Flame spread over horizontal and vertical wires: The role of dripping and core

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Flame spread over horizontal and vertical wires: The role of dripping and core ⁎

Yoshinari Kobayashia, Xinyan Huangb, , Shinji Nakayaa, Mitsuhiro Tsuea, Carlos FernandezPellob a b

Department of Aeronautics and Astronautics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA

A R T I C L E I N F O

A BS T RAC T

Keywords: Polyethylene (PE) Dripping fraction Burning rate Core temperature profile

Dripping of polymer insulations in wire fire has a potential risk of igniting nearby objects and expanding the size of fire, but has not been well studied so far. In this experimental study, dripping behaviors during the flame spread over horizontal and vertical polyethylene (PE) insulated wires were investigated without external airflow. Two different wire dimensions – core/wire diameter of 3.5/8.0 and 5.5/9.0 mm – and three different PE insulations were tested. To identify effects of the core, wires with solid copper (Cu) core, hollow stainless steel (SS) core, and without core were tested, and both core and insulation temperatures were also measured during the flame spread. Experimental results showed that the high-conductance copper core acted as a heat source downstream to increase the flame-spread rate. However, in the upstream burning zone, the copper core also acted as a heat sink to cool the molten insulation and reduce its mobility. Thus, the copper core extended the residence time of molten insulation inside the flame to facilitate the burning while reducing the dripping. Moreover, for the downward flame spread, the heating by the dripping flow of hot molten insulation dominated over the heating by the core. The downward dripping flow is driven by gravity while limited by the viscous and surface tension forces. Therefore, the limited dripping flow along the cooler copper core reduced the downward flame spread. The trend of results was also found to be insensitive to the type of PE insulation. This is the first time that within a single flame, the simultaneous dual effect of the heat source and heat sink for the wire core was observed, and the influence of dripping on the flame spread over the wire was discovered.

1. Introduction Electrical wires with flammable polymer insulation and metal core are responsible for many fire accidents in residential and commercial buildings, nuclear power plants, and space exploration missions. Because of poor contact, short circuiting, external heating, and ground fault, electrical wires and harnesses are easy to ignite. Between 2009 and 2011, the residential electrical fires in the US alone caused 280 deaths, 1125 injuries, and $1.1 billion in property losses, 53% of which involved electrical wires [1]. In nuclear power plants, electrical wires are a major source of fire ignition. In nearly 42% of total fire cases, the wire insulation was the main combustible component [2]. In recent years, space exploration activities have reached new heights, including the growing worldwide collaborations in the International Space Station (ISS), new human spaceflight projects in multiple developing countries, and space transport businesses by private companies like SpaceX, Blue Origin, Virgin Galactic, etc. In

⁎

2015, NASA published its official plans for human exploration and colonization of Mars [3]. Since the Apollo 1 fire claimed lives of three astronauts in 1967, fire in the isolated habitat such as spacecraft cabin has been identified as one of the largest risk factors causing tragic accidents [4,5]. In particular, electrical wires and harnesses have been identified as a potential source of fire in spacecraft [6–8]. The fundamental fire phenomena for thin wires (diameter of ~1 mm) have been studied by several groups in the last two decades, and they mainly focused on the role of wire core (heat sink or source) in the ignition or flame spread over the wire. For example, Leung et al. [9] modeled the influence of core under the external heating and nonflaming pyrolysis. Fujita et al. [10–12] conducted a series of studies on the influence of wire initial temperature, core diameter, oxygen concentration, external flow, pressure, and dilution gas on wire combustion. Umemura et al. [13] proposed a numerical model for flame spread over the wire and found that the copper core acted as a heat sink near extinction. Such heat sink was also observed in the

Corresponding author. E-mail address: [email protected] (X. Huang).

http://dx.doi.org/10.1016/j.firesaf.2017.03.047 Received 25 January 2017; Received in revised form 16 March 2017; Accepted 22 March 2017 0379-7112/ © 2017 Elsevier Ltd. All rights reserved.

