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Proceedings of the Combustion Institute xxx (2012) xxx–xxx

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of the

CombustionInstitute

Effects of low air pressure on radiation-controlledrectangular ethanol and n-heptane pool fires

Ran Tu, Jun Fang ⇑, Yong-ming Zhang, Jun Zhang, Yi Zeng

State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230026, PR China

Abstract

Experiments on rectangular ethanol and n-heptane pool fires were conducted at different altitudes inHefei (99.8 kPa) and Lhasa (66.5 kPa). The burners tested had the same fuel area of 900 cm2, but withaspect ratio of long side to short side (n = l/w) varied from 1 and 8. The individual and combined influencesof low pressure and aspect ratio on burning rate, temperature, puffing frequency, flame height and radia-tion for the two fuels were interpreted and formulated. First, burning rate was found to be proportional toambient air pressure under radiation control, the main reason is that radiative heat flux decreased withpressure due to the pressure affecting the soot absorption coefficient. Flame temperature slightly increased,leading to higher flame puffing frequency at low pressure. Flame height was almost insensitive to pressureas H / p0. Second, for aspect ratio n, flame temperature was constant and independent of fuel type andburner shape. With increasing n, burner wall temperature increased at the long side, and decreased dras-tically at the short side, especially n = 8. This was attributed to the change of flame tilt and heating of theburner side, caused by variation of entrainment motion. Flame puffing frequency was found to increasewith n as a function of f �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðDT=T1Þðnþ 1Þ=2

ffiffiffinpp

. The flame was observed to split into small clustersby enhanced asymmetric entrainment, and H decreased with increasing n as H � ð1=

ffiffiffinpÞ2=5 _Q4=15. Consid-

ering fuel differences, with increasing n, the burning rate of the ethanol pool fire decreased, and n-heptaneshowed the opposite trend.� 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Low pressure; Aspect ratio; Burning rate; Flame characteristics; Radiation controlled

1. Introduction

Low air pressure has been shown to affect poolfire burning behavior by experimental studies [1–6], from which empirical correlations have beenobtained. The burning rate was found to be_m00 � pa, where a � 1.3 in Wieser et al. [1]. Similarresults were reported by Fang et al. [2] and Liet al. [4], but a larger a was suggested in Hu

1540-7489/$ - see front matter � 2012 The Combustion Instithttp://dx.doi.org/10.1016/j.proci.2012.06.036

⇑ Corresponding author. Fax: +86 551 3606430.E-mail address: [email protected] (J. Fang).

Please cite this article in press as: R. Tu et al., Proc.j.proci.2012.06.036

et al. [5]. In 2011, Fang et al. [6] used more burn-ers with side sizes from 4 to 33 cm, a was found tovary in three ranges, �0.4 to 1, 1–1.45, 1 by con-duction, convection and radiation heat feedback-control, respectively. With the same square burnerat low air pressure, flame temperature and puffingfrequency showed little increase.

Theoretical modeling of air pressure influenceson fires has mainly focused on confined laminar orjet fires at elevated pressures [7–9]. However, lam-inar flame theory cannot fully explain turbulentfire dynamic mechanisms. The principal workfor turbulent pool fires has been the pressure

ute. Published by Elsevier Inc. All rights reserved.

Combust. Inst. (2012), http://dx.doi.org/10.1016/

http://dx.doi.org/10.1016/j.proci.2012.06.036

mailto:[email protected]




Nomenclature

_m00 mass burning rate per unit area (g/m2 s)

_q00 heat flux (kW/m2)_Q heat release rate or HRR (kW)q density (kg/m3)D equivalent burner diameter length (m)l long side length of rectangular burner

(m)w width or short side length of rectangu-

lar burner (m)S area (m2)p pressure (kPa)DHc heat of combustion (kJ/g)

DHg heat of gasification (kJ/g)H flame height (m)Uf 0 vapor velocity at source (m/s)f flame puffing frequency (Hz)g acceleration of gravity (m/s2)cp specific heat capacity for constant

pressurer Stephan–Boltzmann constant

Subscriptsf flame1 ambients fuel surface

Radiant heat flux sensor

T1 T21.5 mBurner

2 R. Tu et al. / Proceedings of the Combustion Institute xxx (2012) xxx–xxx

modeling and radiation fire modeling of De Riset al. [10,11], based on scale principles. Thesemodels provide an important experimental guide,but cannot be directly applied for comparison ofsame-scale pool fires in two different pressureenvironments.

