Investigation of flame propagation over an inclined fuel wettedporous bed

Jafar Zanganeh n, Behdad MoghtaderiPriority Research Centre for Energy Faculty of Engineering & Built Environment, The University of Newcastle, Australia

a r t i c l e i n f o

Article history:Received 28 June 2013Received in revised form15 April 2014Accepted 31 May 2014Available online 19 June 2014

Keywords:Flame spreadInclined bedFlammable liquidPorous bedFlame behaviour

a b s t r a c t

This experimental study was conducted to investigate the rate of flame spread over an inclined poroussolid (sand) wetted with finite quantities of fuel (iso-propanol). The study comprised experiments thatwere conducted over 151 and 301 inclined beds with depths ranging from 13.3 mm to 39.9 mm andconsisting of average sand particle diameters ranging from 0.5 mm to 5 mm under quiescent, assistedand opposed airflow conditions.

Analysis of the resulting data indicate that the rate of flame spread is significantly decreased byincreasing the bed inclination angle or the airflow velocity and is applicable for both assisted andopposed directions. Furthermore, the rate of flame spread is decreased to the minimum value andactually ceased halfway along the bed with a 301 inclination angle. This behaviour was observed mainlyfor beds containing coarse sand particles. The rate of flame spread was higher for thinner beds rathercoarse beds under any given airflow conditions. Finally, the rate of flame spread in upward direction wasrelatively quicker in comparison with downward direction counterpart.

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1. Introduction

Images of large scale fires in industrial settings or residentialareas often demonstrate the destructive power of fire and the rateat which it can spread to nearby areas. Flame spread is a difficultand complex concept to explain given the large numbers ofphysical, chemical and environmental aspects; and the largenumber of variables involved in combustion at different stages ofthe process. Of the many types of fires, those occurring inindustrial settings, particularly those in petrochemical industries,are responsible for considerable loss of life and property in manyparts of the world every year. Quite often the accidental spillageand subsequent ignition of combustible liquids is the cause of firesin large-scale industrial settings (e.g. petrochemical industry).In many such fires the liquid fuel spills over a porous inert surface(e.g. a concrete slab or gravel) penetrating into its open pores and/or cavities. If the fuel is ignited, a stable flame may form andsubsequently spread over the surface of the porous bed. If nottreated flames may rapidly spread and envelop nearby buildingsand components leading to massive destruction and losses. Thecharacteristics of the flame spread phenomenon over porous bedsare significantly different from those over non-porous solids andliquid pools. While there are many papers on pool fires for

example [1–4] and flame spread over porous bed flushed-up withliquid fuel [4–19], there has been very little research on the rate offlame spread and flame behaviour over a bed soaked with a finiteamount of liquid fuel [4–7,9,12,16,17,19]. Ishida [6–9], Takeno andHirano [15] performed broad experimental studies of the flamespread over glass, sands and steel beads. These studies exclusivelyfocused on scenarios where an unlimited supply of liquid fuel wasavailable to soak the inert porous bed. They found that the flamespread rate is strongly dependent on the size of the solid particles[7]. It was also found that the rate of flame spread is generallyslower than that of pool fires. The porous bed fuel content is asignificant parameter in the flame spread phenomenon. The flamespread velocity and flame behaviour is strongly affected by theinitial amount of liquid fuel in the porous bed [7]. For a bed withan unlimited fuel supply, the surface of the porous bed is flushedwith fuel. In the flushed bed, if a fire occurs, the flame behavessimilarly to a flame on a liquid pool. The majority of previousstudies have been conducted on this type of fuel-flushed beds,while in practical situations there is typically only a limited fuelsupply. As such the porous bed is not soaked, but rather wetted bythe liquid fuel which slowly penetrates through the bed. The finitequantity of the liquid fuel in this case has a significant impact onthe flame, altering its propagation behaviour and/or other char-acteristics [7]. To narrow down this knowledge gap we undertooka series of combined experimental and theoretical investigationswere undertook at the University of Newcastle (Australia). Resultsobtained from these investigations [20–29] revealed that the flame

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Fire Safety Journal

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n Corresponding author. Tel.: þ61 249854416; fax: þ61 249216893.E-mail address: jafar.zanganeh@newcastle.edu.au (J. Zanganeh).

