LAMINAR PREMIXED LAMINAR PREMIXED FLAMESFLAMES

OVERVIEWOVERVIEWApplications: Applications: Heating appliancesHeating appliances Bunsen burnersBunsen burners Burner for glass product manufacturingBurner for glass product manufacturing

Importance of studying laminar premixed flames:Importance of studying laminar premixed flames: Some burners use this type of flames as shown by Some burners use this type of flames as shown by

examples aboveexamples above Prerequisite to the study of turbulent premixed Prerequisite to the study of turbulent premixed

flames. Both have the same physical processes flames. Both have the same physical processes and many turbulent flame theories are based on and many turbulent flame theories are based on underlying laminar flame structure.underlying laminar flame structure.

PHYSICAL DESCRIPTIONPHYSICAL DESCRIPTIONPhysical characteristicsPhysical characteristics Figure 8.2 shows typical flame temperature profile, Figure 8.2 shows typical flame temperature profile,

mole fraction of reactants,mole fraction of reactants,RR, and volumetric heat , and volumetric heat release, .release, .

Velocity of reactants entering the flame, Velocity of reactants entering the flame, uu = flame = flame propagation velocity, Spropagation velocity, SLL

Products heated Products heated product density ( product density (bb) < reactant ) < reactant density (density (uu). Continuity requires that burned gas ). Continuity requires that burned gas velicity, velicity, bb >= unburned gas vel., >= unburned gas vel., uu

uu uu A = A = bb bb A A (8.1) (8.1)

Q

For a typical hydrocarbon-air flame at PFor a typical hydrocarbon-air flame at Patmatm, , uu//bb 7 7 considerable acceleration of the considerable acceleration of the gas flow across the flame (gas flow across the flame (b b toto uu).).

A flame consists of A flame consists of 2 zones2 zones:: Preheat zonePreheat zone, where little heat is released, where little heat is released Reaction zoneReaction zone, where the bulk of chemical energy , where the bulk of chemical energy

is releasedis releasedReaction zoneReaction zone consists of 2 regions: consists of 2 regions: Thin regionThin region (less than a millimeter) (less than a millimeter), where , where

reactions are very fastreactions are very fast Wide regionWide region ( (several millimeters)several millimeters), where , where reactions reactions

are sloware slow

In In thin region (fast reaction zone), destruction of the fuel destruction of the fuel molecules and creation of many intermediate species molecules and creation of many intermediate species occur. This region is dominated by bimolecular reactions to occur. This region is dominated by bimolecular reactions to produce COproduce CO. .

Wide zoneWide zone (slow reaction zone)(slow reaction zone) is dominated by radical is dominated by radical recombination reactions and recombination reactions and final burnout of COfinal burnout of CO via via CO + CO + OH OH CO CO22 +H +H

Flame colours in Flame colours in fast-reaction zonefast-reaction zone:: If If air >air > stoichiometric proportions, stoichiometric proportions, excited CH radicalsexcited CH radicals

result in result in blue radiationblue radiation. . If If air <air < stoichiometric proportions, the zone appears stoichiometric proportions, the zone appears blue-blue-

greengreen as a result of radiation from as a result of radiation from excited Cexcited C22..

In In both flame regionsboth flame regions, , OH radicalsOH radicals contribute to contribute to the visible radiation, and to a lesser degree due to the visible radiation, and to a lesser degree due to reaction reaction CO + O CO + O CO CO22 + h + h. .

If the flame is If the flame is fuel-rich (much less air)fuel-rich (much less air), , sootsoot will will form, with its consequent blackbody continuum form, with its consequent blackbody continuum radiation. Although soot radiation has its radiation. Although soot radiation has its maximum maximum intensityintensity in the infraredin the infrared (recall Wien’s law for (recall Wien’s law for blackbody radiation), the spectral sensitivity of the blackbody radiation), the spectral sensitivity of the human eye causes us to see a human eye causes us to see a bright yellowbright yellow (near (near white) to dull white) to dull orange emissionorange emission, depending on the , depending on the flame temperatureflame temperature

Figure 1. Spectrum of flame colours

Typical Laboratory Premixed FlamesTypical Laboratory Premixed Flames The typical Bunsen-burner flame is a dual flame: The typical Bunsen-burner flame is a dual flame: a a

fuel rich premixed inner flamefuel rich premixed inner flame surrounded by surrounded by a a diffusion flamediffusion flame. Figure 8.3 illustrates a Bunsen . Figure 8.3 illustrates a Bunsen burner.burner.

The diffusion flame results when The diffusion flame results when CO and OHCO and OH from from the rich inner flame encounter the ambient air. the rich inner flame encounter the ambient air.

The shape of the flame is determined by the The shape of the flame is determined by the combined effects of the velocity profile and heat combined effects of the velocity profile and heat losses to the tube wall. losses to the tube wall.

For the flame to remain For the flame to remain stationarystationary, , SSLL = normal component of = normal component of uu = = uu sin sin (8.2) (8.2). . Figure 8.3b illustrates vector diagram.Figure 8.3b illustrates vector diagram.

Example 8.1Example 8.1. A premixed laminar flame is . A premixed laminar flame is stabilized in a one-dimensional gas flow where the stabilized in a one-dimensional gas flow where the vertical velocityvertical velocity of the unburned mixture, of the unburned mixture, uu, varies , varies linearly with the horizontal coordinate, x, as shown linearly with the horizontal coordinate, x, as shown in the lower half of Fig. 8.6. Determine the flame in the lower half of Fig. 8.6. Determine the flame shape and the distribution of the local angle of the shape and the distribution of the local angle of the flame surface from vertical. Assume the flame surface from vertical. Assume the flame flame speed Sspeed SLL is independent of position and equal to is independent of position and equal to 0.4m/s (constant)0.4m/s (constant), a nominal value for a , a nominal value for a stoichiometric methane-air flame. stoichiometric methane-air flame.

