A study of the flow field surrounding interacting line fires

Research ArticleA Study of the Flow Field Surrounding Interacting Line Fires

Trevor Maynard1 Marko Princevac2 and David R Weise3

1Bureau of Alcohol Tobacco Firearms and Explosives Fire Research Laboratory Beltsville MD 20705 USA2Department of Mechanical Engineering Bourns College of Engineering University of California Riverside Riverside CA 92521 USA3USDA Forest Service Pacific Southwest Research Station Forest Fire Laboratory Riverside CA 92507 USA

Correspondence should be addressed to Trevor Maynard trevormaynardatfgov

Received 31 August 2016 Revised 21 October 2016 Accepted 24 November 2016

Academic Editor Michael A Delichatsios

Copyright copy 2016 Trevor Maynard et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The interaction of converging fires often leads to significant changes in fire behavior including increased flame length angleand intensity In this paper the fluid mechanics of two adjacent line fires are studied both theoretically and experimentally Asimple potential flowmodel is used to explain the tilting of interacting flames towards each other which results from amomentumimbalance triggered by fire geometryThemodel was validated by measuring the velocity field surrounding stationary alcohol poolfires The flow field was seeded with high-contrast colored smoke and the motion of smoke structures was analyzed using a cross-correlation optical flow technique The measured velocities and flame angles are found to compare reasonably with the predictedvalues and an analogy between merging fires and wind-blown flames is proposed

1 Introduction

As two or more freely burning fires converge their behaviorcan change sometimes significantly (Figure 1) Flame lengthflame angle heat release rate and propagation rate (forspreading fires) have all been observed to increase duringflame merging [1 2] Aside from being an intriguing physicalproblem fire interactions can prove challenging for firefight-ers who are often required to adjust tactics to maintain con-trol of the fire Fire interactions are used frequently to controlintensity of prescribed vegetation fires in order to achievenatural resource management objectives [3ndash5]

Flame interactions are common in both vegetation andstructure fires During wildland fires interactions may occurnaturally or may be induced to produce desired behavior(Figure 2) Increased flame length and fire intensity can beespecially problematic in prescribed (controlled) vegetationfires as this can lead to undesired tree and plant mortality [1]In addition the ability of awildland fire to propel embers overlong distances (which can serve as new ignition sources) isdirectly related to its intensity [6] Flame interactions are alsoprevalent in urban area fires Countryman [7] cites numerousconflagrations in the early 20th century including the bomb-ings of Dresden and Hamburg Germany during World War

II as prime examples of destructive fire behaviorThese citieswere principally damaged not by the bombs themselves butby the resulting groups of fires (ldquomass firesrdquo) which inducedextreme winds and burning rates

The physical interaction of two flames is a complexprocess which has been examined both theoretically andwithnumerical physical models [8] Liu et al [9] showed that theburning rate of pool fire arrays increased as their separationdistance decreased This effect occurred until a critical sep-aration was reached below which the burning rate began todecreaseThey explained the initial rise in combustion rate asa result of an increased radiation view factor (enhancementof heat feedback to burning fuels) while the eventual declinewas due to restriction of airflow into each fire For spreadingfires as flames converge the radiant energy emitted by eachflame heats the intervening fuels leading to accelerated firespread [10] More recently Lu et al [11] studied the mergingbehaviors of flames ejected from neighboring windows inreduced-scale compartment fires at constant rates of heatrelease As distance between windows decreased the indi-vidual flames eventually merged into a single flame Theyobserved three regimes of merging continuous intermittentand unmerged Intermittent merging began at a separationdistance of119863119885 lt 03 where119863 is the separation distance and

Hindawi Publishing CorporationJournal of CombustionVolume 2016 Article ID 6927482 12 pageshttpdxdoiorg10115520166927482

2 Journal of Combustion

Figure 1 Merging of a ring of fire burning in longleaf pine understory (Pinus palustrisMill) Note the significant change in fire behavior asthe flame fronts converge

Win

d

Merging zone

RoadBackfire from fuel break

Advancing flame front

(a)

Merging zones

Advancing spot fire

(b)

Fire array (pool fires structures etc)

Merging zones

(c)Figure 2 Example scenarios for fire interactions (a) backfiring from a fuel break to stop an advancing wildfire (b) merging of individualvegetation fires and (c) interaction of multiple burning objects (structures pool fires etc)

119885 is the unmerged flame height Flames were continuouslymerged for 119863119885 lt 01 The probability of merging was pri-marily a function of window separation but window dimen-sion also had an effect Kuwana et al [12] studied the behaviorof two adjacent microscale slot flames and noted that theoverall heat release increased as burner space decreased butboth flames eventually merged into a unified flame

While much of the work on merging fires has focused onradiant heat transfer entrainment and convection also appearto play a significant role in interactions As two flames con-verge their independent entrainment fields interact resultingin an inward tilting of the flames [13 14] Flame tilt affects firebehavior by increasing the amount of radiant heat transfer(view factor) to the surface [15] by increasing the horizontalcomponent of convective heat flux forward of the flame [16]Baldwin et al [17] theorized that flame tilt is a product of theflow restriction between flames which causes a pressure dropthat competes with buoyancy A similar mechanism has alsobeen proposed for noncombusting buoyant plumes at labo-ratory scale [18] Recent work on wind-blown flames (thoughnot interacting) has provided additional insight into themechanisms of flame tilt Jiang and Lu [19] measured theburning rate and flame angle of wind-blown pool fires anddemonstrated that flame tilt was a function of Froude number(Fr) Flame tilt initially increased rapidly in the range of 0 ltFr lt 1 but quickly moderated for Fr gt 2 Hu et al [20] corre-lated flame tilt angle against the ratio of cross-flow speed to

the characteristic buoyant velocity of heptane pool fires andthese results were recently extended to optically thin heptanefires in cross-flow [21] Tang et al [22] demonstrated thatfor small pool fires flame tilt was more easily influenced bywind speed as opposed to larger fires Similar studies havebeen done for pool fires in momentum-dominated regimes[23 24] and flame angle was shown to be a function of thecross-flow to burner verticalmomentum ratio Tang et al [25]studied the behavior of wind-blown gas burner flames inthe presence of walls (walls parallel to cross-flow) whichare potentially analogous to merging flames (entrainmentrestricted) Interestingly as the flame was moved closer tothe wall for the same cross-flow speed flame tilt decreasedTheir observations of rate of flame angle change with cross-flow speed were similar to that of Jiang and Lu [19] Tang et al[26] performed experiments with rectangular pool fires ofvarying aspect ratio and demonstrated that flame angleincreased with cross-flow velocity but aspect ratio did nothave a major impact

Flame length for interacting fires has also been studiedFor gas burners with constant heat release rate Wan et al[27] demonstrated that the dependency of flame length onfirespacing was coupled with heat release rate For smaller heatrelease rates flame length was largely unchanged as spacingbetween fires decreased while it was affected at higher rates ofheat releaseThey also observed that merging occurred whenflames were at a spacing of less than 30 percent of the single

Journal of Combustion 3

flame height Lu et al [11] also demonstrated that the heightof merging facade flames increased as separation distancedecreased For noninteracting pool fires in cross-flows flamelength has been shown to increase linearly with the Froudenumber based on wind speed [22] For buoyant line-sourcejet flames in cross-flows Zhang et al [24] showed that verticalflame height correlated with the ratio of fuel jet to cross-flowmomentum to the 25 power and flame length (horizontal)correlated with the product of the momentum ratio and Fr tothe 13 power

For line fires Baldwin et al [17] used Bernoullirsquos equationcombined with the entrainment assumption to develop amodel for flame length and angle as a function of separationdistance line length and flame zone depth (width of flame)However as discussed by Smith et al [28] classical plumemodels which assume that entrainment is due only to the tur-bulent diffusion of momentum as the plume expands [29] arenot completely appropriate for characterizing the inductionof air into large fires Unlike isothermal buoyant plumes thecombustion process releases a tremendous amount of heatand requires significant amounts of oxygen for sustenanceTurbulent entrainment alone cannot provide a sufficientvolume of air leading to the existence of a horizontal inflowover the fire perimeter called the fire windThey note that thisis far-field entrainment where the dynamic pressure field isthe medium which communicates the effect of buoyancy tothe surrounding fluid

In this paper we develop a simple model to describe thetilting and interaction of adjacent flames The model usesthe conservation of linearmomentum coupledwith potentialflow theory to describe the behavior of the flowfield surroun-ding two fires as a function of separation distanceThemodelis compared with experiments to determine the velocity fieldoutside of adjacent alcohol pool fires using cross-correlationoptical flow methods The model and experimental resultsare discussed in the context of potential effects on overall firebehavior and an analogy between merging flames and wind-driven single flames is suggested

