
03.1
ent mQx053.0m && =No Yes
Tokunaga et
al.
1982
)0337.0Q/x(QD070.0m 4.0
002/1
ent =&Yes Yes
Beyler 1983 25.1ent )06.0x(073.0m +=&
Yes No
Cetegen et
al.
1984 3/5v
3/1p0
2ent )xx()TC/Qg(21.0m = &
No Yes
Delichatsios
and Orloff
1984 2/52/1ent xg034.0m =&
No No
Delichatsios 1987 2/1
f
f
ent
D
x086.0Fr
m)1S(
m
=
+ &&
2/3
ff
ent
D
x093.0Fr
m)1S(
m
=
+ &&
2/5
ff
ent
D
x018.0Fr
m)1S(
m
=
+ &&
Yes No, but
dependent
on fuel
type
Koseki and
Yumoto
1988
S)D/x2(26.3m 56.0
ent=&Yes No, but
dependent
on fuel
type
Zukoski 1994
fent mxD62.0m && =Yes Very
weakly
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An Example of Application of
Some Air Entrainment Correlations
x / D
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Fr
fm
ent
/(S+1)m
f
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
Predicted air entrainment rate by different correlations7.1 cm toluene pool fire, no floor, mf = 0.083 g/s
Q = 3.4 kW, XA= 90%, X
R=30%, S=13.5, Fr
f=0.109
Delichatsios (1987)
McCaffrey (1979)Cox and Chitty (1980)
McCaffrey and Cox (1982)
Delichatsios and Orloff (1984)
Zukoski (1994)Beyler (1983)
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1. Consider air entrainment as a fire induced flow field using
Baum s kinematic model, which involves flow componentsinduced by vorticity and thermal expansion.
2. Develop and utilize techniques to measure the fire induced flowfield for model validation.
3. Develop and utilize techniques to measure the vorticity andthermal expansion that induce the fire induced flow, to avoiduncertainties of combustion models.
4. Compare the measured and predicted fire induced flow field tovalidate the overall model.
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SPECIFIC OBJECTIVES
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Decomposition of the entrainment flow field:
V~
VVr
where
0V, the irrotational thermal expansion,
and 0V~ , the incompressible flow caused by vorticity
1. THE IRROTATIONAL FLOW Q
QVr
and V)V~
V(Vr
,
the governing equation of the irrotational component:
QV
Written is terms of a potential function (
rx er
ex
V):
Q)r
r(rr
1
x2
2(a)
2. THE INCOMPRESSIBLE FLOW
Q
pVr
and V~
)V~
V(Vr
,
the governing equation of the imcompressible component is:
pV~
Written is terms of a stream function (
rx err
1e
xr
1V~ ):
p2
2
2
2
rrr
1
rx
(b)
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Correlations of Buoyant Diffusion Flame
Structures (McCaffrey, 1983)
n***)x(A)x(U
1n2**)x(B
T
TT)x(
})]x(R/r[exp{)x(U)r(u2
xr
})]x(R/r[exp{)x()r( 2r
Centerline Axial Velocity and Excess Temperature
Assuming Gaussian profiles, the axial velocity and
excess temperature distributions are
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The Source Terms based on Correlations
The Flame Radius as a function of x from analysis
of the advected energy balance:
Thermal Expansion Source Term Distribution:
d21RL
I1U
X1xR
/**
})]()[x(
{)(
)x(R)X1(
})]x(R/r[exp{
x
)x(H)r(Q
2R
2r
Vorticity Distribution:
}})](/[{)(
{)(
)()(p
2xRrexp
xR
r
xR
x2Urr
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Boundary Conditions: with Floor
0 at x = 0 for all r
0r
0
0x
at r = 0 for all x
Floor and Axis:
Free Boundaries:
22
R
xr2
X1
)()1(9
