Xinyan Huang

Department of Mechanical Engineering

Imperial College London, x.huang12@imperial.ac.uk

Michael Gollner

Department of Fire Protection Engineering

University of Maryland, mgollner@umd.edu11th International Symposium on Fire Safety Science

9-14 Feb. 2014, University of Canterbury, New Zealand

1. Introduction and Previous Work

2. Description of Flame

3. Flame Length and Mass-loss Rate

4. Flame Thickness and Tilt Angle

5. Conclusions

211th International Symposium on Fire Safety Science

9-14 Feb. 2014, University of Canterbury, New Zealand

1. Introduction and Previous Work

2. Description of Flame

3. Flame Length and Mass-loss Rate

4. Flame Thickness and Tilt Angle

5. Conclusions

311th International Symposium on Fire Safety Science

9-14 Feb. 2014, University of Canterbury, New Zealand

4[1] Gollner et al., Proc. Combust. Inst., 34 (2) (2013) 2531-2538

PMMA: 20×10×1.27 cm

3 camera (top, side, and

back)

Load cell: 15 Hz, ±0.5 g

o K-type TCs × 7

o Thin-skin heat flux

sensor × 19

o Ignition: 1 cm wick

soaked with fuel

ignites for 1 min

5

6

-60 -45 -30 0 30 45 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Angle of Inclination,

Spre

ad R

ate,

Vp (

cm/s

)

Vp (This study, w=10cm)

Pizzo (model)

Pizzo (exp, w=20cm)

Drydale and Macmillian (w=6cm)

Xie and DesJardin (model)

[1] Gollner et al., Proc. Combust. Inst., 34 (2) (2013) 2531-2538[2] Y. Pizzo, J.L. Consalvi, B. Porterie, Comb. Flame. 156 (2009) 1856-1859.[3] D. Drysdale, A. Macmillan. Fire Safety J. 18, no. 3 (1992): 245-254.

[4] W. Xie, P. Desjardin, Comb. Flame. 156 (2009) 522-530.[5] H. Ohtani, K. Ohta, Y. Uehara, Fire Mat. 18 (1991) 323-193.[6] de Ris, J, L. Orloff. Proc. Comb. Inst. 15 (1975) 175-182.

-80 -60 -40 -20 0 20 40 60 800

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Angle of Inclination,

Spre

ad R

ate

(cm

/s)

Vp (This Study, w=10cm)

Pizzo (Model)

Pizzo (Exp, w=20cm)

Drydale and Macmillian (w=6cm)

Xie and DesJardin (Model)

May 15, 2012 6

Flame Spread Steady Burning

-60 -45 -30 0 30 45 602

3

4

5

6

7

8

9

10

Gas Burner, 65 cm [5]

PMMA, Steady Burning

PMMA, Spreading

Angle of Inclination, θAngle of Inclination, θ

Spre

ad R

ate,

Vp

(c

m/s

)

Mas

s-lo

ss R

ate

(g/m

2s)

Spread rate peaks nears vertical wall fire

Burning rate increases with inclination (𝜃)

1. Introduction and Previous Work

2. Description of Flame

3. Flame Length and Mass-loss Rate

4. Flame Thickness and Tilt Angle

5. Conclusions

711th International Symposium on Fire Safety Science

9-14 Feb. 2014, University of Canterbury, New Zealand

8[1] Gollner et al., Proc. Combust. Inst., 34 (2) (2013) 2531-2538

1. Flame height (𝑥𝑓): 𝑥𝑓 ~ 𝑥𝑝~ 𝑡, 𝑥𝑓~ 𝑚′

2. Flame thickness (𝐻 = 𝑦𝑓,𝑚𝑎𝑥)

3. Tilt angle (𝜙): degree of lift off

9

For this small-scale test (𝑥𝑝<20 cm), the spread

rate (𝑉𝑝) was previously found to be constant [1].

Two measurements of 𝑥𝑓 from front-view and

side-view overlap well.

