Institution of Fire Engineers

Rasbash Lecture 40th Anniversary Symposium

John L. de Ris

University of Edinburgh May 15th 2014

Radiation and Incomplete

Combustion of Buoyant

Turbulent Diffusion Flames

FM Global

• Rayleigh-Taylor Instability drives combustion of flamelets

• mixing time independent of fire size

• independent of fire size

• Radiant Fraction, , independent of fire size

• Incompleteness of Combustion, , independent of fire size

“Mechanism of Buoyant Turbulent Diffusion Flames” Procedia Engineering 62 (2013) 13-27

Introduction

A 1983 discussion with David Rasbash in led to the recent paper

Global fV Q

31110q kW m

R

I

Rasbash Lecture

R T

2

• Rayleigh-Taylor Instabilities drive of buoyant turbulent

diffusion flames.

• Smoke-Point, , correlates .

• Diagrammatic and Mathematical models for and .

• Comparison of model with experiment for burning in air.

• Correlation of measurements in general atmospheres.

• Model for flame radiation absorption coefficients in terms of

.

• Recommendations

I

R

q

I

, and C SH S

S

R

Outline

3

Conservation of Energy

; ;convR IR conv I

C C C

QQ Q

M H M H M H

Theory

1

1

R conv I

R conv I

C R conv IM H Q Q Q

Definitions:

Rasbash Lecture

Available chemical energy per unit flame mass

0 1 ch Ch h H S

is the stoichiometric air/fuel mass ratio S 4

Smoke Point & Incompleteness

Smoke Point

Soot formation rate is inversely proportional to smoke point flame height

S

1 1

c S

0.0

0.1

0.2

0.3

0.4

1 10 100 1000

XI,

YS

1/ls

0.072ln 0.36I S

0.039ln 0.36S SY

Smoke point correlates the soot yield, , and

incompleteness of combustion, , of buoyant

turbulent diffusion flames burning in air.

Rasbash Lecture

, Yi & Sunderland Xi, Tewarson FPA

Incompleteness vs. inverse smoke point

S

SY

I

is constantR T

5

Rasbash Lecture Theory Temperatures

0 03 4Rf convT T T T

adT 2300K

1900K

1500K

1100K

300K

convT

RfT

avT

0T x

FUEL AIR AIR

peak gas

flame radiative

average gas

Radiative

loss

Coupling between effective flame radiation temperature

[ ] and peak gas temperature 41/4

RfT convT

RfT is sometimes called the Schmidt temperature6

Schmidt Temperature Measurement

oven Rf SchmidtT T T

Flame Absorption equals Flame Emission when the

temperature of the block body source,

Rasbash Lecture

oven RfT T

Effective Flame Radiation Temperature - RfT

Measurement Concept

Black Body

4

oven ovenI T

ovenT

4 4

oven Rf ovenI I T T

Ray Radiometer

7

Rasbash Lecture

adT

00

0 0

41 1

3

P RfconvR

ch ch

C T Th h

h h h h

Mathematical Model 1

2300K

0 03 4Rf convT T T T

convT

RfT

avT

0T x

0

0

convconv I

ch

h h

h h

1R conv I

1900K

1500K

1100K

300K

typical

8

Energy Diagram

Rasbash Lecture

00

0 0

41 1

3

P RfconvR

ch ch

C T Th h

h h h h

Mathematical Model 2

00

00

41500 ; 2.79 ; ; ;

3

;1

Ref Ref Ref

Ref Ref

Ref Ref

Rf

P

ch Cch

T TT K h C T kJ g

T T

h h H

h h S

0 0 0

0 0 0

4 3 4 31 1 1

Ref

Ref

P Rf P

R

ch ch ch

C T T C T

h h h

0

chR

ch

Non-Dimensional Transformation

Governing Equation

mathematical equation relating &R 9

Radiant Fraction

4 4

0 1 expR f Rf mQ A T T

31110f fQ q V kW m V

4 4

0 1 expfR

R Rf m

f

AQT T

Q q V

3.6 3.6f f

m

f f m

V A

A V Mean Beam Length

4 4 4 4

0 0

1 exp3.6 3.6

0

m

R Rf Rf

mm

T T T Tq q

Flame radiation comes from both soot and gases

Rasbash Lecture Mathematical Model 3

10

Rasbash Lecture

0 4 40

0

0 0

4 3.61 1

3

P RfconvR Rf

ch ch

C T Th hT T

h h h h q

Mathematical Model 4

00

4

00

41500 ; 2.79 ; ; ;

3

1 exp3.6;

1

Ref Ref Ref

Ref Ref

Ref

Ref Ref

Rf

P

mch Cch

m

T TT K h C T kJ g

T T

h h H TU

h h S q

0 0 4 400

0 0 0

4 3 4 31 1 1

Ref

Ref

P Rf P

R

ch ch ch

C T T C TU

h h h

4 4

0

0

chR

ch

U

Non-Dimensional Transformation

Physical Governing Equation

Mathematical Equation to be solved 11

Mathematical Model 5 Rasbash Lecture

0 0 0

1 1 in airch ch

Ra a Ia

ch ch ch

Ia

What is ?