Please cite this article as: Kobayashi, Y., Fire Safety Journal (2017), http://dx.doi.org/10.1016/j.firesaf.2017.03.047

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Nomenclature

Greeks

Symbols

α γ δ ρ λ μ

A c d f g ΔH lm m ṁ Mdr N q̇" S t T V Y

cross-section area (mm2) specific heat (kJ/kg/K) diameter (mm) frequency (Hz) gravity acceleration (m/s2) heat of reaction (MJ/kg) length of the molten layer (m) mass (g) mass-loss rate (mg/s) mass of one drip (mg) number (-) heat flux (kW/m2) flame-spread rate (mm/s) time (s) temperature (°C ) speed (m/s) mass fraction (%)

angle (degree) surface tension (Pa) length (mm) density (kg/m3) thermal conductivity (W/m/K) dynamic viscosity (Pa -s)

subscripts b c dr f h g m o p t v

burning core dripping flame horizontal gas melting outer pyrolysis/plastic total vertical

2. Experimental setup

experiments of Miyamoto et al. [14]. Nakamura et al. [15,16] revealed that the flame-spread rate over polyethylene (PE) insulated wires increased with decreasing pressure and increasing core conductance (both the size and thermal conductivity). Huang et al. [17] found that wire core acted as a heat sink during the ignition and its transition to flame spread. Bakhman et al. [18,19] first studied the flame spread over thin wires with both horizontal and vertical orientations. Hu et al. [20] further studied the effect of wire inclination on the flame spread. However, in the literature there were very few temperature measurements for the wire core and insulation or the quantification of the heat sink or heat effect of the core, especially for the larger wire (diameter of ~1 cm). Moreover, the melting and dripping phenomena of wire insulation are potential fire risks since they can ignite other objects and expand fire. Only a few studies have addressed their fire hazards. Moreover, the dripping phenomenon only occurs under gravity [21], so it is expected not to affect microgravity wire combustion. Williams [22] suggested the melting and dripping flow of burning fuel might control the downward flame spread. Cahill [23] tested the dripping behaviors of several commercial electrical wires for the aircraft safety application. NASA previously designed an empirical test (Test 4 of NASA-STD-6001B) to evaluate the fire hazard of dripping: if the dripped flaming debris does not ignite a piece of K-10 paper placed 20 cm below the sample, the insulation material is judged to be “safe” [24]. Miyamoto et al. [14] found that the easier dripping of molten PE insulation reduced the wire flammability near the limiting oxygen concentration (LOC). He et al. [25] showed that the melting and dripping of wire insulation increased with the overload current. Lim et al. [26] observed that the excessive dripping of molten PE insulation under high AC frequency in wires led to flame extinction. Kim et al. [27–29] simulated the melting and dripping of polymer subjected to external heating using the methods of the volume of fluid and enthalpy-porosity and studied the influence of material properties. However, the influence of core on dripping and the effect of dripping on flame spread have not been studied. In this work, temperatures of core and insulation were measured in the opposed flame spread over both horizontal and vertical oriented wires. Then, the dripping behaviors of molten insulation in the wire fire were investigated experimentally for different wire configurations and orientations. The discussion focuses on the effect of dripping and core.

The tested wires were specially made for the research purpose and could be manually assembled by mating a plastic tube and a metal core. Fig. 1(a) shows the tested wire samples with different dimensions: (I) dc/do =3.5/8.0 and (II) 5.5/9.0 mm (the same samples used in [14]), and Table 1 lists their configurations. Note that these wires were almost 10 times thicker than those tested in [10–12,15,17–19,25,26]. Also, three core conditions were used to investigate the core effect: (i) a solid copper (Cu) core, (ii) a low-conductance stainless steel (SS) hollow core, and (iii) a 1 mm steel hollow bar which only held the position of insulation tube and simulated the no-core case. The test wires were 100 mm long and had three different PE insulations: (1) the semitransparent low-density polyethylene (LDPE), (2) the white opaque high-density polyethylene (HDPE), and (3) black LDPE (B-LDPE). The physicochemical properties of PE insulations and cores are shown in Table 2. The B-LDPE was produced by doping 5wt% black carbon particles into the pure LDPE, and had a higher melt viscosity [30]. Thermally, LDPE had lower temperature and heat of both melting (Tm and ΔHm ) and pyrolysis (Tp and ΔHp ), and a smaller thermal inertia (ρλc [31]) than HDPE. Without external radiation, their flammability ranked as LDPE > B-LDPE ≥ HDPE [14]. Fig. 1(b–d) illustrated the experimental apparatus, including the wire, scale, sample holder, and the configuration of wire and thermocouple. The entire apparatus was placed inside laboratory without external airflow. The wire was fixed by an aluminum sample holder with the same diameter, and the insulation was extended out of the core by 10 mm as the ignition zone. For each test, a regular lighter was used to heat the ignition zone for 10 s to start a uniform ignition. To measure the temperature of Cu core and SS tube wall, three 1-mm holes were drilled in each core, and the hole was used to tightly accommodate the bead (about 0.5 mm diameter) of the K-type thermocouple (TC). The surface temperature of PE insulation at the same position was also measured by the same type of TC, as shown in Fig. 1(b). The TC bead was embedded half in the insulation and half in the air using a soldering rod. The total mass-loss rate (ṁ t ) of wire is equal to the melting rate of insulation (ṁ m ), which is the sum of burning rate (ṁ b ) and dripping rate (m˙ dr ) as