2 Theory

Fires produce strongly buoyant plumes composed of rapidlyascending gases Continuity requires this rising fluid mass tobe replaced by a horizontal inflow For line fires the inflow isprimarily perpendicular to the firersquos axis (entrainment at theedges becomes insignificant) As two line fires converge flowon the inboard side of each flame (nearest to the neighboringflame) is restricted resulting in asymmetric entrainmentThis leads to an imbalance of forces acting on the fire plumecausing it to tilt in the direction of least inflow velocity

A two-dimensional slice of a line fire is shown in Figure 3We assume the fire is a fully developed turbulent diffusionflame If the control volume surrounding the flame is of height119871 width 119863 and depth (into the page) 119882 the plume anglefrom vertical can be estimated as

120579 = tanminus1 (119865119884119865119885) (1)

i oni no

120579z+

y+

w nu

D

L

Figure 3 Control volume for momentum balance

where 119865119884 and 119865119885 represent the horizontal and vertical forcesacting on the control volume respectively These forces canbe determined using the conservation of linear momentum

119865119884 = 120597120597119905 [int119881 120588119900V119900119889119881 + int119881 120588119894V119894119889119881]+ int119860120588119900V119900 (119900 sdot V119900) 119889119860 + int

119860120588119894119906119894 (119894 sdot V119894) 119889119860

119865119885 = 120597120597119905 [int119881 120588119901119908119900119889119881] + int119860 120588119901119908 (119906 sdot 119908) 119889119860

(2)

where V and 119908 are the components of horizontal and verticalvelocity respectively 120588 is the fluid density and subscripts 119900119894 and 119901 represent the outboard inboard and interior regionsof the plume respectively If we assume that all inflows andoutflows are steady (implying that the fire has achieved quasi-steady state and is not influenced by variations in atmosphericflow) that combusting fuel vapor enters the control volumewith negligible momentum and that the ambient density onthe inner side (inboard) of the flame is equivalent to theoutside (2) can be simplified and expressed as force per unitlength of flame front

1198651015840119884 = 120588119900119871 (V1199002 minus V1198942)

1198651015840119885 = 1205881198751198631199082(3)

Flame angle is then represented as

tan 120579 = 119860(V1198902

1199082 ) (4)

where V119890 is the ldquoexcessrdquo inflow velocity from the outboardedge

V119890 = radicV1199002 minus V1198942 (5)

and 119860 is a dimensionless parameter

119860 = 120588119900119871120588119901119863 (6)


Although 119863 is the width of the control volume it is alsoapproximately the width of the base of the flame 119871119863 forflames has been related to heat release rate for a number offire configurations [30 31] most commonly to 119876lowast11986325 where119876lowast119863 is the dimensionless heat release rate

119876lowast119863 = 12058801198881199011198790radic11989211988211986332 (7)

where is the rate of heat release and 1205880 119888119901 and 1198790 are thedensity specific heat and temperature of ambient air respec-tively Sugawa et al [32] performed experiments on interact-ing line fires with gas burners and showed that 119871119863 is pro-portional to119876lowast11986323 For natural fires119876lowast119863 ranges from approx-imately 01 to 5 [33] The parameter 119860 can then be expressedas

119860 sim 120588119900120588119901119876lowast119863

119899(8)

and is of order 01ndash1 for natural fires for 119899 lt 1Note that (4) requires the velocities to be known Since

the horizontal inflow is driven by buoyancy we expect thesevelocities to be related to the vertical velocity of the plume

As a first approximation we propose that the horizontalflow field surrounding the fires is analogous to the potentialflow field generated by two adjacent line sinks of fluid Thisconcept is not new as Baldwin et al [17] mentioned usingpotential flow in the study of merging flames by modelingindividual fires as point sinks of fluidThe idea was employedby Weihs and Small [34] who studied the interaction of fireplumes by modeling each fire as a vertical distribution ofpoint sinks (in the flaming region) and point sources (in theupper ldquothermal plumerdquo region) Additionally the existenceof sink-like inflow near fires is supported by Smith et al[28] who studied natural convection above strongly heatedline sources of finite width but infinite length More recentlyKaye and Linden [35] used potential flow to approximatethe entrainment field surrounding adjacent axisymmetricplumes Since a line sink can be approximated as a series ofclosely spaced point sinks this is a natural extension of thisconcept Lu et al [11] also proposed that the interaction ofmerging facade flames is due to interactions of the potentialflows generated by the firesrsquo entrainment fields

An incompressible potential flow field is one which satis-fies Laplacersquos equation Since solutions to Laplacersquos equationcan be linearly combined the solutions of multiple flowfeatures (sources sinks uniform flows etc) can be added toconstruct the aggregate velocity field [36] Of course poten-tial flow is not without its limitations To satisfy Laplacersquosequation the velocity field must be both incompressible andirrotational Incompressibility is a reasonable assumptionthough the combustion process itself is one of rapid expan-sion the flow field surrounding the fire is of minimal velocityIrrotationality however is more difficult to justify The flowfield surrounding fires often exhibits rotation at multiplescales This is evident by the well-organized convectioncolumns observed above large fires and by the existence offire whirls highly rotational vertical columns of combusting

Line sinksy

x

S2

1

985747

y = 0

x = 0

o

i

+Δs

minusΔs

Figure 4 Schematic for potential flow of two adjacent line sinks

gas However large convection columns only appear to play asignificant role for very large fires or groups of fires [2] whichare beyond the scope of this study Moreover fire whirls andother vortices are highly transient so it may be argued thatpotential flow represents an average velocity field which isperiodically perturbed by these local events

This complex potential for a distributed line sink whichconsists of an infinite number of closely spaced point sinksdistributed over a defined length is given by Paraschivoiu[37]

120601 (119911) = minus1198962120587ℓ [119911 ln 119911 minus (119911 minus ℓ) ln (119911 minus ℓ)] (9)

where 119911 is the complex number 119909 + 119894119910 ℓ is the length of theline sink and 119896 is the strength of the sink The derivative of(9) yields the complex velocity

119881 (119911) = 119889120601119889119911 =minus1198962120587ℓ ln

119911119911 minus ℓ (10)

where119881 = 119906minus 119894V and 119906 and V are the components of velocityparallel and normal to the line sink respectivelyThe complexvelocity for two neighboring line sinks is

119881 (119911) = 1198891206011119889119911 + 1198891206012119889119911= minus1198962120587ℓ [ln(

11991111199111 minus ℓ) + ln( 11991121199112 minus ℓ)] (11)

where subscripts 1 and 2 reference the line sinks shown inFigure 4 and 119896ℓ is the strength of the sink per unit lengthwhich has units of velocity Physically 119896ℓ represents theamount of fluid terminating in the sink per unit length perunit time In a fire buoyancy causes fluid to rise with velocity119908 This rising fluid acts as a sink since it has to be replacedthrough the horizontal inflow Thus for fires we make theassumption that 119896ℓ is equivalent to the vertical velocity ofthe fire plume 119908

The effect of separation distance on the potential flowfieldfor two distributed line sinks is shown in Figures 5 and 6Each line sink draws in fluid from all directions at a constantrate As the separation distance between lines decreases themagnitude of the inboard velocity component normal to theline sink is reduced To satisfy continuity this decrease is


S985747 = 10 S985747 = 025

Figure 5 Streamlines and velocity field for two converging line sinks

00 05 10 15S985747

Inboard velocityOutboard velocity

0

01

02

03

04

05

06

07

08

09

1

vw

Figure 6 Potential flow model effect of separation distance oninboard and outboard velocities normal to the line sink at 119909 = 0normalized to vertical velocity

balanced by an increase in flow velocity on the outside of thesink (Figure 6) Since the magnitude of the inflow velocityis proportional to the source strength the velocity differenceacross each line sink normalized to vertical velocity is afunction of 119878ℓ only

Qualitatively the velocity difference can be explained byconsidering the path of fluid parcels as they enter the regionbetween sinks As shown in Figure 5 streamlines enteringthe central region are nearly parallel to the sinks and parcelsenter the region with almost no 119910-component of velocityOnce the parcel is between the sinks it will start acceleratingtowards the nearest one As the separation distance decreasesso does the length scale of parcel acceleration which ulti-mately limits the inboard velocity Additionally the neighbor-ing fire imposes a horizontal pressure gradient force whichopposes parcel acceleration further reducing velocity

3 Experiments

31 Experimental Setup To investigate the validity of theproposed model for merging flames experiments were per-formed to measure the velocity field surrounding stationaryline fires A schematic of the experiment is shown in Figure 7Two rectangular steel pans (ℓ = 150 cm 119863 = 7 cm) eachcontaining equal volumes of liquid fuel (isopropyl alcohol91 by volume) were placed next to each other at six differentseparation distances from 119878ℓ of 01 to 15 For line fires Yuanand Cox [38] give a functional relationship between flamelength and heat release rate per unit length

