Ignition-to-Spread Transition of Electrical Wire fires

August 21, 2014 1

Ignition-to-Spread Transition of Externally

Heated Electrical Wire

Xinyan Huang and Forman A. Williams

University of California, San Diego

Yuji Nakamura

Hokkaido University, Japan

August 3, 2012 ● 34th international symposium on Combustion, Warsaw, Poland

August 21, 2014 2

Outline

• Motivation

• Simplified Ignition-to-Spread Model

• Experimental Setup

• Experimental Results and Discussion

• Conclusions and Future Work

2August 3, 2012 ● Ignition-to-Spread Transition of Externally Heated Electrical Wire

August 21, 2014 3

Motivation

In 2010, electrical fires accounted for 28,600 incidents and $ 1.1 billion in property losses, 53% of which involved electrical wiring.

Electrical wire fires account for 42% of total fire cases in Nuclear Power Plants. Also, fire scenarios for wire fires in sub-atmospheric pressure and oxygen-enriched (space) applications should be determined.

Previous study showed flames spread faster in a higher-conductivity wire and the spread rate increases as pressure decreases [1]. But no systematic experimental study or theory for wire ignition by externally heating exists.

How do the thermal conductivity, dimension of wire and atmospheric conditions (pressure and oxygen concentration) affect ignition and the consequent transition to spread?


[1] Y. Nakamura et al., Proc. Combust. Inst., 32 (2009), pp. 2559–2566

August 21, 2014 4

Outline

• Motivation






August 21, 2014 5

Ignition Model at Flashpoint

5

Assumptions:

Uniform heat flux within 𝐿

Thermally thin: δ ~ 0.2 mm ≪ 𝛼𝑡𝑖𝑔

Uniform cross-sectional temperature: 𝐵𝑖𝑐 ≪ 𝐵𝑖𝑝 < 0.3

𝜆𝑝 ≪ 𝜆𝑐 and 𝜌𝑐𝜆 𝑝 ≪ 𝜌𝑐𝜆 𝑐

Governing Equations

∑𝜌𝑐𝐴𝜕𝑇

𝜕𝑡= 𝐴𝑐𝜆𝑐

𝜕2𝑇

𝜕𝑥2+ 𝑃𝑜 𝑞𝑒

′′ − 𝑞𝑙𝑜𝑠𝑠′′ 0 < 𝑥 <

𝐿

2



𝜕2𝑇

𝜕𝑥2− 𝑃𝑜ℎ 𝑇 − 𝑇𝑎 𝑥 >

𝐿

2

August 3, 2012 ● Ignition-to-Spread Transition of Externally Heated Electrical Wire

where 𝑇𝐿/2− = 𝑇𝐿/2+ ,𝜕𝑇

𝜕𝑥𝐿/2−

=𝜕𝑇

𝜕𝑥𝐿/2+

,

𝜕𝑇

𝜕𝑥0

= 0, d 𝑇∞ = 𝑇𝑎 , aafor 𝑡 > 0.

Flashpoint: pyrolysis vapors achieve a

fuel’s lower flammability limit, defined

by a critical mass flux or temperature

(at 𝑇𝑚𝑎𝑥 = 𝑇𝑖𝑔 ≥ 𝑇𝑝).

August 21, 2014 6

Ignition Model at Flashpoint

6

Ignition time

𝑡𝑖𝑔 ≈𝑓 𝜆, 𝑑𝑐 , 𝛿, 𝐿

𝑞𝑒′′𝑛

where 𝑛 denotes ignition properties.

𝑛 ≈ 1 (thermally thin)

𝑛 ≈ 2 (thermally thick)

Critical/minimum ignition heat flux:

𝜕𝑇 𝜕𝑡 = 0, 𝑇0~𝐿/2 = 𝑇𝑖𝑔

⇒ 𝑞𝑒,𝑐𝑟𝑡′′ = 𝑞𝑙𝑜𝑠𝑠

′′ +𝑃𝑜𝐿

𝑇𝑖𝑔 − 𝑇𝑎 ℎ𝜆𝑐𝑑𝑜

Increase with the conductance

(conductivity and core diameter)

Decrease with heating length (𝐿)


Governing Equations



𝜕2𝑇

𝜕𝑥2+ 𝑃𝑜 𝑞𝑒

′′ − 𝑞𝑙𝑜𝑠𝑠′′ 0 < 𝑥 <

𝐿

2



𝜕2𝑇

𝜕𝑥2− 𝑃𝑜ℎ 𝑇 − 𝑇𝑎 𝑥 >

𝐿

2

𝑇𝐿/2− = 𝑇𝐿/2+ , 𝜕T/𝜕x 𝐿/2− = 𝜕T/𝜕x 𝐿/2+ ,

𝜕T/𝜕x 0 = 0, d 𝑇∞ = 𝑇𝑎 , aafor 𝑡 > 0.