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Fig. 1. (a) Photo of tested wires with different PE insulations and core materials; schematic diagrams of experimental apparatus: (b) configurations of wire sample and thermocouples, (c) flame spread over horizontal wire, and (d) downward flame spread over vertical wire.

m˙ t = m ˙m = m ˙b + m ˙ dr

(1)

were only conducted for PMMA insulated wires [18] and the metal core of PE-insulated wires [15], but at thinner diameters (~1 mm). Because of the large thermal conductivity of Cu and a small Biot number, a uniform temperature distribution is expected in the cross-section of the Cu core. The temperature measurement of the SS tube wall should be the more local, like that of insulation. Nevertheless, the relative position of temperature profiles between core and insulation were consistent in three TC locations and repeating tests. For the PE insulation temperature, a rapid temperature increase was observed when the flame was reaching the thermocouple because of the TC detachment from the molten insulation. During this detaching process, TC might get in contact with the hot flame shortly, which was denoted as a sharp peak before cooling down by air. Comparatively, the temperature of core varied more smoothly. The temperature variations for HDPE and B-LDPE wires (not shown here) were found to be similar to LDPE wires. For the core temperature (solid line), initially, it was slightly higher than that of insulation (dashed line) at the same position, indicating a heat source effect. Before the arrival of flame (i.e. in the preheat zone), the heating by core controlled the flame spread, and its effective heating length (δc ) should be larger than that in the gas phases (δg ), as illustrated in Fig. 4(b-c). Such a higher core temperature (Tc > TPE ) was particularly clear for the high-conductance solid Cu cores in both horizontal and vertical spread. This temperature measurement is a direct proof for the heat source effect of the solid metal core. Interestingly, although this initial heating process lasted for several minutes, the heat source only occurred when TPE was below 150 °C or the melting point of PE (Tm ).

For the horizontal wire, ṁ t was monitored by a scale (precision up to 0.1 mg). At the same time, the dripped molten insulation was caught by a steel plate beneath (see Fig. 1(c)), and its mass increment due to dripping was measured with another scale to acquire m˙ dr . For the vertical wire, it was difficult to measure the transient ṁ t and m˙ dr because the molten insulation first flowed downward in the form of droplets (like the candle drips, see Fig. 2) along the wire before the detachment. Instead, by catching all dripping insulation with the steel plate, ṁ b was measured with a scale, as illustrated in Fig. 1(d). The mass of wire was also measured before and after the test to obtain the total mass loss ( Δmt ). During the flame spread, the position and behavior of flame were recorded by a digital video camera (Canon PC1742, 24 fps). Once the flame reached the end of insulation, nitrogen was used to quickly extinguish the flame. To synchronize all measurements, the video camera, scales, and TCs were started at the same time. For each condition, 3–6 tests were repeated to quantify the random uncertainty. 3. Results and discussion Fig. 2 shows a group of snapshots of flame-spread and dripping behaviors in the 8-mm horizontal and vertical LDPE wires without core and with the Cu core. Once heated, the PE insulation first melt and became a transparent liquid. For the no-core wire, a blue flame was observed surrounding the melting insulation, above which was a yellow luminous flame. Specifically, for the vertical Cu core, mainly a blue flame was observed. The blue flame could indicate a fuel-lean condition, caused either by the large oxygen supply due to the strong convection or by the small fuel supply attributed to the weak pyrolysis (burning). For both horizontal and vertical wires, a frequent dripping of molten PE insulation was observed. For the vertical wire, the dripping flow may re-solidify beneath the flame because of environmental cooling. Such re-solidification process could be clearly observed as the transparent liquid PE changed back to the white solid.

