Combustion, Explosion, and Shock Waves, Vol. 43, No. 6, pp. 619–627, 2007

Tracer Method in Numerical Simulation of Combustion Processes V. A. Bunev,1 A. V. Baklanov,1 I. G. Namyatov,1 V. V. Zamashchikov,1 and V. S. Babkin1

UDC 536.46

Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 6, pp. 3–12, November–December, 2007. Original article submitted December 21, 2005; revision submitted March 29, 2007.

Fuel-rich laminar flat hydrogen–methane–air flames are studied numerically using the tracer method. It is found that, in the near-limit mixture, hydrogen has an advantage in the oxidation by oxygen. As the stoichiometric compositions are approached, this advantage decreases and then disappears. It is shown that H∗2 O and CO∗2 labeled additives participate in the reactions and the labels from these molecules move to other products. Small additives of CH∗4 in the mixture completely react to form HH∗ O, H∗2 O, CO, CO2 , HH∗ , and H∗2 . Quantitative data on the distribution of the tracer atoms in products are given. The interaction of the hydrogen and methane oxidation schemes is studied. It is shown that in the presence of restriction on the interaction of these schemes, the laminar flame velocity increases by a factor of 5–7. Key words: tracer method, numerical simulation, laminar flame, inhibition, selectivity of oxidation, inert additives, superadiabatic flame temperatures.

The tracer method [1] proved to be effective for studying chemical reaction mechanisms. The kinetic tracer method developed in the last century by Neiman and coworkers has made it possible to establish the sequence of transformations of substances. The essence of this method is that, by adding a particular substance labeled by an appropriate isotope to a reacting system at the initial time, one can find the sequence of chemical transformations of substances in the reaction considered and the rate of transformation of the substances at various times during the reaction. The tracer method has been employed to study many chemical processes: the cold-flame oxidation of butane, the thermal oxidation mechanism of methane, the oxidation reactions of propane, n-pentane, and n-butane, the photochemical decomposition of phenylmercury hydroxide, C6 H5 HgOH, in methyl and ethyl alcohols with deuterium-labeled hydroxyl groups, isotope exchanges, etc. [1]. Numerical simulations of combustion, flame propagation, self-ignition, etc. also allow the use of the tracer 1

Institute of Chemical Kinetics and Combustion, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090; [email protected].

method. In numerical simulation studies, the tracer method can also be productive. In this method, one can use a tracer not only in the form of an isotope but also a labeled atom with the same physical and chemical characteristics as the unlabeled atom. A simple version of the tracer method in numerical simulation was used in a study [2] of the role of a CO2 additive to a methane flame, where the CO2 additive was shown to be not only an inert diluent but to participate in the reactions. Two versions were considered: (a) a CO2 molecule was added, and it participated in the corresponding reactions; (b) the added CO2 molecule was denoted by FCO2 , and it did not participate in the reactions. In this simple version, however, it is possible to elucidate the behavior of the CO2 molecule itself: how, at what rate, and to what species the atoms from CO2 moved. In the present work, the tracer method is used in a numerical study of some questions related to the propagation of fuel-rich laminar flat hydrogen–methane–air flames, such as the possibility of selective oxidation of hydrogen in multicomponent systems, the contribution of each component to the excess of the maximum flame temperature of these mixtures over the equilib-

c 2007 Springer Science + Business Media, Inc. 0010-5082/07/4306-0619 

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rium value, the participation of H2 O or CO2 additives in the reactions, the interaction of hydrogen and methane oxidation schemes, the degree of transformation of small additives of methane in rich hydrogen–air mixtures.

NUMERICAL SIMULATION The numerical simulation of flame propagation in hydrogen–methane–air mixtures was performed using the software package of [3, 4] and the GRI-Mech 3.0 kinetic scheme [5], which consists of 325 reactions involving 53 species. Several versions of using the tracer method in numerical simulations were considered. To show the possibility of preferential oxidation of one of the fuels during flame propagation over a multicomponent mixture by means of numerical simulation, it is necessary to show that oxygen, which is in deficit, it can be consumed preferentially in the oxidation of one of the components. This problem can be solved by numerical simulation if atoms of one of the fuels are labelled, i.e., if the tracer method is employed in the numerical simulation. Unlike in the tracer method in physicochemical experiments, in the case considered, labeled atoms can possess the same properties as unlabeled ones. In our work, the hydrogen molecule was labeled, i.e., the flame propagation velocity and all profiles were calculated for H∗ H∗ –CH4 –air mixtures. In this case, the H∗ and H atoms are identical physically and chemically. The appearance of a tracer in one of the components of the initial mixture led to the need to modify the GRI-Mech 3.0 scheme. Among the existing complete schemes of hydrocarbon oxidation, this is the most convenient one for combustion studies. The scheme was modified by adding new species that could arise from the labeling of the hydrogen atoms in the initial hydrogen molecule and by adding new reactions involving these species. The new species were assigned the properties corresponding to the unlabeled species. The appearance of molecules with tracer atoms in the kinetic scheme requires that the reaction rate constants be corrected since we now differentiate between reactions channels with the presence or absence of tracer atoms in the reactants and products. Let us consider as an example the reaction of an oxygen atom with molecular hydrogen: O + H2 → OH + H. ∗

