LAMINAR PREMIXED FLAMES

LAMINAR PREMIXED FLAMESApplications:

Heating appliancesBunsen burnersBurner for glass product manufacturing

Importance of studying laminar premixed flames:

Some burners use this type of flames as shown by examples above.Prerequisite to the study of turbulent premixed flames. Both have the same physical processes and many turbulent flame theories are based on underlying laminar flame structure.OverviewPHYSICAL DESCRIPTIONPhysical characteristicsFigure 1 shows typical flame temperature profile, mole fraction of reactants, R, and volumetric heat release, .Velocity of reactants entering the flame, u = flame propagation velocity, SLProducts heated product density (b) < reactant density (u). Continuity requires that burned gas velicity, b >= unburned gas vel., u u SL A = u u A = b b A(1)

For a typical hydrocarbon-air flame at Patm, u/b 7 considerable acceleration of the gas flow across the flame (b to u).

Fig. 1 Laminar flame structure, temperature and heat rate profiles based on experiments of Friedman and BurkeA flame consists of 2 zones:Preheat zone, where little heat is releasedReaction zone, where the bulk of chemical energy is releasedReaction zone consists of 2 regions:Thin region (less than a millimeter), where reactions are very fast Wide region (several millimeters), where reactions are slowIn thin region (fast reaction zone), destruction of the fuel molecules and creation of many intermediate species occur. This region is dominated by bimolecular reactions to produce CO.

Wide zone (slow reaction zone) is dominated by radical recombination reactions and final burnout of CO via CO + OH CO2 +H

Flame colours in fast-reaction zone:If air > stoichiometric proportions, excited CH radicals result in blue radiation. If air < stoichiometric proportions, the zone appears blue-green as a result of radiation from excited C2.

In both flame regions, OH radicals contribute to the visible radiation, and to a lesser degree due to reaction CO + O CO2 + h.

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

Figure 2. Spectrum of flame coloursTypical Laboratory Premixed Flames

The typical Bunsen-burner flame is a dual flame: a fuel rich premixed inner flame surrounded by a diffusion flame. Figure 3 illustrates a Bunsen burner.

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

The shape of the flame is determined by the combined effects of the velocity profile and heat losses to the tube wall. For the flame to remain stationary, SL = normal component of u = u sin (2) Figure 3b illustrates vector diagram.

Fig. 3 a Bunsen burner schematic b Laminar flame speed equals normal component of unburned gas velocity Example 1. A premixed laminar flame is stabilized in a one-dimensional gas flow where the vertical velocity of the unburned mixture, u, varies linearly with the horizontal coordinate, x, as shown in the lower half of Fig. 6. Determine the flame shape and the distribution of the local angle of the flame surface from vertical. Assume the flame speed SL is independent of position and equal to 0.4 m/s (constant), a nominal value for a stoichiometric methane-air flame. SolutionFrom Fig. 7, we see that the local angle, , which the flame sheet makes with a vertical plane is (Eqn. 2) = arc sin (SL/u), where, from Fig. 6,u (mm/s) = 800 + (1200 800)/20 x (mm) (known).u (mm/s) = 800 + 20x.So, = arc sin (400/(800 + 20x (mm))and has values ranging from 30o at x = 0 to19.5o at x = 20 mm, as shown in the top part of Fig. 6.To calculate the flame position, we first obtain an expression for the local slope of the flame sheet (dz/dx) in the x-z plane, and then integrate this expression with respect to x find z(x). From Fig. 7, we see that:

,which, for u=A + Bx,

becomes

Integrating the above with A/SL = 2 and B/SL =0.05 yields

-10 ln[(x2+80x+1200)1/2+(x+40)]-203+10 ln(203+40)The flame position z(x) is plotted in upper half of Fig. 8.6.