Table 1 Configurations of PE insulation tubes (125 mm long) and cores (100 mm long) [14]. Type

dc (mm)

do (mm)

δp (mm)

Ac / Ao

I

3.5

8.0

2.25

19% (Cu) 4% (SS) < 1% (no core)

II

5.5

9.0

1.75

37% (Cu) 5% (SS) < 1% (no core)

3.1. Temperature profile of core and insulation Fig. 3 shows an example of measured temperature profiles of core and insulation for the LDPE wire. Similar temperature measurements 3

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3.2. Dripping of molten insulation

Table 2 Physicochemical properties of (solid) PE insulations and cores where thermal properties are evaluated near the room temperature, and ΔH > 0 represents endothermic [14].

ρ [32] (kg/ m3)

λ [32] (W/ m/K)

c [32] (kJ/kg/ K)

Tm [33] (°C )

ΔHm [33] (MJ/ kg)

Tp [33] (°C )

LDPE B-LDPE HDPE

927a 929a 944a

0.23b 0.24b 0.32b

1.55

0.50

387

1.8

0.81

404

2.3

Cu [34] SS [34] Air [34]

8954 8000 1.18

398 13.8 0.026

0.400 0.384 1.07

105– 110 130– 135 – – –

– – –

– – –

– – –

a b

2.00

Fig. 4(a) shows a detailed dripping process for a horizontal flame spread over an 8 mm LDPE insulated wire within 300 ms. At the flame leading edge, the insulation first melted, and then accumulated in the burning zone. This molten ball hung below the core and pyrolyzed (boiling or burning) due to the heating from both flame and core. As the size and width of molten layer increased, the flame size also increased to enhance the heating to the molten ball and the core. If the burning rate is equal to the melting rate (m˙ b = m˙ m ), the molten insulation is completely burnt, and there is no dripping. If the burning rate is smaller than the melting rate (m˙ b < m˙ m ), the size of molten layer continues to increase. When the molten ball grows big enough to counteract the surface tension and viscous forces, it drips off and is mostly surrounded by a flame which is initially merged to the flame in wire. The flow and dripping of molten insulation are complex processes, probably controlled by the surface tension, viscosity, gravity and burning rate. The flow of molten insulation involves natural and Marangoni convection, which is driven by the density and surface tension gradient. It can be seen in Fig. 4(a) that the flow of molten insulation can be indicated by the motion of black soot agglomeration and sometimes vapor bubbles. To better describe dripping phenomenon, we introduce several parameters in the following analysis, i.e. the dripping rate (m˙ dr ), dripping fraction (Ydr ), dripping frequency ( fdr ) and mass of one drip (Mdr ). First, we define the dripping fraction (Ydr ) as the ratio of dripping rate to the total mass-loss rate as

ΔHp [33] (MJ/kg)

Measured in experiment ( ± 2 kg/m3). Measured by 1-D reference bar method ( ± 5%) at 50 °C [17].

As the flame approached the preheat zone, the temperature of insulation quickly exceeded that of the core because of the direct heating from the flame leading edge. Unlike the TCs for insulation which eventually got detached, the TCs inside the core could continuously monitor the core temperature in the burning zone. For the Cu core in the 8-mm wire, it took several minutes to reach the pyrolysis temperature of PE (Tp ). For the Cu core in the 9-mm wire, it might never reach Tp . Comparatively, the temperature increase of SS tube core was much faster. After all insulation around core was burned out, the core temperature eventually reached a peak value in the flame tail. Moreover, after extinction, a very thin layer of PE was left around the Cu core, i.e. not complete burnout. The pyrolysis temperature is the minimum temperature to initiate a strong pyrolysis and sustain a burning flame. In other words, in the burning zone, Cu core mainly acted as a heat sink to cool the insulation. Such simultaneous dual effect of the heat source and heat sink for wire core was observed for the first time, and was expected to influence the dripping and flame spread behaviors.

