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Seik Mansoor AliSafety Research Institute,

Atomic Energy Regulatory Board,

Kalpakkam-603 102, India

Vasudevan Raghavan1

e-mail: [email protected]

Department of Mechanical Engineering,

Indian Institute of Technology Madras,

Chennai-600 036, India

K. VelusamyIndira Gandhi Center for Atomic Research,

Kalpakkam-603 102, India

Shaligram TiwariDepartment of Mechanical Engineering,

Indian Institute of Technology Madras,

Chennai-600 036, India

A Numerical Study of ConcurrentFlame Propagation OverMethanol Pool Surface

Concurrent flame spread over methanol pool surface under atmospheric conditions andnormal gravity has been numerically investigated using a transient, two-phase, reactingflow model. The average flame spread velocities for different concurrent air velocitiespredicted using the model are quite close to the experimental data available in the litera-ture. As the air velocity is increased, the fuel consumption rate increases and aids infaster flame spread process. The flame initially anchors around the leading edge of thepool and the flame tip spreads over the pool surface. The rate of propagation of flame tipalong the surface is seen to be steady without fluctuations. The flame spread velocity isfound to be nonuniform as the flame spreads along the pool surface. The flame spread ve-locity is seen to be higher initially. It then decreases up to a point when the flame haspropagated to around 40% to 50% of the pool length. At this position, a secondary flameanchoring point is observed, which propagates toward the trailing edge of the pool. As aresult, there is an increasing trend observed in the flame spread velocity. As the air veloc-ity is increased, the initial flame anchoring point moves downstream of the leading edgeof the fuel pool. The variations of interface quantities depend on the initial flame anchor-ing location and the attainment of thermodynamic equilibrium between the liquid- and

gas-phases. [DOI: 10.1115/1.4005111]

Keywords: concurrent flame spread, methanol pool, liquidgas interface, flame spreadvelocity, flame anchoring point

1 Introduction

Flame propagation over spilled combustible liquid fuels is aserious fire safety issue and presents a practical fire safety prob-lem. Over the years, a number of theoretical, experimental, andnumerical studies have appeared in literature on flame spreadover condensed fuel surfaces. Early theories [1] on flame spreadover liquid fuels reported the development of fluid motion belowthe propagating flame when fuel is at sub flash temperatures. Theconcept of flame spread on liquid pool surfaces and the variousmechanisms controlling it have been discussed by many research-ers [25]. The role of liquid fuel temperature on the flame spreadprocess has also been elucidated in some of these early studies.Flame spread phenomena were classified into four groups basedon the initial temperature of liquid [6]. According to this classifi-cation, in the subflash regime, the spread could be pseudo-uniform or pulsating in nature, whereas in the near-flash andsuper-flash regime, the flame propagation would be uniform. Thepulsating behavior was shown to be a consequence of flame inter-action with surface flow, which leads to abrupt periodic accelera-tion of the flame front [6,7]. Excellent review articles on flamespread literature and discussions on the predominant mechanismsof heat transfer that control the flame spread rate in each regime

are available [8,9]. Model problems demonstrating integral analy-sis on flame spread under wind aided conditions have also beenreported [10].

Based on detailed experimental investigations, the mechanismof flame propagation over methanol surfaces in super-flash andnear-flash regime, under concurrent as well as opposed air flowconditions were elucidated [11,12]. Later, experimental investiga-tion on flame spread over porous solids soaked with kerosene

brought out the role played by behavior of fuel in the mixedmedia. The two-phase heat transfer in controlling the flame spreadprocess was explained [13,14]. Different experimental techniques[1517] have been applied to investigate the pulsating flamespread across various liquid fuels. Experimental studies have beenconducted on flame spread over n-butanol pool under normal aswell as microgravity environment and the effect of low speed con-

current and opposed air flow on the flame spread characteristicshave been brought out [18]. Recently, experimental studies werereported on the effect of oxygen on the flame spread over severalcombustible liquids [19].

