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LAMINAR PREMIXED FLAMES

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OVERVIEW Applications: Heating appliances Bunsen burners Burner 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.

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PHYSICAL DESCRIPTION Physical characteristics Figure 8.2 shows typical flame temperature profile, mole fraction of reactants, R, and volumetric heat release,. Velocity of reactants entering the flame, u = flame propagation velocity, S L Products heated product density ( b ) = unburned gas vel., u u u A = b b A(8.1)

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

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A flame consists of 2 zones: Preheat zone, where little heat is released Reaction zone, where the bulk of chemical energy is released Reaction zone consists of 2 regions: Thin region (less than a millimeter), where reactions are very fast Wide region (several millimeters), where reactions are slow

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In destruction of the fuel molecules and creation of many intermediate species occur. This region is dominated by bimolecular reactions to produce CO. In 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 CO 2 +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 C 2.

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In both flame regions, OH radicals contribute to the visible radiation, and to a lesser degree due to reaction CO + O CO 2 + 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 Wien’s 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

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Figure 1. Spectrum of flame colours

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Typical Laboratory Premixed Flames The typical Bunsen-burner flame is a dual flame: a fuel rich premixed inner flame surrounded by a diffusion flame. Figure 8.3 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.

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For the flame to remain stationary, S L = normal component of u = u sin (8.2). Figure 8.3b illustrates vector diagram.

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Example 8.1. 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 Determine the flame shape and the distribution of the local angle of the flame surface from vertical. Assume the flame speed S L is independent of position and equal to 0.4m/s (constant), a nominal value for a stoichiometric methane-air flame.

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Solution From Fig. 8.7, we see that the local angle, , which the flame sheet makes with a vertical plane is (Eqn. 8.2) = arc sin (S L / u ), where, from Fig. 8.6, u (mm/s) = (1200 – 800)/20 x (mm) (known). u (mm/s) = (1200 – 800)/20 x (mm) (known). u (mm/s) = x. u (mm/s) = x.So, = arc sin (400/( x (mm)) and has values ranging from 30 o at x = 0 to19.5 o at x = 20 mm, as shown in the top part of Fig. 8.6.

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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. 8.7, we see that

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,which, for u =A + Bx, becomes Integrating the above with A/S L = 2 and B/S L = 0.05 yields -10 ln[(x 2 +80x+1200) 1/2 +(x+40)] -20 3+10 ln(20 3+40) The flame position z(x) is plotted in upper half of Fig. 8.6.

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SIMPLIFIED ANALYSIS Turns (2000) proposes simplified laminar flame speed and thickness on one-dimensional flame. Assumptions used: One-dimensional, constant-area, steady flow. One-dimensional flat flame is shown in Figure 8.5. Kinetic and potential energies, viscous shear work, and thermal radiation are all neglected. The small pressure difference across the flame is neglected; thus, pressure is constant.

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The diffusion of heat and mass are governed by Fourier's and Fick's laws respectively (laminar flow). Binary diffusion is assumed. –The Lewis number, Le, which expresses the ratio of thermal diffusivity, , to mass diffusivity, D, i.e., is unity,

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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 is 1 kg fuel + kg oxidiser ( + 1)kg products The oxidizer is present in stoichiometric or excess proportions; thus fuel is completely consumed at the flame.

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For this simplified system, S L and found are (8.20) and or (8.21) where is volumetric mass rate of fuel and is thermal diffusivity. Temperature profile is assumed linear from T u to T b over the small distance, as shown in Fig. 8.9.

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FACTORS INFLUENCING FLAME SPEED (S L ) AND FLAME THICKNESS ( ) 1. Temperature (T u and T b ) Temperature dependencies of S L and can be inferred from Eqns 8.20 and Explicit dependencies is proposed by Turns as follows (8.27) where is thermal diffusivity, T u is unburned gas temperature,, T b is burned gas temperature.

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(8.28) where the exponent n is the overall reaction order, R u = universal gas constant (J/kmol-K), E A = activation energy (J/kmol) Combining above scalings yields and applying Eqs 8.20 and 8.21 S L (8.29) (8.30)

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For hydrocarbons, n 2 and E A J/kmol (40 kcal/gmol). Eqn 8.29 predicts S L to increase by factor of 3.64 when T u is increased from 300 to 600K. Table 8.1 shows comparisons of S L and The empirical S L correlation of Andrews and Bradley [19] for stoichiometric methane-air flames, S L (cm/s) = [T u (K)] 2 (8.31) which is shown in Fig. 8.13, along with data from several experimenters. Using Eqn. 8.31, an increase in T u from 300 K to 600 K results in S L increasing by a factor of 3.3, which compares quite favourably with our estimate of 3.64 (Table 8.1).