Fire Safety Journal 67 (2014) 113–120

spread rate under both assisted and opposed airflow configura-tions noticeably decreased as the air speed was increased althoughthe extent of decay in the flame spread rate was more pronouncedin the case of the opposed airflow configuration [20,21]. However,regardless of airflow speed and/or direction the rate of flamespread was found to decrease as either the bed depth or particlesize are increased [22]. Moreover, the investigations revealed thatthe fuel penetration rate into the porous bed was a function of bedpermeability and the mass of the liquid fuel. The permeability ofthe porous bed and consequently the rate of fuel penetration werefound to decrease as either the tortuosity or specific surface areawere increased [23]. Knowing the flame spread behaviour in firecaused by fuel spillage will help responders to take proper actionto control and suppress the fire at the beginning of the combustionprocess. The present study which builds upon our previousinvestigations [20–29], aims to examine in detail: (1) the flamespread rate over an inclined porous bed wetted with flamm-able liquid and (2) the effect of assisting and opposing airflowon the rate of flame spread. Moreover the rate of flame spreadfor different inclinations and various particle sizes under air-flow configuration is examined by applying the concept of theDamköhler number.

2. Experimental set-up and procedure

Experiments were performed using the set-up shown schema-tically in Figs. 1 and 2. The set-up consisted of: a rectangularchannel mounted on a support frame; a hydraulic jack for traversemovement; a heat exchanger unit fitted to the bottom of thechannel to maintain its temperature around the ambient tem-perature; a water bath; a thermocouple grid (type K, Ni/Cr – Ni/Al,�200–1370 1C) for temperature measurements; a ducted fan; afuel distributor (not shown in Fig. 1); a canopy hood connected toan exhaust fan; a high speed digital camera; and a data acquisitionsystem comprising a data logger and a computer. A scaled channelwas designed to mimic the spread of flames over a range of porousmedia under realistic conditions within a controlled laboratorysetting (Fig. 1). The 1500�80�40 mm3 channel shown in Fig. 2was made out of stainless steel. It was fixed to the support frameat one end through the hinge point (displayed by “A” letter inFig. 1) and was mounted on the hydraulic jack at the opposite end.This arrangement allowed us to vary the inclination angle of thechannel if needed. The external surfaces of the channel werecovered with a 5 mm thick insulating material (calcium silicatesheet) to prevent heat losses. The channel was filled with 6 differ-ent particle sizes of sand (0.5, 1, 2, 3, 4 and 5 mm; densi-ty¼2680 kg/m3) in three different depths (13.3, 26.6 and39.9 mm) as the porous bed. The effect of air flow on the flame

spread was simulated using the 1300�200�200 mm3 ducted fan.The duct was used to have a uniform airflow at the duct outlet. Theairflow was measured at the duct outlet using a grid frame and anaccurate anemometer. In this technique the duct outlet crosssection is divided into numbers of small imaginary squares. Theairflow velocity is then measured and recorded at the centre ofeach square. The fan air flow velocity is calculated by averagingthese recorded air velocities. To avoid any turbulence the duct waskept clear of any deformation, protrusion and indent. The air flowpassageway was kept open and all other air sources (openwindow, air condition, etc.) were eliminated to prevent interfer-ence with the airflow coming from the fan.

2-Propenol was used as the liquid fuel and uniformly distrib-uted by a liquid fuel distributor all over the porous bed. The ratioof fuel volume to the weight of the sand bed (i.e. fuel volume/sands weight) in all experiments was kept at about 0.1 L/kg. Thisratio was calculated based on the bed volume, fuel and sandparticles density and void fraction. The void fraction for this typeof particles and bed formation was assumed to be 0.41 [30].Ignition was achieved using a pilot flame. The flame speed andhence the spread rate were digitally determined from high-speedvideo cinematography, video image processing techniques andvisual observation. In these techniques the recorded video is splitto frames, then frames are analysed and studied.

To assure data validity and reliability, three experiments wereconducted for each data point. To eliminate any possible errorwhich could come from the operator, instrumentation and envir-onmental conditions, all instruments were calibrated prior con-ducting experiments. To minimise personnel (operator) errors allsamples preparation were carried out by one person only. Thesupport person provided quality assurance in terms of ensuringthat all procedures were correctly followed.

The rates of flame spread over porous bed were digitallydetermined from high-speed video cinematography, video imageprocessing techniques and visual observation. In these techniquesthe rates of flame spread for each individual experiments wascalculated based on the recorded videos, time and distancetravelled by flame front.

3. Results and discussion

The channel was initially filled with desired sand particlesaccording to the experimental plan. The surface of the porous sandbed then was smoothed out using a very small trowel with nocompaction. The fan airflow was regulated (if required) to plannedairflow prior to fuel distribution. The fuel was uniformly distrib-uted over the porous bed with zero inclination (θ¼0) by the liquidfuel distributor described earlier in Section 2. The bed then wasthen tilted up to the desired inclination angle and lit by a gaslighter.

Fig. 1. Experimental set-up to measure flame spread rate over fuel wetted porousbed.