Over the years, various numerical models to study the structureof subsurface liquid flows preceding a flame, spreading at a steadyrate, have been reported [20,21]. The effect of Reynolds number,Prandtl number and the liquid surface tension was investigated toelucidate the role played by the hydrodynamics of the liquid layerin controlling the flame spread process. Some of these early mod-els were concerned with liquid-phase only and neglected the gasliquid phase coupling that is essential to describe the flame spreadprocess. An effective conductivity model for flame spread overshallow sub flash liquid pool layer has been presented [22]. Atwo-dimensional numerical model that coupled both the phases to

capture the oscillatory flame spread over a liquid (methanol) atsub flash initial temperatures and employing a finite-rate chemicalkinetics model has also been reported [23,24]. In these works, theimportance of surface tension induced liquid-phase convectivemotion was investigated by varying the viscosity over a widerange. A detailed, transient two-dimensional numerical model toprovide an accurate description of flame spread over liquid poolsin both pulsating and uniform regimes was presented later [25].This model could correctly predict the instantaneous flame speedin steady and pulsating modes. Besides, it could also predict thepool temperature at which transition from pulsating to steadyflame spread occurs. Numerical studies to examine the influenceof forced opposed air flow conditions on flame spread overn-propanol pools are available [26,27]. Flame propagation at

1 Corresponding author.Contributed by the Heat Transfer Division of ASME for publication in the JOUR-

NAL OF HEAT TRANSFER. Manuscript received April 20, 2011; final manuscriptreceived September 12, 2011; published online February 15, 2012. Assoc. Editor:Ali Ebadian.

Journal of Heat Transfer APRIL 2012, Vol. 134 / 041202-1CopyrightVC 2012 by ASME

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normal as well as zero gravity conditions has been discussed. Sim-ilar numerical studies were also reported [28] on axisymmetricflame propagation over propanol pools in quiescent (no flow) con-ditions under both normal and zero gravity.

Based on the above literature survey, it appears that numericalstudies on flame propagation over a liquid fuel maintained aboveits flash point temperature and subjected to a concurrent air floware rare. The probable reason for this could be that, in such cases,the propagation mechanism over the fuel surface is directly influ-enced by the presence of sufficient amount of fuel vapor that forms

a combustible mixture, especially for volatile fuels such as metha-nol. However, it is known that the flame spread rate for these condi-tions could be very fast depending on the concurrent air velocityand hence could be complex. Furthermore, in case of flammableliquid spills exposed to such conditions, especially those of alcoholssuch as methanol and ethanol, this could lead to a serious fire safetyissue. The prediction of flame spread rate under concurrent air flowconditions, along with the details of flow and thermal fields, formsthe motivation for the present study.

2 Description of Numerical Model

The following assumptions are made in formulating the mathe-matical model for transient flame propagation on fuel poolsurfaces:

1. Flow is two-dimensional and laminar.2. Fuel undergoes complete combustion through a global single-

step reaction mechanism. However, dissociation of CO2 isalso considered through a partial equilibrium approach.

3. Radiative heat addition to the liquid fuel pool is negligiblewhen compared to the conductive heat addition.

4. Properties are functions of temperature and compositiononly.

5. Dufour effect and species diffusion due to pressure are negli-gible in the gas and liquid-phase. Soret effect is alsoassumed to be negligible.

6. Liquid surface regression is slow enough to be neglected.7. Gasliquid (interface) remains planar throughout the

transients.

In this formulation, since the fuel is an alcohol, the liquid-phase

has two species including water in addition to the methanol.Therefore, solutal as well as thermal Marangoni convectioneffects have been modeled at the gasliquid interface. The govern-ing differential equations in gas- and liquid-phases for two-dimensional, transient, reacting flow simulations are providedbelow. The initial and boundary conditions are also presentedsubsequently.

2.1 Governing Equations. The governing equations formass, momentum, species, and energy conservation in the gas-and the liquid-phases are given in conservative differential formin Cartesian coordinates (x, y), in terms of variables such as veloc-ities (u, v), pressure (p), density (q), mass fraction of species i(Yi), and temperature (T).