August 21, 2014 7

To calculate the temperature profile, the heat-transfer equation during spread is

𝐴𝑐𝜆𝑐𝑑2𝑇

𝑑𝑥2+ 𝜌𝑐𝐴 𝑐𝑉𝑓

𝑑𝑇

𝑑𝑥= 𝑞𝑅

′

𝑞𝑅′ : heat transfer in radial direction

Spread Point

7

Flame spread rate (𝑉𝑓) and flame width

(𝑊𝑓) are the eigenvalue of the system,

which quantify the wire conductance.

To sustain the flame spread, the wire temperature profile should be higher than that at steady-state flame-spread .


Four Regions:

I. Unburned wire, 𝑞𝑅,1′ = 𝑃𝑜ℎ1 𝑇 − 𝑇𝑎

II. Boiling polymer within the flame

𝑞𝑅,2′ = 𝑃𝑐 𝑞𝑏

′′ = 𝑃𝑐ℎ𝑏 𝑇 − 𝑇𝑖𝑔

III. The wire core exposed to the flame

𝑞𝑅,3′ = 𝑃𝑐 𝑞𝑓

′′ − 𝜎 𝑇4 − 𝑇𝑎4 − ℎ𝑐 𝑇 − 𝑇𝑎

IV. The wire core exposed to atmosphere

𝑞𝑅,4′ = 𝑃𝑐ℎ4 𝑇 − 𝑇𝑎

August 21, 2014 8

Spread Point

8

* Alternatively, the temperature profile can be measured by a fixed thermocouple [3], and the result agrees with the current semi-analytical estimation.


[2] J.L. Torero et al., Combust. Sci. Tech., 174 (2002), pp. 187–203[3] Y. Nakamura et al., J. Therm. Sci. Tech., 3 (2008), pp. 430–441

𝑻𝒎𝒂𝒙 ?⇒ temperature profile

Burning rate [2]

𝑚′′ =𝛿𝜌𝑝

𝑊𝑓𝑉𝑓 ≈

𝑁𝑢 ∙ 𝜆𝑔

𝑐𝑔𝑑𝑜ln 1 + 𝐵 ,

where 𝐵 =𝑌𝑂2,∞ ∆𝐻𝑐/𝜙 + 𝑐𝑔 𝑇𝑎 − 𝑇𝑖𝑔

𝐿𝑣 − 𝑞𝑏′′/ 𝑚′′

= 4 ~ 5

Additional heating source from wire core

𝑞𝑏′′ = ℎ𝑏 𝑇2 − 𝑇𝑖𝑔 , ℎ𝑏~

𝜆

𝛿

𝑇2 = 𝑇𝑚𝑎𝑥 + 𝑇𝑖𝑔 /2, (linear)

Measuring 𝑽𝒇,𝒆𝒙 & 𝑾𝒇,𝒆𝒙 ⇒ 𝑻𝟐 ⇒ 𝑻𝒎𝒂𝒙

August 21, 2014 9

Ignition-to-Spread Transition

9

Transition from flashpoint to spread point

Flame is weak during the transition

Large conductive heat losses along the metal core may quench the flame

Additional heating may be required

Additional heat & heating duration

𝛥𝑄 = 𝐻𝑠𝑝 − 𝐻𝑓𝑙 − 𝛥𝑚 𝜂𝛥𝐻𝑐 ; 𝛥𝑡 =𝛥𝑄

𝑄𝑒′′𝑃𝑜𝐿/2

Enthalpy at spread point: 𝐻𝑠𝑝 = 0∞∑𝜌𝑐𝐴 𝑇 𝑑𝑥 (blue line)

Enthalpy at flashpoint: 𝐻𝑓𝑙 = 0∞∑𝜌𝑐𝐴 𝑇 𝑑𝑥 (red line)

Heat from flame: 𝛥𝑚 𝜂𝛥𝐻𝑐


o For high-conductivity wire or short heating length, 𝐻𝑠𝑝 − 𝐻𝑓𝑙 is large and a

long additional heating time is expected;

o Thick coating may produce more flame heating and reduce the additional heat.

