4. Combustion mechanism of fuel gases. 4.1 Reaction sequence Reaction mechanism. Reactions like (4-1) (4-2)

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1 4. Combustion mechanism of fuel gases 4.1 Reaction sequence Reaction mechanism Reactions like or CH 4 + O CO + H O (4-1) CO + 1 O CO (4-) do not actually take place. These equations are the summarizing result of a number of individual reactions. Consequently, they are called gross reaction equations. Actual reactions (elementary reactions) proceed in the molecular range like for example the bimolecular reactions. H + O O + OH (4-3) CO + OH CO + H (4-4) and the unimolecular reaction O O + O. (4-5) The conversion is mainly effected by the radicals O, H and OH under formation of intermediate products. Radicals are radiating in the short-wave visible range (ultraviolet range). Therefore, the gas flames emit a bluish light. This effect is called luminescence. The combustion of methane is the sum of some 4 elementary reactions. The kinetics of the individual reactions must be known for exact description of the overall reaction mechanism. The conversion speed of an elementary reaction is proportional to the product of molar density concentrations of starting materials. or unimolecular reactions like (4-5) the following shall apply: d ~ ρ 1 d ~ ρ = dt = k ρ O O ~ dt O (4-6) and correspondingly to a bimolecular reaction like equation (4-3) d ~ ρ dt d ~ ρ = dt d ~ ρ = dt d ~ ρ = dt H O O OH ~ ~ = ~ k ρ ρ H ρ O. (4-7) In case of time-constant overall density the following equation is obtained with ~ ρ ~ ~ i = ρ x i dx ~ dt dx ~ dx ~ dx ~ = = = = ρ ~ k x~ H O. (4-8) dt dt dt H O O OH ~ x

2 The corresponding reverse reaction is dx ~ H ~ s = ρ k x~ ~ x O dt OH. (4-9) The formation and disintegration rates are the same in the state of equilibrium. The correlation of both reaction coefficients can be derived therefrom as follows: k = k s K with K = the equilibrium number according to paragraph... (4-1) The temperature dependence of the reaction coefficient is described by the Arrhenius approach E k = k exp. (4-11) R T The pre-exponential coefficient is slightly temperature-dependent in many cases which may be approximately determined by * n E k = k T exp. (4-1) R T The activation energy E corresponds to the energy threshold to be overcome for the reaction. It reaches the value of bonding energies as maximum e.g. in case of dissociation reactions but may even adopt very small values down to zero if new bonds are established simultaneously with bond breaking. The exponential term approaches 1 in case of extremely high temperatures so that the preexponential coefficient gives the maximum value of reaction coefficient. The latter has different physical meanings in relation to unimolecular and bimolecular reactions. In case of the unimolecular reaction the reciprocal value of k represents the mean life of the molecule. The latter is determined by the oscillation frequency of atoms which participate in the molecular compound. Application of the statistical thermodynamics results in k s -1. In case of bimolecular reactions the pre-exponential factor corresponds to a collision number. In case of very high temperatures the reaction speed is limited by the time-wise number of collisions between two molecules. Values amounting to k m 3 kmol -1 s -1 can be derived from the kinetic theory of gases. The activation energies and the pre-exponential coefficient are given for a great number of elementary reactions in the publication of Warnatz et al The reaction mechanism resulting from the calculation of the conversion kinetics of all elementary reactions is shown as example for a premixed methane-air flame in ig This mechanism is shown in a simplified diagram in ig. 4-. As a result of this, one hydrogen atom will be successively split off from the hydrocarbons and further transformed into water steam. If only one or two hydrogen atoms are left, one oxygen atom is attached. Carbon monoxide is formed by further splitting-off of hydrogen which is finally oxidized to carbon dioxide.

3 The lowest reaction speeds are decisive for the overall combustion speed. ig. 4-3 shows the result of a sensitivity analysis of reaction speeds in a premixed methane-air flame according to Nowak et al Consequently, the reactions H + O OH + O and CO + OH CO + H show the smallest speeds. These reactions are fuel-independent and are applicable both to the combustion of oil vapours and the volatile matters of carbons. Therefore, the OH concentration is preferentially measured for determination of shape and burn-off of flames. The number of reactions to be considered for the practical flame calculations is dependent on the problem to be solved and the accuracy. The local distribution of radicals and temperature and, consequently, the local heat release is of great importance for the calculation of NO x emissions. In this case to 4 of the slowest reactions must be considered (Görner 1991). The mere conversion of fuel however may be approached with a much smaller number of reactions especially in case of non-premixed flames where the conversion rate is mainly determined by the degree of mixing. In the most simple case the reaction speed of fuel components B may be approached by statements according to the gross reaction equations dx ~ dt B ~ E a b = ρ k ~ ~ exp xb xo, (4-13) R T where the exponents of concentrations differ from 1. Table 4-1 gives such reaction equations for a number of essential fuel components. The oxidation of carbon monoxide is largely dependent on the water steam concentration in the air which must be considered through an extra term. Therefore, a dry CO and O mixture is difficult to ignite since the OH radicals are missing. The given equation is no longer applicable in case of water steam concentrations of more than some 1 % since the conversion speed is now independent of this concentration. ig. 4-4 shows the measured values of the reaction coefficient of the CO oxidation as an example. This makes evident that the values ascertained by different authors are extremely differing from each other in some cases. Therefore, literature gives drastically differing values for the reaction coefficients and the exponents of concentration. Oxidation of higher hydrocarbons may be defined by a three-stage reaction sequence in the most simple case, i.e. the disintegration into CO and H in the first stage and the subsequent oxidation into CO and H O in the second and/or third stage (Görner 1991). inally it should be underlined once more that the conversion of fuel is effected by the radicals. However, NO x emission is a secondary effect. Analogous to that, in human life the reaction progress of established groups is only possible by means of radicals. Too much of them, however, will have a detrimental effect.