Fig. 2. Porous bed sketch.

J. Zanganeh, B. Moghtaderi / Fire Safety Journal 67 (2014) 113–120114

Results obtained for the rate of flame spread over inclinedporous bed wetted with 2-propanol under airflow conditions areshown in Figs. 3–8. Figs. 3 and 4 show the variations of the flamespread rate over inclined porous beds consisting of mono-sizedsand particles (i.e. 0.5 mm) under various airflow conditions. Fig. 3shows the rate of flame spread in upward and downward direc-tions for a 151 inclined bed. As indicated, the rate of flame spreaddramatically decreases for all depths as the airflow increases. Inupward direction the highest flame spread rate is about 1.5 m/s

related to the shallowest bed (13.3 mm) under quiescent (i.e.no airflow) condition. For the same bed depth (i.e. 13.3 mm),however, the rate of flame spread decreases to 0.625 m/s as theairflow is increased to 1.5 m/s. A drop of 58% in comparison withthe rate of flame spread under quiescent condition. More intensiveresults are observed for deeper beds (26.6 and 39.9 mm). The rateof flame spread over the bed of 39.9 mm depth, for instance,significantly decreases from 1.103 m/s to the lowest value of0.08 m/s for the quiescent and airflow velocity of 1.5 m/s.

Airflow Velocity (m/s)

FlameSpreadRate(m/s)

0 0.5 1 1.5

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Depth 13.3 mmDepth 26.6 mmDepth 39.9 mm

Downward Flame SpreadBed Inclination: 15 DegreeParticle Size: 0.5 mm

Airflow Velocity (m/s)

FlameSpreadRate(m/s)

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Depth 13.3 mmDepth 26.6 mmDepth 39.9 mm

Upward Flame SpreadBed Inclination: 15 DegreeParticle Size: 0.5 mm

Fig. 3. Upward and downward flame spread rates over an inclined porous bed of 151 consisting of sand particles of size 0.5 mm under various airflow conditions.

AirflowVelocity(m/s)

FlameSpreadRate(m/s)

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Depth13.3mmDepth26.6mmDepth39.9mm

UpwardFlameSpreadBedInclination:30DegreeParticleSize:0.5mm

AirflowVelocity(m/s)

FlameSpreadRate(m/s)

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Depth13.3mmDepth26.6mmDepth39.9mm

DownwardFlameSpreadBedInclination:30DegreeParticleSize:0.5mm

Fig. 4. Upward and downward flame spread rates over an inclined porous bed of 301 consisting of sand particles of the size 0.5 mm under various airflow conditions.

J. Zanganeh, B. Moghtaderi / Fire Safety Journal 67 (2014) 113–120 115

Similarly to upward flame spread, in downward direction therate of flame spread decreases as airflow increases. However,the rate of flame spread is significantly lower in comparison tothe upward flame spread rate counterpart. Results correspondingto the downward flame spread show a significant decrease for anincrease at both bed depth and opposed airflow velocity. The rateof flame spread decreases from 1.25 m/s to 0.095m/s for the13.3 mm bed depth as the airflow increases from 0 to 1.5 m/s.

A similar trend is observed for deeper beds; however, for deeperbeds (413.3 mm) the flame spread in downward direction isalmost impossible as the airflow exceed 1 m/s.

Fig. 4 shows the rate of flame spread in upward and downwarddirections over a 301 inclined bed. It shows that the rate of flamespread decreases considerably as the bed inclination angleincreases. In upward direction, the highest flame spread rate isapproximately 1.25 m/s related to the bed of 13.3 mm depth inquiescent condition. For the same condition the rate of flamespread was measured about 0.75 m/s for 39.9 mm bed depth.A drop of 40% in comparison with the rate of flame spread over abed depth of 13.3 mm inclined bed counterpart.

Results obtained for the downward flame spread over aninclined bed of 301 demonstrate the rate of flame spread isnoticeably slower in comparison to the flame spread rates inupward direction. The rate of flame spread decreases from0.65 m/s to 0.08 m/s over the bed of 13.3 mm depth as theopposed airflow is increased from zero to 1.5 m/s. In addition,flame dose not spread for any bed depth as the airflow exceeds0.5 m/s. Overall, from the flame spread profiles it is deduced thatfor any given airflow, the minimum flame spread rate is related tothe deepest beds (39.9 mm) either in upward or downwardorientation.