119871119891 = 003411987123 (12)

where 119871119891 is the total length of flame (m) (equal to 119871 forvertical flames) and 119871 is the heat release rate per unit length(kWm) For the flame lengths observed in our experiments(10) yields a heat release rate per unit length of approximately50 kWm which is in the low range of intensity for vegetationfires in surface fuels [39]

For each separation distance the behavior of the leftmostfire was captured by a high-definition video camera with aframe rate of 30 frames per second (standard frame rate for aconsumer-grade video camera) with the fire placed directlyin the center of the frame Prior to testing the frame wasspatially calibrated (using a meter stick) to determine thelinear dimension per pixel at the center of the fire To visualizethe surrounding flow field colored smoke cartridges (ammo-nium chloridepotassium chlorate) were placed on bothsides of the fire (Figure 8) The high-contrast smoke fromcartridges made it easy to identify fluid structures as theywere drawn into the fire plumes Each fire was ignited simul-taneously and allowed to burn for at least 10 seconds prior tocapture Although 10 seconds was the minimum many wereallowed to burn for a period closer to 30 seconds priorto video capture Video was captured for approximately 60seconds during the steady burning period

32 Analysis To obtain the best possible insight intomergingfire entrainment a method of nonintrusive quantitative


Video camera

Entraining smoke plumes

S

oo

i

985747

Figure 7 Schematic of pool fire experiments Pool fires were seededby colored smoke plumes which were entrained into the regionssurrounding the flames

Figure 8 Use of smoke cartridges for flow field visualizationExaggerated flame angle on right is fictitious due to perspectivedistortion (figure is cropped camera is actually centered on left fire)

visualization capable of determining the entire velocity fieldover a relatively large region was desired One common tech-nique for this is particle image velocimetry (PIV) In PIVthe velocity field is ldquoseededrdquo by reflective particles which areassumed to follow the flow A pulsed laser is used to illumi-nate the particles in a thin plane and two images are thencaptured in rapid succession The images are compared todetermine particle displacement using a cross-correlationalgorithm yielding the velocity field [40] PIV has success-fully been deployed on pool fires [41] as well as for fires invegetative fuel beds [42] However for the scale of the presentexperiments PIV has several distinct limitations The spatialresolution of PIV is directly related to the size density andhomogeneity of seeding particles In our case the region ofinterest spans several meters (both horizontally and verti-cally) which presents severe difficulties in obtaining adequateparticle density and exceeds the size of plane produced bythe focused lasers Since our goal was to determine the bulkmotion of the entrainment field over a large region wedetermined that PIV would not be the ideal option Insteadwe chose to pursue a more general ldquooptical flowrdquo analysis ofwhich PIV may be considered a specialized type

The optical flow field is the velocity field which resultsfrom the motion of an object within an image frameThoughnumerous classes of optical flowmethods exist the two mostcommon approaches involve the gradient-based analysis ofa conserved image signal [43] and the cross-correlationof image features [40] Cross-correlation has been used toobtain the time-averaged velocity field for plumes with highvisible contrast consisting of discrete fluid structures whichrotate translate and deform as they rise namely oceanhydrothermal vents [44] These plumes are analogous to thesmoke used for flow visualization in our experiments In ourcase the smoke originates from a point source (the cartri-dge) but rapidly assimilates to the local flow field In cross-correlation optical flow the image cross-correlation coeffi-cient is defined as

119862119891119892 (119898 119899) = sum119894

sum119895

119891 (119894 119895) times 119892 (119894 + 119898 119895 + 119899) (13)

where 119891(119894 119895) and 119892(119894 119895) are the image intensity distributionsin the first and second images respectively and 119898 and 119899 arethe pixel offsets between each image Essentially the cross-correlation function attempts to match the progression ofimage features from frame to frame Images are parsed intointerrogation regions which are compared between frames ofknownΔ119905The displacement vector is then calculated by find-ing the displacement of the correlation peak between framesthat is the locations where the regions best match each otherA similar technique using thermal images from IR cameraswas used to estimate flow fields within a flame [45]

33 Experimental Methods

331 Velocity Field For each experiment three separateintervals each with a duration of five seconds (150 frames)were analyzed For each separation distance the experimentwas replicated three times to estimate error Image analysiswas performed using OpenPIV [46] an open-source cross-correlation algorithm designed for use with PIV imagery Foreach capture three separate regions outboard inboard andupper (Figure 9) were analyzed to determine the relevantvelocity fields The inboard and outboard regions extendedlaterally from the location of the respective smoke cartridge(25 cm from the reservoir) to the approximate flame edgeand vertically to the approximate flame tip The upper plumeregion was located directly above the flame tip and spannedseveral flame widths Each region was approximately 200 times200 pixels An interrogation window of 32 times 32 pixels andan overlap of 8 times 8 pixels were used for the cross-correlationanalysis

Themean velocity fields were obtained by taking the aver-age of the instantaneous fields over the capture duration (fiveseconds) For the horizontal inflow (outboard and inboard)themean velocity value was determined by taking the averagevalue of the horizontal velocity profile from the base of theflame to its tip directly next to the flame Vertical velocitywas determined by taking the maximum value of the verticalvelocity in a horizontal plane at the top of the intermittentflame zone as defined by McCaffrey [47]


(a) (b) (c)

Figure 9 Outboard (a) inboard (b) and upper (c) plume instantaneous velocity fields from OpenPIV processing

0 5 10 15 20x (cm)

y (c

m)

0

5

10

15

20

25

v (cm

s)

0

2

4

6

8

10

12

minus2

minus4

(a)

v (cm

s)

0 5 10 15 20x (cm)

y (c

m)

0

2

4

6

8

10

12

minus2

minus40

5

10

15

20

25

(b)

Figure 10 Time-averaged outboard (a) and inboard (b) velocity fields for 119878119867119878 = 325 (119867119878 = height of single flame) Duration of averagingperiod is 5 seconds

332 Flame Height and Angle Mean flame height and anglewere determined by analyzing the spatially calibrated videoframes Since the flamersquos brightness was much greater thanthe smoke and background an algorithmwas used to identifythe location of the flame boundary in each frame by searchingfor continuous regions of maximum pixel intensity Similarmethods have been used to determine statistical propertiesof flame geometry and luminous intensity [48 49] Howeverthis method was not amenable to determining flame anglesince the flame shape is irregularmaking it difficult to detect ahorizontal midpoint at the flame tip Instead flame angle wasdetermined by measuring the angle between a line parallelto the flamersquos axis and a line normal to the surface this wasdone for five sample frames per capture via image processingsoftwareThe length of the flame (119871119891) was calculated from theflame height and angle [50]

119871119891 = 119867cos 120579 (14)

where 119867 is the maximum height of visible flame above thesurface

4 Results

41 Velocity Field An example of the time-averaged outboardand inboard velocity fields is shown in Figure 10 Data isshown for the separation distance relative to the height of asingle flame of 325 (119878119867119878 = 325) For the outboard plumehorizontal inflow velocities of approximately 10 cms werepresent for all experiments which is comparable to thevalues measured by Zhou and Gore [51] using laser Dopplervelocimetry around a 71 cm toluene pool fire Mean outboardand inboard velocities normalized to vertical velocity as afunction of 119878119867119878 are presented in Figure 11 As expected thevelocity on the inboard side of the flame was lower anddecreased with decreasing separation distance while the out-board velocity increased slightly (Figure 11) For the smallestseparation distance (119878119867119878 = 03) flames were almost com-pletely merged For this case inboard velocity could not bemeasured but was assumed to be zero Immediately evidentis the existence of a velocity differential at even the largestseparation (119878119867119878 = 5) which suggests that fire interactionscan begin to occur at even larger distances Overall the dataagree reasonably with the behavior predicted by the poten-tial flow model except at the smallest separation distance


00 10 20 30 40 50

vw

Outer (exp)Outer (model)

Inner (exp)Inner (model)

0

02

04

06

08

1

12

14

16

18

SHS

Figure 11 Mean outboard and inboard velocities normalized tovertical velocity Error bars represent one standard deviation of themean

(119878119867119878 = 03) At this distance the flames are fully mergedat a short distance above the surface and the inboard edge ofthe flame can no longer entrain in the 119910-direction above themerging height Comparison of vertical and inflow velocitiesfor the merged plume becomes more complicated since theyare both dependent on the degree of merging Two fullymerged plumes of equal strength have twice the buoyancyflux of each plume [50] but this is not necessarily manifestin the vertical velocity since destructive interference betweenplumes may cause it to decrease [52]

Vertical velocity increased slightly with decreasing sep-aration distance until 119878119867119878 lt 2 below which it decreasedrapidly (Figure 12) This is likely an effect of burning ratewhich is proportional to the heat release rate (HRR) of the fire[53] For line plumes vertical velocity scales with buoyancyflux and thusHRR to the 13 power As discussed by Liu et al[9] as proximate pool fires approach each other augmentedradiant feedback accelerates burning However as separationdistance becomes very small entrainment becomes restrictedand burning rate decreases Our measurements of verticalvelocity appear to agree with this notion though burning ratewas not explicitly measured

