Module 3: Laminar Premixed Flames

Transcription

1 Module 3: aminar Premixed Flames Objectives Scoe Reading Assignments Assignment Schedule Objectives By the end of this module, students should be able to: Define what is meant by Premixed Flame Understand the Hugoniot Curve Understand the basic theory for flame seed in a remixed system Identify various methods used to measure flame seed Exlain what factors can influence flame seed Exlain the factors that can affect the stability of aminar Premixed Flames Define flammability limits Understand ressure effects of flammability limits Understand flame stabilization at low velocities Define Flashback and Blow-off Define Flame Quenching Scoe Review the Hugoniot Relation Analysis of the basic structure of remixed flames Analysis of remixed flame seed and variables that effect the seed Analysis of flammability limits Reading Assignments Turns: Chater 8, Chater 6 Drysdale: Chater 3 Assignment Schedule Five roblems worth oints each (0 total) are to be comleted and submitted online. There are also two extra credit roblems available (4 oints). See the last age of this module for more details. There are also discussion exercises (3., 3., and 3.3) that will count towards your class articiation grade.

2 aminar Premixed Flames Introduction We can now use the knowledge that we have gained in the first two modules to begin talking about flames. As resented in the introduction, our discussion of flames will begin with develoing an understanding of laminar, remixed flames. First, let us review what we mean by laminar, remixed flames. aminar vs. turbulent flow laminar describes the nature of the gaseous flow field in which the flame is occurring. Of articular imortance is the fact that thermal transort in the vicinity of the flame can be assumed to occur largely by conduction rather than by convection. Premixed vs. diffusion flame as we discussed in Module, in remixed flames reactants are comletely mixed rior to entering the flame zone. By comarison, diffusion flames deend on mixing of the fuel and air at the flame front by diffusion. In Module, we talked about homogeneous thermal exlosions and chain branching exlosions as a way to achieve raid release of the heat of combustion of a fuel-oxidizer system. However, for most fuel-oxygen combinations at room temerature and atmoshere ressure, the system is unreactive. As we now know, desite the large (negative) heat of reaction associated with fuel-oxidizer reactions, at room temerature the kinetics of such reactions are simly too slow for them to occur sontaneously in a self-sustaining manner. We learned that if the mixture was heated sufficiently or sufficient radicals were introduced, an exlosion would occur. In most cases, this exlosion corresonds to a self-sustaining flame which roagates at subsonic velocity. Such a flame roagation is usually referred to as a deflagration. However, if the exlosion leads to a suersonic flame roagation, the result is a detonation. If we begin with a fuel/oxidizer mixture and a local ignition source is alied to the mixture which raises the temerature or concentration of radicals, a region of raid reaction and high heat release will roagate through the mixture rovided the mixture is within flammability limits. We will hold our discussion of local thermal ignition and flammability limits until later in this Module. Right now let us focus on the structure of a laminar, remixed flame. Consider a long tube containing a flammable fuel/oxygen mixture as shown below. If an ignition source is alied at one end, a combustion wave will roagate down the tube from the burned gases into the unburned gases. Burned unburned Flame front

3 For a tube that is oen at both ends, the velocity of roagation of this flame front (sometimes referred to as a flame wave),v, is tyically in the range of 0 00 cm/sec. For most hydrocarbon/air combinations this flame seed is aroximately 45 cm/sec. The flame wave velocity is controlled rimarily by transort rocesses, i.e. heat conduction and the diffusion of radicals. This low seed (i.e. subsonic) flame roagation is called a Deflagration. Note, that the range of V s given above is much less than the sound seed. If the tube is closed at the ignition end, the flame will accelerate in the tube as it roagates. Eventually it will transition from subsonic to suersonic. This suersonic rocess is called a Detonation. In a detonation, the shock wave which occurs at suersonic velocity raises T and P of the mixture to create an exlosive reaction and energy release to sustain wave roagation. To better understand the structure of this flame wave henomenon (whether subsonic or suersonic) we will aly the rincials of fluid mechanics. As usual when analyzing a fluids roblem, we will start with the conservation equations. Conservation Equations A u = u A = m& (continuity) + u = + u CT + ½ u + q = CT + ½ u (momentum) (energy) H H Also we can use the ideal gas equation of state. However, note that the final state equation is not indeendent of the initial state equation. = RT ( = RT ) (not indeendent) Thus, we have a system of 4 equations, 5 unknowns. However, by assuming A = A = in the continuity equation and combining continuity and momentum we can obtain a fifth equation given as: or ( ) ( ) = u - u u u = = m& 3