(1) Continuity equation (for both gas-phase and liquid-phase)

@q

@t

@

@xqu

@

@yqv 0 (1)

(2) Species conservation equationsThere are six species in the gas-phase: CH3OH and O2

(reactants), CO, CO2, and H2O vapor (products) and N2 (an inertspecies). Two species, CH3OH (liquid) and H2O are consideredin the liquid-phase. For any particular species i, the conservationequations in gas- and liquid-phases are of the following form:

Gas-phase:

@

@tqYi

@

@xquYi

@

@yqvYi

@

@xqDi;m

@Yi

@x

@

@yqDi;m

@Yi

@y

_xi (2)

In Eq. (2), _xi denotes the net mass based rate of production ofspecies i per unit volume and Di,m is the mass diffusivity of anyspecies diffusing into the mixture. For liquid-phase, only fuel con-

servation is solved in the binary system. In the absence of chemi-cal reaction in liquid-phase, the species conservation is written as

Liquid-phase:

@

@tqYf

@

@xquYf

@

@yqvYf

@

@xqD12

@Yf

@x

!

@

@yqD12

@Yf

@y

!(3)

In Eq. (3), D12 represents the binary diffusion coefficient inliquid-phase and subscript frepresents fuel.

(3) x-Momentum equation (for both gas-phase and liquid-phase)

@

@t qu

@

@x quu

@

@y quv

@rxx@x

@syx@y

(4)

(4) y-Momentum equationGas phase: This includes a term to simulate buoyancy induced

flow due to density difference q1 q g, where the subscript 1represents the ambient conditions and g is acceleration due togravity

@

@tqv

@

@xquv

@

@yqvv

@

@xsxy

@

@yryy

q1 q g (5)

Liquid-phase:

@@t

qv @@x

quv @@y

qv2

@sxy@x

@ryy@y

(6)

The stress terms, r and s, in Eqs. (5) and (6), can be writtenusing viscosity (l) as

rxx p 2l@u

@x; ryy p 2l

@v

@y;

sxy syx l@u

@y@v

@x

(7)

(5) Energy equationThe energy conservation equation for gas-phase includes en-

thalpy transport by species, heat generation due to chemical reac-tion and radiative heat flux. In the liquid-phase, only enthalpytransport by species is considered in the present formulation. Thegoverning equations for gas- and liquid-phases are given below.

Gas-phase:

@

@tqCpT

@

@xquCpT

@

@yqvCpT

@

@xk@T

@x

@

@yk@T

@y

Xni1

_xiDhf;i _q000

R Xni1

@

@xqDi;mCp;iT

@Yi

@x

@

@yqDi;mCp;iT

@Yi

@y

!(8)

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Liquid-phase:

@

@tqCpT

@

@xquCpT

@

@yqvCpT

@

@xk@T

@x

@

@yk@T

@y

X2j1

@

@xqD12Cp;jT

@Yj

@x

@

@yqD12Cp;jT

@Yj

@y

!(9)

The quantity Dhf;i in Eq. (8) is the enthalpy of formation for ithspecies, k represents mixture thermal conductivity, Cp representsmixture specific heat, and Cp,i represents specific heat of ith spe-cies. The radiative heat loss _q000R is calculated assuming the opti-cally thin approximation with emission-only formulation aspresented in Ali et al. [29]. The overall reaction rate in gas-phasehas been calculated assuming a single-step global reaction mecha-nism for methanol-air oxidation and considering only the dissocia-tion of CO2 through a partial equilibrium approach. A detaileddiscussion of the methodology used to obtain the overall reactionrate is provided in Ali et al. [29].

2.2 Computational Domain. For the present two-dimensionalconfiguration, the methanol pool is taken to be 100 cm long and3 cm deep. Thin flat plates having 25 cm length are assumed to beplaced in flush with the top surface of the fuel pool at its leading aswell as the trailing edges. Initially, the fuel pool consists of puremethanol. The computational domain in the present problem con-sists of a liquid-phase region of 100 cm 3 cm and a gas phaseregion of 150 cm 150 cm. The fuel is ignited at the leading edgeby placing an ignition source at a height of 0.05 cm from its sur-face. The size of the ignition source is 0.25 cm 0.05 cm, which issmall enough to provide a localized volumetric heat source close tothe fuel surface. The free stream air flow over the fuel surface isfrom left to right in all the cases. The direction of gravity vector isin the perpendicular direction to the liquid pool surface. The com-putational domain is shown in Fig. 1.