42 Flame Angle Observed flame angle versus V11989021199082 is

shown in Figure 13 Flame angle for the two closest separationdistances is not shown since the flames weremerged for theseexperiments The slope of the linear fit in Figure 13 gives avalue of 0843 for 119860 (see (6))

Overall both the observed and measured values (see(4)) agree reasonably with each other and with the anglepredicted by potential flow formost of the experimental rangebut diverge from the model as the flames begin to merge(Figure 14) This is to be expected since at small separationdistances 119878119867119878 lt 2 the flames are forced to merge withthe neighboring buoyant plume gradually straightening until

00 10 20 30 40 500

02

04

06

08

1

12

14

SHS

ww

s

Figure 12 Vertical velocity normalized to single flame verticalvelocity Error bars represent one standard deviation of the mean

00 01 02 03 04 05 060

01

02

03

04

05

06

R2 = 07926

y = 08432x

tan(

120579) (

calc

ulat

ed)

w2 (observed)e2

Figure 13 Observed flame angle versus V11989021199082 for nonmerged

separation distances

they eventually return to the vertical as a fully merged singleplume

43 Flame Length In general flame length was not signifi-cantly affected by interaction (Figure 15)This differs from theresults obtained by other researchers using gas burners whoobserved increases in flame length as fires converged [12 54]However in their studies the burning rate was kept constantFor freely burning pool fires burning rate is not controlledFor line fires flame length is related to heat release rate whichis proportional to the burning rate Asmentioned above fromour measurements of vertical velocity it was inferred thatburning decreased as the flames began to merge Thus thepotential increase in flame length due to merging effects wasmasked by the reduced burning rate This issue is worthy offurther study since flame lengths are observed to increasein merging vegetation fires where burning rate is inherentlycoupled with fire behavior


00 10 20 30 40 50

Calculated (Eq 4)Observed

Model

Flames merged

0

10

20

30

40

50

60

70

80

90

SHS

Ang

le (120579

)

below SHS asymp 2

Figure 14 Flame angle versus separation distance Measured valuecalculated using119860 = 0843 Flames began to merge at spacing below119878119867119878 = 2 Error bars represent one standard deviation of the meanLarge uncertainty in measured value is due to the summation ofrelative uncertainty of the squares of three measured values

0

02

04

06

08

1

12

14

SHS

LH

S

00 10 20 30 40 50 60 70

Figure 15 Flame length versus separation distance Flames beganto merge below 119878119867119878 = 2

5 Discussion

51 Do Interacting Flames Become ldquoWind-Blownrdquo FlamesMany of the effects observed during fire merging are similarto those which occur with single flames burning under theinfluence of an ambientwind including increased flame angleand rate of spread [50 55] Asmentioned in the introductionwind can have a marked effect on fire behavior

The model and experiments discussed in this papersuggest that converging line fires are subject to nonuniformentrainment as a result of their position relative to each otherThis leads to the development of a velocity difference normalto each flame front causing the flame angle to depart fromvertical Of interest is whether this velocity difference has thesame effect as an ambient wind of equal magnitude which

could suggest that merging flames may transition to ldquowind-drivenrdquo fire behavior as their separation distance reaches acritical value

At present there is no universally accepted definition forwhat constitutes a wind-driven fire Byram [55] made oneof the earliest attempts to classify fire behavior relative tothe influence of ambient wind He introduced the convectionnumber

119873119862 = 21198921198681205881198861198881199011198791198861199061198863 (15)

where 119868 is the fireline intensity (energy released per unitlength of fire front) 120588119886 is the density of ambient air 119888119901 isthe specific heat of air at constant pressure 119879119886 is the ambientair temperature and 119906119886 is the ambient wind velocity Theconvection number represents the rate at which thermalenergy is converted to kinetic energy in the convectioncolumn (ldquopower of the firerdquo) relative to the horizontal fluxof kinetic energy from the mean flow (ldquopower of the windrdquo)Based on analysis of several large fires Rothermel [47] useda convection number of unity to differentiate between plume(buoyancy) dominated andwind-driven firesThe convectionnumber for a line fire can be represented as the inverse of aFroude number based on buoyancy flux [50 56 57]

119865119877 = 1199061198863

119887119865 = 2119873119862minus1 (16)

where 119887119865 is the buoyancy flux per unit length of source

119887119865 = 119892119868120588119886119888119901119879119886 =

11990611988631198731198882 (17)

Nelson et al [57] derived (16) by relating line fire plumeswith those from ocean outfall diffusers which were studiedby Roberts [58] Based on his analysis and experiments heproposed three distinct regimes for line plumes subject to amean flow For small Froude numbers (FR lt 02) the plumeis dominated by buoyancy and the flow is strongly verticalFor large Froude numbers (FR gt 1) there is an excess ofinflow forcing the plume to stay attached to the surface andpropagate downstreamThe intermediate regime (02 lt FR lt1) represents a transition between the two extremes Nelsonet al [57] applied this criterion to line fires Using (16) theyproposed that 119873119862 gt 10 implies that wind has a minimaleffect on the fire plume while119873119862 lt 2 implies a strong windinfluence

Rouse et al [59] studied interacting turbulent line plumesand showed that the vertical velocity scaled with the buoy-ancy flux per unit length as

119908 = 11988711986513 (18)

Substitution of this vertical velocity into (16) suggests theconvection number for line fires scales as a function of inflowand vertical velocities only

119873119862 asymp ( 119908119906119886)3 (19)


00 10 20 30 40 50

ExperimentModel

01

1

10

100

1000

SHS

Nc

Figure 16 Convection number Error bars represent one standarddeviation of the mean

An identical result can be obtained by substituting thecharacteristic buoyant velocity for a fire defined by NelsonJr [60]

119908119861 = ( 2119892119868120588119886119888119901119879119886)

13

(20)

into the first equality of (17) If we assume the asymmetricentrainment caused by fire convergence to have the sameeffect as an ambient wind of equal magnitude then theconvection number can be represented a function of 119878119867

119873119862 = ( 119908V119900 minus V119894

)3 = 119891( 119878119867) (21)

Using (21) the convection number from our experiments isplotted in Figure 16 Using the abovementioned criteria thetransition to wind-driven fire behavior in our experimentsbegins at 119878119867 sim 1 It must be mentioned that the convectionnumber was developed as a metric to study the behavior ofconvection columns above large fires As such it was origin-ally derived using a complex coupled atmospherethermody-namicmodel [60 61] effects which are clearly not consideredin our analysis However its representation as a function ofbuoyancy flux clearly illustrates its local importance on thebehavior of wind-driven flames as indicated by the exper-iments of Nelson Jr and Adkins [62] and Weise and Biging[56]

6 Conclusions

Theeffects associatedwith flame interaction are important forboth the physical understanding and practical control of fireThis paper developed and validated a simplemodel to explainflame tilt inmerging flames as a result of asymmetric entrain-ment Asymmetric entrainment causes flames to tilt as if exp-osed to an ambient wind which may explain why interacting

fires often exhibit behavior similar to wind-blown flamesTheproposed mechanism resulted from an imbalance of hor-izontal momentum across the flame front caused by flowrestriction on the inboard edge of the flame due to the com-bined effects of reduced acceleration length and the opposingdynamic pressure gradient generated by the neighboring firePotential flow was found to be a reasonable assumption forthe entrainment field surrounding interacting fires Cross-correlation optical flow analysis proved to be a useful methodfor estimating the flow field surrounding fires however thismethod is inherently less accurate than planar measurementtechniques such as particle image velocimetryMeasurementsat field scale are recommended to determine if the laboratoryresults scale to larger spreading fires such as prescribed burnswhere ignition patterns intentionally produce merging flamezones If the similarity of flames from merging line fires withflames from wind-blown fires remains at field scale simpleimprovements to existing fire models to include merging firebehavior may be possible

Nomenclature

119860 Dimensionless parameter 120588119900119871120588119901119863119887119891 Buoyancy flux per unit length of source119862 Image cross-correlation coefficient119888119901 Specific heat at constant pressure119863 Control volume width119865 Force acting on control volume119891 First image in cross-correlation119892 Second image in cross-correlation119892 Gravitational acceleration constant 981ms2

119867 Maximum visible flame height119868 Fireline intensity119896 Strength of line sink119871 Control volume height119871119891 Flame length (equal to 119871 for vertical flames)ℓ Length of line sink119898 Horizontal pixel offset for cross-correlation119899 Vertical pixel offset for cross-correlation119873119862 Convection number Heat release rate119876lowast119863 Dimensionless heat release rate119878 Separation distance between fires119879 Temperature119906 Ambient wind velocity for convection number119881 Complex velocity 119906 minus 119894V for a distributed line sinkV Horizontal velocity component119882 Flame depth119908 Vertical velocity component119911 Complex number 119909 + 119894119910120579 Fire plume angle (from vertical)120588 Density120593 Complex potential for a distributed line sink