4 ( ) = = m u & This is the definition of a so-called Rayleigh line. If we remember that the Mach number, M, is defined as the local gas velocity divided by the local seed of sound, C, such that C U M = where = = T R C γ γ Where V P C C = γ gives γ γ = P P P u = γ M or Recall C C v = R And γ = V C C so C - V C C C = R Or 4

5 C - R C = γ So C = R R = γ γ γ Then the energy equation gives U T C q U T C + = + + using equation of state R T =, then ( ) q U U R C R C = or ( ) q U U = γ γ but U U U U + + = so we get ( ) q = + γ γ (Rankine) Hugoniot Relation For the remixed flame wave rocess described above, this equation defines the relationshi between the initial state (unburned gases) and the final state (burned gases) for a given heat of combustion, q. For a fixed q and a given P and, the Rankine-Hugoniot equation describes a curve on a lot of versus / that corresonds to a family of solutions to this equation. As we will see below, one region of the solution leads to deflagrations while the other region leads to detonations. 5

6 Hugoniot Curve As shown in Figure M3- below, for fixed q: the Rankine-Hugoniot relation leads to a curved line on lot of vs. Also shown on the lot are tangent lines to the uer and lower branches of the curve. The tangent oints are called the Chaman-Jouguet oints. These oints hel divide the curve into three regions. Figure M3-: Hugoniot Plot (From Combustion 3 rd Ed. by Glassman, age ) Region I in the figure corresond to final states where the ressure and density are greater than the initial ressure and density. This is the region of detonations and the flame wave roagation velocity is suersonic. The tangent oint J is the uer Chaman-Jouguet oint. Region II arises when the final ressure and density are lower than the initial state. These regions corresond to deflagrations and the flame wave roagation velocity is subsonic. The tangent oint K is the lower Chaman-Jouguet oint. Region III is a region that, although mathematically valid as a solution to the Rankine-Hugoniot relation, is not hysically valid (since U would be imaginary). Although, in theory, a range of detonations and deflagrations can occur, in ractice, only the solution corresonding to the Chaman-Jouguet oint (oint J) is observed for detonations and only solutions corresonding to the Chaman- Jouguet (oint K) and less (area C on the curve) are observed for deflagration. Note, M = for both Chaman-Jouguet oints; thus, since flow cannot go from subsonic to suersonic in a constant area duct, no values greater than Chaman-Jouguet oint are allowed for deflagrations. For deflagrations, the rate of heat release of the fuel-air mixtures rovides the 5 th equation that determines where the subsonic region in the final state exists. This oint along the weak deflagration region of the curve defines the deflagration velocity. This deflagration velocity is by definition the laminar flame seed. That is, the laminar flame seed is the seed at which a flame wave will roagate through a given fuel-air mixture in a tube with both ends oen. 6

7 At this oint, it is worthwhile to discuss the term exlosion in light of our newfound understanding of deflagrations and detonations. If a fuel-air mixture is confined, such as a natural gas leak in a home, and an ignition source is resent, a flame wave will roagate through the mixture. As we all know this generally leads to an exlosion which destroys the home. However, in almost all cases, this is not a detonation. It is only a confined deflagration. That is, the rate of roagation of the flame in this situation will be subsonic. And, although the ressure inside the home will rise for a eriod of time until it is vented, generally, the rocess will stay subsonic. This has an imortant imlication for most exlosions we encounter in Fire Protection. If an exlosion is caused by a deflagration, since the rocess is subsonic, the ressure will rise uniformly everywhere in the vessel (e.g. the closed ortion of the house in which the mixture is contained). As a result, the exlosion will not vent closest to the source of ignition, but rather it will vent wherever the weakest art of the structure containing the exlosion is (for many houses this means the doors or windows blow out first). This henomenon can be understood by remembering that the seed of sound is the seed at which ressure waves roagate through a gas. Therefore, in a deflagration, the ressure waves roagate significantly faster than the flame does. As a result, the ressure rises aroximately uniformly within the volume containing the deflagration. Discussion Exercise 3.: Assume a roane torch with a one ound suly bottle leaks into a large conference room and remixes with air (within its flammability limits) before it is ignited by an electrical motor for an HVAC unit. If the conference room measures 40 meters by 5 meters by 4 meters in height will the exlosion blow out the windows? The walls? (Assume windows break at 0.5 sig and that cinderblock walls fail at sig). Discuss with your fellow students the level of hazard that you believe such a roane bottle constitutes. Instructions: Determine the level of hazard this constitutes. Once determined, ost your findings and discuss it with fellow students. Answering the roblem is the beginning of this exercise. Discuss the imlications and how this alies to you in your field of Fire Protection Engineering. There is a toic M3-Exlosion in the discussion area created for this discussion. aminar Flame Structure We are now ready to look at the structure of the flame zone itself. We can start by remembering the simle Bunsen burner flame from Module. 7