2.3 Initial and Boundary Conditions. The initial flow fieldswithin the gas- and liquid-phases are assumed to be stationary.Both air and fuel are present at the ambient temperature of 300 Kinitially. Therefore,

Ambient conditions: p1

101325 N/m2; T1

300 K;YO2 0.23, YN2 0.77

Initial conditions for gas-phase: T0 T1; p0 p1; u v 0;YO2 0.23; YN2 0.77

Initial conditions for liquid-phase (subscript 0): T0 T1;u v 0; Yf0 1

Gas-phase boundary conditions: The following conditions existat the gas-phase boundaries (Fig. 1):

(1) InletAtmospheric air with uniform inlet velocity u

1and tempera-

ture T1

enters the domain. The mass fractions of oxygen andnitrogen correspond to those of ambient air. Hence, at the gas-phase domain inlet, u u

1, v 0, T T

1, YO2 0.23, and

YN2

0.77.

(2) WallAt the walls exposed to the gas-phase, located before and after

the fuel pool surface, no-slip and impermeability boundary condi-tions are prescribed for velocities, while temperature and speciesmass fractions are prescribed zero diffusive flux values.

(3) TopA free boundary condition is employed at the top of the domain.

The height of the gas-phase domain is selected in such a way thatthis free boundary condition can be implemented. All the solutionvariables are extrapolated in the direction normal to this boundaryfrom the interior nodes using three point polynomial fits usingzero diffusive flux in the normal direction (n). In the case of anyreverse flow (v< 0) at this boundary, the temperature is set as 300K and mass fractions of oxygen and nitrogen, are set as 0.23 and

0.77, respectively. These conditions can be represented asfollows:

@/

@n 0, where / u; v;T;Yi, forv>0 and T T1, YO2 0.23,

YN2 0.77, and p p1 forv 0 T T1, YO2 0.23,YN2 0.77, and p p1 foru< 0

Liquid-phase: The following conditions exist at the gas-phaseboundaries:

(1) Container walls

No-slip boundary conditions are prescribed for velocities. Fortemperature and mass fractions a zero diffusive flux in the normaldirection (n) is prescribed. Therefore

u 0; v 0;@T

@n

@Yi

@n 0

Pool interface conditionsIn order to solve the governing equations, the values of temper-

ature and species mass fractions in the gas-phase and the velocitycomponents in both gas and liquid-phase are required at the inter-face. The relevant governing equations for the interface are asfollows:

(1) Conservation of mass: The mass flux at any location onpool surface ( _m00x ) is given as:

_m00x qsvs g qsvs l (10)

where the subscript s represents interface and g, l represent thegas- and liquid-phases, respectively.

(2) Continuity of tangential velocity

ug;s ul;s (11)

(3) Continuity of shear stress: This includes the gradient of sur-face tension (rs) along x-direction. Further, the surface tension isevaluated as a function of temperature and concentrations of fueland water at the interface.Fig. 1 Computational domain

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lg;s@u

@y@v

@x

!g;s

ll;s@u

@y@v

@x

!l;s

@rs

@x

s

(12)

(4) Conservation of species

Fuel : _m00x Yf;s qs Df;m@Yf

@y

s

!g

_m00x Yf;s qs D12@Yf

@y

s

!l

(13a)

Water: _m00x Yw;s qs Dw;m@Yw

@y

s

!g

_m00x Yw;s qs D12@Yw

@y

s

!l

(13b)

Other species : _m00x Yi;s qs Di;m@Yi

@y

s

!g

0 (13c)

(5) Conservation of energy

X2

j1

_m00x Yj;sLj X2

j1

qs D12Lj@Yj

@y " #l

ksdT

dys

!g

ksdT

dy

s

!l

0 (14)

where Lj is the latent heat of vaporization ofjth species.