Compared with idealized circular or square poolfires, rectangular or line fires are more common infire engineering [12–14]. Because of the irregularshapes, burning behavior shows obvious asymmetryrelative to axisymmetric pool fires. Moreover, sootand radiation differences between experimental fuelswere ignored by some prior works. These differencesshould be considered in practical engineering.

In this paper, rectangular pool fires with aspectratio n = l/w varying from 1 to 8 were studiedunder 99.8 kPa (Hefei) and 66.5 kPa (Lhasa) pres-sures. Phenomenological models of low pressureand aspect ratio effects on burning rates, flameheight, puffing frequency and radiation wereestablished and validated by experimental results.Ethanol and n-heptane pool fires were chosen forgood repeatability and their different soot produc-tion abilities.

T3

R1

R2

1.5

m Top view

Front view of pool fire

High speed camera

Thermal infrared imager

T1 (T2)T30.8 cm

10 cm

30 cm

50 cm

70 cm

90 cm

110 cm

130 cm

ThermocoupleHeight above burner

Electric balance

Burner

T4

T5T6

T7T8

T9

T10

Heat insulation frame

Fig. 1. Sketch of experimental setup.

2. Experiments

The experimental setup is shown in Fig. 1. Fuelparameters [6,15] are listed in Table 1. Experi-ments were conducted in EN54 standard fire testrooms with dimensions 10 m long, 7 m wide and4 m high [16] at the two locations respectively.

Four rectangular burners with the same900 cm2 fuel area but different aspect ratios wereused: n = 1 (30 cm/30 cm); n = 2 (42.4 cm/21.2 cm); n = 4 (60 cm/15 cm); n = 8 (84.8 cm/10.6 cm). Burners were made of steel plate,2 mm thick with inner depth 4 cm. The height ofthe liquid fuel surface above the pan bottom ineach test was 1.4 cm (ethanol: 1000 g; n-heptane:860 g). The fire source was set on the center ofthe test room floor.


Electronic balance (Mettler Toledo, Excel-lence-Plus XP) was used to record mass loss withprecision 0.01 g. Temperatures were obtained byType K armored thermocouples with diameter0.5 mm, uncertainty within 0.75%, and responsetime less than 1 s [17]. In the figure, T1 and T3show temperatures at long and short exterior sidewalls, respectively, and T2 shows interior fueltemperature. Axial flame temperature was mea-sured by thermocouple array T4–T10. Two radi-ant heat flux sensors (Captec, TS-30) ofresolution 0.0015 kW/m2 were placed 5 cm abovethe burner surface and 1.5 m away from burnercenter at the long and short sides, respectively.A high-speed camera (Fastec, Trouble Shooter)with 250 frames per second was used to recordthe visible flame information. A thermal infraredimager (SAT, HY 6850) with temperature range�40 to 2000 �C and spectral range 8–14 lm wereused to capture flame thermal images, and IR




Table 1Properties of ethanol and n-heptane.

Fuelmaterial

Molecularformula

Density (g/cm3)

Boiling point (�C) Heat of combustion(kJ/g)

Soot yield (g/g)

Hefei Lhasa

Ethanol C2H6O 0.789 78.3 67.0 29.64 0.012n-Heptane C7H16 0.680 98.5 89.0 47.97 0.037

R. Tu et al. / Proceedings of the Combustion Institute xxx (2012) xxx–xxx 3

temperature was further calibrated by the data ofthermal couple. Any use of trade names is fordescriptive purposes only.