∗

(1)

∗

If the system contains HH and H H labeled hydrogen molecules, the scheme needs to be supplemented by the reactions O + H∗ H∗ → OH∗ + H∗ , ∗

∗

O + HH → OH + H ,

(2) (3)

O + HH∗ → OH∗ + H.

(4)

The ratio of the reaction constants (1)–(4) is given by the relation k1 = k2 = 2k3 = 2k4 . The reaction constants (1) and (2) are equal since the H2 and H∗ H∗ molecules are symmetric. For the reaction constants (3) and (4), it is necessary to introduce a coefficient of 0.5 because on the left of these reaction equations are the same species and on the right are different products formed with an equal probability. Thus, a factor of two decrease of ki in reactions (3) and (4) is due to a reduction in the symmetry of the HH∗ molecule compared to HH and H∗ H∗ . To formalize the consideration of molecular symmetry in the expression for the rate constant in terms of transient-state theory, one uses the ratio of symmetry numbers from the rotational partition functions of the transient state and the initial reactants [6], or the degeneracy factor of the reaction path [7], or the so-called statistical factors [8]. We will use the easily interpreted statistical reaction factors, whose applicability was verified in [8]. Following the paper cited, for the bimolecular reaction k

i products, A + B −→

we write the reaction constant in terms of transientstate theory as   0 kT f= ε0 ki = l# exp − , (5) h fA0 fB0 RT 0 , fA0 , and fB0 are the partition functions of where f= the transient state and reactants calculated without using the symmetry numbers, h is Planck’s constant, k is Boltzmann’s constant, ε0 is the value of the barrier activation [8], R is the universal gas constant, and T is the temperature. The entire information on the symmetry of the reacting system is contained in the statistical factor l# . This factor, according to [8], is defined as the possible number of transient states that can be formed if identical atoms are differentiating, for example, by numbering. In reaction (1), the reactant H2 contains two identical atoms and, accordingly, there are two differentiable (if the H atoms are numbered) ways to form the transient state (O· · · ·H· · · ·H). Thus, for reaction (1), the statistical factor l# is 2, the same for reaction (2), and for reactions (3) and (4) this factor is 1. Since the physical and chemical properties of the H and H∗ atoms are identical, all partition functions f 0 and the value of ε0 in expression (5) remain unchanged under the labeling, and the change in the reaction constant is only determined by the change in the factor l# . Naturally, the reaction constants thus obtained do not lead to a change in the total rate of the reaction of atomic oxygen with hydrogen. This rate equals

Tracer Method in Numerical Simulation of Combustion Processes w = (k1 [H2 ] + k2 [H∗ H∗ ] + k3 [HH∗ ] + k4 [HH∗ ]) · [O] ∗

∗

∗

= k1 ([H2 ] + [H H ] + [HH ]) · [O]. The equality is obtained taking into account the above ratio of the reaction constants (1)–(4). It is obvious that the expression reduces to the product of the reaction constant k1 by the total concentration of molecular hydrogen and the concentration of atomic oxygen, as in the situation with no labeling. Similarly for monomolecular reactions, for example, methane dissociation, we have CH4 → CH3 + H, ∗

(6) ∗

CH3 H → CH3 + H ;

(7)

the statistical factor l# for reaction (6) equals 4, and for reaction (7), it equals 1. Therefore, the ratio of reaction constants of these processes equals k6 /k7 = 4. For all forward reactions involving species containing H∗ tracer atoms, the reaction constants were calculated from the values for the reactions with the unlabeled species taking into account the change in the statistical factor l# of the reactions due to the presence of the tracer. The rate constants of the reverse reactions, including the processes involving labeled molecules, were calculated from the values of the equilibrium constants. In the software [3, 4] the equilibrium constant at a constant pressure is calculated from the formula   ΔSi ΔHi − Kpi = exp . R RT Here ΔSi is the entropy change in the ith reactions and ΔHi is the enthalpy change in the same reaction in transition from the reactants to products. The entropy and enthalpy of the kth species are calculated from the formulas T2 Sk = a1k log T + a2k T + a3k R 2 3 4 T T + a5k + a7k , + a4k 3 4 T T2 Hk = a1k + a2k + a3k RT 2 3 3 4 a6k T T + a5k + . + a4k 4 5 T The coefficients ajk for two temperature regions are given in the thermodynamic database (a total of 14 values for the same reactant). For the compounds containing a tracer, it is necessary to take into account that a symmetry change leads to change in the symmetry number σ of the molecule, resulting in a change in the rotational partition function and, hence, in the entropy of the molecule. Since the rotational partition