(6) Phase equilibrium: Using the activity coefficient c the phaseequilibrium is represented as

Xi;g ciXi;lpi

p(15)

3 Numerical Method

3.1 Grid system. The physical domain consists of gas-phaseand liquid-phase regions as described earlier. A partially stag-gered grid arrangement with quadrilateral cells is employed forthe numerical solution. Two separate types of control volumes areused; variables like u, v, T, and Yi are all evaluated at the centroidof a control volume. Only pressure is offset and is evaluated sepa-rately in another control volume. Both these control volumesrequire separate calculations for volume, area of control volumefaces as well as an appropriate interpolation scheme for fluxesacross the control volume faces. An attractive feature of the above

grid system is that pressure need not be specified at the walls in ei-ther the liquid- or the gas-phase regions.

3.2 Discretization Method and Solution Procedure. An in-house numerical code is used for solving the governing conserva-

tion equations. The gas and liquid-phase governing equations arediscretized using the conventional finite volume method on anEulerian domain, using the partially staggered grid arrangementas described earlier. The finite volume integration of these equa-tions over space and time generates a set of algebraic equationsfor the conservation of relevant dependent variables. Solution ofthese algebraic equations ensures that these dependent variablessatisfy the integral form of the conservation equation for eachcontrol volume and also for the entire computational domain. Thenumerical method uses upwind scheme for convective terms andSIMPLE [30] algorithm for the pressure velocity coupling. Themass fraction conservation equations and the energy equation aresolved using a smaller time step value for a certain number ofinner iterations due to the nonlinear source terms present in thoseequations. All the thermophysical properties are updated as afunction of temperature using appropriate correlations. The tran-

sient explicit marching procedure is carried out until either asteady-state or a time independent oscillatory solution is obtained.

4 Results and Discussion

Concurrent flame spread over a 1 m long methanol pool, underatmospheric conditions and normal gravity is analyzed systemati-cally. Free stream air flow parallel to the fuel surface is variedfrom 1.3 m/s to 5.1 m/s. The corresponding free stream Reynolds

Fig. 2 Temporal variations of (a) the flame tip location and (b) the fuel consumption rate inkg/m2s

Fig. 3 Variation of flame spread velocity along the poolsurface



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number, taking the pool length and free stream air velocity as thecharacteristic length and characteristic velocity respectively, fallsin the range of 43,000 to 340,000. The flow is laminar in thisrange, as reported for the same configuration [12]. Time step of1 105 s is used for the computations. A grid independencestudy has been conducted as reported in Ali et al. [29]. After set-ting the initial conditions, the ignition source is added as a local-

ized volumetric heat generation.

4.1 Flame Spread Velocity. Figure 2(a) shows the temporalvariation of flame tip location for different air velocities. Clearly,the flame spread is accelerated as the air velocity increases. Theinitial temperature of the liquid pool is equal to the ambient tem-perature (300 K), which is higher than the flash point temperature

(284 K) of methanol. Besides, methanol is a high volatile fuelwith a low boiling point (338 K). As the air velocity parallel tothe surface is increased, there will be an increase in the availabil-ity of oxidizer near the pool surface. As a result, the gradient ofthe fuel mass fraction at the pool surface increases [29]. The evap-oration rate is controlled, in general, by the gradient of the massfraction of the fuel at the surface as per the Ficks law. Further,the flame stand-off is reduced at higher air velocities, since thefuel need not travel a larger distance to mix with required amountof air in those cases. Therefore, due to enhanced heat and mass

transfers, the flame will able to heat up the portion of the fuelahead to a significant length and facilitate continuous and rapidevaporation. It is also clear from Figure 2(a) that the movement offlame tip along the pool surface is steady, without any oscillationsor pulsations, as observed in the cases of opposed flow flamespread [23,25] or when the pool temperature is below the flashpoint of the fuel [22,25], even though it is not linear. This is dueto the combined effect of concurrent flow as well as the initialtemperature of the pool (300 K) being larger than the flash pointof methanol (284 K). Figure 2(b) shows the temporal variation ofintegrated fuel consumption rate for different air velocities. It isclear that the fuel consumption rate increases with air velocity.