SolutionSolution From Fig. 8.7, we see that the local angle, From Fig. 8.7, we see that the local angle, , which , which

the flame sheet makes with a vertical plane is (Eqn. the flame sheet makes with a vertical plane is (Eqn. 8.2)8.2) = arc sin (S= arc sin (SLL//uu), where, from Fig. 8.6,), where, from Fig. 8.6,

uu (mm/s) = 800 + (1200 – 800)/20 x (mm) (mm/s) = 800 + (1200 – 800)/20 x (mm) (known).(known).

uu (mm/s) = 800 + 20x. (mm/s) = 800 + 20x.

So,So, = arc sin (400/(800 + 20x (mm))= arc sin (400/(800 + 20x (mm))and has values ranging from 30and has values ranging from 30oo at x = 0 to19.5 at x = 0 to19.5oo at x at x = 20 mm, as shown in the top part of Fig. 8.6.= 20 mm, as shown in the top part of Fig. 8.6.

To calculate the flame position, we first obtain an To calculate the flame position, we first obtain an expression for the local slope of the flame sheet expression for the local slope of the flame sheet (dz/dx) in the x-z plane, and then integrate this (dz/dx) in the x-z plane, and then integrate this expression with respect to x find z(x). From Fig. expression with respect to x find z(x). From Fig. 8.7, we see that8.7, we see that

,which, for ,which, for uu=A + Bx, =A + Bx,

becomes becomes

Integrating the above with A/SIntegrating the above with A/SLL = 2 and B/S = 2 and B/SLL = =

0.05 yields0.05 yields

-10 ln[(x-10 ln[(x22+80x+1200)+80x+1200)1/21/2+(x+40)]+(x+40)]-20-203+10 ln(203+10 ln(203+40)3+40)

The flame position z(x) is plotted in upper half of The flame position z(x) is plotted in upper half of Fig. 8.6.Fig. 8.6.

1/ 22 2

2tan u L

L

x Sdzdx S

1/ 22

1L

dz A Bxdx S

x2 0.5

0

dz xz(x) dx (x 80x 1200) 1dx 40

SIMPLIFIED ANALYSISSIMPLIFIED ANALYSISTurns (2000) proposes simplified laminar flameTurns (2000) proposes simplified laminar flamespeed and thickness on one-dimensional flame.speed and thickness on one-dimensional flame.Assumptions used:Assumptions used: One-dimensional, constant-areaOne-dimensional, constant-area, steady flow. , steady flow.

One-dimensional flat flame is shown in Figure 8.5. One-dimensional flat flame is shown in Figure 8.5. Kinetic and potential energies, viscous shear work, Kinetic and potential energies, viscous shear work,

and thermal radiation are all neglected.and thermal radiation are all neglected. The small pressure difference across the flame is The small pressure difference across the flame is

neglected; thus, neglected; thus, pressure is constantpressure is constant..

The diffusion of heat and mass are governed by The diffusion of heat and mass are governed by Fourier's and Fick's lawsFourier's and Fick's laws respectively ( respectively (laminar laminar flowflow). ).

Binary diffusion is assumed.Binary diffusion is assumed.– The Lewis number, Le, which expresses the The Lewis number, Le, which expresses the

ratio of thermal diffusivity, ratio of thermal diffusivity, , to mass , to mass diffusivity, D, i.e., diffusivity, D, i.e., is is unityunity, , p

kLeD C D

u p

kC

The The Cp mixture Cp mixture ≠ f(≠ f(temperature, composition).temperature, composition). This is equivalent to assuming that individual This is equivalent to assuming that individual species specific heats are all equal and species specific heats are all equal and constant.constant. Fuel and oxidizer form products in a single-step Fuel and oxidizer form products in a single-step

exothermic reaction. Reaction isexothermic reaction. Reaction is

1 kg fuel + 1 kg fuel + kg oxidiser kg oxidiser ( ( + 1)kg + 1)kg productsproducts The oxidizer is present in stoichiometric or The oxidizer is present in stoichiometric or

excess proportions; thus excess proportions; thus fuel is completely fuel is completely consumed at the flame. consumed at the flame.

For this simplified system, For this simplified system, SSLL and and found are found are (8.20)(8.20)

and and

or or (8.21)(8.21)

where is where is volumetric mass ratevolumetric mass rate of fuel and of fuel and is is thermal diffusivity. Temperature profile is assumed thermal diffusivity. Temperature profile is assumed linear from Tlinear from Tuu to T to Tbb over the small distance, as shown over the small distance, as shown in Fig. 8.9.in Fig. 8.9.

1/ 2

2 1 FL

u

mS

2

1u

Fm

2

LS

Fm

FACTORS INFLUENCING FLAME FACTORS INFLUENCING FLAME SPEED (SPEED (SSLL) AND FLAME THICKNESS () AND FLAME THICKNESS ())

1. Temperature (T1. Temperature (Tuu and T and Tbb)) Temperature dependencies of STemperature dependencies of SLL and and can be can be

inferred from Eqns 8.20 and 8.21. Explicit inferred from Eqns 8.20 and 8.21. Explicit dependencies is proposed by Turns as followsdependencies is proposed by Turns as follows

(8.27)(8.27)

where where is thermal diffusivity, T is thermal diffusivity, Tuu is unburned gas is unburned gas temperature, temperature, , T, Tbb is burned is burned gas temperature.gas temperature.