Figs. 5–8 demonstrate the rate of flame spread over differentinclined porous beds under airflow conditions. Figs. 5 and 6indicate the rate of flame spread over the 151 inclined bed. Resultscorresponding to the flame spread rate show that under bothopposed and assisted airflow configurations the rate of flamespread decreases as the air flow increases. For any given airflowvelocity and particle size, the minimum rate of flame spreadcorresponds to the downward flame spread particularly underthe opposed airflow configuration. The flame spread decelerationbehaviour is observed to be more pronounced for larger bedparticles and deeper beds. Similar trends are observed at 301inclination (Figs. 7 and 8). But, as a general observation the rate offlame spread corresponding to 301 inclination is lower in compar-ison with the fame spread rate over 151 inclined bed. Furthermore,With the exception of 0.5 mm particles, the flame spread for otherparticle sizes in downward orientation under airflow velocitygreater than 1 m/s is considered not possible. Unlike flame spreadin a downward direction, in an upward direction flame propagatesrelatively is faster under otherwise identical conditions; however,the flame typically extinguished halfway along the bed.

Figs. 5–8 clearly indicate that regardless of bed particle size andairflow direction and/or velocity when finite amount of liquid fuelare available, the rate of flame spread along the bed surface isdecreased as the inclination angle is increased. It is noted however

Fig. 5. Upward flame spread over a 151 inclined porous bed of 13.3 mm depthunder assisted airflow condition.

Fig. 6. Downward flame spread over a 151 inclined porous bed of 13.3 mm depthunder opposed airflow condition.

Fig. 7. Upward flame spread over a 301 inclined porous bed of 13.3 mm depthunder assisted airflow condition.

Fig. 8. Downward flame spread over a 301 inclined porous bed of 13.3 mm depthunder opposed airflow condition.

J. Zanganeh, B. Moghtaderi / Fire Safety Journal 67 (2014) 113–120116

that the flame reduction rate is more pronounced in a downwarddirection. These results show a clear distinction with cases whereunlimited supply of liquid fuel is available [4,6,7,9,12]. For exam-ple, experimental studies by Ishida [6,7] showed that regardless ofthe effect of porous bed temperature on the rate of flame spread,in downward direction, the rate of flame spread is smaller forlarger inclination, whilst in upward direction the rate of flamespread is higher for larger inclination angles. Ishida stated that thisphenomenon is attributed to the moving a large amount ofoverhanging hot gas from the flame towards the unburned surfacelocated ahead of the flame leading edge, leading to increase in theheat flux of the unburned surface. In addition, he found that therate of flame spread in horizontal and upward configurationdecreases as the airflow velocity increases up to 0.4 m/s [6,7].For the airflow velocities between 0.4 and 1.6 m/s the rate of flamespread in the upward and horizontal configuration does notchange significantly, however, beyond this airflow velocity therate of flame spread in upward direction significantly increases toattain its maximum value that corresponds to the airflow velocityof 2.4 m/s. Unlike the upward direction, the rate of flame spread indownward and horizontal configuration dramatically decreases asthe airflow increases.

Results obtained in this study show that the rate of flamespread is smaller in upward and downward direction comparedwith horizontal configuration when there is a limited quantity ofliquid fuel available in the porous bed which is in contrast withIshida's results. Furthermore, it indicates that for any given airflowvelocity or particle size the rate of flame spread is always inverselyproportional to the inclination angles of 151 and 301 for bothupward and downward configurations.

These significant differences in the rate of flame spread canoccur due to a number of reasons such as supply of flammable fuel,supply of oxidiser (i.e. oxygen), heat flux, and buoyancy. Of thesefactors the fuel supply rate from the bed to the surface isconsidered to be the key element which drives the mechanismof flame spread. The rate of fuel evaporation at the surface of thebed considered as an affective parameter on the rate of flamespread. In the case of flame spread along an inclined porous bed,the rate of fuel evaporation depends on the quantity of fuel supplyin the bed, the net heat flux at the surface, the distance betweenthe level of fuel to the surface of bed, and other thermo-physicalproperties of the fuel (e.g. flash point, viscosity, etc.). Among theseparameters and for the case of flame spread over an inclined bedthe degree of inclination has the greatest influence on the rate offuel supply and consequently flame spread rate. When an inclinedporous bed is soaked with a limited quantity of liquid fuel, a higherconcentration of liquid fuel is formed at the lower end due togravity. This phenomenon leads to alteration of the fuel level atdifferent parts of porous bed. Therefore, increasing the bedinclination angle leads to an increase in the distance that fuelparticles should travel from the porous bed to the surface. Thisdistance is known as capillary rise thickness which attains amaximum at the upper end and a minimum at the lower end foran inclined porous bed. Our findings show that with the exceptionof very fine particles (0.5 mm) flame spread over coarse beds indownward direction becomes impossible when the airflow speedexceed 1 m/s. On the other hand, in upward direction the flamedoes not reach to the end and extinguished halfway along thesurface. Moreover, the flame travelled distance in upward direc-tion becomes shorter with increasing the inclination angle or sizeof particles. Therefore some variations in the rate of flame spreadmay be attributed to this parameter.