In contrast to air pressure, similar ambient tem-peratures and humidities were applied at the twolocations (Lhasa: 18 ± 2.0 �C, 50 ± 4%; Hefei:20 ± 2.0 �C, 55 ± 3%). Each test was repeated sev-eral times to ensure reproducible results withinpermitted error ranges.

0 1 2 3 4 5 6 7 8 90

5

10

15

20

25

30

35 (a)

Aspect ratio n

Burn

ing

rate

(g/m

2 s)

99.8 kPa-ethanol 66.5 kPa-ethanol 99.8 kPa-n-heptane 66.5 kPa-n-heptane

3. Results and analysis

3.1. Burning rate

The burning rates of pool fires in the steadyburning stage (from the linear fit shown inFig. 2) are shown in Fig. 3(a). Figure 3(b) shows_m00Lhasa= _m00Hefei vs. n at the two locations. For thesame burner and fuel, _m00Lhasa= _m00Hefei is approxi-mately equal to the ratio of air pressures, and isunaffected by aspect ratio n. A similar result wasreported by Fang et al. [6] for square pool fireswith diameter exceeding 20 cm. However, noquantitative theory has been given to explain thecorrelation. Here, based on radiation fire model-ing [10] and experimental correlation, a quantita-tive theoretical analysis is as follows.

The burning rate corresponds to three types ofheat feedback and is radiation-dominated whenD > 20 cm [18], i.e. _m00 � _q00rad=DH g. _q00rad is simpli-fied as [10]:

_q00rad ¼ rT 4f ½1� expð�jsLÞ� ð1Þ

0 200 400 600 8000.0

0.5

1.0

1.5 Derivation

Steady burning state

Time (s)

Burn

ing

rate

(g/s

) 0

400

800Fuel: ethanol

Case No. 3 in Hefei

Linear fit

Mas

s (g

)

Fig. 2. Experimental data of mass variation. Burningrate _m00 is determined by derivation of mass loss insteady burning state.


First, based on the hypothesis of radiation firemodeling that by holding D � p2 ¼ constant,js ð� p2 � D�1Þ is the soot absorption coefficientand ðL � DÞ beam length [10]. T f is flametemperature considered insensitive to fire scaleand ambient pressure, as confirmed in Section3.2. Since jsL remains invariant, _q000;rad ¼ _q00d;rad ,and thus _m000 ¼ _m00d , where subscript 0 denotes theprototype fire at 1 atm, and d is for the model fireunder decreased pressure.

Second, burner scale varies with pressure dueto D � p2 ¼ constant in radiation fire modeling.Therefore, to compare _m00 at different pressureswith the same scale burner, scale transformationis done subsequently.

0 1 2 3 4 5 6 7 8 90.0

0.2

0.4

0.6

0.8

1.0

/Lhasa Hefeim m′′ ′′/Lhasa Hefeim m′′ ′′

PLhasa/PHefei=0.67

(b)

Rat

io o

f bur

ning

rate

Aspect ratio n

Ethanol N-heptane

Fig. 3. Burning rates of pool fires (a), and ratio of_m00Lhasa= _m00Hefei (b), with various aspect ratios in Hefei(99.8 kPa) and Lhasa (66.5 kPa).




m constantD′′

=

Pan diameter 15 ~ 50 cm

Data by Blinov and Khudiakov [19]

Pan diameter (cm)

(a)

Data by Fang [6]

(b)

(m)

Fig. 4. Burning rate for liquid pools from Blinov andKhudiakov, _m00=

ffiffiffiffiDp� constant between diameter 15 and

50 cm (a), which is also validated by Fang’s study (b).

Table 2Correlations of parameters under different pressureconditions.