Two common correlations

𝑥𝑓 = 𝐴𝑥𝑝

𝑛

𝑘𝑥𝑝 + 𝑏

Front-view

camera

Side-view

camera

[1] Gollner et al., Proc. Combust. Inst., 34 (2) (2013) 2531-2538

Pyrolysis

front (𝑥𝑝)

10

Parabolic fit (𝑥𝑓~𝑥𝑝2) is

better if the spread

time >500 𝑠

Linear fit is good for

t < 500 𝑠

11

Slope 𝒌: 𝑥𝑓 = 𝑘𝑥𝑝 + 𝑏

Exponent 𝒏: 𝑥𝑓 = 𝐴𝑥𝑝𝑛

Burning rate 𝒎′

Steady & Spread

In linear fit, 𝑥𝑓 = 𝑘𝑥𝑝 + 𝑏 (𝑡 < 500 s), slope 𝑘 continuously increases with

inclination angle (𝜃), same trend as the burning rate ( 𝑚′).

For power-law fit, 𝑥𝑓 = 𝐴𝑥𝑝𝑛

𝜃 = 0° (vertical wall fire), 𝑛 = 0.86 agree with 𝑛 = 0.78 and 0.8 in literatures.

Generally, 𝑛 = 0.85 is a good approximation ⇒ 𝒙𝒇~ 𝑽𝒑𝒕𝟎.𝟖𝟓

~𝒕𝟎.𝟖𝟓

(early-stage, small-scale fires, 𝑡 < 500 s)

1. Introduction and Previous Work

2. Description of Flame

3. Flame Length and Mass-loss Rate

4. Flame Thickness and Tilt Angle

5. Conclusions

1211th International Symposium on Fire Safety Science

9-14 Feb. 2014, University of Canterbury, New Zealand

13[7] Delichatsios, M. A. Combust. Sci. & Tech., 39(1-6):195–214, 1984.

[8] Gollner et al., Combustion and Flame, 158(7):1404 – 1412, 2011.

Mass-loss (burning) rate ( 𝒎′) and heat-release rate (HRR, 𝑸′)

𝑄′ = ∆𝐻𝑐 𝑚′ = ∆𝐻𝑐 𝑚′′ 𝑥𝑝

𝑥𝑓 = 𝐹(𝑥𝑝)

Delichatsios’ scaling analysis [7]

𝑚′ = 𝑓𝑥𝑓𝛼𝜌𝑎𝑢𝑔 (𝑢𝑔: characteristic gas velocity)

where 𝑓 is F/A stoich. ratio; 𝛼 is entrainment coefficient; and 𝜌𝑎 is air density.

Turbulent mixing controlled plume: 𝒖𝒈~ 𝒙𝒇𝒈

𝒙𝒇~ 𝑚′/ 𝛼𝜌𝑎𝑓 𝑔 2/3~ 𝒎′ 𝟐/𝟑~ 𝑄′ 2/3(𝑝 = 2/3)

Laminar diffusion controlled plume: 𝒖𝒈~𝑫/𝒂 with 𝑎 = 𝑚′/(𝑓𝜌𝑓)

𝑥𝑓𝑔[8]

𝒙𝒇~ 𝑚′ 4/3/ 𝜌𝑓𝜌𝑎𝑓2𝐷 𝑔

2/3~ 𝒎′ 𝟒/𝟑~ 𝑄′ 4/3

(𝑝 = 4/3)

In vertical wall fire, 𝑝 ≈ 1 for cardboard [8], and 𝑝 = 1~1.25 for PMMA and gas

burner. However, the theoretical limiting values of 𝑝 = 2/3 and 𝑝 = 4/3 have

never been found before.

𝒙𝒇~ 𝑸′ 𝒑~ 𝒎′ 𝒑

14

For 𝜃 > 30°, 𝑝 < 1 and approach limiting value of 2/3.

Boundary-layer separation (turbulence) is clear.

𝑄′ > 20 kW/m suggests that turbulent mixing dominates the flame behavior.

Turbulent

15

For vertical wall fire (𝜃 = 0° ), 𝑝 ≈ 1 and 𝑄′ ≈ 20 kW/m agrees with literature.

Usually, 𝑄′ = 20 kW/m is the critical value from laminar to turbulent transition.

Almost a boundary-layer plume, but the flame tip starts to separate.