The thickness of capillary rise in the bed with limited quantityof liquid supply (i.e. wetted bed) is always quite large in compar-ison with fully saturated bed. Accordingly it takes longer for thefuel to reach the surface and provide the flame with sufficient

flammable material. Therefore due to the insufficient fuel supplythe rate of flame propagation slows down until the occurrence ofspontaneous extinction.

As previously noted, the higher flame spread rate in theupward direction in comparison with downward direction canbe attributed firstly to the larger fuel concentration at the lowerend and secondly to the shorter travel distance (i.e. capillary risethickness) for the fuel to reach the bed surface in lower end. Theeffect of inclination angle on the rate of flame spread becomesmore distinct when the flame spread happens under airflowconditions. Under the assisted airflow configuration the rate ofoxygen supply to the flame leading edge may increase whereas therate of fuel supply to the surface remain constant (i.e. O24Fuel).This lack of equilibrium can potentially shorten or even preventthe combustible vapour fuel from attaining its lower flammabilitylimit (i.e. fuel lean mixture), resulting in a longer reaction time (i.e.retardation of chemical reaction) and thereby lower flamespread rates.

Regardless of airflow speed the direction of airflow also has asignificant impact on the rate of flame spread by accelerating thefuel evaporation rate through the increase of bed temperature. Forinstance in upward flame spread under assisted airflow the flamepillars tilt down towards the bed surface ahead of the flameleading edge, resulting in an increase in the convective andirradiative heat transfer from the flame to the bed surface. There-fore, due to moving of the overhanging hot gas from the flame tothe unburned areas located in front of the flame leading edge, theunburnt regions are preheated which lead to the enhancement offuel evaporation rate, and consequently increase of the rate offlame spread. Noticeably the retardation of the chemical reactioncaused by assisted airflow can partly be compensated by thesurface bed preheating phenomenon.

Unlike assisted airflow, under opposed airflow configurationthe flame tilts backward and approaches the region which hasalready been covered with the flame and its temperature isrelatively high. Therefore, the increase of porous bed temperatureand preheating bed surface due to the heat transfer from the flameto the bed does not have a significant impact on the enhancementof fuel evaporation rate and accordingly flame spread rate. Therate of flame spread is also affected by buoyancy effect which ismuch distinct when the flame spread occurs in downward direc-tion under opposed airflow. The opposed airflow push back theflame leading edge and blow-off some flammable gas from thesurface of bed. Thereby, the flame spread rate under this conditionbecomes very unstable, and decreases as the airflow speedincreases. The flame stops spreading when either the opposedairflow or inclination angle are increased [9]. For the porous bedsoaked with unlimited quantities of liquid fuel, the fuel supply tothe surface is largely conducted by the liquid fuel motion in thebed [19,31]. With finite quantities of liquid fuel the fuel ceases toexist across the entire bed, thus the rate of fuel supply to thesurface is not necessarily determined by the liquid motion.

4. Damköhler number analysis

The relationship among the flame spread rate, inclination angleof porous bed, airflow speed, and particle size of the bed observedin this study can be greatly explained and discussed if onecompares the relative importance of the underlying chemicalreaction and transport phenomena. This can be best achieved ifthe rate of flame spread over the inclined bed is plotted against theDamköhler number (Da) which is proportional to the ratio ofairflow transient time through the flame (tflow which underpinsthe transport of heat and mass) to the time for completion ofchemical reaction, tchem [32]. The Damköhler equation for this

J. Zanganeh, B. Moghtaderi / Fire Safety Journal 67 (2014) 113–120 117

reaction is presented below:

Da ptf lowtchem

p1

V2a

where Va denotes the speed of air.Figs. 9–12 illustrate the logarithmic plots of flame spread rate

versus Da for a particle size ranging from 0.5 mm to 5 mm and abed depth of 13.3 mm. In each case the rate of flame spread (Uf)has been normalised by a theoretical flame spread rate (Utheo)which has been equated to the flame spread rate under quiescentconditions, Uf0. This is justified since past studies [16–18] haveshown that at the airflow close to zero (i.e. DaZO½103�) the ratio ofUf/Utheo approaches unity, implying Uf0 ¼Utheo.