0.75 1( )( ) u

u p

k T T T PC T

0.5 b uT T T

(8.28)(8.28)

where the exponent n is the overall reaction order, where the exponent n is the overall reaction order, RRuu = universal gas constant (J/kmol-K), E = universal gas constant (J/kmol-K), EAA = = activation energy (J/kmol) activation energy (J/kmol)

Combining above scalings yields and applying Eqs Combining above scalings yields and applying Eqs 8.20 and 8.218.20 and 8.21

SSLL (8.29)(8.29)

(8.30)(8.30)

/F um 1. exp( /( )n n nub u A u b

TF T P T E R TP

0.375 / 2 ( 2) / 2exp2

n nAu b

u b

ET T T PR T

0.375 / 2 / 2exp2

n nAb

u b

ET T PR T

For hydrocarbons, For hydrocarbons, n n 2 and E 2 and EAA 1.67.10 1.67.1088 J/kmol J/kmol (40 kcal/gmol). Eqn 8.29 predicts (40 kcal/gmol). Eqn 8.29 predicts SSLL to increase by to increase by factor of 3.64factor of 3.64 when T when Tuu is increased from 300 to is increased from 300 to 600K. Table 8.1 shows comparisons of S600K. Table 8.1 shows comparisons of SLL and and

The empirical SThe empirical SLL correlation of Andrews and Bradley correlation of Andrews and Bradley [19] for stoichiometric methane-air flames,[19] for stoichiometric methane-air flames,SSLL (cm/s) = 10 + 3.71.10-4[T (cm/s) = 10 + 3.71.10-4[Tuu(K)](K)]22 (8.31)(8.31)which is shown in Fig. 8.13, along with data from which is shown in Fig. 8.13, along with data from several experimenters. several experimenters.

Using Eqn. 8.31, an increase in TUsing Eqn. 8.31, an increase in Tuu from 300 K to from 300 K to 600 K results in 600 K results in SSLL increasing by a factor of 3.3 increasing by a factor of 3.3, , which compares quite favourably with our estimate which compares quite favourably with our estimate of 3.64 (Table 8.1).of 3.64 (Table 8.1).

Table 8.1Table 8.1 Estimate of effects of T Estimate of effects of Tuu and T and Tbb on S on SLL and and using Eq 8.29 and 8.30 using Eq 8.29 and 8.30

Case A: referenceCase A: reference Case C: TCase C: Tbb changes due to heat transfer or changes due to heat transfer or

changing equivalent ratio, either lean or rich.changing equivalent ratio, either lean or rich. Case B: TCase B: Tuu changes due to preheating fuel changes due to preheating fuel

CaseCase A (ref)A (ref) BB CCTTuu (K) (K) 300300 600600 300300

TTbb (K) (K) 2,0002,000 2,3002,300 1,7001,700

SSLL/S/SL,AL,A 11 3.643.64 0.460.46

//AA 11 0.650.65 1.951.95

Pressure (P)Pressure (P) From Eq. 8.29, if, again, n From Eq. 8.29, if, again, n 2, S 2, SLL f (P). f (P). Experimental measurements generally show a Experimental measurements generally show a

negative dependence of pressure. Andrews and negative dependence of pressure. Andrews and Bradley [19] found thatBradley [19] found thatSSLL (cm/s) = 43[P (atm)] (cm/s) = 43[P (atm)]-0.5-0.5 (8.32)(8.32)fits their data for P > 5 atm for methane-air flames fits their data for P > 5 atm for methane-air flames (Fig. 8.14). (Fig. 8.14).

Equivalent Ratio (Equivalent Ratio ()) Except for very rich mixtures, the primary effect of Except for very rich mixtures, the primary effect of on Son SLL for similar fuels is for similar fuels is a result of how this a result of how this parameter affects flame temperaturesparameter affects flame temperatures; thus, we ; thus, we would expect S would expect S L,maxL,max at a slightly rich mixture and at a slightly rich mixture and fall off on either side as shown in Fig. 8.15 for fall off on either side as shown in Fig. 8.15 for behaviour of methane. behaviour of methane.

Flame thickness (Flame thickness () shows the inverse trend, ) shows the inverse trend, having a minimum near stoichiometrichaving a minimum near stoichiometric (Fig. 8.16). (Fig. 8.16).

Fuel TypeFuel Type Fig. 8.17 shows SFig. 8.17 shows SLL for C for C11-C-C66 paraffins (single paraffins (single

bonds), olefins (double bonds), and acetylenes bonds), olefins (double bonds), and acetylenes (triple bonds). Also shown is H(triple bonds). Also shown is H22. S. SLL of C of C33HH88 is used is used as a reference. as a reference.

Roughly speaking the CRoughly speaking the C33-C-C66 hydrocarbons all hydrocarbons all follow the same trend as a function of flame follow the same trend as a function of flame temperature. Ctemperature. C22HH44 and C and C22HH22‘ S‘ SLL > the C > the C33-C-C66 group, group, while CHwhile CH44’S’SLL lies somewhat below. lies somewhat below.