Ydr =

m˙ dr (t ) × 100% = 1 − Yb m˙ t (t )

(2a)

where Yb is the burning fraction. For the horizontal flame spread, the mass-loss rate (ṁ t ) and dripping rate (ṁ dr ) were acquired from two scales, as illustrated in Fig. 1(c). During the entire flame spread process, we found that the transient value of Ydr , h was very close to

Fig. 2. Opposed flame spread over an 8 mm LDPE insulated wires: (a) horizontal no-core wire, (b) horizontal Cu-core wire, (c) vertical no-core wire, and (d) vertical Cu-core wire. Resolidification is shown when the color of drips changes from transparent back to its original white.

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Fig. 3. Temperature profiles of the core (Tc) and insulation (TPE) for (a) horizontal and (b) vertical downward flame spread over LDPE insulated wires for three thermocouple locations.

define the wire cross-section thermal conductance as

the time-average value as

Ydr , h

m˙ (t ) ∆mdr = dr × 100 % ≈ × 100 % m˙ t (t ) ∆m t

∑ Ai λi

(2b)

∆mdr ∆mt − ∆mb × 100 % = × 100 % ∆m t ∆m t

(2c)

The dripping frequency is defined as the number of detached drips per unit time

fdr =

Ndr ∆t

(3)

which can be only counted for horizontal wires. Then, the average mass of a single drip (Mdr ) can be calculated as

Mdr =

∆mdr m˙ = dr Ndr fdr

(5)

Fig. 5 shows the measured dripping fraction (Ydr ) as a function of ∑ Ai λi for LDPE insulated wires,1 and that for HDPE and B-LDPE wires are shown Fig. A1. Clearly, for both horizontal and vertical wires and all PE insulations, Ydr decreased with the wire thermal conductance. For example, in the 8-mm horizontal LDPE wire, only 40% of insulation was dripped with Cu core, while 75% was dripped without a core. In other words, the burning fraction (Yb = 1 − Ydr ) significantly increased. If the secondary burning and ignition by dripping were neglected, the Cu core increased 35% (=75−40%) of total burning mass or heat release, that is, a significant increase in a fire hazard. Fig. 5 also shows that Ydr of the vertical wire was larger than that of the horizontal wire. It is probably because the vertical wire was in parallel to the gravitation, and acted as a duct to facilitate the dripping flow. As discussed above, the low-temperature profile of Cu core suggested that it acts as a heat sink in the burning zone to cool the molten insulation inside the flame. Such cooling effect reduced the mobility of molten insulation since the liquid viscosity increased with a decrease in

Therefore, the averaged dripping fraction is used throughout the following discussion. For the vertical downward flame spread, the total mass loss due to burning (∆mb ) was obtained from the scale so that we can calculate Ydr , v as

Ydr , v ≈

= Ap λp + Ac λc

(4)

Both fdr and Mdr were easy to measure for horizontal wires from the video, but not possible for vertical wires because the molten insulation dripped along the wire as seen in Fig. 2(c) and (d). Also, to better investigate the influence of core conductivity and configuration, we

1 The dripping fraction for the no-core vertical wire could not be determined accurately in experiments because part of molten insulation was found to drip inside the insulation tube.

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Fig. 4. (a) Flow and dripping of molten LDPE insulation in the horizontal flame spread, and the corresponding illustrations of (b) the horizontal and (c) vertical wires, where the blue arrows show core’s cooling effect in the burning zone and red arrows shows its heating effect in the preheat zone (dual effect).

Fig. 5. Dripping fraction (Ydr ) as a function of the wire cross-section thermal conductance (∑ Ai λi ) in the flame spread over (a) 8 mm and (b) 9 mm LDPE wires.

ignition capability of dripping should increase with both fdr and Mdr , which is beyond the scope of the current study. As the thermal conductance increased, fdr decreased from about 5 Hz to 1 Hz. On the other hand, Mdr increased with the thermal conductance from about 2 mg to 5 mg. In other words, if assuming the spherical shape for a molten insulation drip, its equivalent diameter increased from 1.6 mm to 2.2 mm. One condition necessary for dripping to occur is that the volumetric gravity force overcomes the surface-tension and viscous forces:

temperature. The large viscosity is also indicated by the difference in the shape of hanging molten insulation around the Cu core, as compared to Fig. 2(a) and (b): below the core, the hanging height of molten ball (lm ) was smaller and the surface was flatter (larger α , see Fig. 4(b)). Therefore, the heat sink effect of Cu core enforced a longer residence time for the molten insulation in the flame, thus, increasing its chance to burn (or pyrolyze) while its chance to drip was reduced. For the same reason, Ydr for LDPE was found to be most sensitive to the core cooling effect because the molten LDPE has the lowest viscosity among three different PE insulations. Fig. 6 shows the average dripping frequency ( fdr ) and the average mass of one drip (Mdr ) as a function of ∑ Ai λi in the horizontal flame spread over the LDPE wire (see HDPE and B-LDPE wires in Fig. A2). In general, the