Subscripts

119886 Ambient condition119894 Inboard region of fire plume119900 Outboard region of fire plume119901 Interior region between fire plumes119904 Single flame119884 Horizontal (119910-direction)119885 Vertical (119911-direction)Additional Points

Summary for Table of Contents The convergence of separateflame fronts is often accompanied by changes in fire behaviorIn this paper a simple fluid entrainment model is used todescribe themechanism of flame tilting formerging line firesThe model was validated with experiments using laboratoryscale line fires and an analogy between merging flames andwind-blown flames is proposed

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Financial support for this research was provided by theNational PERISHIP Fellowship in Hazards Risks and Dis-asters Joey Chong of the USDA Forest Service Pacific South-west Research Station provided a great deal of support duringexperiments The authors would also like to thank ChristianBartolome Stephen Coffer Mitchell Shinn Jitmohan MalayJahangir Ashraf Eric Peng and Shen Ren for their assistanceduring laboratory experiments

References

[1] RW Johansen ldquoPrescribed burningwith spot fires in theGeor-gia Coastal Plainrdquo Georgia Forest Research Paper 49 GeorgiaForestry Commission Macon Ga USA 1984

[2] M A Finney and S S McAllister ldquoA review of fire interactionsand mass firesrdquo Journal of Combustion vol 2011 Article ID548328 14 pages 2011

[3] R E Martin and J D Dell ldquoPlanning for prescribed burning inthe inland northwestrdquo General Technical Report GTR-PNW-076 USDA Forest Service Pacific Northwest Forest and RangeExperiment Station Portland Ore USA 1978

[4] L R Green ldquoBurning by prescription in chaparralrdquo GeneralTechnical Report GTR-PSW-051 USDA Forest Service PacificSouthwest Forest and Range Experiment Station BerkeleyCalif USA 1981

[5] D D Wade J D Lunsford M J Dixon and H E Mobley ldquoAguide for prescribed fire in southern forestsrdquo Technical Publica-tion R8-TP-11 USDA Forest Service Southern Region AtlantaGa USA 1989

[6] F A Albini ldquoTransport of firebrands by line thermalsrdquoCombus-tion Science and Technology vol 32 no 5-6 pp 277ndash288 2007

[7] C M Countryman ldquoMass fires and fire behaviorrdquo ResearchPaper RP-PSW-019 USDA Forest Service Pacific Southwest

Forest and Range Experiment Station Berkeley Calif USA1964

[8] D Morvan C Hoffman F Rego andWMell ldquoNumerical sim-ulation of the interaction between two fire fronts in grasslandand shrublandrdquo Fire Safety Journal vol 46 no 8 pp 469ndash4792011

[9] N Liu Q Liu J S Lozano et al ldquoGlobal burning rate ofsquare fire arrays experimental correlation and interpretationrdquoProceedings of the Combustion Institute vol 32 pp 2519ndash25262009

[10] K G Huffman J RWelker and CM Sliepcevich ldquoInteractioneffects of multiple pool firesrdquo Fire Technology vol 5 no 3 pp225ndash232 1969

[11] K Lu L Hu M Delichatsios F Tang Z Qiu and L HeldquoMerging behavior of facade flames ejected from two windowsof an under-ventilated compartment firerdquo Proceedings of theCombustion Institute vol 35 no 3 pp 2615ndash2622 2015

[12] K Kuwana S Kato A Kosugi T Hirasawa and Y NakamuraldquoInteraction of two micro-slot flames heat release rate andflame shaperdquo Journal of Physics Conference Series vol 557 no1 Article ID 012079 2014

[13] O Sugawa and W Takahashi ldquoFlame height behavior frommulti-fire sourcesrdquo Fire and Materials vol 17 no 3 pp 111ndash1171993

[14] S Schalike K BMishra K-DWehrstedt and A SchonbucherldquoLimiting distances for flame merging of multiple n-heptaneand di-tert-butyl peroxide pool Firesrdquo Chemical EngineeringTransactions vol 32 pp 121ndash126 2013

[15] G M Byram H B Clements M E Bishop and R MNelson Jr ldquoFinal reportmdashProject Fire Model an exploratorystudy of model firesrdquo Contract OCD-PS-65-40 USDA ForestService Southeastern Forest Experiment Station Office of CivilDefense Asheville NC USA 1966

[16] P G Baines ldquoPhysical mechanisms for the propagation of sur-face firesrdquoMathematical and ComputerModelling vol 13 no 12pp 83ndash94 1990

[17] R Baldwin P H Thomas and H G G Wraight ldquoThe mergingof flames from separate fuel bedsrdquo Fire Research Note 551Boreham Wood Fire Research Station Borehamwood UK1964

[18] L Pera and B Gebhart ldquoLaminar plume interactionsrdquo Journalof Fluid Mechanics vol 68 no 2 pp 259ndash271 1975

[19] P Jiang and S X Lu ldquoPool fire mass burning rate and flame tiltangle under crosswind in open spacerdquoProcedia Engineering vol135 pp 260ndash273 2016

[20] L Hu S Liu J L De Ris and L Wu ldquoA new mathematicalquantification of wind-blown flame tilt angle of hydrocarbonpool fires with a new global correlation modelrdquo Fuel vol 106pp 730ndash736 2013

[21] L Hu C Kuang X Zhong F Ren X Zhang and H Ding ldquoAnexperimental study on burning rate and flame tilt of optical-thinheptane pool fires in cross flowsrdquo Proceedings of the CombustionInstitute 2016

[22] F Tang L J Li K J Zhu ZWQiu andC F Tao ldquoExperimentalstudy and global correlation on burning rates and flame tiltcharacteristics of acetone pool fires under cross air flowrdquoInternational Journal of Heat andMass Transfer vol 87 pp 369ndash375 2015

[23] J W Wang J Fang S B Lin J F Guan Y M Zhang and JJ Wang ldquoTilt angle of turbulent jet diffusion flame in crossflowand a global correlationwithmomentumflux ratiordquoProceedingsof the Combustion Institute 2016


[24] X Zhang W Xu L Hu and X Liu ldquoA new mathematicalmethod for quantifying trajectory of buoyant line-source gas-eous fuel jet diffusion flames in cross air flowsrdquo Fuel vol 177pp 107ndash112 2016

[25] F Tang L Li Q Wang and Q Shi ldquoEffect of cross-wind onnear-wall buoyant turbulent diffusion flame length and tiltrdquoFuel vol 186 pp 350ndash357 2016

[26] F Tang L Hu X Zhang X Zhang andMDong ldquoBurning rateand flame tilt characteristics of radiation-controlled rectangularhydrocarbon pool fires with cross air flows in a reducedpressurerdquo Fuel vol 139 pp 18ndash25 2015

[27] HWan J Ji K Li X Huang J Sun and Y Zhang ldquoEffect of airentrainment on the height of buoyant turbulent diffusion flamesfor two fires in open spacerdquo Proceedings of the CombustionInstitute 2016

[28] R K Smith B R Morton and L M Leslie ldquoRole of dynamicpressure in generating fire windrdquo Journal of Fluid Mechanicsvol 68 no 1 pp 1ndash19 1975

[29] B R Morton G Taylor and J S Turner ldquoTurbulent gravita-tional convection frommaintained and instantaneous sourcesrdquoProceedings of the Royal Society of London Series A Mathemat-ical Physical and Engineering Sciences vol 234 pp 1ndash23 1956

[30] E E Zukoski ldquoFluid dynamics of room fires Fire safetysciencerdquo in Proceedings of the 1st International SymposiumWashington DC USA 1986

[31] Y Hasemi and T Tokunaga ldquoFlame geometry effects on thebuoyant plumes from turbulent diffusion flamesrdquo Fire Scienceand Technology vol 4 no 1 pp 15ndash26 1984

[32] O Sugawa H Satoh and Y Oka ldquoFlame height from rectangu-lar fire sources considering mixing factorrdquo in Proceedings of the3rd International Symposium on Fire Safety Science vol 3 pp435ndash444 Tokyo Japan 1991

[33] B J McCaffrey ldquoPurely buoyant diffusion flames some exper-imental resultsrdquo Tech Rep NSBIR 79-1910 National Institutefor Standards and Technology Report Washington DC USA1995

[34] S D Weihs and R D Small ldquoInteractions and spreadingof adjacent large area firesrdquo Pacific-Sierra Research TechnicalReport DNA-TR-86-214 1986

[35] N B Kaye and P F Linden ldquoCoalescing axisymmetric turbulentplumesrdquo Journal of Fluid Mechanics vol 502 pp 41ndash63 2004

[36] R E Meyer Introduction to Mathematical Fluid DynamicsDover Toronto Canada 1982

[37] I Paraschivoiu Subsonic Aerodynamics Presses InternationalsPolytechnique Montreal Canada 2003