HH22's S's SL,maxL,max is many times > that of C is many times > that of C33HH88. Several . Several factors combine to give Hfactors combine to give H22 its high flame speed: its high flame speed:

i.i. the thermal diffusivity (the thermal diffusivity () of pure H) of pure H22 is many times is many times > the hydrocarbon fuels; > the hydrocarbon fuels;

ii.ii. the mass diffusivity (the mass diffusivity (DD) of H) of H22 likewise is much > the likewise is much > the hydrocarbons; hydrocarbons;

iii.iii. the reaction the reaction kinetics for Hkinetics for H22 are very rapid are very rapid since the since the relatively slow CO relatively slow CO COCO22 step that is a major factor step that is a major factor in hydrocarbon combustion is absent. in hydrocarbon combustion is absent.

Law [20] presents a Law [20] presents a compilation of laminar compilation of laminar flame-speed data for flame-speed data for various pure fuels and various pure fuels and mixtures shown in mixtures shown in Table 8.2.Table 8.2.

Table 8.2Table 8.2 S SLL for for various pure fuels various pure fuels burning in air for burning in air for = = 1.0 and at 1 atm1.0 and at 1 atm

FuelFuel SSLL (cm/s) (cm/s)

CHCH44 4040

CC22HH22 136136

CC22HH44 6767

CC22HH66 4343

CC33HH8 8 4444

HH22 210210

FLAME SPEED CORRELATIONS FLAME SPEED CORRELATIONS FOR SELECTED FUELSFOR SELECTED FUELS

Metghalchi and Keck [11] experimentally Metghalchi and Keck [11] experimentally determined Sdetermined SLL for various fuel-air mixtures over for various fuel-air mixtures over a range of temperatures and pressures typical of a range of temperatures and pressures typical of conditions associated with reciprocating internal conditions associated with reciprocating internal combustion engines and gas turbine combustion engines and gas turbine combustors.combustors.

Eqn 8.33 similar to Eqn. 8.29 is proposedEqn 8.33 similar to Eqn. 8.29 is proposedSSLL = S = SL,refL,ref (1 – 2.1Y (1 – 2.1Ydildil) (8.33)) (8.33)

for Tfor Tuu 350 K. 350 K.

,

u

u ref ref

T PT P

The subscript ref refers to reference conditions The subscript ref refers to reference conditions defined bydefined byTTu,refu,ref = 298 K, P = 298 K, Prefref = 1 atm = 1 atm and and SSL,refL,ref = B = BMM + B + B22(( - - MM))2 2 (for reference conditions)(for reference conditions)where the constants where the constants BBMM, B, B22, and , and MM depend on fuel depend on fuel typetype and are given in Table 8.3. and are given in Table 8.3.

Exponents of T and P, Exponents of T and P, and and are functions of are functions of , , expressed asexpressed as = 2.18 - 0.8(= 2.18 - 0.8( - 1) - 1) (for non-reference conditions)(for non-reference conditions) = -0. 16 + 0.22(= -0. 16 + 0.22( - 1) - 1) (for non-reference conditions)(for non-reference conditions)

The term YThe term Ydildil is the mass fraction of diluent present is the mass fraction of diluent present in the air-fuel mixture in Eqn. 8.33 to account for any in the air-fuel mixture in Eqn. 8.33 to account for any recirculated combustion products. This is a common recirculated combustion products. This is a common technique used to control NOtechnique used to control NOxx in many combustion in many combustion systems systems

Table 8.3Table 8.3 Values for B Values for BMM, B, B22, and , and MM used in Eqn used in Eqn 8.33 [11]8.33 [11]

Fuel M BM (cm/s) B2 (cm/s)

MethanolMethanol 1.111.11 36.9236.92 -140.51-140.51

PropanePropane 1.081.08 34.2234.22 -138.65-138.65

Iso octaneIso octane 1.131.13 26.3226.32 -84.72 -84.72

RMFD-303RMFD-303 1.131.13 27.5827.58 -78.54-78.54

Example 8.3Example 8.3Compare the laminar flame speeds of gasoline-airCompare the laminar flame speeds of gasoline-airmixtures with mixtures with = 0.8 for the following three cases: = 0.8 for the following three cases:i.i. At ref conditions of At ref conditions of T = 298 K and P = 1 atmT = 298 K and P = 1 atmii.ii. At conditions typical of a spark-ignition engine At conditions typical of a spark-ignition engine

operating at wide-open throttle: operating at wide-open throttle: T = 685 K and P T = 685 K and P = 18.38 atm= 18.38 atm..

iii.iii. Same as condition ii above, but with Same as condition ii above, but with 15 percent 15 percent (by mass) exhaust-gas recirculation(by mass) exhaust-gas recirculation

SolutionSolution RMFD-303RMFD-303 research fuel has a controlled research fuel has a controlled

composition simulating composition simulating typical gasolinestypical gasolines. The . The flame speed at 298 K and 1 atm is given byflame speed at 298 K and 1 atm is given by

SSL,refL,ref = B = BMM + B + B22(( - - MM))22

From Table 8.3,From Table 8.3, BBMM = 27.58 cm/s, B = 27.58 cm/s, B22 = -78.38cm/s, = -78.38cm/s, MM = 1. 13. = 1. 13. SSL,refL,ref = 27.58 - 78.34(6.8 - 1.13) = 27.58 - 78.34(6.8 - 1.13)22 = = 19.05 cm/s19.05 cm/s To find the flame speed at TTo find the flame speed at Tuu and P other than the and P other than the

reference state, we employ Eqn. 8.33reference state, we employ Eqn. 8.33 SSLL(T(Tuu, P) = S, P) = SL,ref L,ref