1atm

Transformed Pressuredecreased

Correlations

p0 p0 pd pd ¼ bp0D0 Dd Dd Dd ¼ D0=b

2

_m000 _m000t _m00d _m00d ¼ _m000 _m000t ¼ _m000=b ¼ _m00d=b

0 1 2 3 4 5 6 7 8 9800

900

1000

1100

1200

1300

(a)

Averaged flame temperature Ethanol N-heptane Tf-Lhasa=1111 K Tf-Lhasa=1104 K Tf-Hefei=1086 K Tf-Hefei=1091 KFl

ame

tem

pera

ture

Tf (

K)

Aspect ratio n

66.5 kPa-ethanol 66.5 kPa-n-heptane 99.8 kPa-ethanol 99.8 kPa-n-heptane

99.8 kPa: ethanol

66.5 kPa: ethanol

66.5 kPa: n-heptane

1:1

99.8 kPa: n-heptane

1:2 1:4 1:8

(b)

Fig. 5. Flame temperatures (a), and infrared images (b;unit: �C) in Hefei (99.8 kPa) and Lhasa (66.5 kPa) withvarious aspect ratios.


From the results of Blinov et al. [19] under nor-mal pressure, _m00=

ffiffiffiffiDp

is nearly constant for fuelswith D from 15 to 50 cm (Fig. 4). This is animportant experimental result for scale transfor-mation, and also reflects the non-dimensional heatrelease rate _Q�:

_m00

D1=2� _Q� ¼

_Q

q1T1cpffiffiffiffiffiffigDp

D2

� constant; 15 cm < D < 50 cm ð2Þ

Assuming diameters of the prototype fire(1 atm) and model fire (low pressure) are D0 andDd , respectively, and the scale-transformed proto-


type fire (1 atm) has burning rate _m000t and diameterDd (the same scale as the model fire). The follow-ing relation should ultimately exist:

pd D1=2d ¼p0D1=2

0 ; _m00d ¼ _m000 ðradiation fire modelingÞ_m000=D1=2

0 ¼ _m000t=D1=2d ðexperimental correlationÞ

)) _m00d

pd

¼ _m000t

p0

or _m00 /p

ð3Þ

Table 2 summarizes correlations between pro-totype, scale-transformed prototype and modelfires under two different pressures.

For the aspect ratio effect, it is not expectedthat ethanol and n-heptane pool fire burning ratesdevelop oppositely with increasing n, as shown inFig. 3(a). This will be explained in Section 3.3 bycombining temperature and flame height data.

3.2. Flame and burner wall/fuel temperature

Flame temperature T f , defined as constantpeak temperature in the continuous flame regionof turbulent diffusion flames, is shown in Fig. 5.Figure 5(a) shows that T f is nearly independentof the shape or material of the fuel source, but




0 100 200 300 4000

20

40

60

80

100

120

140

160

180 Aspect ratio n=1 (a)

The sudden increase is due to faster burning rate in Hefei (99.8 kPa),thermocouple was exposed to flame earlier

Tem

pera

ture

(o C)

Time (s)

T1 66.5 kPa T1 99.8 kPa T2 66.5 kPa T2 99.8 kPa

0 100 200 300 4000

40

80

120

0 100 200 300 4000

80 1 2 4 8

0

40

80

120T3 (long side) with aspect ratio n

T2 fuel temperature(almost the same for each cases)Tem

pera

ture

(o C) 1 2 4 8

Ethanol pool fires in Lhasa

(b)

Tem

pera

ture

(o C)

Time (s)

T1 (short side) with aspect ratio n

T2 fuel temperature

100


is affected by pressure. Averaged T f measuredunder 99.8 kPa and 66.5 kPa was about 1089and 1108 K, respectively. Although the differenceof T f between the two locations is not obvious,T f in Lhasa was slightly higher, mainly becauseof less radiative heat loss of the flame at low pres-sure, and weaker ambient air entrainment coolingfor lower air density [4,6].

For burner wall temperature T w and fuel tem-perature T fuel, the influence of pressure is notobvious as shown in Fig. 6(a). The aspect ratioeffect upon T w is shown in Fig. 6(b) typically usingethanol pool fires in Lhasa, which has the similartrend of n-heptane. Figure 6(b) reveals that withincreasing n, T w at the long side is increased, whileat the short side, a sharp decrease appears atn = 8. The influence of n on T fuel is not obvious;a comparison is given in Fig. 6(c) for burningtime = 200 s. To further understand the effect ofn on T w, entrainment theory was used forexplanation.