Fig. 5 a) Adiabatic flat flame burner b) Non-adiabatic flat flame burner

Fig. 6 Flow velocity, flame position, and angle from vertical of line tangent to flame

Fig. 7 Definition of flame geometry for Example 1SIMPLIFIED ANALYSISTurns (2000) proposes simplified laminar flame speed and thickness on one-dimensional flame.Assumptions used:1- One-dimensional, constant-area, steady flow. One-dimensional flat flame is shown in Figure5. 2-Kinetic and potential energies, viscous shear work, and thermal radiation are all neglected.3-The small pressure difference across the flame is neglected; thus, pressure is constant.4- The diffusion of heat and mass are governed by Fourier's and Fick's laws respectively (laminar flow). 5- Binary diffusion is assumed.The Lewis number, Le, which expresses the ratio of thermal diffusivity, , to mass diffusivity, D, i.e., is unity,

The Cp mixture f(temperature, composition). This is equivalent to assuming that individual species specific heats are all equal and constant.Fuel and oxidizer form products in a single-step exothermic reaction. Reaction is1 kg fuel + kg oxidiser ( + 1)kg productsThe oxidizer is present in stoichiometric or excess proportions; thus fuel is completely consumed at the flame. For this simplified system, SL and found are(8.20)

and

or (21)

where is volumetric mass rate of fuel and is thermal diffusivity. Temperature profile is assumed linear from Tu to Tb over the small distance, as shown in Fig. 9.

Fig. 9 Assumed temperature profile for laminar premixed flame analysisFACTORS INFLUENCING FLAME SPEED (SL) AND FLAME THICKNESS ()1. Temperature (Tu and Tb)Temperature dependencies of SL and can be inferred from Eqns 20 and 21. Explicit dependencies is proposed by Turns as follows (27)

where is thermal diffusivity, Tu is unburned gas temperature, , Tb is burned gas temperature.

(28)

where the exponent n is the overall reaction order, Ru = universal gas constant (J/kmol-K), EA = activation energy (J/kmol) Combining above scalings yields and applying Eqs. 20 and 21SL (29)

(30)

For hydrocarbons, n 2 and EA 1.67.108 J/kmol (40 kcal/gmol). Eqn 29 predicts SL to increase by factor of 3.64 when Tu is increased from 300 to 600K. Table 8.1 shows comparisons of SL and The empirical SL correlation of Andrews and Bradley [19] for stoichiometric methane-air flames,SL (cm/s) = 10 + 3.71.10-4[Tu (K)]2 (31)which is shown in Fig. 8.13, along with data from several experimenters. Using Eqn. 31, an increase in Tu from 300 K to 600 K results in SL increasing by a factor of 3.3, which compares quite favourably with our estimate of 3.64 (Table 8.1).

Fig. 13 Effect of gas temp. on laminar flame speeds of stoichiometric methane-air mixture at 1 atm, various lines are data from various investigators Table 8.1 Estimate of effects of Tu and Tb on SL and using Eq 29 and 30

Case A: referenceCase C: Tb changes due to heat transfer or changing equivalent ratio, either lean or rich.Case B: Tu changes due to preheating fuelCaseA (ref)BCTu (K)300600300Tb (K)2,0002,3001,700SL/SL,A13.640.46/A10.651.95Pressure (P)From Eq. 29, if, again, n 2, SL f (P).Experimental measurements generally show a negative dependence of pressure. Andrews and Bradley [19] found thatSL (cm/s) = 43[P (atm)]-0.5(32)fits their data for P > 5 atm for methane-air flames (Fig. 14).

Fig. 14 Effect of pressure on laminar flame speeds of stoichiometric methane-air mixture for Tu=16-27oCEquivalent Ratio ()Except for very rich mixtures, the primary effect of on SL for similar fuels is a result of how this parameter affects flame temperatures; thus, we would expect S L,max at a slightly rich mixture and fall off on either side as shown in Fig. 8.15 for behaviour of methane. Flame thickness () shows the inverse trend, having a minimum near stoichiometric (Fig. 16). Fuel TypeFig. 8.17 shows SL for C1-C6 paraffins (single bonds), olefins (double bonds), and acetylenes (triple bonds). Also shown is H2. SL of C3H8 is used as a reference. Roughly speaking the C3-C6 hydrocarbons all follow the same trend as a function of flame temperature. C2H4 and C2H2 SL > the C3-C6 group, while CH4SL lies somewhat below.