As observed in Figs. 9–12, for both upward and downwardflame spread under either assisted or opposed airflow configura-tion, the ratio of the Uf/Utheo remains very close to unity even atthe air speeds up to 0.1 m/s (Da �O½102�). For example the ratio ofthe Uf/Utheo for the flame spread in upward and downwarddirections for the airflow of 0.1 m/s is about 0.97, which is veryclose to the flame spread ratio in quiescent condition. This unityindicates that tflow and tchem is approximately of the same order ofmagnitude, therefore the effect of airflow and inclination angleseems to not be significant. However at higher airflow speeds(i.e. lower Da) tflow and tchem diverge from each other, resulting in adecrease in the ratio of Uf/Utheo. For instance in the case of upwardflame spread (Fig. 5), when the airflow speeds increases to 0.5 the

ratio of Uf/Utheo drops to about 0.82 corresponding to Da¼4. In thecase of downward flame spread at the same Damköhler numbers,the ratio of Uf/Utheo decreases to 0.8. Comparison of these to ratiosindicate that although the airflow speed of 0.5 m/s has some effecton the ratio of Uf/Utheo, however, this effect is not significant. Themost notable declines in the ratio of Uf/Utheo for upward anddownward flame spreads under assisted and opposed airflow areobserved for very low Damköhler numbers (i.e. Da5O(101)). Atthis situation tflow and tchem are no longer the same order ofmagnitude. For example the ratio of Uf/Utheo under airflow speedsof 1 m/s (Da¼1) and 1.5 m/s (Da¼0.44) decreases from 0.33 to0.046 which corresponds to the flame spread in an upwarddirection. For the same Damköhler numbers, a greater drop occursfor the flame spread in a downward direction; Uf =Utheo � 0:15 and0.014. In the case of downward flame spread the ratio of Uf/Utheo

shows a drop of 85% when compared to the flame spread in theupward direction. These significant differences in the rate of flamespread can occur due to a number of reasons such as supply offlammable fuel, supply of oxidiser (i.e. oxygen), heat flux, andbuoyancy. Among these parameters the rate of fuel supply fromthe bed to the surface is pointed as a key factor which drives themechanism of flame spread. The rate of chemical reaction is muchgreater than the rate of flame spread [7]. Hence, the ratio of thecharacteristic time for flame spread tf � ð1=Vf Þ to the fuel supplyts � ð1=VsÞ is considered as the greatest factor for the steadiness ofthe flame spread, where Vf is the rate of flame spread and Vs is therate of fuel supply by capillary rise, vaporisation, and diffusion. tf

Fig. 9. Normalised upward flame spread rate versus Damköhler number upon abed of 151 inclination angle and 13.3 mm deep under the assisted airflowconfiguration.

Fig. 10. Normalised upward flame spread rate versus Damköhler number upon abed of 301 inclination angle and 13.3 mm deep under the assisted airflowconfiguration.

Fig. 11. Normalised downward flame spread rate versus Damköhler number upon abed of 151 inclination angle and 13.3 mm deep under the opposed airflowconfiguration.

Fig. 12. Normalised downward flame spread rate versus Damköhler number upona bed of 301 inclination angle and 13.3 mm deep under the opposed airflowconfiguration.

J. Zanganeh, B. Moghtaderi / Fire Safety Journal 67 (2014) 113–120118

and ts are the characteristic time for the rate of fuel consumptionand rate of fuel supply, respectively [7]. When tf 4ts, the flameneeds longer time to consume the supplied fuel. As such the rateof flame spread is slower compared to the rate of fuel supply (i.e.Vf oVs), leading to more constant flame spread. In the case whenðtf ¼ tsÞ, due to almost unity between the rate of fuel supply andrate of fuel consumption, the rate of flame spread is equal to therate of fuel supply, (i.e. Vf ¼ Vs). In this case the flame often isunsteady.

If tf ots since Vf 4Vs the flame spreads a short distance and,due to the fuel supply shortage, halts halfway along the surface. Asnoted above, the rate of fuel evaporation at the surface of the beddirectly impacts on the rate of flame spread. In the case of flamespread along an inclined porous bed, the rate of fuel evaporationdepends on the quantity of fuel supply in the bed, the net heat fluxat the surface, the distance between the level of fuel to the surfaceof bed, and other thermo-physical properties of the fuel (e.g. flashpoint, viscosity, etc.).

In the case of flame spread over an inclined bed, the degree ofinclination as compared to other parameters has the maximuminfluence on the rate of fuel supply and consequently flame spreadrate. When an inclined porous bed is soaked with a limitedquantity of liquid fuel, a higher concentration of liquid fuel isformed at the lower end due to gravity. This phenomenon leads toalteration of the fuel level at different parts of the porous bed.Therefore, increasing the bed inclination angle leads to an increasein the distance that fuel particles need to travel from the porousbed to the surface. This distance is known as capillary risethickness which attains a maximum at the upper end and aminimum at the lower end for an inclined porous bed. The studyfindings show that with the exception of very fine particles(0.5 mm), flame spread over coarse beds in a downward directionceases when the airflow speed exceeds 1 m/s. On the other hand,in an upward direction the flame does not reach the end and isextinguished halfway along the surface. Moreover, the distancethat the flame travels in an upward direction becomes shorterwith increasing inclination angle or size of particles.