As shown in Fig. 7, with large aspect ratio, sig-nificant inward flame tilt near the short side bystrong airflow entrainment was observed(Fig. 7(b)). Assuming air entrainment velocity V,g indicates the burner characteristic length parallelto the entrainment velocity. Horizontal and verti-cal pressure differences of entrained air by vorticespumping are DpH � qf V 2 and DpV � q1gg [20],giving

DpH

q1�

qf

q1V 2 � DpV

q1� gg) V � g1=2g1=2 ð4Þ

So, for a rectangular pool fire, there is larger Von the short side than on the long side (Fig. 7(a),V w > V l). With increasing n, l, therefore increasedV w and flame inclination, the flame receded fromthe rim of the short side wall (Fig. 7(b)), and tem-perature decreased. For the flame near the longside (Fig. 7(c)), the pushing of inward air becameweaker because of the narrow fire source. Theflame was even closer to the rim, increasing thetemperature as shown in Fig. 6(b).

0 1 2 3 4 5 6 7 8 920

40

60

80

(c)Ethanol pool fires in Lhasaat time=200 s

Tem

pera

ture

(o C)

Aspect ratio n

T1: short side T2: fuel T3: long side
3.3. Flame image characteristic
Digital image processing was used to calculateflame height H and flame puffing frequency f.Flame height was obtained from 60-s sequencedflame images from the steady burning state,using the mean flame height definition ofZukoski et al. [21]. Frequency was obtained bya high-speed camera using the fast Fourier trans-form method.

Fig. 6. Burner exterior wall and fuel temperatures ofethanol pool fires: influence of pressure on wall and fueltemperature (a); influence of aspect ratio on temperaturefor ethanol pool fires in Lhasa (66.5 kPa) at long sidewall and short side wall (b); comparison of temperaturesat a given time (c).

3.3.1. Flame puffing frequencyThe frequency of a circular pool fire was dem-

onstrated to be f / 1=ffiffiffiffiDp

[22]. Cetegen et al.studied the oscillatory behavior of planar buoyant


plumes using a rectangular nozzle [23], by keepingthe long side length 200 mm and varying nozzlewidths from 20 to 70 mm. The frequency of thehot plume without chemical reaction was shownto be:

f ¼ ð1� qp=q1Þ0:45g0:45w�0:55V 0:1

p ð5Þ




Air flow Air flowFlame

Flame

Air flow Air flow

Flame

Air flow

Air flow

(b) Long side view

(a) Top view

(c) Short side view

l

lV

wVw

Fig. 7. Flame shape and air flow at enlarged aspectratio.

0 1 2 3 4 5 6 7 8 91

2

3

4

Averaged standard deviation: 0.08 Hz

(a)

Hefei

Lhasa

Puffi

ng fr

eque

ncy

(Hz)

Aspect ratio n

99.8 kPa-ethanol 99.8 kPa-n-heptane 66.5 kPa-ethanol 66.5 kPa-n-heptane calculated [22]

0 1 2 3 4 5 6 7 8 9

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

0 2 4 6 8

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

(b)

Predicted


Rat

io o

f f/f 0

Aspect ratio n

Fig. 8. Experimental puffing frequencies (a) and f =f0 (b)vs. aspect ratio of rectangular pool fires in Hefei(99.8 kPa) and Lhasa (66.5 kPa).


where qp is the hot plume density, and V p the ver-tical plume velocity. This shows that frequencyhas a strong dependence on qp=q1 (or T1=T p)and w. For a circular pool fire with large Ri num-

ber, Ri ¼ ðq1�qf ÞgD

qf U2f 0

, f could be simplified as [20]:

f ¼ Cffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq1=qf � 1

q�ffiffiffiffigD

r¼ C

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiDTT1� gD

sð6Þ

where C is a proportion factor. For the rectangu-lar burner, a hydraulic diameter defined asD� ¼ 2w � l=ðwþ lÞ is introduced. Consideringfuel area Ss ¼ w � l ¼ constant and l/w = n, substi-tuting D� into Eq. (6) gives:

f ¼ C0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDTT1� gD�

s¼ C0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDTT1� gSs� ðnþ 1Þ

2ffiffiffinp

sð7Þ

First, Eq. (7) shows that for the pressure effect,because of stronger buoyancy convection inducedby higher T f , f is slightly higher at Lhasa than atHefei (independent of fuel type). This is illustratedby Fig. 8(a).