Figure 3 presents the variation of flame spread velocity (Vf)along the pool surface. It is clear that the flame spread velocity isnot uniform at all the x-locations. It has a higher value initiallydue to the effect of ignition and also due to enhanced mass trans-

fer at the leading edge. The flame has an anchoring point close tothe leading edge of the fuel pool. As the flame tip propagates, theflame spread velocity is seen to decrease and the trend continuestill the flame propagates to around 40% to 50% of the pool length.This is due to an increase in the flame stand-off distance along thepool length. After this, there is a slight increase in the flamespread velocity, when the flame moves further downstream toward

Fig. 4 Average flame spread velocity versus air velocity

Fig. 5 Temperature contours and velocity vectors as a function of time in the gas-phase foru53.9 m/s



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almost the trailing edge of the fuel pool. This is due to formationof a secondary flame anchoring point at a particular pool locationand its propagation, in addition to the leading edge anchoringpoint. This trend is explained later along with temperature con-tours for a particular case. At higher air velocities, there is a slight

decrease in the flame spread velocity when the flame approachesthe trailing edge of the pool. During this period, the evaporationrate of fuel vapor from the short pool surface ahead of the flametip is not enough to facilitate flame propagation at the same rate.

Figure 4 shows the average flame spread velocity obtained byintegrating the curves in Fig. 3. Also shown in Fig. 4 are the corre-sponding experimental values reported in literature [12]. It is seenthat the numerical model is able to predict the average flamespread velocity as a function of air velocity reasonably well.

4.2 Flow and Thermal Fields. Instantaneous gas-phase ve-locity vector and grayscale temperature plots are shown in Fig. 5for free stream air velocity of 3.9 m/s. The grayscale temperaturecontours qualitatively indicate the flame zone with the darkest

region indicating the maximum temperature. Velocity vectors areshown in five sections along the pool length at x/L locations start-ing with 0.05 and ending with 0.95. At a time instant of 0.05 s,flame has propagated nearly up to 20% of the pool length. Theflame is seen to stand closer to the surface. This means significantheat and mass transfer occurs between the gas and liquid-phases.Due to this, the flame spread velocity is seen to be much higherinitially, as shown in Fig. 3. The velocity vector at the x/L locationof 0.05 shows velocity overshoot in its profile. At this time instant,u-velocity in the gas-phase does not reach the free stream value atthe downstream locations.

The corresponding liquid-phase quantities are shown in Fig. 6.Since the velocity and temperature scales are much different in liq-uid- and gas-phases, these quantities are presented separately using

different length scales for velocity vector dimensions as indicatedin Figs. 5 and 6. Figure 6(a) shows the instantaneous flow and ther-mal fields in the liquid-phase at the time instant of 0.05 s. The poolsurface has been heated up to approximately 20% of its total length,the location up to which the flame in the gas-phase has propagated.

Due to Marangoni convection and shear stress in the interface, anx-direction velocity has been induced on the pool surface. This isclearly shown by the velocity vectors at x/L location of 0.25. How-ever, due to higher viscosity in the liquid-phase, the induced u-ve-locity gets damped out quickly along the depth as well as the poollength. Furthermore, at the locations where the flame has crossed,the liquid-phase u-velocity value decreases. This is due to reductionin the shear stress at the interface as well as the reduction in thetemperature gradient along the pool surface.

At a time instant of 0.15 s (Fig. 5(b)), the flame has propagatednearly half of the pool length. The flame extent in the y-directionhas also increased, which affects the heat transfer to the pool sur-face. During this time-period, the flame spread velocity shows adecreasing trend as shown in Fig. 3. In the x-locations where theflame has propagated (x/L 0.05 and 0.25), the velocity overshoot

in the vector profile is clearly observed. At x/L location around0.5, where the flame tip nearly touches to the pool surface, trans-verse component of velocity (v-velocity) is induced in the flowfield. Figure 6(b) shows the corresponding liquid-phase thermaland flow fields for this time instant. The surface temperature ofthe pool has increased up to the point where the flame has propa-gated, as seen before. Just after the point where the flame tipnearly touches the pool surface, the liquid-phase u-velocity hasincreased significantly. At the locations where the flame hascrossed, the magnitude ofu-velocity is seen to decrease due to thereasons mentioned previously.