Transition

16

For underside flame (𝜃 < 0° ), 𝑝 ≈ 4/3, 𝑄′ < 20 kW/m, and no boundary-layer

separation is observed, suggesting molecular diffusion is dominant.

The underside burning can delay the transition to a turbulent flame.

Laminar

17

First time to experimentally verify the two theoretical limiting values (𝑝 = 4/3 & 2/3).

In small-scale laboratory tests, flame behavior may be appreciably modified towards

laminar or turbulent, simply by inclining the fuel surface downwards or upwards.

1. Introduction and Previous Work

2. Description of Flame

3. Flame Length and Mass-loss Rate

4. Flame Thickness and Tilt Angle

5. Conclusions

1811th International Symposium on Fire Safety Science

9-14 Feb. 2014, University of Canterbury, New Zealand

19

Flame thickness (𝐻) is defined as the maximum flame standoff distance (𝑦𝑓,𝑚𝑎𝑥)

𝐻 increases during spread and approaches constant after spread stops.

Flame thickness increases with inclination (𝜃), suggesting the radiation heat flux

to the burning region (𝑥 < 𝑥𝑝) and the burning rate ( 𝒎′) increases with 𝜽.

Flame lift off increases with the flame thickness, decreasing the convective heat

flux to unburned region (𝑥 > 𝑥𝑝), and spread rate

⇒ lift-off is inversely proportional to 𝑽𝒑.

20

10 continuous side-view photos are averaged, averaging flame fluctuations.

Flame tilt angle is defined by a line dividing the image into two regions with the

same total luminance → useful to estimate radiation heat flux and view angle

At θ ≤ 0°, tilt angle (𝜙) decreases with time ⇒ a negligible flame separation

At θ = 30°, tilt angle (𝜙) is a constant ⇒ flame starts to separate

At θ > 30°, tilt angle (𝜙) increases with time ⇒ a strong flame separation

Tilt angle (𝜙) in

respect to the

fuel surface

21

Tilt angle (𝜙) can be fitted as 𝜙 = 1.57𝑒0.045𝜃, and reaches the maximum

value of 90° at pool fire (𝜃= 90°).

Follows the trend of 1/𝑉𝑝

⇒ Flame separation decreases the heat flux to the unburnt fuel, therefore

reducing the flame spread rate.

1/𝑉𝑝

𝜙 = 1.57𝑒0.045𝜃

1. Introduction and Previous Work

2. Description of Flame

3. Flame Length and Mass-loss Rate

4. Flame Thickness and Tilt Angle

5. Conclusions

2211th International Symposium on Fire Safety Science

9-14 Feb. 2014, University of Canterbury, New Zealand

23

For early-stage, small-scale PMMA fires, flame length is proportional

to pyrolysis length at all inclinations, and increases as 𝒙𝒇~𝒕𝟎.𝟖𝟓.

Underside flame spread (𝜃 < 0°) is found to be turbulence-

suppressed and diffusion-controlled: 𝒙𝒇~ 𝒎′ 𝟒/𝟑.

Topside flame spread (𝜃 > 0°) satisfies the turbulent-mixing

correlation: 𝒙𝒇~ 𝒎′ 𝟐/𝟑.

Flame thickness increases with inclination, supporting the trends of

flame spread rate and burning rate.

Flame tilt angle increases with inclination, being inversely

proportional to flame-spread rate 𝑉𝑝.

11th International Symposium on Fire Safety Science

9-14 Feb. 2014, University of Canterbury, New Zealand

Valuable comments from Forman Williams and Ali Rangwala

during the first stage of this work.

Assistance from Charles Marcacci, Jeanette Cobian, and Ulrich

Niemann with laboratory experiments.

2411th International Symposium on Fire Safety Science

9-14 Feb. 2014, University of Canterbury, New Zealand

Xinyan Huang

Department of Mechanical Engineering

Imperial College London, x.huang12@imperial.ac.uk

Michael Gollner

Department of Fire Protection Engineering

University of Maryland, mgollner@umd.edu11th International Symposium on Fire Safety Science

9-14 Feb. 2014, University of Canterbury, New Zealand