8 Figure M3-: Schematic of Bunsen Burner This burner flame is a simle laminar remixed flame. The air and fuel are mixed in the tube and flow together out the to of the burner where they enter the remixed flame zone. The flame itself is conical in shae with a dark zone under the flame cone and a luminous region that defines the flame zone itself. The burned gases flow uward out the to of the flame accelerated by the heat release in the flame zone. If we isolate a section of the flame front, we can analyze it to understand more recisely the structure of the remixed flame. We will do this analysis following the theory of Mallard and e Chatelier with the ultimate goal of understanding the structure of the flame and the variable that determine the flame seed for a laminar remixed flame (i.e. the velocity of travel of the deflagration). aminar Flame Seed Mallard and e Chatelier develoed a Two zones theory of a laminar, remixed flame. In their theory, the flame is divided into a reheat region (or region of conduction), Zone I, and a burning region, Zone II, as shown in Figure M3-3 below. Note that the burning zone has a thickness, δ, defined as the laminar flame thickness. 8

9 Figure M3-3: Mallard-e Chatelier Descrition (From Combustion 3 rd Ed. by Glassman, age 6) In their theory, the flame moves by conducting heat from the burning zone to the reheat zone. In order for the flame to be self-sustaining, the amount of heat conducted from the burning zone must be sufficient to raise the temerature of the unburned fuel/air mixture to its ignition temerature. Thus, they theorized that in Zone I the gases are heated from their initial temerature, T 0, to their ignition temerature, T i, by heat from the combustion reaction conducted from Zone II into Zone I. The excess energy released from the combustion reaction then further raises the temerature of the gases from T i to the flame temerature T f. They analyzed this rocess by linearizing the temerature change in Zone II and by setting the sensible heat necessary to raise the unburned gases from T 0 to T i equal to the heat conducted from the flame into Zone I. The energy balance then is given by (. T ) f Ti m C (T i T o ) = λ A δ Where λ = thermal conductivity If we treat this flame roagation as a D roblem then the mass flow rate in the reheat region is given by:. m = Au = As where s = u is defined as the laminar flame seed. So the energy balance around the flame becomes ( T T ) = λ( T T ) δ S C / i o f i or 9

10 S ( T T ) λ f i = (M3-) C ( T T )δ i o but the flame thickness,δ, is unknown. However, we can use chemical kinetics to get an exression for δ as follows. The flame thickness is given by the flame seed times some measure of the reaction time. This reaction time is given by the inverse of the reaction rate, so δ = S τ = S = dε dt S, RR If we substitute the exression for δ into equation (M3-) and solve for S then we get S λ = c T f T T T i i o ( RR) ~ ( αrr) where α = λ c If we eliminate RR by using the fact that RR = S / δ then we get δ = α S That is, the flame thickness is equal to the thermal diffusivity divided by the laminar flame seed. Since for tyical Hydrocarbons Then S = 40 cm/sec. δ 0.cm =. 0mm α And τ = 5 S milliseconds S αrr Note ( ) If we look at the reaction rate, dε n RR= = kε dt So E n RT n n = Ae ε 0

11 S ~ n ~ n ( ) Since for most Hydrocarbon fuels, the reaction rate is overall second order, i.e., n =, then S is aroximately indeendent of ressure. Also note, that since the reaction rate term is dominated by the exonential term in the Arrhenius exression, S ~ E RT e if T i T f then S ~ E f e RT this leads to the conclusion that a higher T f roduces a faster S. Summary Review: Mallard and e Chatelier Thermal theory ( zones): reheat flame Result: S = λ c T f T T T i o o de dt ( ) S ~ α RR δ ~ S α S n o ( ) ~ ~ S ~ E f e RT

12 Flame Seed Measurements In order to measure the seed of a laminar flame it is often necessary to define the exact location of the flame. The flame can be located by a number of different measurement techniques. The first and most obvious is the luminous zone of the flame. However, some other techniques can also be used to define the flame zone. They include the otical methods of shadowgrah and Schlieren, which measure the second derivative and the first derivative, resectively, of the temerature gradient, and interferometry, which measures the temerature or density of the gas. Ways to locate flame a) luminous zone b) shadowgrah ( nd derivative) c) Schlieren ( st derivative) d) Interferometry (temerature or density) Figure M3-4: Temerature regimes in a laminar flame (From Combustion 3 rd Ed. by Glassman, age 49) For a Bunsen Burner (see Figure M3-5 below), these different measures of the flame zone give slightly different definitions of the flame area and, as we will see below, lead to slightly different measures of the flame seed.