[38] L-M Yuan and G Cox ldquoAn experimental study of some linefiresrdquo Fire Safety Journal vol 27 no 2 pp 123ndash139 1996

[39] M E Alexander and M G Cruz ldquoInterdependencies betweenflame length and fireline intensity in predicting crown fireinitiation and crown scorch heightrdquo International Journal ofWildland Fire vol 21 no 2 pp 95ndash113 2012

[40] R J Adrian ldquoParticle-imaging techniques for experimentalfluid mechanicsrdquoAnnual Review of Fluid Mechanics vol 23 no1 pp 261ndash304 1991

[41] S R Tieszen T J OrsquoHern R W Schefer E J Weckman and TK Blanchat ldquoExperimental study of the flow field in and arounda onemeter diametermethane firerdquoCombustion and Flame vol129 no 4 pp 378ndash391 2002

[42] J Lozano W Tachajapong D R Weise S Mahalingam andM Princevac ldquoFluid dynamic structures in a fire environmentobserved in laboratory-scale experimentsrdquo Combustion Scienceand Technology vol 182 no 7 pp 858ndash878 2010

[43] B K P Horn and B G Schunck ldquoDetermining optical flowrdquoArtificial Intelligence vol 17 no 1ndash3 pp 185ndash203 1981

[44] T J Crone R E McDuff andW S D Wilcock ldquoOptical plumevelocimetry a new flow measurement technique for use inseafloor hydrothermal systemsrdquo Experiments in Fluids vol 45no 5 pp 899ndash915 2008

[45] X Zhou L Sun SMahalingam andD RWeise ldquoThermal par-ticle image velocity estimation of fire plume flowrdquo CombustionScience and Technology vol 175 no 7 pp 1293ndash1316 2003

[46] Z J Taylor R Gurka G A Kopp and A Liberzon ldquoLong-duration time-resolved PIV to study unsteady aerodynamicsrdquoIEEE Transactions on Instrumentation and Measurement vol59 no 12 pp 3262ndash3269 2010

[47] B J McCaffrey ldquoPurely buoyant diffusion flames some experi-mental resultsrdquoNational Institute for Standards andTechnologyReport NSBIR 79-1910 National Institute for Standards andTechnology Washington DC USA 1979

[48] L Audouin G Kolb J L Torero and J M Most ldquoAveragecentreline temperatures of a buoyant pool fire obtained byimage processing of video recordingsrdquo Fire Safety Journal vol24 no 2 pp 167ndash187 1995

[49] T Maynard and M Princevac ldquoThe application of a simple freeconvection model to the pool fire pulsation problemrdquo Com-bustion Science andTechnology vol 184 no 4 pp 505ndash516 2012

[50] F A Albini ldquoAmodel for thewind-blown flame from a line firerdquoCombustion and Flame vol 43 pp 155ndash174 1981

[51] X C Zhou and J P Gore ldquoAir entrainment flowfield induced bya pool firerdquo Combustion and Flame vol 100 no 1-2 pp 52ndash601995

[52] R W Macdonald R K Strom and P R Slawson ldquoWater flumestudy of the enhancement of buoyant rise in pairs of mergingplumesrdquo Atmospheric Environment vol 36 no 29 pp 4603ndash4615 2002

[53] D Drysdale An Introduction to Fire Dynamics John Wiley ampSons West Sussex UK 2011

[54] Y Fukuda D Kamikawa Y Hasemi and K Kagiya ldquoFlamecharacteristics of group firesrdquo Fire Science and Technology vol23 no 2 pp 164ndash169 2004

[55] A A Brown and K P Davis Forest Fire Control and UseMcGraw-Hill New York NY USA 1973

[56] D RWeise and G S Biging ldquoEffects of wind velocity and slopeon flame propertiesrdquo Canadian Journal of Forest Research vol26 no 10 pp 1849ndash1858 1996

[57] R M Nelson B W Butler and D R Weise ldquoEntrainment regi-mes and flame characteristics of wildland firesrdquo InternationalJournal of Wildland Fire vol 21 no 2 pp 127ndash140 2012

[58] P J W Roberts ldquoLine plume and ocean outfall dispersionrdquoJournal of the Hydraulics Division vol 105 no 4 pp 313ndash3311979

[59] H Rouse W D Baines and H W Humphreys ldquoFree convec-tion over parallel sources of heatrdquo Proceedings of the PhysicalSociety Section B vol 66 no 5 pp 393ndash399 1953

[60] RMNelson Jr ldquoPower of the firemdasha thermodynamic analysisrdquoInternational Journal of Wildland Fire vol 12 no 1 pp 51ndash652003

[61] R M Nelson Jr ldquoByram derivation of the energy criterion forforest andwildland firesrdquo International Journal ofWildland Firevol 3 no 3 pp 131ndash138 1993

[62] R M Nelson Jr and C W Adkins ldquoFlame characteristics ofwind-driven surface firesrdquo Canadian Journal of Forest Researchvol 16 no 6 pp 1293ndash1300 1986

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Figure 1 Merging of a ring of fire burning in longleaf pine understory (Pinus palustrisMill) Note the significant change in fire behavior asthe flame fronts converge

Win

d

Merging zone

RoadBackfire from fuel break

Advancing flame front

(a)

Merging zones

Advancing spot fire

(b)

Fire array (pool fires structures etc)

Merging zones

(c)Figure 2 Example scenarios for fire interactions (a) backfiring from a fuel break to stop an advancing wildfire (b) merging of individualvegetation fires and (c) interaction of multiple burning objects (structures pool fires etc)

119885 is the unmerged flame height Flames were continuouslymerged for 119863119885 lt 01 The probability of merging was pri-marily a function of window separation but window dimen-sion also had an effect Kuwana et al [12] studied the behaviorof two adjacent microscale slot flames and noted that theoverall heat release increased as burner space decreased butboth flames eventually merged into a unified flame

While much of the work on merging fires has focused onradiant heat transfer entrainment and convection also appearto play a significant role in interactions As two flames con-verge their independent entrainment fields interact resultingin an inward tilting of the flames [13 14] Flame tilt affects firebehavior by increasing the amount of radiant heat transfer(view factor) to the surface [15] by increasing the horizontalcomponent of convective heat flux forward of the flame [16]Baldwin et al [17] theorized that flame tilt is a product of theflow restriction between flames which causes a pressure dropthat competes with buoyancy A similar mechanism has alsobeen proposed for noncombusting buoyant plumes at labo-ratory scale [18] Recent work on wind-blown flames (thoughnot interacting) has provided additional insight into themechanisms of flame tilt Jiang and Lu [19] measured theburning rate and flame angle of wind-blown pool fires anddemonstrated that flame tilt was a function of Froude number(Fr) Flame tilt initially increased rapidly in the range of 0 ltFr lt 1 but quickly moderated for Fr gt 2 Hu et al [20] corre-lated flame tilt angle against the ratio of cross-flow speed to

the characteristic buoyant velocity of heptane pool fires andthese results were recently extended to optically thin heptanefires in cross-flow [21] Tang et al [22] demonstrated thatfor small pool fires flame tilt was more easily influenced bywind speed as opposed to larger fires Similar studies havebeen done for pool fires in momentum-dominated regimes[23 24] and flame angle was shown to be a function of thecross-flow to burner verticalmomentum ratio Tang et al [25]studied the behavior of wind-blown gas burner flames inthe presence of walls (walls parallel to cross-flow) whichare potentially analogous to merging flames (entrainmentrestricted) Interestingly as the flame was moved closer tothe wall for the same cross-flow speed flame tilt decreasedTheir observations of rate of flame angle change with cross-flow speed were similar to that of Jiang and Lu [19] Tang et al[26] performed experiments with rectangular pool fires ofvarying aspect ratio and demonstrated that flame angleincreased with cross-flow velocity but aspect ratio did nothave a major impact

Flame length for interacting fires has also been studiedFor gas burners with constant heat release rate Wan et al[27] demonstrated that the dependency of flame length onfirespacing was coupled with heat release rate For smaller heatrelease rates flame length was largely unchanged as spacingbetween fires decreased while it was affected at higher rates ofheat releaseThey also observed that merging occurred whenflames were at a spacing of less than 30 percent of the single





2 Theory



120579 = tanminus1 (119865119884119865119885) (1)

i oni no

120579z+

y+

w nu

D

L




119860120588119894119906119894 (119894 sdot V119894) 119889119860

119865119885 = 120597120597119905 [int119881 120588119901119908119900119889119881] + int119860 120588119901119908 (119906 sdot 119908) 119889119860

(2)


1198651015840119884 = 120588119900119871 (V1199002 minus V1198942)

1198651015840119885 = 1205881198751198631199082(3)


tan 120579 = 119860(V1198902

1199082 ) (4)


V119890 = radicV1199002 minus V1198942 (5)


119860 = 120588119900119871120588119901119863 (6)



