Air Entrainment Rate Calculations

8/12/2019 Air Entrainment Rate Calculations

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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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2/81

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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Maurice J . Zucrow LaboratoriesSchool of Mechanical Engineering

OUTLINE


3/81

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


4/81

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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&


5/81

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PAST MEASUREMENT TECHNIQUES ( I )

McCaffrey (1979)


6/81


7/81

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PAST MEASUREMENT TECHNIQUES ( III )

Zukoski and Coworkers (1980)


8/81

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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


9/81

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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)


10/81

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


11/81

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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)


12/81

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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


13/81

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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


14/81

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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


15/81

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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


16/81

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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


17/81

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Multigrid Scheme

j,ijm,ijm,ijp,ijp,ij,imj,imj,ipj,ipj,ij,i D~

c~

c~

c~

c~

c


18/81

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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:


19/81

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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)


20/81

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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


21/81

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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


22/81

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The Enclosure


23/81

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The Fuel Supply System


24/81

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Laser Doppler Velocimeter (LDV)


25/81

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Measureed Mean Velocity Field

Zhou and Gore (1995)


26/81

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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

.

.


27/81

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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

.


28/81

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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

.


29/81

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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

.


30/81

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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

.


31/81

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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


Hinterface


Dfloor= 51 cm, r = 4.5 cm

x = 9 cm

x = 5 cm

x = 1 cm

.


32/81

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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


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



x = 12 cm

x = 6 cm

x = 1 cm


33/81

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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



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


Hinterface


Dfloor

= 51 cm

x = 12 cm

x = 6 cm

x = 1 cm


34/81

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Particle Imaging Velocimetry

Based on CW Laser


35/81


36/81

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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


37/81

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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


38/81

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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


39/81


40/81

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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


41/81

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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


42/81

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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


43/81

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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


44/81


45/81


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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


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


Heptane 15 none 385

Toluene 30 none 2850Heptane 30 none 2660

Toluene 15 none 370

0.135(X/D)0.78



47/81


48/81

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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)


49/81


50/81


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Gas Chromatography

Column 1: H2, O2, N2, CH4, CO

Column 2:

CO2, C2H2, C2H4


52/81


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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


54/81

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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


55/81

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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


56/81

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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


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


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


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


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


Natural Gas, Frf= 0.109


First measurement

Predictions


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Date post:	03-Jun-2018
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