F10
d
Fd22
2
F(0) = F(1) = 0
)(F3/5 22 xr cos
The Pool Burnerr(i) The Floor
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Boundary Conditions: without Floor
0r
0 at r = 0 for all x
On inner boundaries:
On outer boundaries:
)()1(9
F10
d
Fd22
2
F(-1) = F(1) = 0
)(F3/5 22
xr cos
PoolBurner
r(i)
22
R
xr4
X1
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Numerical Discretization:
a typical element
N
EPW
S
n
s
ew
r(p)
x(p)
xn(p)
xs(p)
xs(p)
xp(p)
xn(p)
rw(p) re(p)
rw(p)
rp(p)
re(p)
p
2w
2e
pwesn
2w
2e x)
2
rr)(r(Qx)
rr
rr()
xx(
2
rr r
PSSNNWWEEPP daaaaa
)r
r(xa
e
eE
)r
r(xa
w
wW
n
2w
2e
Nx
1
2a
rr
s
2w
2e
Sx
1
2a
rr
SNWEP aaaaa
x)2
rr)(r(Qd
2w
2e
Pr
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Multigrid Scheme
j,ijm,ijm,ijp,ijp,ij,imj,imj,ipj,ipj,ij,i D~
c~
c~
c~
c~
c
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The Velocity Field
)j(x)j(x
)1j,i()1j,i()j,i(u
snx
)i(r)i(r
)j,1i()j,1i()j,i(u
wer
)i(r1
)i(r)i(r)j,1i()j,1i()j,i(u~
pwex
)i(r
1
)j(x)j(x
)1j,i()1j,i()j,i(u~
pnsr
The irrotational velocity field:
The incompressible velocity field:
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Comparison of the predictions and the
correlations of the axial velocities at x = 42.5 cm
Radial Position, cm0 5 10 15 20
AxialVelocity,cm/s
0
50
100
150
200
250
300
Numerical Modeling
Correlations of McCaffrey (1983)
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Effect of the Computational Domain Size
Radial Position, cm
0 10 20 30 40
AxialVelocity,cm/s
-5
0
5
10
15
20
25
30
at x=0.5 cm, r= 1 cm, x= 1 cm
Prediction Computational Domain
1 m by 4 m
2 m by 4 m
1 m by 5 m
0.5 m by 4 m
1 m by 2 m
Radial Position, cm
0 10 20 30 40
AxialVelocity,cm/s
0
50
100
150
200
250
at x= 42.5 cm, r= 1 cm, x= 1 cm
Prediction Computational Domain
1 m by 4 m
2 m by 4 m
1 m by 5 m
0.5 m by 4 m
1 m by 2 m
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Effect of the Grid Spacing Size
Radial Position, cm
0 5 10 15 20
AxialVelocity,cm/s
0
50
100
150
200
250
The predicted axial velocity at x=42.5 cm1 m by 4 m computational domain
r= 1 cm, x= 1 cm
r= 0.5 cm, x= 1 cm
Prediction Grid size
Radial Position, cm
0 5 10 15 20
AxialVelocity,cm
/s
-5
0
5
10
15
2025
30
The predicted axial velocity at x=0.5 cm1 m by 4 m conputational domain
r= 1 cm, x= 1 cm
r= 0.5 cm, x= 1 cm
Prediction Grid size
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The Enclosure
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The Fuel Supply System
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Laser Doppler Velocimeter (LDV)
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Measureed Mean Velocity Field
Zhou and Gore (1995)
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Entrainment Rates Based On LDV
Measured Mean Velocity Field
Correlation
Fr
fm
ent
/(S+1)m
f
0.1 1 100.01
0.1
1
10
100
1000
Delichatsios(1987)
Author Year Fuel Burner Method Symbol
Present 1995 Toluene 7.1 cm LDV, Ri=11.5 cm
LDV, Ri=6.5 cm
LDV, Ri=4.5 cm
LDV, Ri=flame
Weckman 1989 Acetone 30 cm LDV(Axial Velocity)
Beyler 1983 Propane 19 cm Hood
Thomas 1965 Ethanol 91 cm Particle Tracking
19 cm Hood
Cetegen 1984 Nat. Gas 19 cm Hood
50 cm Hood
Toner 1987 Nat. Gas 19 cm Hood
x / D
.
.