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function is inversely proportional to the symmetry number of the molecule [6], to calculate Sk /R of the labeled compound, one needs to add the Napierian logarithm ln(σ/σ ∗ ) — logarithm of the ratio of the symmetry numbers of the unlabeled and labeled compounds — to the coefficient a7k of the unlabeled compounds. For example, for the HH∗ compound, ln 2 is added to a7k . The calculation accuracy and the convergence of the solution are determined by the number of points in the integration region (the cold boundary is located at −8 cm, and hot boundary at +40 cm). In the present work, it was 200–280. The coordinate origin is placed at the point at which the flame front temperature is 400 K. The modified kinetic scheme for calculating the flame propagation velocity was tested by comparing with velocity calculations using the unmodified GRI-Mech 3.0 scheme. The laminar flame velocities and temperatures profiles calculated for the GRI-Mech 3.0 scheme and the modified scheme are in good agreement. In the second version of the tracer method, the reactions involving simultaneously both labeled and unlabeled species are excluded. In this case, labeled hydrogen and unlabeled methane are oxidized separately except for the fact that both oxidation schemes include atomic and molecular oxygen and the heat is common. The labeled species and their corresponding unlabeled species have the same chemical and physical properties, except for species whose symmetry number changes with the appearance of a labeled atom in them. For such species, the entropy used in the code for calculating the constants of the reverse reactions with their participation changes. In trimolecular reactions, the third components M are all species, both labeled and unlabeled, that correspond to the initial reaction scheme. The H∗2 –CH4 –air system was considered. In this version, a total of 38 species participate in 231 reactions. The block of reactions involving nitrogen is excluded from the scheme. In the third version of the tracer method, two labels — on the initial molecular hydrogen and on part of the oxidizer were — were introduced. The (H∗2 + O∗2 )–(CH4 + O2 )–N2 system was considered. Reactions with the simultaneous participation of labeled and unlabeled species were excluded. This version corresponds to a mixture of two reactive systems (labeled hydrogen–labeled oxidizer and methane–oxidize) in an arbitrary ratio. The labeled and their corresponding unlabeled species had the same chemical and physical properties. In this case, the oxidation schemes influence each other only through the heat released separately in hydrogen and methane oxidation reactions. To some extent, this method is an analog of Le Chatilier’s rule [9] for the flammability limits, according to which mixing

622 of two limit mixtures in an arbitrary ratio results in a limit mixture. This is the so-called additive case. In trimolecular reactions, the third components M are all species, labeled and unlabeled, that correspond to the initial reaction scheme. The next version of using the method consisted of labeling an oxygen atom in the initial CO2 molecule. The (16% H2 +8% CH4 +air)–10% CO∗2 system was considered. In this version, CO∗2 participates in all flame reactions and one can trace the behavior of the label on the oxygen atom. The labeled and their corresponding unlabeled species have the same chemical and physical properties, except for species whose symmetry number changes with the appearance of a labeled atom in them. For such species, the entropy used in the code for calculating the constants of the reverse reactions with their participation changes. In this version, a total of 60 species participate in 575 reactions. In trimolecular reactions, third components M are all species, labeled and unlabeled, that correspond to the initial reaction scheme. The block of reactions involving nitrogen is excluded from the scheme. The code for calculating the equilibrium state for each version is transformed with allowance for the features of the oxidation schemes for each version.

RESULTS AND DISCUSSION The behavior of the methane added to rich hydrogen–air flames is of interest. The is due to the fact that there are several concepts on the role of inhibitors in flames. In [10] it is believed that the action of methane can be divided into two constituents and that its effect can be described by three parameters since inhibitors have a complex effect on flame propagation. On the one hand, the presence of an inhibitor in a mixture reduces the maximum concentration of active centers at the flame front. On the other hand, reactions involving inhibitors can proceed with heat release. And, third, there is the effect of dilution of the mixture and its thermal conductivity, diffusivity, and heat capacity change. It is not always possible to distinguish the contribution of a particular constituent to the effect. In [10], a method is proposed to estimate the effect of an inhibitor on deflagration or detonation processes of flame propagation. According to this method, the concept of the depth of inhibition is introduced [10]. This parameter characterizes the maximum capability of an inhibitor as a chemical agent that acts only on the concentration of active centers. Different inhibitors have different depths of inhibition. For hydrogen–air flames, it turned out that methyl, ethyl, and isopropyl

