Prediction of the critical condition for flame acceleration over wood surface with different sample
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Brief CommunicationsPrediction of the critical condition for flame acceleration over wood surface with different sample orientationsYing Zhang,Jie Ji,Qingsong Wang,Xinjie Huang,Qiuhong Wang,Jinhua Sun ⇑State Key Laboratory of Fire Science,University of Science and Technology of China,Hefei 230027,Chinaa r t i c l e i n f o Article history:Received 19January 2011Received in revised form 3December 2011Accepted 16April 2012Available online xxxx Keywords:Flame spread InclinationTransition zone AccelerationCritical conditiona b s t r a c tTo understand the inclination effects on flame spread over wood surface,a set of flame spread experi-ments were carried out for different sample orientation angles from À50°to 20°in the Hefei Plain (at the altitude of 50m)and in the Tibetan plateau (at the altitude of 3658m).At both altitudes,a transition zone was found at 10–20°orientation for flame spread rate,the preheated length and flame angle from the horizontal.The transition zone was an external manifestation of the change of flame spread from steady state to acceleration.A new relationship of P c =1was established to predict the occurrence of acceleration based on theoretical analysis.Experimental data at the two altitudes suggested that the crit-ical value of P c is about 1.1–1.2,which has a good agreement with the theoretical value.Ó2012The Combustion Institute.Published by Elsevier Inc.All rights reserved.1.IntroductionFire accident investigations suggested that the inclination of solid surface is one of the most important factors in flame spread,such as the 30°inclination of the wooden escalator in the King’s Cross fire in 1987[1–4].After that,the experiments were carried out to study flame spread over inclined surfaces and the trench effect [5–14].The inclination effects on flame spread [5–10]indicated that the flame spread rate increased with inclination angle in an exponential way.The trench effects on flame spread were explored [11–14],and it was found that fire eruption occurred over an inclined surface with a sufficient steepness,even when the trench side-walls were removed.Drysdale and Macmillan [12]pointed out a transition zone at a sample orientation of around 15–20°.Wu et al.[14]studied the fire plume interaction with an inclined surface using a schlieren system and proposed two parameters to describe the fire plume features:(1)the length of the fire plume attachment to the surface;(2)the flame tilt angle from the inclined surface.They pointed out that the sharp rise in the plume attachment length identifies the critical inclination angle.However,further discussion about the mecha-nism of transition has not been reported so far and the related critical condition of transition has not been addressed yet.In this study,the experiments under inclination angles ranging from À50°to 20°were conducted at two cities:the Lhasa City (in the Tibetan plateau,3650m altitude)and the Hefei City (in the Hefei Plain,58m altitude).The ambient pressures of the two cities are 65.5kPa and 100.8kPa.The flame shape during flame spread were captured by digital video,and the rate of fire spread and the flame heat flux feedback to the unburned surface were also monitored in experiments.The mechanism of the transition zone and the prediction on the critical condition will be discussed in this paper.2.ExperimentsThe experimental facility is described in [15].A color digital video camera was set outside the observation window and the flame spread process was in a real time record.A steel ruler was fixed aside the sample holder,which can be rotated through 360°,to determine the scale of images.A rotary dial,with 2°preci-sion,was mounted on the sample holder to indicate the inclination of sample surface.A heat flux meter TS30was mounted on the sample surface to measure total flame heat flux to sample surface.The meter’s uncertainty is less than 3%,and its operating temper-ature could not exceed 200°C,so it has to be removed away when the pyrolysis front reaches.The inclination angle h of the sample surface is defined as follows:a horizontal sample surface has an inclination of 0°(h =0°);for a surface inclined at an angle a from the horizontal,the inclination angle h equals to a for upward flame spread;for downward,h =Àa .Whitewood was applied in the series of experiments.The samples had 70mm width,3mm thickness,and 400mm length.Parallel lines were marked at 20mm intervals,perpendicular to0010-2180/$-see front matter Ó2012The Combustion Institute.Published by Elsevier Inc.All rights reserved./10.1016/bustflame.2012.04.007Corresponding author.E-mail address:sunjh@ (J.Sun).the direction of spread.Theflame propagated along the wood grain.To eliminate the influence of the wood moisture content, samples were kept in a drying oven at constant temperature of 80°C until their weights kept constant all times.The rate offlame spread was timed by recording the arrival time of the pyrolysis front at each mark by a stopwatch.Then,the mark line locations and their arrival times were plotted and the slope of the linefit represents the rate of spread.Theflame shape was recorded by a digital camera at25frames per second.The characteristic parameters offlame shape are illus-trated in Fig.1.The general model forflame spread over inclined surface(see Fig.1)consists of three main regions:the burnt zone (x b),the pyrolysis zone extending to region x p,and the preheated zone(the region x fÀx p).In our experiments,the pyrolysis zone is defined as the zone on whichflame attaches to the sample surface.The preheat length d f is defined as the sample distance (x fÀx p).Flame tilt angle a is defined as the angle between the unburned surface andflame centerline,which is the line from flame tip to the center point of pyrolysis zone.The angle between flame and the horizontal direction is represented by h+a.it becomes more sensitive to the inclination angle when the incli-nation angle is greater than0°.Figure3shows theflame spread rate at different orientation an-gles.Theflame fails to spread at high altitude if the angle of inclina-tion is less thanÀ32°,and at low altitude,the extinction angle is À45°.The rates at both altitudes increase with an increase of in-clined angle,and the rate at the high altitude is lower than that at the low altitude.At both altitudes,a significant rise in the rate of spread from10°to20°was observed in Fig.3.Similar results were also found in previous experiments using PMMA samples[12]. 