,

u

u ref ref

T PT P

wherewhere = 2.18-0.8(= 2.18-0.8(-1) = 2.34-1) = 2.34 = -0.16+0.22(= -0.16+0.22(-1) = -1) = -- 0.204 0.204Thus,Thus,SSLL(685 K, 18.38 atm) = (685 K, 18.38 atm) = 19.05 (685/298)19.05 (685/298)2.342.34(18.38/1)(18.38/1)-0.204-0.204 = =73.8cm/s73.8cm/sWith dilution by exhaust-gas recirculation, the With dilution by exhaust-gas recirculation, the flame speed is reduced by factor (1-2.1 Yflame speed is reduced by factor (1-2.1 Ydildil):):SSLL(685 K, 18.38 atm, 15%EGR) = (685 K, 18.38 atm, 15%EGR) = 73.8cm/s[1-2.1(0.15)]= 73.8cm/s[1-2.1(0.15)]= 50.6 cm/s50.6 cm/s

QUENCHING, FLAMMABILITY, QUENCHING, FLAMMABILITY, AND IGNITIONAND IGNITION

Previously Previously steady propagationsteady propagation of premixed of premixed laminar flameslaminar flames

Now Now transient processtransient process: quenching and ignition. : quenching and ignition. Attention to quenching distance, flammability Attention to quenching distance, flammability limits, and minimum ignition energies with heat limits, and minimum ignition energies with heat losses controlling the phenomena.losses controlling the phenomena.

1. Quenching by a Cold Wall1. Quenching by a Cold Wall Flames extinguish upon entering a sufficiently Flames extinguish upon entering a sufficiently

small passageway. If the passageway is not too small passageway. If the passageway is not too small, the flame will propagate through it. small, the flame will propagate through it. The The critical diameter of a circular tubecritical diameter of a circular tube where a flame where a flame extinguishes rather than propagates, is referred to extinguishes rather than propagates, is referred to as the as the quenching distancequenching distance. .

Experimental quenching distances are determined Experimental quenching distances are determined by observing whether a flame stabilised above a by observing whether a flame stabilised above a tube does or does not tube does or does not flashbackflashback for a particular for a particular tube diameter when the tube diameter when the reactant flow is rapidly reactant flow is rapidly shut off. shut off.

Quenching distances are also determined using Quenching distances are also determined using high-aspect-ratio rectangular-slothigh-aspect-ratio rectangular-slot burners. In this burners. In this case, the quenching distance between the long case, the quenching distance between the long sides, i.e., the slit width. sides, i.e., the slit width.

Tube-based quenching distances are somewhat Tube-based quenching distances are somewhat larger (larger (20-50 percent) than slit-based ones [21]20-50 percent) than slit-based ones [21]

Ignition and Quenching CriteriaIgnition and Quenching CriteriaWilliams [22] provides 2 rules-of-thumb governingWilliams [22] provides 2 rules-of-thumb governingignitionignition and and flame extinctionflame extinction. . Criterion 1 -Criterion 1 -IgnitionIgnition will only occur if will only occur if enough enough

energyenergy is added to heat a slab is added to heat a slab thickness steadily thickness steadily propagating laminar flamepropagating laminar flame to the to the adiabatic flame adiabatic flame temperaturetemperature..

Criterion 2 -The rate of Criterion 2 -The rate of liberation of heat by liberation of heat by chemical reactionschemical reactions inside the slab must inside the slab must approximately balance the rate of heat lossapproximately balance the rate of heat loss from from the slab by thermal conduction. This is applicable the slab by thermal conduction. This is applicable to the problem of to the problem of flame quenchingflame quenching by a cold wall. by a cold wall.

Simplified Quenching Analysis.Simplified Quenching Analysis. ConsiderConsider a flame that has just entered a slot a flame that has just entered a slot

formed by two plane-parallel plates as shown in formed by two plane-parallel plates as shown in Fig. 8.18. Applying Williams’ second criterion: Fig. 8.18. Applying Williams’ second criterion: heat produced by reaction = heat conductionheat produced by reaction = heat conduction to to the walls, i.e.,the walls, i.e.,

(8.34)(8.34)

is volumetric heat release rateis volumetric heat release rate (8.35)(8.35)

where where is volumetric mass rate of fuel, is volumetric mass rate of fuel, is heat of combustion is heat of combustion

Thickness of the slab of gas analysed = Thickness of the slab of gas analysed = . .

,cond totQ V Q

F cQ m h

Fmch

Q

FindFind quenching distance, d. quenching distance, d.SolutionSolution (8.36)(8.36)

A = 2A = 2L, where L is slot width (L, where L is slot width ( paper) and 2 paper) and 2 accounts for contact on both sidesaccounts for contact on both sides (left and right). (left and right).

is difficult to approximate. A reasonable is difficult to approximate. A reasonable lower bound of lower bound of = = (8.37)(8.37)where b = 2, assuming a linear distribution of T where b = 2, assuming a linear distribution of T from the centerline plane at Tfrom the centerline plane at Tbb to the wall at T to the wall at Tww. In . In general b > 2.general b > 2.