4 4.1. Ignition Ignition mechanism The radicals OH, H and O are required for initiation of the reaction of a fuel with oxygen. These radicals are initially generated by dissociation of hydrogen and oxygen according to or H O ΟΗ + Η (4-14) O O + O. (4-15) The equilibrium of these reactions is shown in ig. -6. Consequently, H O gets dissociated at lower temperatures than O. Therefore the air humidity has a decisive effect on the generation of radicals. or instance, ignition of carbon monoxide in dry air takes place at much higher temperatures than in humid air. Therefore, for the generation of radicals it is sufficient to heat a small but sufficient gas volume to a high temperature. The energy balance is applicable to the unsteady heating of a gas volume as follows: dt ρ V cp = Q& R Q& α. (4-16) dt In this equation, Q R is the heat flow generated by the reaction, and Q α is the heat flow eliminated by convection and radiation. The following applies to both heat flows: Q & = M & h (4-17) R B R (M B = fuel mass flow, h R = reaction enthalpy) with the reaction approach according to equation (4-13): dx B E a b M & ρ B V k exp x~ B x~ O dt M ~V = ρ = R T (4-18) and for pure convective heat dissipation: ( T ) Q & = α A (4-19) α T u (T U = ambient temperature). The principle course of both heat flows as a function of temperature is shown in ig The heat flow caused by reaction has an S-shaped course in compliance with the Arrhenius approach whereas the flow of lost heat shows a linear progress. Let us initially consider the progress of Q R1 for a large heat production. In case of temperatures T < T Z the heat extraction is higher than the heat production. Ignition and combustion are not possible. In case of T = T Z the equilibrium is established between heat production and heat extraction. However, this equilibrium is unstable. If temperature lowers slightly the loss of heat will exceeds the production of heat, i.e. the gas cools down and the reaction is interrupted. In case of a slight temperature rise, however, the conversion speed drastically increases and the gas is heated until a new equilibrium is established at the

5 combustion temperature T V. The temperature T Z as the initial point of automatic gas heating forms the ignition temperature. Ignition temperature and ignition limits Lean gases have a low conversion rate due to their low concentration of inflammable constituents according to equation (4-18) and, hence, a low heat production, as shown in ig. 4-5 where the principle of the course of Q R is demonstrated. Therefore, a higher ignition temperature and a higher ignition energy would be required in this case. Consequently, they have a bad ignition effect. If fuel or oxygen take only a low concentration in a mixture, the conversion speed is very low according to equation (4-18) again. Heat production can no longer exceed the heat dissipation if the temperature falls below the so-called ignition limit, as it can be seen from the course of Q R3 in ig The ignition limits are dependent on the kind of fuel, temperature, fuel and oxygen concentration and a little dependent on the pressure. ig. 4-6 shows the reference values of ignition limits for natural gas. 4. Premixed flames If fuel gas and air are mixed together prior to ignition, the burner and its associated flame are called premixing burner and premixed flame. Examples are burners for short flames and intensive combustion like ignition burners and overhead burners in industrial kilns, spark ignition engines and gas turbines lame length ig. 4-7 is a photograph of a turbulent premixed flame from a tubular burner, i.e. a long- time photo and a short-time streak photo where the turbulent structures are clearly visible. ig. 4-8 is the schematic view of the premixed flame. The typical flame shape is that of a cone. The reaction front propagates in its surroundings with the speed v. The so-called flame speed may be determined by experiment through the mean outlet speed u _ of the burner and the angle β of the cone v = u sinβ. (4-) The length of the flame may be approximately determined on the basis of the geometric relation d 1 =. (4-1) tanβ L The relation sinβ tanβ is applicable to small angles. Consequently, the following may be derived from both equations above:

6 L d u v =. (4-) If the outlet speed is replaced by the volumetric flow V& π = d u (4-3) 4 the following will be finally obtained for the flame length: L = π V& d 1 v. (4-4) Consequently, the flame length is proportional to the emerging volumetric flow. The flame gets longer if the burner diameter is made smaller. lame length is furthermore dependent on the flame speed to be explained in detail later. A difference is made between the laminar and the turbulent flow. 4.. lame speed lame speed may be interpreted as the distance δ l to be passed by the flame front within the time τ δ v (4-5) τ The propagation of temperature front in a substance corresponds to the dimension-less style of ourier's differential equation δ a G τ, (4-6) where a = λ /(ρ c p ) is the thermal diffusity of the gas. The following may be derived from both equations for the flame thickness a λ G G δ =. (4-7) v ρ cp v Under conditions of ambient pressure the width δ of the flame front amounts to only a few tenths of a millimetre. According to the equation stated above the flame width increases as a function of declining density and declining pressure. Therefore, measurements of concentration and temperature profiles in pre-mixture flames must be made under conditions of negative pressure. Such measurements have been described in literature, for instance by Braun in Time is inversely proportional to the conversion speed of fuel