13 Figure M3-5: Otical fronts in a Bunsen burner flame (From Combustion 3 rd Ed. by Glassman, age 50) Methods of flame seed measurement Burner method S varies Early method: S = Q ~ cm A sec also use cone angle, then: S = U U sin α 3

14 Figure M3-6: Velocity vectors in a Bunsen core flame (From Combustion 3 rd Ed. by Glassman, age 5) Cylindrical tube. horizontal tube oen at one end. ignite at oen end 3. flame is curved S A f = U m R Soa bubble method. gas in soa bubble ignited at center = constant balance gives S xax = u o r xax f or S = u r f o Sherical bomb Constant volume changes must follow and flame 3 3 R r d dr S = 3γ ur dr dt 4

15 Flat Flame burner Figure M3-7: Flat flame burner aaratus Cool burner (From Combustion 3 rd Ed. by Glassman, age 54) Figure M3-8: Cooling effect in flat flame burner aaratus (From Combustion 3 rd Ed. by Glassman, age 55) 5

16 Discussion Exercise 3.: A stoichiometric fuel-air mixing flowing in a Bunsen burner forms a well-defined conical flame. The mixture is then made leaner. For the same flow velocity in the tube, does the cone angle become larger or smaller than the angle for the stoichiometric mixture? Exlain. Instructions: In the discussions sace, there is a toic M3-Flow Velocity. Post your exlanation/oinion there. Be sure to rovide suort for your answer. Comare and discuss your findings with those of other students. Effects on Flame Seed Showed reviously S λ = c T f T T T i o o de dt ( α ) ~ RR e E ~ n RT ~ ( ) n is overall order of reaction. For second order S ~ o For most hydrocarbons (hc), n.5.0 (.75), so there is a slight decrease in S with. Figure M3-9: Variation in laminar flame seeds Cometition between: (From Combustion 3 rd Ed. by Glassman, age 57) 6

17 H+O O+OH H+O +M HO +M Figure M3-0: Variation in laminar flame seeds (From Combustion 3 rd Ed. by Glassman, age 58) S vs φ T max at φ slightly greater than.0 So is S max For H increase in thermal different ushes Max S richer Variation of S for hc follows T f 7

18 Figure M3-: Relative effect of oxygen concentrations on flame seed (From Combustion 3 rd Ed. by Glassman, age 59) S vs 0 O 0 should exect hc factor of 5 higher should exect CO/H factor of 5 lower CO has limited OH hc radical ool increases with O S vs T i small changes in T i give small changes in T f but since S ~ E RT e f can have large effect. 8

19 Figure M3-: Methane laminar flame velocities S vs dilluent (N, AR, He) AR and N have the same diffusivity, but C N > C AR and CAR = C He but α He > αar (From Combustion 3 rd Ed. by Glassman, age 60) Note: attemts to modify flame seed by addition of low temerature intermediate roduces results that are the same as excess fuel. Thus, S is controlled by high temerature reactions. For CO added H, H O increases, then decreases by ~5% due to OH Anti-knocks: no effect on flame seed reduce marginal radicals Halogens: reduce marginal radicals 9

20 Stability of aminar Flames imits due to loss of heat in gas hase: reduced temerature no feed back imits due to quenching at wall loss of heat & radicals imits due to mixture flow Flashback Blow-off Turbulence Flammability imits: Introduction As a function of φ Measured by self sustained roagation Often ignites by sark or flame controlled by heat gain vs heat loss Factors Affecting Flammability imits size of tube energy of sark direction of roagation Table M3-: Flammability imits of Some Fuels in Air Flammability imits broaden with T initial (From Combustion 3 rd Ed. by Glassman, age 63) Note: ower limits aroximately 50% of stoichiometric 0

21 Uer limits aroximately 3 times stoichiometric ower limit is the same for O and air (mixing O like N ) But uer limit is much greater in O because of temerature Table M3-: Comarison of Oxygen and Air Flammability imits Effect of diluent tye on flammability limit. CO > N > He or AR (From Combustion 3 rd Ed. by Glassman, age 64) The trend follows secific heat, C Figure M3-3: imits of flammability of various methane-inert gas-air mixtures (From Combustion 3 rd Ed. by Glassman, age 65)