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Table 8.1 Estimate of effects of T u and T b on S L and using Eq 8.29 and 8.30 Case A: reference Case C: T b changes due to heat transfer or changing equivalent ratio, either lean or rich. Case B: T u changes due to preheating fuel Case A (ref) BC T u (K) T b (K) 2,0002,3001,700 S L /S L,A /A/A/A/A

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Pressure (P) From Eq. 8.29, if, again, n 2, S L f (P). Experimental measurements generally show a negative dependence of pressure. Andrews and Bradley [19] found that S L (cm/s) = 43[P (atm)] -0.5 (8.32) fits their data for P > 5 atm for methane-air flames (Fig. 8.14).

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Equivalent Ratio ( ) Except for very rich mixtures, the primary effect of on S L 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 for behaviour of methane. Flame thickness ( ) shows the inverse trend, having a minimum near stoichiometric (Fig. 8.16).

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Fuel Type Fig shows S L for C 1 -C 6 paraffins (single bonds), olefins (double bonds), and acetylenes (triple bonds). Also shown is H 2. S L of C 3 H 8 is used as a reference. Roughly speaking the C 3 -C 6 hydrocarbons all follow the same trend as a function of flame temperature. C 2 H 4 and C 2 H 2 ‘ S L > the C 3 -C 6 group, while CH 4 ’S L lies somewhat below.

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H 2 's S L,max is many times > that of C 3 H 8. Several factors combine to give H 2 its high flame speed: i.the thermal diffusivity ( ) of pure H 2 is many times > the hydrocarbon fuels; ii.the mass diffusivity (D) of H 2 likewise is much > the hydrocarbons; iii.the reaction kinetics for H 2 are very rapid since the relatively slow CO CO 2 step that is a major factor in hydrocarbon combustion is absent.

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Law [20] presents a compilation of laminar flame-speed data for various pure fuels and mixtures shown in Table 8.2. Table 8.2 S L for various pure fuels burning in air for = 1.0 and at 1 atm Fuel S L (cm/s) CH 4 40 C2H2C2H2C2H2C2H2136 C2H4C2H4C2H4C2H467 C2H6C2H6C2H6C2H643 C3H8C3H8C3H8C3H844 H2H2H2H2210

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FLAME SPEED CORRELATIONS FOR SELECTED FUELS Metghalchi and Keck [11] experimentally determined S L 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 is proposed S L = S L,ref (1 – 2.1Y dil ) (8.33) for T u 350 K.

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The subscript ref refers to reference conditions defined by T u,ref = 298 K, P ref = 1 atm and S L,ref = B M + B 2 ( - M ) 2 (for reference conditions) where the constants B M, B 2, and M depend on fuel type and are given in Table 8.3. Exponents of T and P, and are functions of , expressed as = ( - 1) (for non-reference conditions) = ( - 1) (for non-reference conditions) The term Y dil is the mass fraction of diluent present in the air-fuel mixture in Eqn to account for any recirculated combustion products. This is a common technique used to control NO x in many combustion systems

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Table 8.3 Values for B M, B 2, and M used in Eqn 8.33 [11] Fuel MM B M (cm/s)B 2 (cm/s) Methanol Propane Iso octane RMFD

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Example 8.3 Compare the laminar flame speeds of gasoline-air mixtures with = 0.8 for the following three cases: i.At ref conditions of T = 298 K and P = 1 atm ii.At conditions typical of a spark-ignition engine operating at wide-open throttle: T = 685 K and P = atm. iii.Same as condition ii above, but with 15 percent (by mass) exhaust-gas recirculation

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Solution RMFD-303 research fuel has a controlled composition simulating typical gasolines. The flame speed at 298 K and 1 atm is given by S L,ref = B M + B 2 ( - M ) 2 From Table 8.3, B M = cm/s, B 2 = cm/s, M = S L,ref = ( ) 2 = cm/s To find the flame speed at T u and P other than the reference state, we employ Eqn S L (T u, P) = S L,ref

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where = ( -1) = 2.34 = ( -1) = Thus, S L (685 K, atm) = (685/298) 2.34 (18.38/1) =73.8cm/s With dilution by exhaust-gas recirculation, the flame speed is reduced by factor (1-2.1 Y dil ): S L (685 K, atm, 15%EGR) = 73.8cm/s[1-2.1(0.15)]= 50.6 cm/s

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QUENCHING, FLAMMABILITY, AND IGNITION Previously steady propagation of premixed laminar flames Now transient process: quenching and ignition. Attention to quenching distance, flammability limits, and minimum ignition energies with heat losses controlling the phenomena.

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1. Quenching by a Cold Wall Flames 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.

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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 ( percent) than slit-based ones [21]

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Ignition and Quenching Criteria Williams [22] provides 2 rules-of-thumb governing ignition 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.

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Simplified Quenching Analysis. Consider a flame that has just entered a slot formed by two plane-parallel plates as shown in Fig 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 = .

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Find quenching distance, d. Solution (8.36) A = 2 L, 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 = (8.37) where b = 2, assuming a linear distribution of T from the centerline plane at T b to the wall at T w. In general b > 2. Quenching occurs from T b to T w.