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

1900 2100 2300 2500 2700

Tad

vs. Tad0, ,

0 1

Ref1. is a function of and

2. approximately linear function of

3. empirically, is a linear function of

4. also, if or

C

ad

R

I R

H S T h

T

0

0 0

11 0.81 1

1

Refch

ch ch C

h

H S

12

0,Ia Ra aMax

Rasbash Lecture Diagrammatic Model

0

1500

0.2

1200 ` 15

1. Complete oxidation of soot:

all soot is eventually oxidized

Unusual for fuels burning in air

2. Partial oxidation and release of soot : 0

I

Rf

I

Rf

T K

K T

00 1500

0.2

with

all fuel pyrolyzes in flame

Typical of aliphatic hydrocarbons

3. Copious soot formation:

some fuel decomposes at low temperatures and bypasses flame

conv

I

K T K

` 1200 1500 and

Typical of aromatic hydrocarbons

Rf convT K T K

THREE CASES:

13

Rasbash Lecture

CASE 1. Complete oxidation of soot

adT

convT

RfT

avT

0T x

2400K

2100K

1650K

1200K

300K

FUEL AIR AIR

Radiative loss

0 11500

and Rf

I

T

K

Examples: CH4 or C2H6 burning in O2 enhanced air

Unusual case

1500K

1500Rf KT

Diagrammatic Model

14

CASE 2. Partial oxidation and release of soot

Rasbash Lecture

0 1 0.2 and 0.8I

1200 ` 1500

1500

Rf

conv

K T K

T K

All fuel decomposes in flame

Typical of aliphatic hydrocarbons

adT 2300K

1700K

1500K

1050K

300K

convT

RfT

avT

0T x

FUEL AIR AIR

Radiative

loss

1350K

0.2 0.45R

Diagrammatic Model

15

Comparison with Experiment

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

R

a

Ia

Radiant Fractions Ra vs. I a in Air

Measured Model

CH4

C2H6

C3H8

C2H4

C3H6

C4H8

C2H2

C4H6

Ra a Ia 0.2 5 3 0.8Ra a Ia

0.0

0.1

0.2

0.3

0.4

0.5

0.6

R

a

Fuel

Radiant Fractions in Air

Measured

Model

Rasbash Lecture

Case 2. Case 3.

Comparison with Experiment

16

CASE 3. Extremely sooty flames

Tewarson FPA measurements

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1

R

a

Ia

Radiant Fraction vs. Incomplete Combustion

Tewarson Data

Tewarson Fit

Linear 0.9*(0.8 - Xi)

Tewarson FSJ 39 (2004) 131-141

Rasbash Lecture

17

CASE 3. Copious soot formation with some fuel

decomposing at low temperatures and bypassing flame

Theory Rasbash Lecture

Aromatic hydrocarbons typically burn according to Case 3.

adT 2300K

900K

1500K

1200K

300K

convT

RfT

avT

0T x

FUEL AIR AIR

Radiative

loss

` 1200 1500 and Rf convT K T K 0.2 0.8 and I

1500Also, being less than results in some flame extinguishment.convT K

18

CASE 3. Copious soot formation with some fuel decomposing

at low temperatures and bypassing the flame

Theory Rasbash Lecture

0

0 0

0.2

0.2 1

0.21

1 1 1

11.

11 1

1 1

1

Let be the fuel bypassing the flame.

or

assuming

IB I

R conv IB

convR

IB IB IB

C IB Cch

RIB R

ch chR

IB ch ch

R

H HS

S hS h

0

0.2

0.2

50.2 1 0.2 1.2 0.2 0.8

3

ch

R IB I I

19

Comparison with Experiment

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

R

a

Ia

Radiant Fractions Ra vs. I a in Air

Measured Model

CH4

C2H6

C3H8

C2H4

C3H6

C4H8

C2H2

C4H6

Ra a Ia 0.2 5 3 0.8Ra a Ia

0.0

0.1

0.2

0.3

0.4

0.5

0.6

R

a

Fuel

Radiant Fractions in Air

Measured

Model

Rasbash Lecture

Case 2. Case 3.

Com

20

General Correlations of Radiant Fractions

1 2 for each fuel "j" Rj Raj j aj j ajS S

Linear correlations provide a amazingly good fit.

1400

1600

1800

2000

2200

2400

2600

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

T [

K]

R

C4H8

C3H6

C2H4

C3H8

C2H6

CH4

adia. T

Experiment Rasbash Lecture

21

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Co

rre

lati

on

Measurement

Combined Std. Dev. 3.21 %

for all fuels

Linear correlations provide a amazingly good fit.

Rasbash Lecture Experiment

22

Solving for effective flame radiative temperature

Rasbash Lecture

1500RfT K

1300

1500

1700

1900

2100

2300

2500

2700

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

T [

K]

CH4

C2H6

C3H8

C2H4

C3H6

C4H8

adia.T

Results

,R

23

Dimensionless Absorption Coefficient

Rasbash Lecture

4 4

0

0

From the radiation equation chR

ch

U

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

U

U()

C4H8

C3H6

C2H4

C3H8

C2H6

CH4

43.6 RefTU

q

Results

24

1/2

2

2 2

2200 0.360.15 0.037 0.33ln 15 ; 0.24

; 0.55; 0.65

ad Sa

L H

H L L H

H L

U S P x xT

x xP x x x x

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

U

Fit of Dimensionless Absorption Coefficient, U

C3H6

C3H6 Model

C2H4 Model

C2H4

C3H8 Model

C3H8

C2H6 Model

C2H6

CH4 Model

CH4

Rasbash Lecture Results

43.6 RefTU

q

25

, ,C SU H S

• Rayleigh-Taylor Instabilities drive the combustion of

buoyant turbulent diffusion flames.

• Smoke-Point, , correlates .

• Diagrammatic and Mathematical models for and .

• Excellent comparison with experiment for burning in air.

• Correlation of measurements in general atmospheres.

• Predictions of flame radiation absorption coefficients in

terms of .

I

R I

, and C SH S

S

R

Conclusions Rasbash Lecture

26

1. Apply existing model to predict:

• pool fire burning rates

• wall fire radiant heat transfer rates

2. Measure in general atmospheres using the FPA

3. Model soot mantle surrounding very large pool fires

4. Measure & model effect of wind on pool fires burning rates

I

Recommendations Rasbash Lecture

27