7 1 τ dx ~. (4-8) dt B Accordingly, equation (4-13) is applicable to the conversion speed 1 τ. (4-9) k ρ x x a b G B O Consequently, the following is applicable to the flame speed: v λ k x x. (4-3) G a b B O cp There with the flame speed is dependent through λ, c p and k on the kind of fuel, through k on the temperature and through Π x i on the product and, consequently, on the level of the individual concentrations. ig. 4-9 shows the laminar flame speed for some hydrocarbons as a function of the fuel concentrations. Consequently, the flame speed in close vicinity to the stoichiometric fuel-air composition on the low-air side (unctuous mixture) reaches its maximum value. In case of methane this values is about 45 cm/s. Table 4- summarizes the maximum and the stoichiometric value of the laminar flame speed for three typical fuel gases. Hydrogen shows the highest value. The value of carbon monoxide, however, is much lower and reaches only some 5% of the value for methane. ig. 4-1 shows the influence of the O concentration on the flame speed by taking the example of hexane as fuel (Chomiak 199). ig makes clear that the flame speed increases as a function of air preheating and, consequently, the flame temperature (Chomiak 199). In case of turbulent flow no smooth cone shape will be produced. As shown in ig. 4-7 the formation of a rough cone surface takes place. As example, Warnatz et al made visible the OH concentration measured on the surface, i.e. on the reaction front. It is apparent that the surface consists of a great number of small laminar flames. The co-called lamelet model serves as the basis for the mathematical description of such flames. The turbulent flame is considered as an ensemble of many small laminar flames in a turbulent flow field. The turbulent flame shape is shown in the schematic view in ig The actual surface with the laminar flames should be A lam whereas the mean surface should be A turb. The latter spreads with the turbulent flame speed v turb. Consequently, the following relation may be established: v lam A = v A. (4-31) lam turb turb If the turbulent speed is replaced according to v turb = v lam + v (4-3)

8 by the turbulent fluctuation speed v, the following surface ratio will be established: A lam v = 1+. (4-33) A v turb lam Accordingly the turbulent flame speed is higher than the laminar flame speed: v turb v = 1+. (4-34) v v lam lam ig shows the turbulent flame speed as a function of the fluctuation speed for a C 3 H 8 - air mixture. Proceeding from the laminar value, the flame speed is initially subjected to a strong increase as a function of the fluctuation speed and, consequently, the turbulence. After that, flame speed passes a maximum that will be the higher the lower the air ratio will be. or instance, if the air ratio is 1.1, the maximum turbulent flame speed will exceed the laminar value by the factor 1. After that, the turbulent flame speed will decline again as a function of turbulence until the turbulence finally will get so large again that the flame goes out. The concentration gradients and, thus, the diffusion speed will increase as a function of rising turbulence. inally the kinematics of chemical conversion will be no longer rapid enough. The reactive species are excessively thinned. Thus reaction heat will rapidly decline and the local temperature will drop accordingly. Since reaction speed is exponentially dependent on the temperature, the latter will decelerate drastically so that the flame goes out. Time required for flame extinguishing is only in the range of.1 ms (Warnatz et al. 1996). Extinguishing is described with the so-called stretching effect determined by the tangential speed and concentration gradient (along the flame area). This gradient withdraws radicals and reactands from the reaction zone in addition to the normal mass transport. This stretching is described with the so-called Karlowitz number δ du Ka =. (4-35) v dz Extinguishing takes place if the value of this coefficient exceeds a value of about 1. As shown in ig. 4-13, mixtures are very easily extinguished at higher air ratios. This is one of the reasons why engines running on lean fuel have relatively strong hydrocarbon concentrations although the excessive O should rather promote the complete combustion. Extinguishing takes place rather easily on the cold walls of engines (in contrast to furnaces). By the way, the turbulent flame speed in engines is approximately proportional to the rotational speed. Consequently, the combustion process gets accelerated. Otherwise the combustion in engines would be limited to low speed ranges. Lean gases (high inert share in the fuel) are extinguished very easily as well. Accordingly they are difficult to ignite. Contractions of gas caused by sudden extinguishing are to be considered as the source of flame noises (together with the geometry-related resonance phenomena) (Warnatz et al. 1996).