Quenching occurs from Quenching occurs from TTbb to T to Tww..

dTdx

cond in gas walldTQ kAdx

dTdx

/

b wT Td b

Combining Eqns 8.35-8.37,Combining Eqns 8.35-8.37, (8.38a)(8.38a)

oror (8.38b)(8.38b)

Assuming TAssuming Tww = T = Tuu, using Eqn 8.20 (about , using Eqn 8.20 (about SSLL), and relating ), and relating

.. , Eqn 8.38b becomes, Eqn 8.38b becomes

dd = 2 = 2b b //SSLL (8.39a)(8.39a) Relating Eqn 8.21 (about Relating Eqn 8.21 (about )), Eqn 8.39a becomes, Eqn 8.39a becomes dd = 2 = 2b b Because b Because b 2, value d is always > 2, value d is always > . Values of d for fuels . Values of d for fuels

are shown Table 8.4. are shown Table 8.4.

( )( )) (2 )/

b wF c

T Tm h dL k Ld b

2 2 b w

F c

kb T Td

m h

( 1) ( )c p b uh c T T

Table 8.4 Flammability limits, quenching Table 8.4 Flammability limits, quenching distances and minimum ignition energiesdistances and minimum ignition energies

Flammability limitFlammability limit Quenching distance, dQuenching distance, d

minmin maxmax Stoich-mass Stoich-mass

air-fuel air-fuel ratioratio For For =1 =1 Absolute Absolute

min, mmmin, mm CC22HH22 0.190.19 13.313.3 2.32.3 --

COCO 0.340.34 6.766.76 2.462.46 -- --

CC1010HH2222 0.360.36 3.923.92 15.015.0 2.12.1 --

CC22HH66 0.500.50 2.722.72 16.016.0 2.32.3 1.81.8

CC22HH44 0.410.41 > 6.1> 6.1 14.814.8 1.31.3 --

HH22 0.140.14 2.542.54 34.534.5 0.640.64 0.610.61

CHCH44 0.460.46 1.641.64 17.217.2 2.52.5 2.02.0

CHCH33OHOH 0.480.48 4.084.08 6.466.46 1.81.8 1.51.5

CC88HH1818 0.510.51 4.254.25 15.115.1 -- --

CC33HH88 0.510.51 2.832.83 15.615.6 2.02.0 1.81.8

FuelFuel Minimum ignition energyMinimum ignition energy For For =1 (10=1 (10-5-5 J) J) Absolute Absolute

minimum (10minimum (10-5-5 J) J)

CC22HH22 33 --

COCO -- --

CC1010HH2222 -- --

CC22HH66 4242 2424

CC22HH44 9.69.6 --

HH22 2.02.0 1.81.8

CHCH44 3333 2929

CHCH33OHOH 21.521.5 1414

CC88HH1818 -- --

CC33HH88 30.530.5 2626

Example 8.4Example 8.4. . Consider the design of a laminar-flow, adiabatic, Consider the design of a laminar-flow, adiabatic,

flat-flame burner consisting of a square flat-flame burner consisting of a square arrangement of thin-walled tubes as illustrated in arrangement of thin-walled tubes as illustrated in the sketch below. the sketch below.

Fuel-air mixture flows through both the tubes and Fuel-air mixture flows through both the tubes and the interstices between the tubesthe interstices between the tubes. .

It is desired operate the burner with a It is desired operate the burner with a stoichiometric methane-air mixture exiting the stoichiometric methane-air mixture exiting the tubes at tubes at 300 K300 K and and 5 atm5 atm

Determine the Determine the mixture mass flowrate per unit mixture mass flowrate per unit cross-sectional areacross-sectional area at the design condition. at the design condition.

Estimate the Estimate the maximum tube diametermaximum tube diameter allowed so allowed so that flashback will be prevented.that flashback will be prevented.

SolutionSolution To establish a flat flame, the mean flow velocity must equal To establish a flat flame, the mean flow velocity must equal

the laminar flame at the design temperature and pressure. the laminar flame at the design temperature and pressure. From Fig. 8.14From Fig. 8.14,,

SSLL (300K, 5atm) = 43/ (300K, 5atm) = 43/P (atm) = 43/P (atm) = 43/5 = 5 = 19.219.2cm/s.cm/s. The mass flux, , The mass flux, , isis = = = = uuuu = = uuSSLL

Assuming an ideal-gas mixture, whereAssuming an ideal-gas mixture, where MWMWmixmix = = CH4CH4MWMWCH4CH4 + (1 - + (1 - CH4CH4)MW)MWairair

= 0.095(16.04) + 0.905(28.85)= 0.095(16.04) + 0.905(28.85) = 27.6 kg/kmol =5.61kg/m= 27.6 kg/kmol =5.61kg/m33

(Stoichimetric mass ratio air/ methane = 17.2, see (Stoichimetric mass ratio air/ methane = 17.2, see Table 8.4Table 8.4)) Thus, the mass flux isThus, the mass flux is = = uuSSLL = 5.61(0.192)= = 5.61(0.192)= 1.08 1.08

kg/(s.mkg/(s.m22))

m/m Am

m

We assume that if the tube diameter < the quench We assume that if the tube diameter < the quench distance (d), with some factor-of-safety applied, distance (d), with some factor-of-safety applied, the burner will operate without danger of the burner will operate without danger of flashback. flashback.

Thus, we need to find the quench distance at the Thus, we need to find the quench distance at the design conditions. design conditions.

Fig. 8.16Fig. 8.16 shows that d shows that dslitslit 1.7 mm. Since d1.7 mm. Since dslitslit = d = dtubetube – (20-50%), use d– (20-50%), use dslitslit outrightoutright (our case) with factor (our case) with factor of safety 20-50%. Data in Fig 8.16 is for slit, of safety 20-50%. Data in Fig 8.16 is for slit, design is of tube.design is of tube.