August 21, 2014 10

Outline

• Motivation






August 21, 2014 11

Ignition Experiment

Chamber size: 365 mm (L) × 260 mm (W) × 180 mm (H);

Coil heater: d = 5 mm, L = 1.2 cm, 2.0 cm (wound 10 times), and 3.0 cm;

Change the coil heater power to provide different external heat flux and heating time by regulated DC power (accurate to ±0.01 A) and compact PLC (accurate to ±0.1 s);

Sony HDR-XR 500V video camera (30 fps);

Two pipe line: (1) from air/oxygen tank; (2) to vacuum pump.


August 21, 2014 12

Sample Wires & Test Conditions

12

Wire core: nichrome (NiCr) and copper (Cu) wires

(𝜌𝑐)𝑁𝑖𝐶𝑟

≈ (𝜌𝑐)𝐶𝑢

≈ (𝜌𝑐)𝑃𝐸

, but 𝜆𝑁𝑖𝐶𝑟 ∶ 𝜆 𝐶𝑢 ≈ 1 ∶ 25

Polyethylene coating: 𝛿 ≤ 0.3 mm (thermally thin), 𝜆𝑝 ≪ 𝜆𝑐

At least 5 repeated tests at each case

Ignition curves are plotted along the 50% chance condition (e.g. 3 times flash/spread and 3 time not flash/spread).

Configurations of thin wires used in this study


* 𝜆𝑝 ≈ 0.2 𝑊/𝑚𝐾, 𝜆𝑁𝑖𝐶𝑟 ≈ 16𝑊/𝑚𝐾, 𝜆𝐶𝑢 ≈ 400𝑊/𝑚𝐾

* >3500 runs in this study

August 21, 2014 13

Outline

• Motivation






August 21, 2014 14

Typical Ignition Process at Normal Atmosphere

14

NiCr-A wire: do = 1.0 mm, dc = 0.7 mm, 𝛿 = 0.15 mm,

𝐼 = 10 𝐴, coil heater (2 cm), 𝑃𝑎 = 1 atm

Transition (no-spread)

heating time = 7.4 sec

Flashpoint


Spread point



As heating duration increases:

Blue premix flame (flashpoint) → yellow diffusion flame (fire point) → flame separate and spread to the edge of coil heater

→ spread out (spread point)

August 21, 2014 15

Comparison at Flashpoint

15

I. At flashpoint, experimental results qualitatively agree with modeling results.

II. Index 𝑛 increases with increasing wire conductance, and therefore does not confirm ideality.

III. a wire with a larger conductivity and a larger core diameter, a longer heating duration is required, and critical heat flux or electrical current is larger.

Ignition time by fitting modeling results

𝑡𝑖𝑔 ≈𝑓 𝜆, 𝑑𝑐 , 𝛿, 𝐿

𝑞𝑒′′𝑛


* Note that it is impossible to calculate the exact heat flux from the coil heater.

Conductance ↗

August 21, 2014 16

Transition and Spread point

16

Estimating the experimental heat flux from previous

comparison by connecting 𝐼, 𝑡𝑖𝑔 to 𝑄𝑒′′, 𝑡𝑖𝑔 .

Assuming heating efficiency from the flame: 𝜂 = 5%, and calculate the required heating duration.

Experimental observation:

I. For large-conductance wires, additional heating duration is required in experiments.

II. For low-conductance wires, once flash, flame can spread out.


I. Model qualitatively predicts the experimental trend, ∆𝑡 increases with increasing thermal conductance (Cu-A>Cu-B>NiCr-A>NiCr-B).

II. ∆t decreases as heat flux decrease because a longer heating duration increases 𝐻𝑓𝑙

III. In high-heat-flux experiment, the required heating duration is underestimated because the high-temperature coil continues to heat after power off.

Conductance ↗

August 21, 2014 17

Heating-Length Effect

17

I. Increasing the heating length increases the 𝐻𝑓𝑙 and 𝛥𝑚 𝜂𝛥𝐻𝑐 , which may

converge the spread point to the flashpoint.