22 Rich limits are more resistive to diluents than lean limits. Halogens The effect of halogen comounds on Flammability limits is substantial. The addition of only a few ercent of can make some systems nonflammable. This is not only due to the diluent effect of the added gas, but also due to the ability of the halogens to act as catalysts in reducing the H atom concentrations in the chain branching sequence. In the following comarison, X reresents a halogen atom (F, Cl, Br, or I). The right side of the comarison is much faster that the reactions on the left side. This cometition between reactions reduces the rate of the very imortant H + O reaction. Fast comared to HX + H = H + X H + O HO + O X + X + M = X + M H + RH = R + H X + H = HX + X Total H + H = H Discussion Exercise 3.3: Exlain briefly why halogen comounds are effective in altering flammability limits. Instructions: There is a toic M3-Halogens in the discussion area. Post your exlanation there. Comare and discuss you exlanation with that of other students. Pressure Effects on Flammability imits High Pressure imits for flammability in rich mixtures increase ean mixture limits are aroximately constant ow Pressure Prior belief that high and low limits converged Actually, the limits remain constant

23 Figure M3-4: Effect of ressure increase (From Combustion 3 rd Ed. by Glassman, age 67) Figure M3-5: Effect of reduction of ressure (From Combustion 3 rd Ed. by Glassman, age 68) Flame stabilization at low velocities If the flow velocity > flame seed, then flame will be forced out of tube and it becomes a burner flame. The flame is then stabilized by the burner li, which acts as sink for heat and radicals. As flow increases, the flame cone angle decreases, but the flame is stabilized by the lower velocity near the li of the burner. Eventually, as the flow continues to increase, the flame will blow-off. 3

24 If the velocity is decreased, the flame will roagate into the tube. This is referred to as flashback. Thus, the flame is only stable within certain velocity limits! Flashback and Blow-off Figure M3-6: Stability of flame front near the rim of a Bunsen burner Gradient for flashback is given by: S g F = where S is the flame seed and d P is the enetration distance. d 4

25 Figure M3-7: Burning velocity and gas velocity inside a Bunsen tube (From Combustion 3 rd Ed. by Glassman, age 75) inside tube for: u > S flame blows out of tube u = S flame begins flashback u 3 < S flame flashes back For blow-off: As u increases, the equilibrium osition moves away from rim More dilution slows flame but eventually it blows off. G B = lim r du dr R for Poiseuille flow u d 8 g B F = 5

26 Figure M3-8: Tyical curves of the gradient of flashback and blowoff, resectively (From Combustion 3 rd Ed. by Glassman, age 77) Figure M3-9: Seated and lifted flame regimes for Bunsen burners (From Combustion 3 rd Ed. by Glassman, age 78) 6

27 Figure M3-0: Stability and oeration limits of a Bunsen burner Flame Quenching (From Combustion 3 rd Ed. by Glassman, age 79) The quenching diameter, (d T ) is the smallest diameter of a Bunsen burner that just lets flame flashback. To look at quenching as a heat loss henomenon, let us look at arallel lates: Figure M3-: Parallel Plates Quenching occurs when q RXN = q OSS. q RXN = φ o(rr)(aφ ) Q RXN. dt q OSS = λa d λ.. If T q is lowest flame temerature for roagation and T o is wall temerature, then or Tq To Aλ = φoq d RXN RRAd 7

28 d o ( T T ) q = 4λ φ RRQ o RXN but Q RXN = C ( T f To ) so d 4λ T = φ oc RR T q f T o T o or α d ~ RR remembering ( ) S ~ α RR then S ~ d and d S RR ~ α Note: as RR 0 d which is not true so assumtion breaks down for low RR Note: d = deth of enetration d = d (arallel lates) note for more reactive fuels d decreases. i.e. d < d H HC there is also the affect of diluents d He > d AR > d N > dcd because 8

29 α > α > α > αco He AR N also d T + ~ φ so d T increasing T φ Also, d T increases as P decreases λ α = ~ c RR ~ so n d α ~ ~ RR n + for Hydrocarbons: d ~ nd order The effect of low must also take into consideration the effect of radicals. As decreases, the mean free ath increases, so more radical quench. This enters into the analysis through the RR term. 9

30 Module 3 Assignment In comleting this assignment, you should show all work. The aroach that you use is the essential art of develoing a solution, where obtaining the correct answer in these assignments is only of modest imortance. Formats for submitting assignments Problems that are due on the same date can be comleted in one document and submitted as one electronic file. You may comlete your assignment in the following formats: word rocessed (.doc,.rtf, df, etc.) or scanned. Due Dates: See class schedule for due date. Total Points: 0 All roblems can be found in the m3_roblems.doc in the assignment for module 3. 30