9 4..3 lame stability If the outlet velocity of the burner exceeds the flame speed, the flame takes off and is thus blown out. If the outlet velocity is too small, the flame flash back into the burner. Therefore measures hast to be installed to stabilize the flame. That a flame burns stably, the flow speed has to be equal to the flame speed in one position, as is explained on the basis of ig The flow speed rises from the wall to the centre of the burner. The flame speed is very small at the rims of burner due to the calorific losses. Therefore it goes through a maximum, which is in practical cases relatively close to the rims of the burner. With the distance "" should be alike the flow and the flame speed. If the front of the flame induces itself from the rims to the distance "3" away, the flame speed becomes larger than the flow speed and the flame returns to the distance. If the flame shifts to the distance "1", the flame speed decreases and the flame is blown again to the distance. At this distance thus the flame is stable. If the power of the burner and thus the outlet velocity are reduced, thus the distance can be shifted into the burner, the flame flashes back. Against it if the achievement is shifted constantly increased to the point behind the maximum flame speed, then the flame is finally blown off. The critical states for flash back and blow off depend with burners on the zone of flow and on the distribution of the flame speed (Lewis, from Elbe 1987). or each burner a stability diagram can be therefore provided as is schematically shown in fig The stability of the flame depends according to fig on the speed gradients at the wall. In the case of a laminar pipe flow we get for this gradient du dr w 8 u =, (4-35a) d whereby u the mean flow speed and d the nozzle diameter are. or a turbulent pipe flow the empirical relationship applies du dr w u d,8,3 Re (4-35b) with the Reynolds number u d Re =. (4-35c) ν In the case of a stoichiometric composition a maximum gradient of approximately 5 1/s results according to this picture, before the flame is blown off. With diameters smaller than 1 mm (laminar flow) thus the maximum outlet velocities are in accordance with Eq. (4-3a) below 3,1 m/s. Also with a large diameter of 1 mm (turbulent flow) one receives only about 3.5 m/s from Gl. (4-35b) as maximum outlet velocity. With air numbers of one, and in particular with air numbers more largely than one, with which the value of gradients steeply drops, premixed burnes can be operated thus only with a relatively small outlet velocity and thus power. Within the sub-stoichiometric range the critical gradient for the blown off rises against it strongly. With an excess air number of.7 for example the gradient is about 3 time higher as in the stoichiometric mixture. Premixed burners can be operated thus within the sub-stoichiometric range with higher outlet velocities. Besides the danger of the flash back of

10 the flame is shorter in this range. The stability range is with air-poor mixtures thus larger than with fuel-poor mixtures. or this reason with premixed burners mainly air-poor mixtures are taken and led to the complete oxidation later secondary air is added. The smaller the flame speed is, the more highly is the blown off inclination of the flame. Natural gas flames bend therefore rather to blown off as for example acetylene and hydrogen flames. Accordingly the blown off inclination is the larger, the higher the air number is. or safe ignition and thus stability different measures can be done with premixed burners. A simple method is the installation of a small ignition flame, which possesses its own fuel supply. A further method is the attach of pilotpushes into the zone of flow on the jet axle. Thus an eddy develops with a back flow of hot gas already burned. To the physical description of the effect is referred to the books of Chomiak 199 and Guenther Extinguish distance In the proximity of walls the heat dissipation is very high, in particular if these are relatively cold. If the flame is too close at such a wall, it can come to local extinguishes. The wall distance, within the flame cannot burn, is called extinguish distance. The variables on the extinguish distance can be deduced from the following consideration. The enthalpy q generated in the flame zone has to be conduct within the extinguish distance d q to the wall q λ ( ϑ ϑ ) G δ w. (4-36) dq Here in ϑ and ϑ w are the flame and/or wall temperature and λ the heat conductivity of the gas. The enthalpy has to warm up the gas in the flame zone from the initial or ambient temperature outside of the extinguish distance to the flame temperature G p ( ϑ ϑ ) q δ v ρ c. (4-37) rom both equations follows u d q a v G w (4-38) ϑ ϑ ϑ ϑ u with a G as thermal diffusivity of the gas. The extinguish distance is thus the more largely, the lower the wall temperature and the lower the flame speed is. In ig extinguish distances for different methane air mixtures are shown. According to above equation the extinguish distances is the more largely, the more the mixture from the stoichiometric composition deviates and the lower thereby the flame speed becomes. Ignition electrodes has to lie apart at least the double of the extinguish distance, in order to ensure an ignition. Wire nets with a mesh size, which is smaller than the double extinguish distance, thus flames cannot pass through. Such nets are used as safeties for flash back.

11 4..5 Minimum ignition energy In order to be able to ignite the fuel, one needs a minimum ignition energy H. This one receives from the following consideration. or ignition a gas volume with the width of the flame zone has to be warmed up to flame temperature G p ( ϑ ϑ ) H = A δ ρ c. (4-39) u The expansion of the cross-section area A must be larger in each direction than the extinguish distance A = d q. (4-4) With eq. (4-37) for the width of the flame zone arises then H λ ( ϑ ϑ ) G = dq u. (4-41) v If one replaces the distinguish distance by eq. (4-38) with ϑ w = ϑ, then follows finally u 3 G 3 a H = ρg cp ( ϑ ϑu ). (4-4) v The ignition energy depends thus on the kind of fuel and with the flame speed on the concentration and thus excess air number. rom above equation one receives with the material properties of air at 1 C for example for ϑ = C and a flame speed of 1 m/s for the minimum ignition energy H =,3 mj. In ig exemplarily minimum ignition energies are indicated for some fuels. One recognizes that this possesses the lowest value according to the flame speed during stoichiometric composition. According to the strong dependence on the flame speed the minimum ignition energy with the deviation from the stoichiometric composition rises strongly Swirling of flow The flow and thus the form of a premixed flame can be affected by a Swirling of the mixture before withdrawal from the burner. or this for example the mixture is led through a disk with tangential rotated slots. Depending upon degrees of the tangential position the strength of the swirl can be adjusted. The pattern of flow resulting from swirl is described with ig In the left field the speed profile without swirl is represented. The mixture flowing out of the burner results in a jet, which spreads approximately with 19, as will be still explained in the following section. The flame has the typical cone shape. If the mixture is swirled, then it possesses a radial component after withdrawal from the burner due to the centrifugal force. Starting from a certain swirl, the so-called critical swirl, the radial flow is so strong that on the axle a back flow adjusts itself. In the radially leaking out reacting mixture a funnel shaped flame is formed, as drawn in in the picture schematically. With very high swirl the flame burns nearly to the wall. Such burners are called flat flame burners. To the promotion