At a time instant of 0.25 s (Fig. 5(c)), the flame tip has propa-gated nearly 80% of the pool length. The flame extent in they-direction has increased, especially to a larger extent, near its tip.

Fig. 6 Temperature contours and velocity vectors as a function of time in the liquid-phase foru53.9 m/s



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A continuous single flame zone as observed in the previous timeinstants is not seen in this case. The tip of the flame anchoredaround the leading edge is seen to shift upward at the downstreamlocations, due to buoyancy induced flow. A second anchoringlocation for the flame, closer to the pool surface at x/L around 0.7,is now observed. A secondary flame is seen to propagate. This isthe reason for the slight increase in the flame spread velocity asseen in Fig. 3. The flame tip has propagated ahead of this second-ary flame anchoring point. As seen in previous cases, at thex-locations where the flame has propagated, the velocity over-

shoot is observed. At an x/L location around 0.75, transverse com-ponent of velocity (v-velocity) is induced in the flow field asbefore. Figure 6(c) shows the corresponding quantities in theliquid-phase at this time instant. The surface temperature of thepool has increased up to the point where the flame has its secondanchoring point. Just after this point, an increase in the liquid-phase u-velocity is also noticed.

At a time instant of 0.35 s (Fig. 5(d)), the flame tip has crossedthe entire pool length. The downstream anchoring point hasmoved up to 90% of the pool length. The velocity profilesupstream of this location have become almost similar. The flametip height has increased further due to buoyancy induced flow. At

x/L location around 0.95, transverse component of velocity (v-ve-locity) is induced and a velocity overshoot is also observed. Fig-ure 6(d) shows the corresponding quantities in the liquid-phase atthis time instant. The surface temperature of the pool hasincreased up to 90% of the pool length. At time instant of 0.5 s(Fig. 5(e)), the flame has propagated across the entire pool length.The downstream anchoring point has also moved away beyondthe trailing edge of the pool. All the velocity profiles have becomealmost similar. The flame tip height has reduced as the forced con-vection effects take over the buoyancy induced flow effects. Fig-

ure 6(e) shows the corresponding quantities in the liquid-phase,where the surface temperature has increased over the entire poollength. Significant decrease in the liquid-phase velocity values isalso noticed. The velocity vectors observed at this time instant aredue to temperature gradient along the pool surface; the surfacetemperature decreases from the leading edge of the pool, wherethe flame anchors much closer to the surface, to its trailing edge,where the flame stand-off is at a higher y-location.

4.3 Temporal Variations of Interface Quantities. Figures7(a) and 7(b) show the variations of surface temperature as a func-tion of time for two free stream velocity cases. As mentioned

Fig. 7 Variation of interface quantities (a, b) temperature, (c, d) gas-phase u-velocity (x-compo-nent) and (e, f) gas-phase v-velocity (y-component) along the pool length for various free streamvelocity cases; (a), (c) and (e) for u

51.3 m/s; (b), (d), and (f) for u53.9 m/s



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earlier, the initial temperature of the liquid pool is at the ambienttemperature of 300 K. In general, since methanol has a low boil-ing point (338 K), the surface temperature reaches an equilibriumvalue in the range of approximately 325 K to 328 K, at varioustime instants. As the flame propagates, it heats up the pool surfaceto the equilibrium value, up to the point of propagation. After thispoint, there is a sharp reduction in the surface temperature to theambient value. This has been discussed with respect to Figs. 5 and6. At an air velocity as low as 1.3 m/s (Fig. 7(a)), the flame is ableto anchor very close to the leading edge of the fuel pool, that is, at

x/L 0. Therefore, starting from the leading edge itself, the poolsurface has reached the equilibrium value (Fig. 7(a)). However, asthe air velocity is increased, for example, to 3.9 m/s (Fig. 7(b)),the initial flame anchoring point near to the leading edge of thefuel pool moves slightly downstream. Due to this, the surface tem-perature at the leading edge has a lower value (Fig. 7(b)) than thelower velocity case (Fig. 7(a)). It can also be seen that the valueof the surface temperature at the leading edge decreases as the airvelocity is increased from 1.3 m/s to 3.9 m/s. Further reductionwas noticed when the air velocity was increased to 5.1 m/s (notshown). The temperature then rises to its equilibrium value at thelocation on the pool surface, where the flame has its initial anchor-ing point for that air velocity.