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Combining Eqns , (8.38a) or (8.38b) Assuming T w = T u, using Eqn 8.20 (about S L ), and relating ., Eqn 8.38b becomes d = 2 b /S L (8.39a) Relating Eqn 8.21 (about ), Eqn 8.39a becomes d = 2 b Because b 2, value d is always > . Values of d for fuels are shown Table 8.4.

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Table 8.4 Flammability limits, quenching distances and minimum ignition energies Flammability limit Quenching distance, d min max Stoich-mass air-fuel ratio For =1 Absolute min, mm C2H2C2H2C2H2C2H20.19 CO C 10 H C2H6C2H6C2H6C2H C2H4C2H4C2H4C2H40.41 > H2H2H2H CH CH 3 OH C 8 H C3H8C3H8C3H8C3H

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Fuel Minimum ignition energy For =1 (10 -5 J) Absolute minimum (10 -5 J) C2H2C2H2C2H2C2H23- CO-- C 10 H C2H6C2H6C2H6C2H64224 C2H4C2H4C2H4C2H49.6- H2H2H2H CH CH 3 OH C 8 H C3H8C3H8C3H8C3H

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Example 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

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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.

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Solution To establish a flat flame, the mean flow velocity must equal the laminar flame at the design temperature and pressure. From Fig. 8.14, S L (300K, 5atm) = 43/ P (atm) = 43/ 5 = 19.2cm/s. The mass flux,, is = = u u = u S L Assuming an ideal-gas mixture, where MW mix = CH4 MW CH4 + (1 - CH4 )MW air = 0.095(16.04) (28.85) = 27.6 kg/kmol =5.61kg/m 3 (Stoichimetric mass ratio air/ methane = 17.2, see Table 8.4) Thus, the mass flux is= u S L = 5.61(0.192)= 1.08 kg/(s.m 2 )

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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 shows that d slit 1.7 mm. Since d slit = d tube – (20-50%), use d slit 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:

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Eqn. 8.39a, d /S L Eqn 8.27, T 1.75 /P d 2 = d(5atm) =1.7mm. d design 0.76 mm Check whether d=0.76 mm gives laminar flow (Re d < 2300). Flow is still laminar

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2. Flammability Limits A 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). = (A/F) stoich /(A/F) actual by mass or by mole Flammability 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

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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.

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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].

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Example 8.5. A full C 3 H 8 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 20 o C and 1 atm. After a long time fuel gas and room air are well mixed. Is the mixture in the room flammable? Solution From Table 8.4, we see that C 3 H 8 -air mixtures are flammable for 0.51 < < Our problem, thus, is to determine of the mixture filling the room. Partial pressure of C 3 H 8 by assuming ideal-gas behaviour

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= Pa Propane mole fraction = F = P F /P = 672.3/101,325 = and air = 1 - F = The air-fuel ratio of the mixture in the room is (A/F) act =

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

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Comment Although 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. C 3 H 8 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.

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3. Ignition Most of ignition uses electrical spark (pemantik listrik). Another means is using pilot ignition (flame from very low-flow fuel). Simplified Ignition Analysis Consider 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, R crit, below which flame will not propagate Find minimum ignition energy, E ign, to heat critical gas volume from initial state to flame temperature (T u to T b ).

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Critical radius, R crit, and E ign (8.40) (propagation) (8.41) where is mass flowrate/volume Heat transfer process is shown in Figure 8.20 (8.42) Substitution Eqn 8.42 to 8.41 results in .(8.43) R crit is therefore determined by the flame propagation

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If R h c Substituting from Eqn 8.20 into Eqn 8.43 will give (8.44) Ignition is aimed to increase fluid from T u to T b at the onset of combustion to replace h c (ignition) (8.45) where E ign is minimum ignition energy

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Substitution m crit = b.4 R crit 3 /3 and b using gas ideal formulae to Eqn 8.45 results in (8.47) where R b = R u /MW b and R u = gas constant

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4. Dependencies on Pressure, Temperature and Composition Using Eqn 8.27 and 8.29 on Eqn 8.47 demonstrates effect of pressure to be E ign P -2 (8.48) (see comparison with experimental result in Fig 8.21) Eqn 8.47 implies that in general, T u E ign (see Table 8.5).

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E ign vs %fuel gives U-shaped plot (Figures 8.22 and 8.23). This figure indicates that E ign is minimum as a mixture composition is stoichiometric or near it. If the mixture gets leaner atau richer, E ign increases first gradually and then abruptly. %fuel at E ign = to be ignited are flammability limits

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Figure Effect of %fuel on E ign

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Figure Effect of methane composition on E ign

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Table 8.5 Temperature influence on spark-ignition energy Fuel Initial temp (K) E ign (mJ) n-heptane Iso-octane n-pentane

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Fuel Initial temp (K) E ign (mJ) n-heptane propane

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References: Turns, Stephen R., An Introduction to Combustion, Concepts and Applications, 2 nd edition, McGrawHill, 2000

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