Fig. 15 Effect of equivalence ratio on the laminar flame speed of methane-air mixture at atmospheric pressure

Fig. 16 Flame thickness for laminar methane-air flames at atmospheric pressure

Fig. 17 Relative flame speeds for c1-c6 hydrocarbon fuelH2's SL,max is many times > that of C3H8. Several factors combine to give H2 its high flame speed: the thermal diffusivity () of pure H2 is many times > the hydrocarbon fuels; the mass diffusivity (D) of H2 likewise is much > the hydrocarbons; the reaction kinetics for H2 are very rapid since the relatively slow CO CO2 step that is a major factor in hydrocarbon combustion is absent. Law [20] presents a compilation of laminar flame-speed data for various pure fuels and mixtures shown in Table 2.Table 2 SL for various pure fuels burning in air for = 1.0 and at 1 atmFuelSL (cm/s)CH440C2H2136C2H467C2H643C3H8 44H2210FLAME SPEED CORRELATIONS FOR SELECTED FUELSMetghalchi and Keck [11] experimentally determined SL for various fuel-air mixtures over a range of temperatures and pressures typical of conditions associated with reciprocating internal combustion engines and gas turbine combustors.Eqn 8.33 similar to Eqn. 8.29 is proposedSL = SL,ref (1 2.1Ydil) (8.33) for Tu 350 K.

The subscript ref refers to reference conditions defined byTu,ref = 298 K, Pref = 1 atm and SL,ref = BM + B2( - M)2 (for reference conditions)where the constants BM, B2, and M depend on fuel type and are given in Table 3. Exponents of T and P, and are functions of , expressed as = 2.18 - 0.8( - 1) (for non-reference conditions) = -0. 16 + 0.22( - 1) (for non-reference conditions)The term Ydil is the mass fraction of diluent present in the air-fuel mixture in Eqn. 8.33 to account for any recirculated combustion products. This is a common technique used to control NOx in many combustion systems Table 8.3 Values for BM, B2, and M used in Eqn 8.33 [11]

FuelM BM (cm/s)B2 (cm/s)Methanol1.1136.92

-140.51Propane1.0834.22

-138.65Iso octane1.13

26.32-84.72

RMFD-3031.13

27.58

-78.54Example 8.3Compare the laminar flame speeds of gasoline-airmixtures with = 0.8 for the following three cases:At ref conditions of T = 298 K and P = 1 atmAt conditions typical of a spark-ignition engine operating at wide-open throttle: T = 685 K and P = 18.38 atm.Same as condition ii above, but with 15 percent (by mass) exhaust-gas recirculation SolutionRMFD-303 research fuel has a controlled composition simulating typical gasolines. The flame speed at 298 K and 1 atm is given bySL,ref = BM + B2( - M)2From Table 8.3,BM = 27.58 cm/s, B2 = -78.38cm/s, M = 1. 13.SL,ref = 27.58 - 78.34(6.8 - 1.13)2 = 19.05 cm/sTo find the flame speed at Tu and P other than the reference state, we employ Eqn. 33SL(Tu, P) = SL,ref

where = 2.18-0.8(-1) = 2.34 = -0.16+0.22(-1) = - 0.204Thus,SL(685 K, 18.38 atm) = 19.05 (685/298)2.34(18.38/1)-0.204 =73.8cm/sWith dilution by exhaust-gas recirculation, the flame speed is reduced by factor (1-2.1 Ydil):SL(685 K, 18.38 atm, 15%EGR) = 73.8cm/s[1-2.1(0.15)]= 50.6 cm/sQUENCHING, FLAMMABILITY, AND IGNITIONPreviously steady propagation of premixed laminar flamesNow transient process: quenching and ignition. Attention to quenching distance, flammability limits, and minimum ignition energies with heat losses controlling the phenomena.1. Quenching by a Cold WallFlames extinguish upon entering a sufficiently small passageway. If the passageway is not too small, the flame will propagate through it. The critical diameter of a circular tube where a flame extinguishes rather than propagates, is referred to as the quenching distance. Experimental quenching distances are determined by observing whether a flame stabilised above a tube does or does not flashback for a particular tube diameter when the reactant flow is rapidly shut off. Quenching distances are also determined using high-aspect-ratio rectangular-slot burners. In this case, the quenching distance between the long sides, i.e., the slit width. Tube-based quenching distances are somewhat larger (20-50 percent) than slit-based ones [21]Ignition and Quenching CriteriaWilliams [22] provides 2 rules-of-thumb governingignition and flame extinction. Criterion 1 -Ignition will only occur if enough energy is added to heat a slab thickness steadily propagating laminar flame to the adiabatic flame temperature.Criterion 2 -The rate of liberation of heat by chemical reactions inside the slab must approximately balance the rate of heat loss from the slab by thermal conduction. This is applicable to the problem of flame quenching by a cold wall.