12 of the radial flow the wall at the burner passage is funnel formed, as is suggested in the fig The back flow on the axle consists usually of burned out and thus hot gas. This hot gas favours the ignition. Therefore swirl flames burn relatively stably, although their flow exhibits high speed gradients and shearing stresses. 4.3 Diffusion flames The question if fuel and air are mixed before or after entering the combustion chamber is one of the distinctive features of flames. In the first case the flames are called premixed flames. In the second case the combustion intensity is decisively determined by the mixing speed and, consequently, by the diffusion processes. An old slogan says: Mixed and immediately burnt. Therefore such flames are even called "diffusion flames". The kinetics of combustion of premixed flames are influenced as well by diffusion processes which however take place in the microscopic range. These processes have influences on emissions and extinguishing. Nevertheless the term "diffusion flame" is furthermore used since this term is well established and a better terms is not known. The majority of burners in industrial furnaces are diffusion burners used mainly for liquid and solid fuels. urther examples for diffusion flames are the candle flame and the flames in steam generators, diesel engines, aircraft engines and rocket propulsion units Mixing mechanism (free jet) The fuel-air mixing mechanism in diffusion burners will be explained on the example of the free jet. uel flows from a nozzle into a large air-filled compartment so that the walls cannot influence the flow. The resultant flow field is shown in the schematic view in ig In case of a turbulent flow the jet is propagated in linear direction with an angle of some 18 to degrees. By the way, this jet propagation is well visible on the outlet opening of power station chimneys under conditions of qualm weather. During its propagation the fuel jet draws air from the environment. Consequently, the speed in the jet is reduced continuously. Speed reduction and the increase in mass flow should be considered now in detail. Since the pressure is constant along the jet and no external forces are effective, the momentum flow remains constant (Gersten et al. 199 and Scholz et al. 1984). Consequently, the following shall apply: ( z) I O = I, (4-43) where I o = the momentum flow of nozzle outlet flow. The momentum flow is defined as follows: I = M & u, (4-44) where ū = the mean flow velocity of the jet. The mass flow for round jets is defined as follows: M& π = ρ d u, (4-45) 4

13 where d = jet diameter and ρ = mean jet density. Use of those two equations and equation (4-43) result in: u u d = d ρ ρ. (4-46) As mentioned before, the jet gets wider by the angle α = 18 to so that the following equation can be established for its diameter: α = d + z tan. (4-47) d With tan 9,16 (4-48) and equation (4-46) the speed reduction may be calculated as follows u 1 = u,3 z d + 1 ρ ρ. (4-49) Taking equations (4-43) and (4-49) the mass increase may be calculated as follows: M& M& = 1 +,3 z d ρ ρ. (4-5) Consequently, speed decreases in a certain distance reciprocally to the nozzle distance whereas the mass flow shows a linear increase as shown in ig The fuel flow M takes the ambient air the more intensive the smaller the nozzle diameter is according to equation (4-5). The length z st forms the measure for the intensity of stoichiometric air volume to be taken by the jet. In this case the mass flow of jet amounts to & = M& + M& L. (4-51) Mst Thus the mixing length can be calculated from equation (4-5) z st 1 ρ = ( 1+ L) 1 d. (4-5),3 ρ Consequently, the mixing length is proportional to the nozzle diameter. or instance, in case of natural gas with L = 15 the mixing length of cold jets (ρ /ρ 1) is in the order of 45 diameters and in case of hot jets (ρ /ρ 4) in the order of 9 diameters. The stoichiometric mixing length of the hot jet is shorter than the flame length. The flame length will be discussed later.