119876lowast119863 = 12058801198881199011198790radic11989211988211986332 (7)


119860 sim 120588119900120588119901119876lowast119863

119899(8)





Line sinksy

x

S2

1

985747

y = 0

x = 0

o

i

+Δs

minusΔs






119881 (119911) = 119889120601119889119911 =minus1198962120587ℓ ln

119911119911 minus ℓ (10)


119881 (119911) = 1198891206011119889119911 + 1198891206012119889119911= minus1198962120587ℓ [ln(

11991111199111 minus ℓ) + ln( 11991121199112 minus ℓ)] (11)




S985747 = 10 S985747 = 025


00 05 10 15S985747


0

01

02

03

04

05

06

07

08

09

1

vw




3 Experiments


119871119891 = 003411987123 (12)





Video camera


S

oo

i

985747





119862119891119892 (119898 119899) = sum119894

sum119895

119891 (119894 119895) times 119892 (119894 + 119898 119895 + 119899) (13)






(a) (b) (c)


0 5 10 15 20x (cm)

y (c

m)

0

5

10

15

20

25

v (cm

s)

0

2

4

6

8

10

12

minus2

minus4

(a)

v (cm

s)

0 5 10 15 20x (cm)

y (c

m)

0

2

4

6

8

10

12

minus2

minus40

5

10

15

20

25

(b)



119871119891 = 119867cos 120579 (14)


4 Results



00 10 20 30 40 50

vw



0

02

04

06

08

1

12

14

16

18

SHS







00 10 20 30 40 500

02

04

06

08

1

12

14

SHS

ww

s


00 01 02 03 04 05 060

01

02

03

04

05

06

R2 = 07926

y = 08432x

tan(

120579) (

calc

ulat

ed)

w2 (observed)e2






00 10 20 30 40 50


Model

Flames merged

0

10

20

30

40

50

60

70

80

90

SHS

Ang

le (120579

)

below SHS asymp 2


0

02

04

06

08

1

12

14

SHS

LH

S

00 10 20 30 40 50 60 70


5 Discussion





119873119862 = 21198921198681205881198861198881199011198791198861199061198863 (15)


119865119877 = 1199061198863

119887119865 = 2119873119862minus1 (16)


119887119865 = 119892119868120588119886119888119901119879119886 =

11990611988631198731198882 (17)



119908 = 11988711986513 (18)


119873119862 asymp ( 119908119906119886)3 (19)


00 10 20 30 40 50

ExperimentModel

01

1

10

100

1000

SHS

Nc



119908119861 = ( 2119892119868120588119886119888119901119879119886)

13

(20)


119873119862 = ( 119908V119900 minus V119894

)3 = 119891( 119878119867) (21)


6 Conclusions



Nomenclature




Subscripts



Competing Interests


Acknowledgments


References



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













2 Theory



120579 = tanminus1 (119865119884119865119885) (1)

i oni no

120579z+

y+

w nu

D

L




119860120588119894119906119894 (119894 sdot V119894) 119889119860

119865119885 = 120597120597119905 [int119881 120588119901119908119900119889119881] + int119860 120588119901119908 (119906 sdot 119908) 119889119860

(2)


1198651015840119884 = 120588119900119871 (V1199002 minus V1198942)

1198651015840119885 = 1205881198751198631199082(3)


tan 120579 = 119860(V1198902

1199082 ) (4)


V119890 = radicV1199002 minus V1198942 (5)


119860 = 120588119900119871120588119901119863 (6)



119876lowast119863 = 12058801198881199011198790radic11989211988211986332 (7)


119860 sim 120588119900120588119901119876lowast119863

119899(8)





Line sinksy

x

S2

1

985747

y = 0

x = 0

o

i

+Δs

minusΔs






119881 (119911) = 119889120601119889119911 =minus1198962120587ℓ ln

119911119911 minus ℓ (10)


119881 (119911) = 1198891206011119889119911 + 1198891206012119889119911= minus1198962120587ℓ [ln(

11991111199111 minus ℓ) + ln( 11991121199112 minus ℓ)] (11)




S985747 = 10 S985747 = 025


00 05 10 15S985747


0

01

02

03

04

05

06

07

08

09

1

vw




3 Experiments


119871119891 = 003411987123 (12)





Video camera


S

oo

i

985747





119862119891119892 (119898 119899) = sum119894

sum119895

119891 (119894 119895) times 119892 (119894 + 119898 119895 + 119899) (13)






(a) (b) (c)


0 5 10 15 20x (cm)

y (c

m)

0

5

10

15

20

25

v (cm

s)

0

2

4

6

8

10

12

minus2

minus4

(a)

v (cm

s)

0 5 10 15 20x (cm)

y (c

m)

0

2

4

6

8

10

12

minus2

minus40

5

10

15

20

25

(b)



119871119891 = 119867cos 120579 (14)


4 Results



00 10 20 30 40 50

vw



0

02

04

06

08

1

12

14

16

18

SHS







00 10 20 30 40 500

02

04

06

08

1

12

14

SHS

ww

s


00 01 02 03 04 05 060

01

02

03

04

05

06

R2 = 07926

y = 08432x

tan(

120579) (

calc

ulat

ed)

w2 (observed)e2






00 10 20 30 40 50


Model

Flames merged

0

10

20

30

40

50

60

70

80

90

SHS

Ang

le (120579

)

below SHS asymp 2


0

02

04

06

08

1

12

14

SHS

LH

S

00 10 20 30 40 50 60 70


5 Discussion





119873119862 = 21198921198681205881198861198881199011198791198861199061198863 (15)


119865119877 = 1199061198863

119887119865 = 2119873119862minus1 (16)


119887119865 = 119892119868120588119886119888119901119879119886 =

11990611988631198731198882 (17)



119908 = 11988711986513 (18)


119873119862 asymp ( 119908119906119886)3 (19)


00 10 20 30 40 50

ExperimentModel

01

1

10

100

1000

SHS

Nc



119908119861 = ( 2119892119868120588119886119888119901119879119886)

13

(20)


119873119862 = ( 119908V119900 minus V119894

)3 = 119891( 119878119867) (21)


6 Conclusions



Nomenclature




Subscripts



Competing Interests


Acknowledgments


References



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119876lowast119863 = 12058801198881199011198790radic11989211988211986332 (7)


119860 sim 120588119900120588119901119876lowast119863

119899(8)





Line sinksy

x

S2

1

985747

y = 0

x = 0

o

i

+Δs

minusΔs






119881 (119911) = 119889120601119889119911 =minus1198962120587ℓ ln

119911119911 minus ℓ (10)


119881 (119911) = 1198891206011119889119911 + 1198891206012119889119911= minus1198962120587ℓ [ln(

11991111199111 minus ℓ) + ln( 11991121199112 minus ℓ)] (11)




S985747 = 10 S985747 = 025


00 05 10 15S985747


0

01

02

03

04

05

06

07

08

09

1

vw




3 Experiments


119871119891 = 003411987123 (12)





Video camera


S

oo

i

985747





119862119891119892 (119898 119899) = sum119894

sum119895

119891 (119894 119895) times 119892 (119894 + 119898 119895 + 119899) (13)






(a) (b) (c)


0 5 10 15 20x (cm)

y (c

m)

0

5

10

15

20

25

v (cm

s)

0

2

4

6

8

10

12

minus2

minus4

(a)

v (cm

s)

0 5 10 15 20x (cm)

y (c

m)

0

2

4

6

8

10

12

minus2

minus40

5

10

15

20

25

(b)



119871119891 = 119867cos 120579 (14)


4 Results



00 10 20 30 40 50

vw



0

02

04

06

08

1

12

14

16

18

SHS







00 10 20 30 40 500

02

04

06

08

1

12

14

SHS

ww

s


00 01 02 03 04 05 060

01

02

03

04

05

06

R2 = 07926

y = 08432x

tan(

120579) (

calc

ulat

ed)

w2 (observed)e2






00 10 20 30 40 50


Model

Flames merged

0

10

20

30

40

50

60

70

80

90

SHS

Ang

le (120579

)

below SHS asymp 2


0

02

04

06

08

1

12

14

SHS

LH

S

00 10 20 30 40 50 60 70


5 Discussion





119873119862 = 21198921198681205881198861198881199011198791198861199061198863 (15)


119865119877 = 1199061198863

119887119865 = 2119873119862minus1 (16)


119887119865 = 119892119868120588119886119888119901119879119886 =

11990611988631198731198882 (17)



119908 = 11988711986513 (18)


119873119862 asymp ( 119908119906119886)3 (19)


00 10 20 30 40 50

ExperimentModel

01

1

10

100

1000

SHS

Nc



119908119861 = ( 2119892119868120588119886119888119901119879119886)

13

(20)


119873119862 = ( 119908V119900 minus V119894

)3 = 119891( 119878119867) (21)