Fig. 18 Schematic of flame quenching between two parallel wallSimplified Quenching Analysis. Consider a flame that has just entered a slot formed by two plane-parallel plates as shown in Fig. 8.18. Applying Williams second criterion: heat produced by reaction = heat conduction to the walls, i.e.,(8.34)

is volumetric heat release rate(8.35)

where is volumetric mass rate of fuel, is heat of combustion Thickness of the slab of gas analysed = .

Find quenching distance, d.Solution(36)

A = 2L, where L is slot width ( paper) and 2 accounts for contact on both sides (left and right).is difficult to approximate. A reasonable lower bound of = (37)

where b = 2, assuming a linear distribution of T from the centerline plane at Tb to the wall at Tw. In general b > 2.Quenching occurs from Tb to Tw.

Combining Eqns 8.35-8.37,(38a)

or(38b)

Assuming Tw = Tu, using Eqn 8.20 (about SL), and relating ., Eqn 8.38b becomes

d = 2b /SL(39a)Relating Eqn 8.21 (about ), Eqn 8.39a becomesd = 2b Because b 2, value d is always > . Values of d for fuels are shown Table 8.4.

Table 8.4 Flammability limits, quenching distances and minimum ignition energiesFlammability limit Quenching distance, dmin max Stoich-mass air-fuel ratio For =1 Absolute min, mm C2H20.1913.32.3-CO0.346.762.46--C10H220.363.9215.02.1-C2H60.502.7216.02.31.8C2H40.41> 6.114.81.3-H20.142.5434.50.640.61CH40.461.6417.22.52.0CH3OH0.484.086.461.81.5C8H180.514.2515.1--C3H80.512.83

15.62.01.8

FuelMinimum ignition energy For =1 (10-5 J) Absolute minimum (10-5 J) C2H23-CO--C10H22--C2H64224C2H49.6-H22.01.8CH43329CH3OH21.514C8H18--C3H830.526Example 8.4. Consider the design of a laminar-flow, adiabatic, flat-flame burner consisting of a square arrangement of thin-walled tubes as illustrated in the sketch below. Fuel-air mixture flows through both the tubes and the interstices between the tubes. It is desired operate the burner with a stoichiometric methane-air mixture exiting the tubes at 300 K and 5 atm Determine the mixture mass flowrate per unit cross-sectional area at the design condition.Estimate the maximum tube diameter allowed so that flashback will be prevented.

SolutionTo establish a flat flame, the mean flow velocity must equal the laminar flame at the design temperature and pressure. From Fig. 14,SL (300K, 5atm) = 43/P (atm) = 43/5 = 19.2cm/s.The mass flux, , is= = uu = uSLAssuming an ideal-gas mixture, whereMWmix = CH4MWCH4 + (1 - CH4)MWair= 0.095(16.04) + 0.905(28.85)= 27.6 kg/kmol =5.61kg/m3(Stoichimetric mass ratio air/ methane = 17.2, see Table 4)Thus, the mass flux is = uSL = 5.61(0.192)= 1.08 kg/(s.m2)

We assume that if the tube diameter < the quench distance (d), with some factor-of-safety applied, the burner will operate without danger of flashback. Thus, we need to find the quench distance at the design conditions. Fig. 16 shows that dslit 1.7 mm. Since dslit = dtube (20-50%), use dslit outright (our case) with factor of safety 20-50%. Data in Fig 8.16 is for slit, design is of tube.Correction for 5 atm:Eqn. 39a, d /SLEqn 27, T1.75/Pd2 =

d(5atm) =1.7mm.

ddesign 0.76 mmCheck whether d=0.76 mm gives laminar flow (Red < 2300).