14 The fuel concentration continuously decreases as a function of length due to the admixture of air. The concentration profile of fuel gets wider and more flat as a function of nozzle distance analogous to the speed profile. If fuel and air are in reaction with each other, they get into each other only in a small reaction zone as shown in the schematic view in ig The reaction zone is very small as compared with the jet width. The reaction products CO and H O are diffusing both into the environment and even towards the jet centre. The reaction zone and, consequently, the flame front are established in those areas where fuel and air are in the stoichiometric ratio when cold mixing takes place. L ρ / ρ z st /d z /d CO.47 8/ CH / H 34.5 / The table above shows the stoichiometric mixing length for three typical fuel gases. The flame length is given as well. It is obvious that the flame length of the individual fuel gases is very different. Thus the flames of natural gas are the longest whereas the flames of carbon monoxide are the shortest. Since the flame length is much longer than the stoichiometric mixing length, the flame takes an air volume that corresponds to an excess air number of - 3. Thus it may be stated that burners with diffusion flames but without air control (so-called atmospheric burners) yield rather poor efficiency rates from the standpoint of fuel engineering. Therefore, burners used in today's domestic heating systems are air-controlled in order to reach excess air numbers of some 1.1 to Diffusion flame with partial premixing Premixed flames are often sub-stoichiometrically operated, since, as described before, then the stability range is larger. Usual air numbers lie in range about λ =,7. With smaller air numbers the flame speed increases strongly and the flame length accordingly. Air for premixing is called primary air. Air for the complete oxidation of the fuel has to be sucked in as with the diffusion flame from the environment. This air is called secondary air. In this case a form of the flame adjusts, as is represented in ig. 4-4 in principle. Two flames are formed out, an interior and an above external flame. The interior flame is conical like the typical premixed flame. The above flame has the typical form of a diffusion flame. Also with fuel concentrations more largely than the upper ignition limit one observes still an interior flame. This is justified in the fact that at the flame root by the free jet effect additional air is interfered Stability Similar to the premixed flames criteria has to be kept also for the diffusion flames, so that these burn stably. With a small outlet velocity of the fuel the flame touch the burner rim. With rising outlet velocity increasingly holes form in the basis of the flame. The flame takes off. It begins to burn only in a distance from some nozzle diameters. Starting from a certain outlet velocity the flame is finally blown off. or safety reasons therefore the outlet velocities may lie not too close to the blown off speed.

15 or the explanation of the flame distance three different theories (Turns 1996) exist. The first theory means that the height of the flame is, where the flow speed at local stoichiometric mixture is equal to the turbulent flame speed of a premixed flame. This is the oldest theory. The second theory assumes the local shear stress speed (aspect ratio) exceeds the critical extinguish speed of a laminar flamelets. The third theory contains: The time for the back mixture of a turbulent eddy of hot combustion gas with the unreacted gas is smaller than the critical time for the reaction, which is needed for an ignition. In ig. 4-5 taking off heights are shown as a function of the outlet velocity, for free jet flames of the three gaseous fuels methane, progane and ethyls. It is remarkable that the height is independent of the nozzle diameter and the height rises with decreasing flame speed. According to fig. 4-9 the maximum flame speeds amount to that gases v (CH 4 ) = 4 cm/s and v (C 3 H 8 ) = 5 cm/s. This result is interpreted with the first theory. Kalghatgi 1984 gives the approximation for the taking off height of hydrocarbon flames h v ν max u = 5 v max ρ ρl 1,5 (4-97) whereby ρ L the density of surrounding air is. or the blown off of the flame one goes out with a similar mechanism as with premixed flames. The basis and the edge of the diffusion flame are regarded as pre-mixed. The flame is blown off therefore if the turbulent maximum flame speed with the distance drops faster than the flow speed. or the critical speed of the blown off Kalghatgi 1981 gives the approximation. u v crit 6 =,17 Re ) L (1 3,5 1 ReL max ρ ρ L 1,5 (4-98) whereby the Reynolds number Re L v L ν max = (4-99) is defined. or the characteristic length L L d 1 =,5 x st ρ ρl,5 1,5 (4-1) is valid, what corresponds with the flame length. In ig. 4-6 measured blown off speeds for different gaseous fuel are depicted according to eq. (4-98), from which the applicability is evident. rom the three above equations for the critical outlet velocity follows concerning the blown off u d crit L max (4-11),17,5 ρ ρ v ν x st

16 or 1,5 crit ρ L v max u d L,17. (4-1) ρ ν The blown off speed depends on the square of the flame speed. In Table 4-5 are for some gases these on the diameter and/or on the flame length referred critical outlet velocity specified. or acetylene and in particular for hydrogen these speeds lie substantially more highly than concomitantly for methane and natural gas. Carbon monoxide and concomitantly weak gases possess clearly lower critical speeds than natural gas. Therefore flames of these gases are extremely stability sensitive. Remarkable it is still that the blown off speed rises proportionally with the nozzle diameter. Therefore it is so difficult to blow out flames of boreholes. Measures to Stability or stable burning of diffusion flames can be met several measures. or burners with large power often small ignition burners are used, which always burn with a premixed flame. or small and middle power in a small distance from the burner mouth on the axle a pilot disk are attached. Thereby develops a flowing back eddy, which returns hot gas for ignition. One reaches a back flow also by a swirling of the supplied combustion air. 4.4 Explosions and Detonations The controlled combustion with constant pressure one calls deflagration. The explosion is combustion with increase in pressure, e.g. combustion with constant volume. With a detonation a progressive pressure wave is formed. Explosions Explosions takes place with combustion at constant volume, then an increase in pressure follows. Due to this increase in pressure a damage can occur (exception engines), why explosions are unwanted usually. With explosions fuel and air are pre-mixed, so that it comes to a fast propagation of the flame front. So that an explosion can occur, three conditions must be fulfilled: - enclosed room - defined fuel air mixture - ignition source. Typical dangerous room for explosion are combustion chambers and boilers. In the cold condition an explosive mixture can occur, e.g. by unburned remainder fuel after switching off, or by leakages. By igniting the flame after the start of a burner it comes then to an explosion. Such advices must be sufficiently rinsed therefore for safety reasons before igniting the burner. That an explosion is possible, the fuel air mixture must lie within the ignition limits. The ignition limits were already treated in section urther an ignition source must be