The thickness of capillary rise in the bed with limited quantityof liquid supply (i.e. wetted bed) is quite large compared with afully saturated bed. Therefore in a wetted bed, it takes longer forthe fuel to reach the surface and provide the flame with sufficientflammable material. Therefore due to the insufficient fuel supplythe rate of flame propagation slows until spontaneous extinctionoccurs.

The effect of inclination angle on the rate of flame spreadbecomes more distinct when the flame spread happens underairflow conditions. Under the assisted airflow configuration therate of oxygen supply to the flame leading edge may increasewhereas the rate of fuel supply to the surface remain constant (i.e.O24Fuel). This disequilibrium can potentially shorten or evenprevent the combustible vapour fuel reaching its lower flamm-ability limit (i.e. fuel lean mixture), resulting in a longer reactiontime (i.e. retardation of chemical reaction) and thereby resulting inlower Damköhler (Da) and flame spread rates.

5. Conclusion

In this study an investigation was conducted to assess therate of flame over an inclined porous bed of sand wetted with2-propanol under diverse conditions. The experimental resultsobtained from this study show that the rate of flame spread overinclined porous beds wetted/soaked with liquid fuel is smaller incomparison with the horizontal configuration. In both upward anddownward direction flame propagation the rate of flame spreaddecreases as either the bed inclination angle or the airflow velocity

increases. Similar flame spread decreases were observed fordeeper beds containing larger particles. Furthermore, relativelylarge inclination angles (i.e.4151) prevented flame spread overthe beds containing large particles in a downward direction underopposed airflow condition. In an upward direction, given the samelarge inclination angles, the flame was consistently quenchedhalfway along the bed. The variation in the rate of flame spreadassociated with some key controlling parameters (e.g. bed geo-metry, airflow speed, etc.) can be explained in terms of theDamköhler number which defines the relative importance of tflowand tchem. The Damköhler number for 151 and 301 inclinationangles is inversely proportional to the airflow speed. As such therate of flame spread is proportional to the Damköhler number. Thefindings from this study will provide designers and facility ownersalike with important information with which to more effectivelymanage accidental fuel spills and provide an opportunity to avoidfuture fires in industrial settings.

Acknowledgement

The authors wish to thank Mr. Jeffrey Marley (The Universityof Newcastle-Australia) for collaboration and constrictive supportin this study. Moreover, the authors like to acknowledge thefinancial support provided to them by the University of NewcastleAustralia.

References

[1] H. Hayasaka, Unsteady burning rates of small pool fires, in: Proceeding of 5thInternational Symposium on Fire Safety Science 1997.

[2] M.J. Murphy, Flame spread rates over methanol fuel spills, Combust. Sci.Technol.42 (1985) 223–227.

[3] T. Suzuki, et al. Flame spread over thin layers of crude oil sludge, in:Proceedings of the 1st International Symposium on Combustion, USA, 1985.

[4] T. Suzuki, T. Hirano, Flame propagation across a liquid fuel in an air stream, in:Proceedings of the 19th International Symposium on Combustion, 1982.

[5] C.Y.H. Chao, J.H. Wang, W. Kong, Effect of fuel properties on the combustionbehavior of different types of porous beds soaked with combustible liquid, Int.J. Heat Mass Transfer 47 (2004) 5201–5210.

[6] H. Ishida, Flame spread over fuel-soaked ground, Fire Saf. J. 10 (1986) 163–171.[7] H. Ishida, Flame spread over ground soaked with highly volatile liquid fuel,

Fire Saf. J. 13 (1988) 115–123.[8] H. Ishida, Initiation of fire growth on fuel-soaked ground, Fire Saf. J. 18 (3)

(1992) 213–230.[9] H. Ishida, Propagation of precursor flame tip in surrounding airflow along the

ground soaked with high-volatile liquid fuel, J. Fire Sci. 23 (2005) 247–259.[10] H. Ishida, Flame tip propagation with assisted flow along fuel-soaked ground,

J. Fire Sci. 29 (2011) 99–110.[11] H. Ishida, Flame tip travelling in boundary layer flow with flammable mixture

along fuel-soaked ground, J. Fire Sci. 30 (1) (2011) 17–27.[12] H. Ishida, T. Ido, and T. Sato, Flame propagation in counter airflow along the

ground soaked with highly-volatile liquid fuel, Research report, Japan, 2004.[13] H. Ishida, Y. Kenmotsu, Flame spread in opposed flow along the ground soaked

with high-volatile liquid fuel, J. Fire Sci. 10 (2009) 285–297.[14] H. Ishida, et al., Flame spread over fuel-spilled and/or snow-covered asphalt

road, J. Fire Sci.14 (1996) 50–66.[15] K. Takeno, T. Hirano, Flame spread over porous solids soaked with a

combustible liquid, in: Proceedings of the 21st International Symposium onCombustion, 1988.