Second, for the aspect ratio effect, Eq. (7) indi-

cates that f /ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðnþ 1Þ=2

ffiffiffinpp

when p remainsconstant. Figure 8(b) shows experimental and pre-dicted values of f =f0 vs. n. Here, subscript 0 is forthe square burner. The correlation predicted byEq. (7) appears to scale with experimental data.

3.3.2. Flame heightFlame height is expressed as H=D ¼

3:7 _Q�2=5 � 1:02 [24], as _Q� ¼ pD2 _m00DHc4q1T1cp

ffiffiffiffigDp

D2


� _m00=pffiffiffiffiDp

and _m00 / p shown above, giving_Q� � p0, and thus H=D � p0. This means that airpressure has no conspicuous influence on flameheight as Fig. 9 shows.

With increasing n, H became lower for bothethanol and n-heptane pool fires. However, forethanol, the decrease of H was greater. A qualita-tive analysis is given below.

Taking the 99.8 kPa condition as an example,for a square pool fire, the assumed flame heightand theoretical HRR are H 0 and _Q0 ¼ Ss _m00DH c

respectively. For a rectangular pool fire, they areH and _Q ¼ d _Q0. d is a coefficient based on exper-imental data above; d ¼ 0:77 � 1:18. The flameheight of an axisymmetric pool fire is classicallyexpressed as Eq. (8) [24]. The classical correlationof H for a rectangular fire was suggested byHasemi et al. as Eq. (9) [14]:

Square : H 0 ¼ 0:235 _Q2=50 � 1:02D ð8Þ

Rectangular : H ¼ 0:035ðd _Q0=lÞ2=3; n > 3 ð9ÞSo, for the same fuel area condition, there is

the approximation:




0 1 2 3 4 5 6 7 8 90

20

40

60

80

100

Flame height bymethod of Zukoski

Ethanol

N-heptane


Flam

e he

ight

(cm

)

Aspect ratio n

Fig. 9. Flame heights of pool fires with aspect ratio inHefei (99.8 kPa) and Lhasa (66.5 kPa).

0 1 2 3 4 5 6 7 8 90.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Predicted by Eq. (10)

H/(H

0+1.

02D

)

Aspect ratio n

Theory: n-heptane Theory: ethanol Exp: n-heptane Exp: ethanol

Fig. 10. Experimental and predicted flame heightscorrelated with aspect ratio and heat release rate.

0 1 2 3 4 5 6 7 8 90

80

160

240

320

400

480

Rad

iant

hea

t flu

x (W

/m2 )

Aspect ratio n

66.5 kPa-R1 66.5 kPa-R2 99.8 kPa-R1 99.8 kPa-R2

R1

R2

Burner

(a)

Hefei 99.8 kPa

Lhasa 66.5 kPa

0 1 2 3 4 5 6 7 8 90.0

0.2

0.4

0.6

0.8

1.0

PLhasa/PHefei=0.67(b)

Rat

io o

f rad

iant

hea

t flu

x

Aspect ratio n

R1- R2-

Fig. 11. Comparison of radiant heat flux of ethanol poolfires in Hefei (99.8 kPa) and Lhasa (66.5 kPa).


H1:02Dþ H 0

¼ 0:149ð 1ffiffiffiffiffiffiffinSsp Þ2=5 � d2=3 _Q4=15

0 ; n

> 3 ð10Þ

Eq. (10) shows that H decreases with increasing n,and the larger _Q0 is, the more slowly H decreaseswith n. Compared with ethanol, n-heptane has agreater burning rate, meanwhile, DHc is nearlytwo times that of ethanol, leading to a larger _Q0,so H of an ethanol pool fire decreases faster withincreasing n. Eq. (10) is validated by Fig. 10.