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Vorticity Distributions
0
5
10
15
20
25
30
Hinterface
= 64 cm
Dfloor
= 51 cm
Lip Height=0.2cm
mf
= 83 mg/sD=7.1cm, Toluene
Vorticity,1/sec
0
5
10
15
20
Radial Position, cm
0 2 4 6 8 10 12 14 160
5
10
15
20
Flame Boundary
Farthest Visible
Flame Boundary
Average Visiblex = 1 cm
x = 5 cm
x = 9 cmPOOL EDGE
.
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Probability Density Function (PDF)
of Radial Velocities at r = 3.5 cm
0.00
0.05
0.10
0.15
0.20
ProbabilityDensityFunction,s/cm
0.00
0.05
0.10
0.15
Radial Velocity, cm/s
-20 -15 -10 -5 0 5 10 15 20 25 300.00
0.05
0.10
0.15
D = 7.1 cm, Toluenem
f= 83 mg/s
Hinterface = 64 cm
Lip Height = 0.2 cmD
floor= 51 cm
r = 6.5 cm
x = 1 cm
ur= 5.0 cm/su
r' = 7.9 cm/s
x = 5 cm
ur= 6.3 cm/s
ur' = 5.6 cm/s
x = 9 cm
ur= 12.2 cm/s
ur' = 5.5 cm/s
.
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Probability Density Function (PDF)
of Axial Velocities at r = 3.5 cm
0.00
0.05
0.10
0.15
0.20
ProbabilityDensityFunction,s/cm
0.00
0.05
0.10
0.15
Vertical Velocity, cm/s
-20 -10 0 10 20 30 40 500.00
0.05
0.10
0.15
D = 7.1 cm, Toluenem
f= 83 mg/s
Hinterface = 64 cm
Lip Height = 0.2 cmD
floor= 51 cm
r = 3.5 cm
x = 1 cm
ux= 42.72cm/su
x' = 42.04 cm/s
x = 5 cm
ux= 22.71 cm/s
ux' = 28.18 cm/s
x = 9 cm
ux= 6.44 cm/s
ux' = 9.37 cm/s
.
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Power Spectral Density (PSD)
of Radial Velocities at r = 4.5 cm
10-3
10-2
10-1
100
101
PowerSpectrumDensityofRadialVelocity
10-3
10-2
10-1
100
Frequency, Hz
0.1 1 10 10010-3
10-2
10-1
100
D = 7.1 cm, Toluene, mf= 83 mg/s
Hinterface
= 64 cm, Lip Height = 0.2 cm
Dfloor= 51 cm, r = 4.5 cm
x = 9 cm
x = 5 cm
x = 1 cm
.
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Power Spectral Density (PSD)
of Axial Velocities at r = 4.5 cm
10-3
10-2
10-1
100
101
PowerSpectrumDensityofVerticalVe
locity
10
-3
10-2
10-1
100
Frequency, Hz
0.1 1 10 10010-3
10-2
10-1
100
D = 7.1 cm, Toluene, mf= 83 mg/s
Hinterface
= 64 cm, Lip Height = 0.2 cm
Dfloor= 51 cm, r = 4.5 cm
x = 9 cm
x = 5 cm
x = 1 cm
.