Correction for 5 atm:Correction for 5 atm:

Eqn. 8.39a, Eqn. 8.39a, d d /S/SLL

Eqn 8.27, Eqn 8.27, T T1.751.75/P/P dd22 = =

d(5atm) =1.7mm.d(5atm) =1.7mm.

dddesigndesign 0.76 mm0.76 mm Check whether d=0.76 mm gives laminar flow (ReCheck whether d=0.76 mm gives laminar flow (Redd

< < 23002300). ).

Flow is still laminarFlow is still laminar

,1 ,12 11 1

1 ,2 2 ,2

L L

L L

S SPd dS P S

6

5.61(0.00076)(0.192)Re 51.515.89.10

u design Ld

d S

1 43 /5 19.2 /atm cm satm cm s

2. Flammability Limits2. Flammability Limits A flame will propagate only within a range of A flame will propagate only within a range of

mixture the so-called lower and upper limits of mixture the so-called lower and upper limits of flammability. The limit is the leanest mixture (flammability. The limit is the leanest mixture ( < < 1), while the upper limit represents the richest 1), while the upper limit represents the richest mixture (mixture ( > 1). > 1). = (A/F) = (A/F)stoich stoich /(A/F)/(A/F)actual actual by mass or by mass or by moleby mole

Flammability limits are frequently quoted as Flammability limits are frequently quoted as %fuel %fuel by volume in the mixtureby volume in the mixture, or as a , or as a % of the % of the stoichiometric fuel requirementstoichiometric fuel requirement, i.e., (, i.e., ( x 100%). x 100%). Table 8.4 shows flammability limits of some fuels Table 8.4 shows flammability limits of some fuels

Flammability limits for a number of fuel-air Flammability limits for a number of fuel-air mixtures at atmospheric pressure is obtained from mixtures at atmospheric pressure is obtained from experiments employing "tube method". experiments employing "tube method".

In this method, it is ascertained whether or not a In this method, it is ascertained whether or not a flame initiated at the bottom of a vertical tube flame initiated at the bottom of a vertical tube (approximately 50-mm diameter by 1.2-m long) (approximately 50-mm diameter by 1.2-m long) propagates the length of the tube. propagates the length of the tube.

A mixture that sustains the flame is said to be A mixture that sustains the flame is said to be flammable. By adjusting the mixture strength, the flammable. By adjusting the mixture strength, the flammability limit can be ascertained.flammability limit can be ascertained.

Although Although flammability limitsflammability limits are physico-chemical are physico-chemical properties of the fuel-air mixture, experimental properties of the fuel-air mixture, experimental flammability limits are related to losses from the flammability limits are related to losses from the system, in addition to the mixture properties, and, system, in addition to the mixture properties, and, hence, generally hence, generally apparatus dependentapparatus dependent [31]. [31].

Example 8.5. Example 8.5. A full A full CC33HH88 cylinder from a camp stove leaks its cylinder from a camp stove leaks its

contents of 1.02 lb (contents of 1.02 lb (0.464 kg0.464 kg) in 12' x 14' x 8' (3.66 ) in 12' x 14' x 8' (3.66 m x 4.27 m x 2.44 m) room at 20m x 4.27 m x 2.44 m) room at 20ooC and 1 atm. C and 1 atm. After a long time fuel gas and room air are well After a long time fuel gas and room air are well mixed. Is the mixture in the room mixed. Is the mixture in the room flammableflammable??

SolutionSolution From Table 8.4, we see that CFrom Table 8.4, we see that C33HH88-air mixtures are -air mixtures are

flammable for 0.51 < flammable for 0.51 < < 2.83. Our problem, thus, < 2.83. Our problem, thus, is to determine is to determine of the mixture filling the room. of the mixture filling the room. Partial pressure of CPartial pressure of C33HH88 by assuming ideal-gas by assuming ideal-gas behaviourbehaviour

= 672.3 Pa= 672.3 Pa Propane mole fraction =Propane mole fraction = FF = P = PFF/P = 672.3/101,325 = 0.00664/P = 672.3/101,325 = 0.00664 and and airair = 1 - = 1 - FF = 0.99336 = 0.99336 The air-fuel ratio of the mixture in the room isThe air-fuel ratio of the mixture in the room is (A/F)(A/F)actact = =

/ 0.464(8315/44.094)(20 273)3.66(4.27)(2.44)

F u FF

room

m R MW TP

V

97.880.99336 (28.85)0.00664 (44.094)

air air

fuel fuel

MWMW

From the definition of From the definition of and the value of ( and the value of (A/FA/F))stoichstoich from Table 8.4 (i.e. 15.6 by from Table 8.4 (i.e. 15.6 by mass ratiomass ratio), we have), we have = (= (A/FA/F))stoichstoich /(A/F) /(A/F)actact = 15.6/97.88 = 0.159 = 15.6/97.88 = 0.159

Since Since = 0.159 < = 0.159 < lower limitlower limit (= 0. 51), the mixture in (= 0. 51), the mixture in the room is not capable of supporting a flame.the room is not capable of supporting a flame.

CommentComment Although our calculations show that in the fully Although our calculations show that in the fully

mixed state the mixture is not flammable, it is quite mixed state the mixture is not flammable, it is quite possible that, during the possible that, during the transient leaking processtransient leaking process, , a flammable mixture can exist somewhere within a flammable mixture can exist somewhere within the room. the room.

CC33HH88 is heavier than air is heavier than air and would tend to and would tend to accumulate near the floor until it is mixed by bulk accumulate near the floor until it is mixed by bulk motion and molecular diffusion. motion and molecular diffusion.