II. A shorter heating zone requires more heating duration to ensure spread.

III. Critical heat flux decreases with increasing heating length.


𝛥𝑄 = 𝐻𝑠𝑝 − 𝐻𝑓𝑙 − 𝛥𝑚 𝜂𝛥𝐻𝑐 ;

⇒ 𝛥𝑡 =𝛥𝑄

𝑄𝑒′′𝑃𝑜𝐿/2

𝑄𝑒,𝑐𝑟𝑡′′ = 𝑄𝑙𝑜𝑠𝑠

′′ +𝑃𝑜𝐿

𝑇𝑖𝑔 − 𝑇𝑎 ℎ𝜆𝑐𝑑𝑜

(Additional heat time)

Heating length ↗

August 21, 2014 18

Ignition and Spread at Reduced Pressures

18

𝑷𝒂 = 𝟒𝟎 kPa

Cu-B wire: 𝐼 = 11 𝐴, heating time = 9.0 sec,

coil heater (2 cm)

𝑷𝒂 = 𝟐𝟎 kPa

Cu-B wire: 𝐼 = 11 𝐴, heating time = 10.0 sec,

coil heater (2 cm), no steady-state spread


Blue, weak, and spherical flame during ignition

Flame spread faster as pressure decreases

August 21, 2014 19

Pressure Effect

19

Modeling results at flashpiont

Experimental results

o Simulation results show that reducing the ambient pressure reduces the convective cooling (ℎ𝑐), resulting in a short heating time at flashpoint.

o Dash line indicates the limiting condition of no gravity.

o In general, pressure effect should be small.

In low-pressure experiments, the heating time at flashpoint increases with decreasing pressure because the convective heating (from both coil and flame) decreases remarkably.

The same reason for a longer the heating time at spread point.

Thus, when consider the ignition difficulty in low pressures, how the pressure affects the heating source should not be neglected.


August 21, 2014 20

Oxygen-Concentration Effect

20

Heating time decreases as oxygen concentration increases (𝑋𝑂2 < 40%),

even under the low pressure environment, because a higher flaming temperature increases the heating efficiency (𝜂).

𝑋𝑂2 > 40%, spread point always

converges to the flashpoint, indicating a different mechanism to control the spread point.

Ignition model failsIgnition model works


August 21, 2014 21

Ignition Delay at High Oxygen Concentrations

21

Cu-B wire

o do = 0.8 mm, dc = 0.5 mm, 𝛿 = 0.15 mm,

o 𝑿𝑶𝟐 = 𝟔𝟎%, 1 atm

o coil heater (2 cm), 𝐼 = 11 𝐴

Heating time = 4.1 sec

Flashpoint = 10.4 sec (~ 6 sec delay)


[4] O. Fujita et al., Proc. Combust. Inst., 33 (2011), pp. 2617–2623

Ignition delay is observed that ignition occurs several seconds after the end of heating, which is also observed in the overloading ignition (microgravity) experiments [4].

In high oxygen concentrations, this heat-transfer based ignition model is no longer appropriate.

Both mixing and chemical kinetics in gas phase should be considered.

August 21, 2014 22

Outline

• Motivation






August 21, 2014 23

Conclusions

23

• A simplified ignition-to-spread model for thin electrical wires is developed, which qualitatively agrees with experimental results.

• For a higher-conductance wire, a longer heating duration is required to achieve both flashpoint and spread point, and the weak flame is easier to be quenched during the transition.

• Ignition becomes difficult in reduced pressures because the heating source becomes weak.

• In high oxygen concentration, flashpoint converges to the spread point and ignition delay occurs, which cannot be included in this heat-transfer based ignition model.


August 21, 2014 24

Future Work

24

Future work can be focused on

1) looking for the critical/minimum coating thickness for ignition/flame-spread;

2) Quantify the effective conductivity (𝑘𝑒𝑓𝑓) of wire by

including the conductance of wire core to calculate both ignition time and spread-rate by classical theories;

3) For some coating materials, a different transition to smoldering ignition;

4) evaluating the applicability of the theory to other more widely used wires.


August 21, 2014 25

Acknowledgements

25

Hokkaido University for offering this internship opportunity

Gao Jian, Junya Iwakami and Yangkyun Kim (Hokkaido Univ.) for their help to my experiments

Prof. Michael Gollner (Maryland), Prof. Kal Seshadri, and Ulrich Nieman (UCSD) for valuable discussions

Financial support for this research provided by JSPS (Grants-in-aid for Young Scientists: #21681022) and the Japan Nuclear Energy Safety Organization (JNES).


August 21, 2014 26

QUESTIONS?

Thanks for your attention!

Presented by Xinyan Huang

University of California, San Diego

Documents

Ignition-to-Spread Transition of Electrical Wire fires