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Measurements and Predictions of Axial Velocities
around a 7.1 cm Toluene Pool Fire
Radial Position, cm
3.5 5.5 7.5 9.5 11.5 13.5-20
0
20
40
60
-20
0
20
40
60
80
Ve
rticalVelocity,cm/s
-20
0
20
40
60
D = 7.1 cm, Toluene, mf= 83 mg/s
Hinterface= 64 cm, Lip Height = 0.2 cmDfloor = 51 cm
x = 12 cm
x = 6 cm
x = 1 cm
Radial Position, cm
3.5 5.5 7.5 9.5 11.5 13.5-20
0
20
40
60
-20
0
20
40
60
80
Ve
rticalVelocity,cm/s
-20
0
20
40
60
D = 7.1 cm, Toluene, mf= 83 mg/s
Hinterface= 64 cm, Lip Height = 0.2 cmDfloor = 51 cm
x = 12 cm
x = 6 cm
x = 1 cm
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Measurements and Predictions of Radial Velocities
around a 7.1 cm Toluene Pool Fire
Radial Position, cm
3.5 5.5 7.5 9.5 11.5 13.50
10
20
30
0
10
20
30
40
RadialVelocity,cm/s
0
10
20
30
D = 7.1 cm, Toluene, mf= 83 mg/s
Hinterface= 64 cm, Lip Height = 0.2 cmDfloor = 51 cm
x = 12 cm
x = 6 cm
x = 1 cm
Radial Position, cm
3.5 5.5 7.5 9.5 11.5 13.50
10
20
30
0
10
20
30
40
Ra
dialVelocity,cm/s
0
10
20
30
D = 7.1 cm, Toluene, mf= 83 mg/s
Hinterface
= 64 cm, Lip Height = 0.2 cm
Dfloor
= 51 cm
x = 12 cm
x = 6 cm
x = 1 cm
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Particle Imaging Velocimetry
Based on CW Laser
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Instantaneous Velocity Vectors around a 7.1
cm Toluene Pool fire without a Floor
Radial Position, cm
1 2 3 4 5 6 7 8 9 10 11
AxialPosition,cm
0
1
2
3
4
5
6
7
8
9
10
50 cm/s
Pool Edge
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Instantaneous Velocity Vectors around a 15
cm Toluene Pool fire with a Floor
Radial Position, cm
7 9 11 13 15 17 19 21
AxialPo
sition,cm
0
2
4
6
8
10
12
14
25 cm/sPool Edge
A
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Instantaneous Velocity Vectors around a 15
cm Toluene Pool fire without a Floor
Radial Position, cm
7 9 11 13 15 17 19 21
AxialPo
sition,cm
0
2
4
6
8
10
12
14
25 cm/sPool Edge
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Mean Velocity Vectors around a 7.1 cm
Toluene Pool fire with a Floor
Radial Position, cm
2.5 4.5 6.5 8.5 10.5
A
xialPosition,cm
0
1
2
3
4
5
6
7
8
9
10
10 cm/s
Pool Edge
Radial Position, cm
2.5 4.5 6.5 8.5 10.5 12.5
Pool Edge
PIV Measurements LDV Measurements
Mean entrainment flow field, Toluene, D = 7.1 cm, With a Floor
mf= 83 mg/s, Dfloor= 51 cm, Hinterface= 64 cm, Hflame= 32 cm
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Mean Velocity Vectors around a 7.1 cm
Toluene Pool fire without a Floor
Radial Position, cm
1 2 3 4 5 6 7 8 9 10 11
AxialPosition,cm
0
1
2
3
4
5
6
7
8
9
10
50 cm/s
Pool Edge
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Mean Velocity Vectors around a 15 cm
Toluene Pool fire with a Floor
Radial Position, cm
7 9 11 13 15 17 19 21
AxialPo
sition,cm
0
2
4
6
8
10
12
14
25 cm/sPool Edge
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Mean Velocity Vectors around a 15 cm
Toluene Pool fire without a Floor
Radial Position, cm
7 9 11 13 15 17 19 21
AxialPo
sition,cm
0
2
4
6
8
10
12
14
25 cm/sPool Edge
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Normalized Air Entrainment Rate for 15 and
30 cm Pool Fires without a Floor
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Fr
fm
ent
/(S+1)m
f
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
Fuel Pool(cm) Floor(cm) mf(mg/s) Data
Methanol 30 none 980
Heptane 15 none 385