Mdr g > σm lm + μm lm Vdr

(6)

where lm ~ (Mdr / ρM )1/3 is the characteristic size of the drip; σm is the surface tension; and Vdr is the dripping flow speed (see Fig. 4(b-c)). In the horizontal spread, the surface tension is the largest resistance to 6

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Fig. 6. Dripping frequency ( fdr ) and mass of one drip (Mdr ) as a function of the wire cross-section thermal conductance (∑ Ai λi ) in the horizontal flame spread over (a) 8-mm. and (b) 9mm LDPE wires.

average flame-spread rate in 3–6 repeating tests was found to be very consistent. Such fluctuation was a result of the pulsating/flickering flame, which was observed at the flame leading edge in each test. Note that PE is a low-viscosity polymer and has a large temperature gap between melting and pyrolysis point (Tp − Tm ≈ 270 °C ). Therefore, the flame spread over PE insulation should adopt some certain nature of flame spread across the liquid, e.g. the pulsating flame and the surface-tension-driven flow. Fundamentally, this pulsating flame was a premixed flame (or flash) which periodically occurs between the flashpoint and the fire point [36,37]. Previously, a different zigzag (go-and-stop) motion was observed in the thin wire, but it was more likely governed by the dripping dynamics (e.g. sliding over the surface) and solidification timing [38]. Fig. 8 shows the average flame-spread rate over wires as a function of ∑ Ai λi for LDPE wire (see Fig. A3 for HDPE and B-LDPE wires). Firstly, the vertical flame spread was found to be faster than the horizontal flame spread (Sv > Sh ). Also, the horizontal flame spread increased with the wire conductance

dripping, while in the vertical downward spread, viscous force may become more important. Both surface-tension and viscous forces (i.e. σm and μm ) decrease with increasing temperature [35], and their contributions are expected to change if the wire is inclined. Eq. (6) suggests that a larger Mdr is needed under the larger surface tension and viscosity (or a cooler molten insulation). Because Cu core cools in the burning zone (also see Fig. 3), σm and μm for molten PE surrounding the Cu core should be larger. Therefore, the observed larger Mdr for the Cu wire also supported the heat sink effect of the high-conductance core in the burning zone.

3.3. Opposed flame-spread rate The duration of flame spread was defined from the moment of flame reaching the core to the moment of flame reaching the end of insulation. The transient flame-spread rates were calculated by tracking the leading edge of the flame using a MATLAB image processing code. Fig. 7 shows an example of measured transient and average flamespread rate in the LDPE insulated wires. Despite the zigzag motion, the

Sh (no core) < Sh (SS tube) < Sh (Cu core)

Fig. 7. Transient and average flame-spread rate for the horizontal and vertical LDPE insulated wires.

7

(7a)

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Fig. 8. Flame-spread rate over LDPE wires as a function of the cross-section thermal conductance (∑ Ai λi ).

its heating controlled the vertical downward flame spread over the wire, as suggested in the review of [22]. Note that the flame spread behaviors over the tested wires have a strong size and transient effect, so caution is required if extending current conclusions to other wires of a larger length and different material.