In environments employing flammable gases, In environments employing flammable gases, monitors should be located at both low and high monitors should be located at both low and high positions to detect leakage of heavy and light positions to detect leakage of heavy and light fuels, respectively.fuels, respectively.

3. Ignition3. Ignition Most of ignition uses electrical spark (pemantik Most of ignition uses electrical spark (pemantik

listrik). Another means is using pilot ignition (flame listrik). Another means is using pilot ignition (flame from very low-flow fuel).from very low-flow fuel).

Simplified Ignition AnalysisSimplified Ignition Analysis Consider Williams’ second criterion, applied to a Consider Williams’ second criterion, applied to a

spherical volume of gas, which represents the spherical volume of gas, which represents the incipient propagating flame created by a point incipient propagating flame created by a point spark. Using the criterion:spark. Using the criterion:

Find a critical gas-volume radius, Find a critical gas-volume radius, RRcritcrit,, below which below which flame will not propagateflame will not propagate

Find minimum ignition energy, Find minimum ignition energy, EEignign,, to heat critical to heat critical gas volume from initial state to flame temperature gas volume from initial state to flame temperature ((TTuu to T to Tbb).).

Critical radius, RCritical radius, Rcritcrit, and E, and Eignign (8.40)(8.40)

((propagationpropagation)) (8.41)(8.41)

where is mass flowrate/volumewhere is mass flowrate/volume Heat transfer process is shown in Figure 8.20Heat transfer process is shown in Figure 8.20

(8.42)(8.42)

Substitution Eqn 8.42 to 8.41 results inSubstitution Eqn 8.42 to 8.41 results in

.. (8.43)(8.43)

RRcritcrit is therefore determined by the flame propagation is therefore determined by the flame propagation

conductionQ V Q

3 24 / 3 4crit

F c crit critR

dTm h R k Rdr

crit

b u

R crit

T TdTdr R

3 b ucrit

F c

k T TR

m h

If R < RIf R < Rcritcrit, it would require exothermic heat > , it would require exothermic heat > hhcc

Substituting Substituting from Eqn 8.20 into Eqn 8.43 will givefrom Eqn 8.20 into Eqn 8.43 will give (8.44)(8.44)

Ignition is aimed to increase fluid from TIgnition is aimed to increase fluid from Tuu to T to Tbb at at the onset of combustion to replace the onset of combustion to replace hhc c ((ignitionignition))

(8.45)(8.45)

where Ewhere Eignign is minimum ignition energy is minimum ignition energy

6 6 / 2 critL

RS

ign crit p b uE m c T T

Substitution mSubstitution mcritcrit==bb.4.4RRcritcrit33/3 and /3 and bb using gas using gas

ideal formulae to Eqn 8.45 results inideal formulae to Eqn 8.45 results in (8.47)(8.47)

where Rwhere Rbb = R = Ruu/MW/MWbb and R and Ruu = gas constant = gas constant

3

61,6

p bign

L

u

b b

c T TPR

EST

4. Dependencies on Pressure, Temperature4. Dependencies on Pressure, Temperatureand Compositionand Composition

Using Eqn 8.27 and 8.29 on Eqn 8.47 Using Eqn 8.27 and 8.29 on Eqn 8.47 demonstrates effect of pressure to bedemonstrates effect of pressure to be

EEignign P P-2-2 (8.48)(8.48)(see comparison with experimental result in Fig (see comparison with experimental result in Fig 8.21)8.21)

Eqn 8.47 implies that in general, Eqn 8.47 implies that in general, TTuu E Eignign (see (see Table 8.5). Table 8.5).

EEignign vs %fuel gives U-shaped plot (Figures 8.22 vs %fuel gives U-shaped plot (Figures 8.22 and 8.23). This figure indicates that and 8.23). This figure indicates that EEignign is is minimum as a mixture composition is minimum as a mixture composition is stoichiometric or near it. stoichiometric or near it.

If the mixture gets If the mixture gets leaner atau richer, Eleaner atau richer, Eignign increasesincreases first gradually and then abruptly. %fuel first gradually and then abruptly. %fuel at Eat Eignign = = to be ignited are flammability limits to be ignited are flammability limits

Figure 8.22. Effect of %fuel on EFigure 8.22. Effect of %fuel on E ignign

Figure 8.22. Effect of %fuel on Eign

Figure 8.23. Effect of methane composition on EFigure 8.23. Effect of methane composition on E ignign

Table 8.5Table 8.5 Temperature influence Temperature influence

on spark-ignition energyon spark-ignition energy

FuelFuel Initial temp (K)Initial temp (K) EEignign (mJ) (mJ)n-heptane n-heptane 298298 14.514.5

373373 6.76.7444444 3.23.2

Iso-octaneIso-octane 298298 27.027.0373373 11.011.0444444 4.84.8

n-pentanen-pentane 243243 45.045.0253253 14.514.5

FuelFuel Initial temp (K)Initial temp (K) EEignign (mJ) (mJ)n-heptane n-heptane 298298 7.87.8

373373 4.24.2444444 2.32.3

propane propane 233233 11.711.7243243 9.79.7253253 8.48.4298298 5.55.5331331 4.24.2356356 3.63.6373373 3.53.5477477 1.41.4

References:References: Turns, Stephen R., An Turns, Stephen R., An Introduction to Introduction to

Combustion, Concepts and ApplicationsCombustion, Concepts and Applications, 2, 2ndnd edition, McGrawHill, 2000edition, McGrawHill, 2000