Toluene 30 none 2850Heptane 30 none 2660
Toluene 15 none 370
0.135(Z/D)0.78
Methanol 15 none 245
X / D
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Fr
fm
ent
/(S+1)m
f
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
Fuel Pool(cm) Floor(cm) mf(mg/s) Data
Methanol 30 none 980
Heptane 15 none 385
Toluene 30 none 2850Heptane 30 none 2660
Toluene 15 none 370
0.135(X/D)0.78
Methanol 15 none 245
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THE PHYSICAL SIGNIFICANCE OF
THERMAL EXPANSION SOURCE TERM Q
State Equation:
t
1
R
P
t
T
2
, and
2
1
R
PT (1)
The Energy Equation:
QTTVCt
TC pp
&r
(2)
The Mass Conservation Equation:
0VV
t
rr(3)
Substitute eq. (1) into eq. (2) and add to TCp eq. (3):
)TQ(TC
1V
p
&r
(4)
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Gas Chromatography
Column 1: H2, O2, N2, CH4, CO
Column 2:
CO2, C2H2, C2H4
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Radial Distribution of Mixture Fraction in
the Near Field of 7.1 cm Natural Gas Flame
0.0
0.2
0.4
0.6
0.8
1.0
Natural Gas, D = 7.1 cm, no floor
Frf= 0.109, H
flame= 36.4 cm,
Mixtu
reFraction
0.0
0.2
0.4
0.6
0.8
r, cm
0 1 2 3 40.0
0.2
0.4
0.6
0.8
Gaussian Logistic
X = 1.5 cm
= 1.0 cm
= 0.5 cm
Data
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Radial Distribution of Mixture Fraction in the
Higher Region of 7.1 cm Natural Gas Flame
0.0
0.1
0.2
0.3
Natural Gas, D = 7.1 cm, no floorFr
f= 0.109, H
flame= 36.4 cm,
MixtureFraction
0.0
0.1
0.2
0.3
0.4
r, cm
0 1 2 3 40.0
0.2
0.4
0.6
0.8
Gaussian Logistic
X = 10.0 cm
= 5.0 cm
= 2.0 cm
Data
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Mole Fraction of Reactant Species as a
Function of Mixture Fraction
0.0
0.2
0.4
0.6
0.8
1.0
Mole
Fraction
0.00
0.05
0.10
0.15
0.20
Mixture Fraction
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
CH4
O2
Data X, cm
OPPDIF Prediction
0.00.51.01.52.0
3.05.0
Data X, cm
N2
Natural Gas, D = 7.1 cm, no floorFrf= 0.109, Hflame = 36.4 cm
Data X, cm
0.00.51.01.52.0
3.05.0
10.012.0
7.0
Data X, cm
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Mole Fraction of Intermediate Combustion
Products as a Function of Mixture Fraction
Chemkin Prediction
0.00
0.01
0.02
0.03
0.04
MoleFraction
0.000
0.002
0.004
0.006
0.008
0.010
Mixture Fraction
0.0 0.2 0.4 0.6 0.8 1.00.00
0.01
0.02
0.03
C2H
4
C2H
2
H2
OPPDIF Prediction
Natural Gas FlameD = 7.1 cm, without floorFrf= 0.109, Hflame = 36.4 cm
Data X, cm
0.00.51.01.5
2.03.05.0
10.012.0
7.0
Data X, cm
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Mole Fraction of Combustion Products as a
Function of Mixture Fraction
0.00
0.02
0.04
0.06
0.08
MoleFraction
0.00
0.01
0.02
0.03
0.04
Mixture Fraction
0.0 0.2 0.4 0.6 0.8 1.00.00
0.05
0.10
0.15
CO2
CO
H2O
OPPDIF Prediction
Natural Gas Flame
D = 7.1 cm, without floorFrf= 0.109, H
flame= 36.4 cm
Data X, cm
0.00.51.01.5
2.03.05.0
10.012.0
7.0
Data X, cm
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Specific Volume Calculated Based on Species
Concentration as a Function of Mixture Fraction
chemkin predictionchemkin predictionchemkin prediction
Mixture Fraction Z
0.0 0.2 0.4 0.6 0.8 1.0
,m
3/kg
0
1
2
3
4
5
6
7
OPPDIF prediction
Data X, cm
0.5
1.0
1.5
2.0
Natural Gas FlameD = 7.1 cm, without floorFr
f= 0.109, H
flame= 36.4 cm
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Diffusivity Calculated Based on Species
Concentration as a Function of Mixture Fraction