On the contrary, the vertical downward flame spread decreased with the wire conductance

Sv (no core) > Sv (SS tube) > Sv (Cu core)

(7b)

As confirmed by the thermocouple measurement in Fig. 3, no matter in the horizontal or vertical flame spread, the metal core acted as a heat source to preheat the insulation downstream and accelerate the flame spread. In other words, the effective heating length of core in the solid phase should be larger than that of flame in the gas phase,

δc (core) > δg (flame)

4. Conclusion In this work, the dripping behaviors during the opposed flame spread over horizontal and vertical PE insulated wires were investigated experimentally. Two different wire dimensions (dc / do = 3.5/8.0 and 5.5/ 9.0 mm), three insulations (LDPE, HDPE, and B-LDPE), and three core conditions (Cu, SS, and no-core) were tested. Experimental results showed that the Cu core acted as a heat source downstream to increase the flamespread rate. Thus, for the horizontal wire, the flame-spread rate increased with wire thermal conductance. However, in the upstream burning zone, the Cu core acted as a heat sink to cool and limit the motion of the molten insulation. The cooling from the Cu core extended the insulation’s residence time in flame to facilitate the burning while reducing the dripping. Therefore, the smaller dripping fraction and frequency, as well as a larger mass of drip, were found for the Cu wire. Moreover, in the vertical downward flame spread, the dripping flow of molten insulation preheats the wire downstream and increases the flamespread rate. Such heating of dripping flow dominated over the heating from the core. Therefore, the vertical downward flame-spread rate was faster than that in the horizontal flame spread, and it increased with increasing dripping flow and decreased with increasing wire thermal conductance. This is the first time that the simultaneous dual effect of the heat source and heat sink for wire core was observed, and the influence of dripping on the flame spread over the wire was discovered.

(8a)

Therefore, the flame-spread rate should increase with wire thermal conductance. However, only the horizontal flame-spread rate (Sh ) satisfied this trend. For the downward flame spread, a close look at Fig. 2(c) and (d) revealed that the dripping of hot molten insulation from the burning zone to the preheat zone acted as an extra heat source. This heating process due to dripping is illustrated in Fig. 4(c). Naturally, the heating of dripping flow should increase with the dripping rate (m˙ dr ) and the dripping fraction (Ydr ). Recall that in Fig. 5 both m˙ dr and Ydr decrease with increasing core conductance because of the cooling (heat sink effect) of the core in the burning zone. Therefore, the heating of dripping flow decreases with the core conductance. If the effective heating length of dripping (δdr ) is larger than that of core (δc ) as

δdr (dripping) > δc (core) > δg (flame)

(8b)

the heating of dripping flow dominates over the core heating and controls the vertical downward flame spread. Therefore, we may express the observed vertical downward spread rate as

Sv = Sm + Sdr

(9)

Acknowledgements

where Sm is the fuel regression rate due to the melting, and Sdr , v is the speed of the dripping flow. On the other hand, we have Sh = Sm for the horizontal flame spread. As results, two phenomena should be expected: (1) the downward flame spread should be faster than the horizontal spread controlled by the core heating, i.e. Sv > Sh , and (2) the flame-spread rate should decrease with the core thermal conductance. Both phenomena were observed in Fig. 8, so it was highly possible that the dripping flow and

This study was supported by NASA Grant NNX14AF01G and JAXA as a candidate experiment for the third stage use of JEM/ISS titled “Evaluation of gravity impact on combustion phenomenon of solid material towards higher fire safety” (called as “FLARE”). The authors would like to thank Yusuke Konno (Hokkaido Univ.) and Andy Rodriguez (UC Berkeley) for their assistance in experiments.

Appendix A In experiment, there are slight difference in measured quantities among different PE insulations (LDPE, HDPE, and B-LDPE). However, the trend of flame spread and dripping behavior is very similar. 8

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Fig. A1 shows the measured dripping fraction (Ydr ) as a function of ∑ Ai λi for the HDPE and B-LDPE insulated wires. Compared to LDPE in Fig. 5, their trends are essentially the same. Similar observation can be found by comparing between Fig. 6 and A2 for the average dripping frequency ( fdr ) and the average mass of one drip (Mdr ), and between Fig. 8 and A3 for the flame-spread rate.(See Figs. A2 and A3).

Fig. A1. Dripping fraction (Ydr ) as a function of the wire cross-section thermal conductance (∑ Ai λi ) in the flame spread over (a) 8 mm and (b) 9 mm HDPE and B-LDPE wires.

Fig. A2. Dripping frequency ( fdr ) and mass of one drip (Mdr ) as a function of the wire cross-section thermal conductance (∑ Ai λi ) in the horizontal flame spread over (a) 8-mm and (b) 9-mm HDPE and B-LDPE wires.

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Fig. A3. Flame-spread rate over HDPE and B-LDPE insulated wires as a function of the cross-section thermal conductance (∑ Ai λi ).

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