Flow is still laminar

2. Flammability LimitsA flame will propagate only within a range of mixture the so-called lower and upper limits of flammability. The limit is the leanest mixture ( < 1), while the upper limit represents the richest mixture ( > 1). = (A/F)stoich /(A/F)actual by mass or by moleFlammability limits are frequently quoted as %fuel by volume in the mixture, or as a % of the stoichiometric fuel requirement, i.e., ( x 100%). Table 8.4 shows flammability limits of some fuels Flammability limits for a number of fuel-air mixtures at atmospheric pressure is obtained from experiments employing "tube method". In this method, it is ascertained whether or not a flame initiated at the bottom of a vertical tube (approximately 50-mm diameter by 1.2-m long) propagates the length of the tube. A mixture that sustains the flame is said to be flammable. By adjusting the mixture strength, the flammability limit can be ascertained.Although flammability limits are physico-chemical properties of the fuel-air mixture, experimental flammability limits are related to losses from the system, in addition to the mixture properties, and, hence, generally apparatus dependent [31].Example 8.5. A full C3H8 cylinder from a camp stove leaks its contents of 1.02 lb (0.464 kg) in 12' x 14' x 8' (3.66 m x 4.27 m x 2.44 m) room at 20oC and 1 atm. After a long time fuel gas and room air are well mixed. Is the mixture in the room flammable?

SolutionFrom Table 8.4, we see that C3H8-air mixtures are flammable for 0.51 < < 2.83. Our problem, thus, is to determine of the mixture filling the room. Partial pressure of C3H8 by assuming ideal-gas behaviour= 672.3 PaPropane mole fraction =F = PF/P = 672.3/101,325 = 0.00664and air = 1 - F = 0.99336The air-fuel ratio of the mixture in the room is(A/F)act =

From the definition of and the value of (A/F)stoich from Table 8.4 (i.e. 15.6 by mass ratio), we have = (A/F)stoich /(A/F)act = 15.6/97.88 = 0.159Since = 0.159 < lower limit (= 0. 51), the mixture in the room is not capable of supporting a flame.

CommentAlthough our calculations show that in the fully mixed state the mixture is not flammable, it is quite possible that, during the transient leaking process, a flammable mixture can exist somewhere within the room. C3H8 is heavier than air and would tend to accumulate near the floor until it is mixed by bulk motion and molecular diffusion. In environments employing flammable gases, monitors should be located at both low and high positions to detect leakage of heavy and light fuels, respectively.3. IgnitionMost of ignition uses electrical spark (pemantik listrik). Another means is using pilot ignition (flame from very low-flow fuel).

Simplified Ignition AnalysisConsider Williams second criterion, applied to a spherical volume of gas, which represents the incipient propagating flame created by a point spark. Using the criterion:Find a critical gas-volume radius, Rcrit, below which flame will not propagateFind minimum ignition energy, Eign, to heat critical gas volume from initial state to flame temperature (Tu to Tb).

Critical radius, Rcrit, and Eign(8.40)

(propagation)(8.41)

where is mass flowrate/volumeHeat transfer process is shown in Figure 8.20

(8.42)

Substitution Eqn 8.42 to 8.41 results in

.(8.43)

Rcrit is therefore determined by the flame propagation

If R < Rcrit, it would require exothermic heat > hcSubstituting from Eqn 8.20 into Eqn 8.43 will give (8.44)

Ignition is aimed to increase fluid from Tu to Tb at the onset of combustion to replace hc (ignition) (8.45)

where Eign is minimum ignition energy

Substitution mcrit=b.4Rcrit3/3 and b using gas ideal formulae to Eqn 8.45 results in(8.47)

where Rb = Ru/MWb and Ru = gas constant

4. Dependencies on Pressure, Temperatureand Composition

Using Eqn 8.27 and 8.29 on Eqn 8.47 demonstrates effect of pressure to beEign P-2(8.48)(see comparison with experimental result in Fig 8.21)

Eqn 8.47 implies that in general, Tu Eign (see Table 8.5). Eign vs %fuel gives U-shaped plot (Figures 8.22 and 8.23). This figure indicates that Eign is minimum as a mixture composition is stoichiometric or near it. If the mixture gets leaner at au richer, Eign increases first gradually and then abruptly. %fuel at Eign = to be ignited are flammability limits

Figure 8.22. Effect of %fuel on Eign

Figure 8.22. Effect of %fuel on EignFigure 8.23. Effect of methane composition on Eign

Table 8.5 Temperature influenceon spark-ignition energy FuelInitial temp (K)Eign (mJ)n-heptane 29814.53736.74443.2Iso-octane29827.037311.04444.8n-pentane24345.025314.5FuelInitial temp (K)Eign (mJ)n-heptane 2987.83734.24442.3propane 23311.72439.72538.42985.53314.23563.63733.54771.4References:Turns, Stephen R., An Introduction to Combustion, Concepts and Applications, 2nd edition, McGrawHill, 2000