We now return to the question in Section 3.1,regarding the opposite development of ethanoland n-heptane pool fire burning rates vs. n at thetwo locations. Figure 10 indicates the decreaseof H vs. n, so does L � H in Eq. (1). Since T f

remains nearly constant, _q00rad also decreases withincreasing n. This effect will degrade the burningrate _m00. Considering that H-ethanol decreases fas-ter than n-heptane as shown above, the degrada-tion effect on ethanol is therefore stronger. Onthe other hand, for the rectangular burner, theincreasing T w vs. n at the long side wall cannotbe ignored, which enhances the burning rate.Finally, _m00 vs. n is determined by the couplingeffects of increasing wall heating and decreasingradiation heat feedback, which produces theopposite development for the two fuels.

3.4. Radiation heat flux

The radiant heat of a pool fire depends on theradiation fraction and burning rate _q00 / vr _m00.The radiation fraction, vr ¼ _Qrad= _Q, is provento be independent of pressure when D�p2 ¼ constant according to radiation fire modeling[10]:

vr ¼ _Qrad= _Q ¼Sf rT 4

f ½1� expð�jsLÞ�SsDH c _m00

� p0 ð11Þ

Considering that the radiation fraction showsno dependence on pan diameter between 7.6 and122 cm [25], vr should be almost the same for


low pressure and normal pressure, i.e., vr�Lhasa ¼vr�Hefei for a mid-scale pool fire. For the radiationheat flux measured at the same position in Hefeiand Lhasa, combining Eq. (3) gives

_q00Lhasa= _q00Hefei ¼ _m00Lhasa= _m00Hefei ¼ pLhasa=pHefei ð12Þ

Figure 11 compares the radiant heat flux ofethanol pool fires at the two locations. Figure11(a) shows that for the same measuring position,





_q00 in Hefei is much larger than in Lhasa, and _q00

facing the long side of the burner (R2) is largerthan that facing the short side (R1). This isbecause of the different geometric radiation coeffi-cients and stronger extinction of soot through thelong side. The _q00Lhasa= _q00Hefei is shown in Fig. 11(b),which agrees with the prediction of Eq. (12).

4. Conclusions

Rectangular ethanol and n-heptane pool fireswith the same fuel area but different aspect ratioswere conducted under 99.8 and 66.5 kPa condi-tions. Major results are summarized as follows:

(1) Burning rate and radiant heat flux wereproportional to air pressure _m00 � _q00 / punder radiation-controlled, which wasinterpreted by formulas based on radiationfire modeling and experimental correlation.

(2) At low air pressure, flame temperatureslightly increased, leading to higher flamepuffing frequency. Flame height was nearlyindependent of pressure.

(3) Regarding the aspect ratio effect, flame tem-perature was constant and independent ofburner shape. Burner wall temperatureincreased at the long side, and drasticallydecreased at the short side for n = 8, owingto variation of entrainment movement.

(4) Flame puffing frequency was found to be

f /ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðDT=T1Þðnþ 1Þ=2

ffiffiffinpp

, which reflectsthe combined effects of p and n. Flameheight decreased with increasing n as

H � ð 1ffiffinp Þ2=5 _Q4=15

0 .

(5) For the fuel difference, with increasing n,flame heights of the ethanol pool firedecreased at a greater extent; burning rateof the ethanol pool fire decreased,whereas n-heptane showed the oppositetrend, it is caused by the coupling effectsof wall heating and radiation heatfeedback.

Acknowledgments

This research was supported by the NationalNatural Science Foundation of China (No.51036007) and National Key Technology R&DProgram (No. 2011BAK03B02). Fang Jun wassupported by China NSFC 51074147, the ChineseUniversities Scientific Fund and the Fund of KeyLaboratory of Microgravity of Institute ofMechanics of CAS. The authors express sincereappreciation to Dr. John L. De Ris of FM Global


for his generous help and suggestions on thiswork.

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