chemkin predictionchemkin predictionchemkin prediction
Mixture Fraction Z
0.0 0.2 0.4 0.6 0.8 1.0
DiffusionCoefficient,m
2/s
0e+0
1e-4
2e-4
3e-4
4e-4
5e-4
6e-4
OPPDIF prediction
D Data X, cm
0.5
1.0
1.5
2.0
Natural Gas Flame
D = 7.1 cm, without floorFr
f= 0.109, H
flame= 36.4 cm
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Thermal Expansion Source Term as a
Function of Radial Distance in the Near Field
-5
0
5
10
15
20
Natural Gas FlameD = 7.1 cm, without floorFr
f= 0.109, H
flame= 36.4 cm
d
/d/Z/d/dr(r
DdZ/dr)/r,1/s
-5
0
5
10
15
20
r, cm
0 1 2 3 4-5
0
5
10
15
20
25
Measured
Correlations
Visible Flame
X = 2.0 cm
= 1.5 cm
= 0.5 cm
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Particle Imaging Velocimetry
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Instantaneous Velocity Vectors in the
Near Field of a 7.1 cm Natural Gas Flame
Radial Position, cm
-4 -3 -2 -1 0 1 2 3 4
Axial
Position,cm
0
1
2
3
4
5
6
7
8Natural Gas, Fr
f= 0.109
D = 7.1 cm, Hflame
= 36.4
Buoyant Diffusion Flame
No Floor
2.0 m/s
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Instantaneous Velocity Vectors in the intermittent
Region of a 7.1 cm Natural Gas Flame
Radial Position, cm
-4 -3 -2 -1 0 1 2 3 4
AxialPosition,cm
24
25
26
27
28
29
30
31Natural Gas, Fr
f= 0.109
D = 7.1 cm, without floor
Buoyant Diffusion Flame
Diffuser Burner
4.0 m/s
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Mean Velocity Vectors in the Near Field
of a 7.1 cm Natural Gas Flame
Radial Position, cm
-4 -3 -2 -1 0 1 2 3 4
Axia
lPosition,cm
0
1
2
3
4
5
6
7
8
Natural Gas, Frf= 0.109
D = 7.1 cm, Hflame
= 36.4
Buoyant Diffusion FlameNo Floor
2.0 m/s
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Mean Velocity Vectors in the Intermittent
Region of a 7.1 cm Natural Gas Flame
Radial Position, cm
-4 -3 -2 -1 0 1 2 3 4
Axia
lPosition,cm
24
25
26
27
28
29
30
31Natural Gas, Fr
f= 0.109
D = 7.1 cm, without floor
Buoyant Diffusion FlameDiffuser Burner
4.0 m/s
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Radial Profiles of Mean Axial Velocities in
the Near Field of a 7.1 cm Natural Gas Flame
0
40
80
120
160
200
AxialVelocity,cm/s
0
40
80
120
0
20
40
60
Radial Position, cm
-5 -4 -3 -2 -1 0 1 2 3 4 50
10
20
30
x = 6 cm
x = 4 cm
x = 2 cm
x = 1 cm
Second measurement
Buoyant Diffusion FlameNatural Gas, Frf= 0.109
D = 7.1 cm, without floor
First measurement
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Radial Profiles of Vorticities in the Near
Field of a 7.1 cm Natural Gas Flame
-20
0
20
40
6080
100
120
Vorticity,1/sec
-20
0
20
40
60
80
-40
-20
0
20
40
60
Radial Position, cm
-5 -4 -3 -2 -1 0 1 2 3 4 5-40
-20
0
20
40
x = 6 cm
x = 4 cm
x = 2 cm
x = 1 cm
from velocity field on 0.5 cm grid
Buoyant Diffusion FlameNatural Gas, Fr
f= 0.109
D = 7.1 cm, without floor
from velocity field on 0.25 cm gridfrom smoothed velocity field on 0.25 cm grid
r
u
x
u xr
)j,1i(r)j,1i(r
)j,1i(u)j,1i(u
)1j,i(x)1j,i(x
)1j,i(u)1j,i(u)j,i(
xx
rr
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Measurements and Predictions of Radial
Profiles of Axial Velocities
0
40
80
120
160
200
AxialVelocity,cm/s
0
40
80
120
0
20
40
60
Radial Position, cm
-5 -4 -3 -2 -1 0 1 2 3 4 50
10
20
30
x = 6 cm
x = 4 cm
x = 2 cm
x = 1 cm
Second measurement
Buoyant Diffusion Flame
Natural Gas, Frf= 0.109
D = 7.1 cm, without floor
First measurement
Predictions
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