3.2.Discussion on the transition zoneIn this study,two parameters are measured from the video information:the preheated length(d f)and theflame angle from the horizontal direction(h+a),and the results are shown in Fig.4.A transition zone around10–20°can be observed in thefig-ures of the preheated length and the angle as a function of sample orientation at both altitudes.The preheat length shows a slight rise from h=0°to h=10°,but a further increase in the inclined angleα1x2Flame heatflux to unburned surface under different inclination at altitudes.3.Flame spread rates on plateau and plain as a function of orientation[12]Fig.4.Flame angle from horizontal direction and preheated length as a function of orientation at both altitudes.Figure 5shows the time evolution of the pyrolysis front position at two altitudes.The movement of the pyrolysis front has signifi-cantly different behavior at the angles of 0°,10°,and 20°.The posi-tion of pyrolysis front moves linearly with time at h =0°and 10°.For h =20°,the position of the pyrolysis front moves exponentially with time,which implies that the flame spread rate accelerates.Based on the analysis on the preheat length,the angle h +a and the flame spread rate,the mechanism of the transition zones around 10–20°could be explained as follows.Firstly,the interac-tion between the flame and the inclined surface is changed due to the Coanda effect,which is a response to the pressure differential induced by differences in the capacity for entrainment of air ups-lope and down-slope of the fire plume [16,17].Thus,the fire plume attaches to the inclined surface.The flame attachment is observed from the sharp drop of the angle h +a :at the inclined angle of 0°and 10°,both of the angles h +a at the two altitudes almost equals to 90°,which indicates that the flame is mainly influenced by buoy-ancy and remains in the vertical direction.Once the inclined angle exceeds 10°,the interaction between the flame and the unburned surface becomes significant and the angle between them decreases sharply.Then,the tilted flame is close to the inclined surface and can result in the enhancement of heat transfer from the flame to the unburned surface,which is indicated by the sharp rise of the preheated length.The flame spread changed from steady-state to acceleration due to the change of the heat transfer process (see Fig.5).Therefore,the transition zones reflect the change in flamedepends on the heat flux over the visible flame extension and is roughly constant [19].Therefore,t f does not vary with time in the flame spread process.From Eq.(1),we know the critical condition of flame acceleration is:d v p dt ¼d d f dt ¼d ðx f Àx p Þdt¼0ð2ÞFor upward flame spread over an inclined surface,fires will quickly become turbulent.In our experiments,turbulent flame were found after flame spread for 100mm at both altitudes even at h =0°.Quintiere [19]suggested an empirical formula to predict the length of turbulent flame spread over solid surface with an in-clined angle h :x f ¼1:02l cY o 2;1ð1ÀX r Þ1=3ð3Þwhere Y o 2;1¼0:233is the ambient oxygen mass fraction,and X r is the flame radiation fraction,which means the ratio of heat from flame radiation to heat released by fuel combustion.In general,X r %0.1.The convective plume length scale l c is a function of x p :l c ¼_q 00f D h c x pq 1c p T 1L ffiffiffiffiffiffiffiffiffiffiffiffiffiffig sin hp !2=3ð4Þwhere T 1and q 1are the ambient temperature and the air density in ambient condition,g is the acceleration due to gravity,9.8m/s 2,Table 1Some key characteristic parameters of flame shape.h (°)High altitudeLow altitudea (°)h +a (°)d f (mm)x p (mm)a (°)h +a (°)d f (mm)x p (mm)082±882 2.3±0.822981±981 5.1±1.26471072.5±17.582.512.6±2.374972±188215.7±4.32552029.4±2449.4110.4±33.86543±476393.4±1.38.685Fig.5.The time evolutions of pyrolysis front position under different inclinations:(a)at high altitude;(b)at low altitude.Y.Zhang et al./Combustion and Flame xxx (2012)xxx–xxx3P ¼1:8ð1À1=c Þðp 1Y 3=2o 2;1Þð1ÀX r Þ1=2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix p g sin h p _q 00f D h c =Lð6ÞOnce P exceeds 1,the acceleration of flame spread occurs.Therefore,the semi-empirical formula of P c ,th =1is postulated to predict the occurrence of acceleration.Moreover,the P number can also be calculated from our experimental results,and the calculated results are presented in Fig.6.As observed at both altitudes,the transition occurred around 10–20°,so the critical dimensionless number P c ,ex obtained in our experiments is in the range of 1.1–1.2.The experimental result of P c ,ex %1.1–1.2is consistent with the theoretical value of 1,which also suggests that the present theoretical analysis is reasonable.4.ConclusionsIn order to explore the inclination effects on flame spread over a wood sample surface,experiments with various sample orienta-tions were carried out in the Tibetan plateau and the Hefei plain.Some key characteristic parameters of flame spread were analyzed,such as the flame heat flux,the rate of spread and the flame shape.The main conclusions are summarized as following:(1)At both altitudes,the flame heat flux,and thus the flamespread rate increase with the inclined angle.A transition zone of the flame spread rate was found when the angle of inclination ranged from 10°to 20°.for the Doctoral Program of Higher Education of China (No.20113402110023).The authors gratefully acknowledge these supports.References[1]D.Fennel,Investigation into the King’s 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