6 Conclusions



Nomenclature




Subscripts



Competing Interests


Acknowledgments


References



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










S985747 = 10 S985747 = 025


00 05 10 15S985747


0

01

02

03

04

05

06

07

08

09

1

vw




3 Experiments


119871119891 = 003411987123 (12)





Video camera


S

oo

i

985747





119862119891119892 (119898 119899) = sum119894

sum119895

119891 (119894 119895) times 119892 (119894 + 119898 119895 + 119899) (13)






(a) (b) (c)


0 5 10 15 20x (cm)

y (c

m)

0

5

10

15

20

25

v (cm

s)

0

2

4

6

8

10

12

minus2

minus4

(a)

v (cm

s)

0 5 10 15 20x (cm)

y (c

m)

0

2

4

6

8

10

12

minus2

minus40

5

10

15

20

25

(b)



119871119891 = 119867cos 120579 (14)


4 Results



00 10 20 30 40 50

vw



0

02

04

06

08

1

12

14

16

18

SHS







00 10 20 30 40 500

02

04

06

08

1

12

14

SHS

ww

s


00 01 02 03 04 05 060

01

02

03

04

05

06

R2 = 07926

y = 08432x

tan(

120579) (

calc

ulat

ed)

w2 (observed)e2






00 10 20 30 40 50


Model

Flames merged

0

10

20

30

40

50

60

70

80

90

SHS

Ang

le (120579

)

below SHS asymp 2


0

02

04

06

08

1

12

14

SHS

LH

S

00 10 20 30 40 50 60 70


5 Discussion





119873119862 = 21198921198681205881198861198881199011198791198861199061198863 (15)


119865119877 = 1199061198863

119887119865 = 2119873119862minus1 (16)


119887119865 = 119892119868120588119886119888119901119879119886 =

11990611988631198731198882 (17)



119908 = 11988711986513 (18)


119873119862 asymp ( 119908119906119886)3 (19)


00 10 20 30 40 50

ExperimentModel

01

1

10

100

1000

SHS

Nc



119908119861 = ( 2119892119868120588119886119888119901119879119886)

13

(20)


119873119862 = ( 119908V119900 minus V119894

)3 = 119891( 119878119867) (21)


6 Conclusions



Nomenclature




Subscripts



Competing Interests


Acknowledgments


References



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Video camera


S

oo

i

985747





119862119891119892 (119898 119899) = sum119894

sum119895

119891 (119894 119895) times 119892 (119894 + 119898 119895 + 119899) (13)






(a) (b) (c)


0 5 10 15 20x (cm)

y (c

m)

0

5

10

15

20

25

v (cm

s)

0

2

4

6

8

10

12

minus2

minus4

(a)

v (cm

s)

0 5 10 15 20x (cm)

y (c

m)

0

2

4

6

8

10

12

minus2

minus40

5

10

15

20

25

(b)



119871119891 = 119867cos 120579 (14)


4 Results



00 10 20 30 40 50

vw



0

02

04

06

08

1

12

14

16

18

SHS







00 10 20 30 40 500

02

04

06

08

1

12

14

SHS

ww

s


00 01 02 03 04 05 060

01

02

03

04

05

06

R2 = 07926

y = 08432x

tan(

120579) (

calc

ulat

ed)

w2 (observed)e2






00 10 20 30 40 50


Model

Flames merged

0

10

20

30

40

50

60

70

80

90

SHS

Ang

le (120579

)

below SHS asymp 2


0

02

04

06

08

1

12

14

SHS

LH

S

00 10 20 30 40 50 60 70


5 Discussion





119873119862 = 21198921198681205881198861198881199011198791198861199061198863 (15)


119865119877 = 1199061198863

119887119865 = 2119873119862minus1 (16)


119887119865 = 119892119868120588119886119888119901119879119886 =

11990611988631198731198882 (17)



119908 = 11988711986513 (18)


119873119862 asymp ( 119908119906119886)3 (19)


00 10 20 30 40 50

ExperimentModel

01

1

10

100

1000

SHS

Nc



119908119861 = ( 2119892119868120588119886119888119901119879119886)

13

(20)


119873119862 = ( 119908V119900 minus V119894

)3 = 119891( 119878119867) (21)


6 Conclusions



Nomenclature




Subscripts



Competing Interests


Acknowledgments


References



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c)


0 5 10 15 20x (cm)

y (c

m)

0

5

10

15

20

25

v (cm

s)

0

2

4

6

8

10

12

minus2

minus4

(a)

v (cm

s)

0 5 10 15 20x (cm)

y (c

m)

0

2

4

6

8

10

12

minus2

minus40

5

10

15

20

25

(b)



119871119891 = 119867cos 120579 (14)


4 Results



00 10 20 30 40 50

vw



0

02

04

06

08

1

12

14

16

18

SHS







00 10 20 30 40 500

02

04

06

08

1

12

14

SHS

ww

s


00 01 02 03 04 05 060

01

02

03

04

05

06

R2 = 07926

y = 08432x

tan(

120579) (

calc

ulat

ed)

w2 (observed)e2






00 10 20 30 40 50


Model

Flames merged

0

10

20

30

40

50

60

70

80

90

SHS

Ang

le (120579

)

below SHS asymp 2


0

02

04

06

08

1

12

14

SHS

LH

S

00 10 20 30 40 50 60 70


5 Discussion





119873119862 = 21198921198681205881198861198881199011198791198861199061198863 (15)


119865119877 = 1199061198863

119887119865 = 2119873119862minus1 (16)


119887119865 = 119892119868120588119886119888119901119879119886 =

11990611988631198731198882 (17)



119908 = 11988711986513 (18)


119873119862 asymp ( 119908119906119886)3 (19)


00 10 20 30 40 50

ExperimentModel

01

1

10

100

1000

SHS

Nc



119908119861 = ( 2119892119868120588119886119888119901119879119886)

13

(20)


119873119862 = ( 119908V119900 minus V119894

)3 = 119891( 119878119867) (21)


6 Conclusions



Nomenclature




Subscripts



Competing Interests


Acknowledgments


References



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00 10 20 30 40 50

vw



0

02

04

06

08

1

12

14

16

18

SHS







00 10 20 30 40 500

02

04

06

08

1

12

14

SHS

ww

s


00 01 02 03 04 05 060

01

02

03

04

05

06

R2 = 07926

y = 08432x

tan(

120579) (

calc

ulat

ed)

w2 (observed)e2






00 10 20 30 40 50


Model

Flames merged

0

10

20

30

40

50

60

70

80

90

SHS

Ang

le (120579

)

below SHS asymp 2


0

02

04

06

08

1

12

14

SHS

LH

S

00 10 20 30 40 50 60 70


5 Discussion





119873119862 = 21198921198681205881198861198881199011198791198861199061198863 (15)


119865119877 = 1199061198863

119887119865 = 2119873119862minus1 (16)


119887119865 = 119892119868120588119886119888119901119879119886 =

11990611988631198731198882 (17)



119908 = 11988711986513 (18)


119873119862 asymp ( 119908119906119886)3 (19)


00 10 20 30 40 50

ExperimentModel

01

1

10

100

1000

SHS

Nc



119908119861 = ( 2119892119868120588119886119888119901119879119886)

13

(20)


119873119862 = ( 119908V119900 minus V119894

)3 = 119891( 119878119867) (21)


6 Conclusions



Nomenclature




Subscripts



Competing Interests


Acknowledgments


References



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00 10 20 30 40 50


Model

Flames merged

0

10

20

30

40

50

60

70

80

90

SHS

Ang

le (120579

)

below SHS asymp 2


0

02

04

06

08

1

12

14

SHS

LH

S

00 10 20 30 40 50 60 70


5 Discussion





119873119862 = 21198921198681205881198861198881199011198791198861199061198863 (15)


119865119877 = 1199061198863

119887119865 = 2119873119862minus1 (16)


119887119865 = 119892119868120588119886119888119901119879119886 =

11990611988631198731198882 (17)



119908 = 11988711986513 (18)


119873119862 asymp ( 119908119906119886)3 (19)


00 10 20 30 40 50

ExperimentModel

01

1

10

100

1000

SHS

Nc



119908119861 = ( 2119892119868120588119886119888119901119879119886)

13

(20)


119873119862 = ( 119908V119900 minus V119894

)3 = 119891( 119878119867) (21)


6 Conclusions



Nomenclature




Subscripts



Competing Interests


Acknowledgments


References



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00 10 20 30 40 50

ExperimentModel

01

1

10

100

1000

SHS

Nc



119908119861 = ( 2119892119868120588119886119888119901119879119886)

13

(20)


119873119862 = ( 119908V119900 minus V119894

)3 = 119891( 119878119867) (21)


6 Conclusions



Nomenclature




Subscripts



Competing Interests


Acknowledgments


References



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Subscripts



Competing Interests


Acknowledgments


References



































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









A study of the flow field surrounding interacting line fires

Documents

Transcript of A study of the flow field surrounding interacting line fires