17 releases with sufficient energy. After Remenyi (1987) the explosion pressures can amount for hydrogen and acetylene (C H ) up to 16.5 bar, for methane up to 7.5 bar and for coal dust up to 4. bar. Measures to the explosion protection are therefore preventing possible ignition sources and injecting of inert gas. or transportation and storage of oxidation able types of dust, e.g. coal dust, therefore burned out gas, N or CO were used. Detonations or the explanation of a detonation a long pipe is regarded according to ig , in which a pre-mixed fuel air mixture is contained. If the mixture at the open right side is ignited, then an almost even burn front spreads to the left into the mixture. With this front a stationary speed usually adjusts itself. The speed of this burn wave lies much below the speed of sound. The burned and thus hot gas expands and flows to the right away. If the mixture is ignited against it at the closed right end, then the pressure of the burned gas rises on the right side strongly. This works then like a piston, which presses the reaction front into the unburned mixture. The burn wave is accelerated and the speed can reach a multiple of the speed of sound, what leads to a detonation. The structure of the detonation wave is described on the basis ig. 4-4., in that the axial change of the pressure is schematically represented. The front of the detonation consists of a so-called shock wave, in which from the starting situation the pressure, the density and the temperature rise steeply. The thickness of this layer is very small and lies in the order of magnitude of few free distances of the molecules. Starting from a certain temperature, which depends on the kind of the mixture, the fuel ignites. The ignition range is called induction zone. The temperature rises due to the low reaction rate still slowly. Pressure and temperature rise according only little. Afterwards in the so-called reaction zone the temperature rises steeply to very high values. If the reaction is ended, temperature, pressure and density have nearly reached the equilibrium state. The distance from the shock front to the burn off lies in the magnitude of 1 cm. On the mechanism of the acceleration of the reaction front which first spreads with the laminar flame speed and then exceeds the speed of sound is not dealt with here. or this is referred to the book of Kuo In the following however the height of the detonation speed is regarded still briefly. In the ig , this speed is shown for the two fuels propane and acetylene as a function of their concentration in the mixture. The detonation speeds lie within the range of 15 to 3 m/s and amount to thus a multiple of the speed of sound. It is remarkable that the maximum value arises not with the stoichiometric concentration, but within the range with substantially higher fuel concentration. The maxima lie somewhat above the stoichiometric concentration for the conversion to CO and H O. This can be explained thereby that the reaction time is too short with a detonation, to convert the CO completely to CO. This reaction is as well known relatively slow. So that a detonation can occur, the mixture must lie within certain limits similar to the ignition. In Table 4-6 experimentally determined limits for the detonation and ignition of some fuels are confronted. rom this it is evident that the limits for a detonation are closer than for combustion. ig. 4-3: Ignition of fuel-air-mixture in a long pipe

18 ig Structure of a detonation wave ig. 4-3 Mixture Detonation speeds in dependence on fuel concentration in oxygene Combustion Detonation Detonation Combustion lower limit in Vol % fuel upper limit in Vol % fuel H -O 4, ,9 H -air 4 18, CO-O (wet) 15, ,9 (CO + H ) O 1,5 17, 91 9 (CO + H ) air 6, ,8 NH 3 O 13,5 5, C 3 H 8 O,4 3, C H O,8 3, C 4 H 1 O air 1,85,8 4,5 36,5 Tab. 4-6: Ignition and detonation limits due to Kuo (1986)

19 CH 4 C H 6 +H +H,O,OH +CH 3 +H,O,OH +H +H,O,OH +O +M CH 3 C H 5 CH3CHO CH3CO +CH 3 +O +CH 3 +H +M,O CH 3 CH O +H,O,OH C H +O,OH 4 CH 3,CH O,CHO +H CHO CO +M,O,H +H C H 3 +OH C H +O CHCO +H CH 3 +OH CH +H CH CH O,CHO +O,O +O,O CO CO,CO ig. 4-1: Integral reaction-flow analyse in a premixed stoichiometric CH 4 -air-flame at 1 bar and 98 K (Warnatz 1984) CH 4 C H 6 CH 3 C H 5 CH O C H 4 CHO C H 3 CO C H CO CH CH ig. 4-: Schematic mechanism of oxidation of carbon-hydrogen (Warnatz 1981 a)

20 Relative sensitivity 1 H+O OH+O Lean flame Stoichiometric flame at flame,5 CO+OH CO +H -,5 OH+O H+O H+O +M HO +M H + CH 3 CH4 Reaction H -Ox CO-Ox C -Ox 1 ig. 4-3: Analysis of sensitivity of the reactions in a premixed methane flame (Warnatz 1984) K CO+1/ O CO. ml / mole sec -9 N(RT/P) x1 f f.5 f.5 CO O H O Inverse temperature 1/T 1x1-4 ig. 4-4: Standardized reaction rate of the CO burning (Howard 1973)

21 Q.. Q R1. Q R. Q α Q.. Q α1. Q R. Q R3. Q α T z1 T z T v1 T v T T z T z1 T v1 T v T ig. 4-5: Mechanism of ignition 3 Vol. % Upper ignition limit CH 4 Rapid ignition 1 Lower ignition limit Temperature ig. 4-6: Ignition temperature of methane (Zelkowski 1969) o C