[16] F. Pello, S.R. Ray, I. Glassman, Flame spread in an opposed forced flow: theeffect of ambient oxygen concentration, in: Proceedings of the 18th Interna-tional Symposium on Combustion, 1981, pp. 579–589.

[17] I.S. Wichman, Theory of opposed-flow flame spread, Prog. Energy. Combust.Sci. 18 (1992) 553–593.

[18] R.A. Altenkirch, R. Eichhorn, P.C. Shang, Buoyancy effects on flame spreadingdown thermally thin fuels, Combust. Flame 37 (1980) 71–83.

[19] K. Takeno, T. Hirano, Behavior of combustible liquid soaked in porous bedsduring flame spread, in: Proceedings of the 22nd International Symposium onCombustion, 1988.

[20] J. Zanganeh, B. Moghtaderi, Flame propagation over a porous media wettedwith flammable liquid in a channel of finite cross section, in: Proceedings ofthe Australian Combustion Symposium, The University of Queensland, Aus-tralia, 2009.

J. Zanganeh, B. Moghtaderi / Fire Safety Journal 67 (2014) 113–120 119

[21] J. Zanganeh, B. Moghtaderi, Flame spread over porous sand beds wetted withpropenol, J. Fire Mater. 35 (2) (2011) 61–70.

[22] J. Zanganeh, B. Moghtaderi, Experimental study of temperature distributionand flame spread over an inert porous bed wetted with liquid fuel, Int. J.Emerg. Multidiscip. Fluid Sci. 2 (1) (2010) 1–14.

[23] J. Zanganeh, B. Moghtaderi, Experimental and mathematical analysis of fuelpenetration through unconsolidated porous media, J. Fire Mater. 37 (2) (2013)160–170.

[24] J. Zanganeh, B. Moghtaderi,. Flame spread under opposed and assisted airflowconfigurations over inclined porous beds soaked with combustible liquids, in:Proceedings of the 9th International Symposium Fire Safety Science, Germany,2008.

[25] J. Zanganeh, Flame Spread Over Inert Porous Solids Wetted With FlammableLiquids Under Conditions Pertinent to Industrial Fires, Priority ResearchCentre for Energy, Discipline of Chemical Engineering, School of Engineering,Faculty of Engineering & Built Environment, The University of Newcastle:Newcastle, 2010, 245.

[26] J. Zanganeh, B. Moghtaderi, Flame spread over a porous bed soaked withliquid fuel under assisted and opposed airflow condition, in: Proceedings of

the 20th National and 9th International Conference of Heat and Mass Transfer,ISHMT-ASME, Mumbai, India, 2010.

[27] J. Zanganeh , B. Moghtaderi, Effect of fuel ratio and flame initiation delay onthe rate of flame spread over a porous bed wetted with a flammable liquid,in: Proceedings of the Australian Combustion Symposium, The University ofNewcastle, Australia, 2011.

[28] J. Zanganeh, B. moghtaderi, Effect of fuel soaked time and fuel ratio on theflame spread rate over a porous bed wetted with liquid fuel, Fire Saf. J. 59(2013) 151–159.

[29] J. Zanganeh, B. Moghtaderi, H. Ishida, Combustion and flame spread on fuelsoaked porous solids, Prog. Energy Combust. Sci. 39 (4) (2013) 320–339.

[30] W.C. Yang, Handbook of Fluidization and Fluid Particle Systems, vol. 1, MarcelDekker, USA, 2003.

[31] K. Takeno, T. Hirano, Flame spread over porous solids soaked with acombustible liquid, in: Proceedings of the 21st International Symposium onCombustion, 1986.

[32] J.G. Quintiere, Surface flame spread, in: C.L. Beyler, R.L.P. Custer, W.D. Walton(Eds.), SFPE Handbook of Fire Protection, D.P. Engineering, NFPA, 1995,pp. 205–210.

J. Zanganeh, B. Moghtaderi / Fire Safety Journal 67 (2014) 113–120120