Figures 7(c) and 7(d) present the temporal variations of u-ve-locity for two air velocity cases. Based on the flame anchoringposition, a negative u-velocity is induced near to the leading edge

of the fuel pool. At the lower air velocity of 1.3 m/s, when theflame anchors just above the leading edge of the pool, the u-velocity is seen to be mostly positive. It sharply increases to amaximum value in the range of around 0.6 m/s to 0.8 m/s at alocation in the pool surface just ahead of the point that is heatedup by the flame. At higher velocities, since the initial flameanchoring point is on the downstream location of the leading edgeof the fuel pool, there is a positive temperature gradient in thenegative x-direction between the point of flame anchoring and thepool leading edge. As a result, a negative u-velocity is induced atthose locations. It can also be noted that at higher air velocities,there is a reduction in the induced u-velocity as compared to thecase of 1.3 m/s. This is mainly due to increased uniformity in theflame tip propagation at higher air velocities.

Figures 7(e) and 7(f) show the temporal variations of gas-

phase v-velocity for two air velocity cases. This component rep-resents the Stefan velocity induced due to vaporization of the liq-uid fuel. Based on the mass fraction of the fuel vapor at theinterface, it gradient value is calculated. Using this interface fuelvapor mass fraction and its gradient, this velocity is calculatedby Ficks Law. At the lower air velocity of 1.3 m/s, when thefuel vapor mass fraction is around its equilibrium value at theleading edge, the v-velocity has its highest value of around0.0067 m/s at that location. Then, its value decreases along thepool surface. Its value spikes up to a local maximum at variouslocations on the pool surface at various time instants, based onthe flame propagation velocity (or the air velocity). At higher airvelocity of 3.9 m/s, the maximum v-velocity is observed at theinitial flame anchoring location, which is just ahead of the poolleading edge.

5 Conclusions

Concurrent flame spread over methanol pool surface underatmospheric conditions and normal gravity has been numericallyinvestigated using a transient, two-phase, reacting flow numericalmodel. Variable thermo-physical properties, single-step globalreaction mechanism with partial equilibrium based dissociation ofcarbon-dioxide, optically thin approximation based radiationmodel and thermodynamic equilibrium at the interface forms thesalient features of the numerical model. The average flame spreadvelocities for different concurrent air velocities predicted by themodel are quite close to the reported experimental measurement[12]. The fuel consumption rate increases as the air velocity is

increased, due to increased availability of oxidizer near the poolsurface, and this also enhances the flame spread velocity. Whenignited, the flame anchors near the leading edge of the pool andthe tip propagates. The rate of propagation of flame tip along thesurface is seen to be steady without fluctuations, since the initialliquid pool temperature is higher than the flash point temperature.The flame spread velocity is found to be nonuniform along thepool surface. It is seen to be higher initially due to the effect ofignition and also due to enhanced mass transfer at the leadingedge caused by flame anchoring. It then decreases up to a point

when the flame has propagated to around 40% to 50% of the poollength, due to increased flame stand-off from the pool surface. Atthis position, a secondary flame anchoring point is observed,which propagates toward the trailing edge of the pool. As a result,there is an increasing trend observed in the flame spread velocityduring this period. As the air velocity is increased, the initial flameanchoring point moves downstream of the leading edge of the fuelpool. The variations of interface quantities in both gas and liquid-phase sides depend on the initial flame anchoring location and theattainment of thermodynamic equilibrium between the liquid- andgas-phases.

Acknowledgment

Authors thank Department of Science and Technology India for

funding the purchase of Xeon workstations.

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