22 ig. 4-7: Short duration schlieren photographs of turbulent premixed propane-air flames (Tsuji 1979) ϕ L u ϕ u o d o v ig. 4-8: Length of premixed flames

23 1. m. s -1.8 V.6.4 N-C H 7 16 C 3 H 8 C 4 H C H 3 6 C H (v /) CH Vol % 15 uel concentration ig. 4-9: Laminar flame velocity in dependence on concentration of fuel-air-mixtures at bei 1 bar (Warnatz 1993).8-1 m. s.4. V %O 8 %O 67 %O 51 %O 4 %O 8 %O %O 16 %O Vol.% X C H 6 14 ig. 4-1: Laminar flame velocity of hexane-o -nitrogen mixtures (Shchetinkov 1965)

24 . m. s Kerosene Naphtalene v o C 4 Temperature ig. 4-11: Influence of the initial velocity on the laminar flame velocity during the stoichiometric burning of kerosene and naphthalene (Shchetinkov 1965) A lam A turb ig. 4-1: Actual and mean flame surface

25 6 m. s -1 λ =.9 λ = λ = 1.5 v Extinction λ = v in m/s ig. 4-13: Turbulent flame velocity in dependence on turbulent intensity of C 3 H 8 -air mixture (Abdel-Gayed et al. 1984)

26 r Burner flow 1 z 3 v 1 < v < v 3 Burnerrim ig. 4-14: Stability of flames Blow-off region Velocity gradient at the boundary 1/s Region of stable flame lash-back region rec. Excess air number 1/λ ig. 4-15: lame stability diagram for natural gas-air-mixture (Merzhanov et al. 1988)

27 1 mm 6 4 O /(O + N ) Extinction distance Vol.-conc. of Methane % ig. 4-16: Distance of extinction for mixtures of methane, O and N (Lewis and Ebbe 1951) Minimum ignition energy 6 4 mj Propane H /O /He H /O /N Acetylene n-pentane Butane. H.1 /O /Ar uel concentration fraction of stoichiometric ig. 4-17: Minimum ignition energies for various fuel-air-mixtures. H (II)-hydrogen and air; H (I)-hydrogen and air with N replaced by argon; H (III)-hydrogen and air with N replaced by helium (Calcote et al. 195)

28 d 19 o r r z.. u/u M / M o o 1,,8,6,4, 1 Core region Transition region Similarity region z / d o z / d o ig. 4-18: Turbulent open jet (Scheme) with velocity field and axial profile Mass increasing in a round free jet

29 d z/d ig. 4-19: Principle forming of free jet flame X O B r r st r st r X B CO, H O O r Reaction zone r st r ig. 4-: Radial concentration profile with a fuel jet in air without (above) and with reaction (below)

30 ig. 4-1: Photo of a free jet flame 5 CH 4 Lift of of height h in in mm C 3 H 8 C H 4 d in mm Jet exit velocity u in m/s ig. 4-3: Lift of heights of free jet flames

31 U v ρ ρ L Methane Propane Ethylene Butane Acetylene X Hydrogen 4.17 Re L ( Re L ) Re L ig. 4-4: Blow out velocities of free jet flames unburnt gas ρ 1, p 1, T 1 u combustion front burnt gas ρ, p, T ig. 4-3: Ignition of a fuel-air-mixture in a long pipe ig. 4-31: Structure of a detonation wave

32 ig. 4-3: Detonation speeds in dependence on fuel concentration in oxygen

33 CH 4 + O CO + H O d ~ x ~ CH4 1/,7,8 = ρ k x~ ~ CH x O dt 4 k = 5, 1 11 Dryer et al CO + ½ O CO kj / mol exp R T 3 m kmol 1/ 1 s dx ~ dt CO = ρ ~ k x~ CO x~ 1/ O x~ 1/ HO k = 1, Howard et al kJ / mol m 1 exp R T kmol s Table 4-1: Global approaches for fuel reactions uel Symbol Ignition temperature in air Ignition limit in air ( C) lower upper C Vol.-% Vol.-% Hydrogen H 53 4,1 7,5 Carbon monoxide CO 61 19,6 7,9 Methane CH ,1 13,5 Acetylene C H 335,3 8, Ethylene C H , 17,7 Ethane C H ,1 11,7 Propylene C 3 H 6 46,6 1, Propane C 3 H 8 51,1 9,5 n-butane C 4 H ,5 8,5 n-pentane (*) C 5 H ,3 7,6 n-hexane (*) C 6 H , 7,4 Top gas Coke gas Naturel gas L Naturel gas H (*) condensate at standard condition Table 4-: Ignition temperature and limits of gaseous fuels

34 v max [m/s ~ x max [%] v st [m/s] ~ x st [%] Methane CH 4,43 1,,4 9,5 Hydrogene H 3,64 4,5,37 9,6 Carbonmonoxide CO,195 41,5,174 9,6 Table 4-: Laminar flame speeds Gas ν O M ~ B 3 kgo kg B m B O x st x~ st 3 kgb kgg mg kg L kg L B λ x ( st ) h u MJ kg B H 1/ 8,8,96 34,5,1 1 CO 1/ 8,57,9,96,5,8 1,1 CH ,55,95 17,3,1 5, C 3 H ,6,6,4 15,7,1 46,4 Table 4-3: Gas data to the evaluation of the flame length and the excess air number