Bunev, Baklanov, Namyatov, et al. alcohols exhibit the same depth of inhibition. This implies that, as chemical agents interfering the branching of active centers, these alcohols exhibit the same effect. However, as sources of additional heat, they are different. Isopropyl alcohol is the most active in this respect. Propane and isooctane also have the same depth of inhibition although their molecular weights differ significantly. Ethylene, which has a double bond, has a greater effect as a chemical agent on hydrogen flames, although, as a source of additional heat, it acts at the level of nitrogen, an inert diluent [10]. The data given in [10] support the conclusion made in [11] on the role of the structure of inhibitors in their efficiency as chemical agents. The thermal factor of the of effect of inhibitors (heat release or absorption, changes in thermal conductivity, diffusivity, and heat capacity) also depends on the structure of the inhibitor molecule. This conclusion differs somewhat from that formulated in [12]. According to [12], hydrogen is more reactive than hydrocarbons. Flame velocity data are given as an argument in favor of this claim. The laminar flame velocity in hydrogen–air mixtures is an order of magnitude higher than that in hydrocarbons, including methane. In addition, since the flame propagation velocity is proportional to the square root of the chemical reaction rate [13], the above relation between laminar burning velocities implies that the rate of hydrocarbon oxidation is a few tens of times lower than the rate of hydrogen oxidation. The logic of [12] is valid if hydrogen and hydrocarbon oxidation reactions are considered separately. However, in a complex mixture containing hydrogen and hydrocarbon, the oxidations of hydrogen and hydrocarbon are not independent of each other. The same active species O, H, and OH play an important role in the oxidation of both hydrogen and hydrocarbon. However, since the bond energy in the hydrogen molecule is significantly higher than that in hydrocarbon molecules, hydrocarbons react with the active species to greater advantage than molecular hydrogen even in the low-temperature region. In this respect, it can even be said that under flame conditions in a complex mixture, hydrocarbons is more reactive than hydrogen. As a result, at the flame front there is simultaneous oxidation of hydrogen and hydrocarbons. The contribution to the heat release from their oxidation corresponds to the ratio between them in the initial mixture. It is only necessary to take into account that hydrocarbons are oxidized not to CO2 and H2 O but to CO, CO2 , H2 O, and H2 to form smaller hydrocarbons, such as acetylene or methane. The second argument of [12] is that the inhibition of detonation of hydrogen-rich mixtures containing additives of propane–butane mixtures cannot be due to oxygen con-

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Fig. 2. Concentration profiles of species in a 21% H∗ H∗ + 10.5% CH4 + air flame. Fig. 1. Concentration profiles of species in a 55% H2 + 1% CH∗4 + air flame.

sumption in the reaction with the hydrocarbon additive; otherwise, propylene and isopropyl alcohol would show identical inhibition efficiency. This conclusion is based on the fact that the heats of combustion of propylene and isopropyl alcohol are close, the stoichiometric coefficients in the reactions with oxygen are identical, and the rich flammability limits are close. However, according to [10], for isopropyl alcohol as the third component in the hydrogen–air mixture, the thermal factor, equal to 9.9, is higher than that for propylene (for propane, which is close to propylene, it is 6.6). This is due to the fact that the depth of inhibition for isopropyl alcohol (0.12 as for methyl and ethyl alcohols) is approximately half that for propylene (for propane, it is 0.28). If propylene and isopropyl alcohol were not to inhibit hydrogen flame propagation, their thermal factors, according to [10], would be almost identical since the rich limits for these fuels are close (11% for propylene and 12.7% for isopropyl alcohol [14]). The use of the tracer method in the numerical simulation provided an answer to the question of the behavior of hydrocarbons added to rich hydrogen–air mixtures. In the present work, simulation was performed for a flame propagating in a 55% H2 –air mixture doped with 1% CH∗4 . It is known that methane acts as an inhibitor reducing the concentration of radicals in flames and as an additional fuel. The numerical simulation shows (Fig. 1) that the added methane CH∗4 completely disappears in the zone of the flame front. The products, however, contain methane which consists of carbon atoms from the initial methane and hydrogen

atoms from the initial hydrogen molecules. In other words, methane partially remains in the form of CH4 but with hydrogen atoms from the initial hydrogen. In the products, the fraction of carbon in CH4 molecules is 29% of the initial content. The fraction of carbon in CH3 H∗ molecules is 4.2% of the initial content. The fraction of carbon in the larger C2 H4 molecules is 8.6%; 51.3% of carbon from the initial methane forms CO and 6.7% forms CO2 . Labeled hydrogen in the initial methane is distributed in the combustion products as follows: 65.5% of the initial amount of H∗ moved to HH∗ molecules, and 29.9% to HH∗ O water molecules. The remaining amount of the labeled atom is in the form of H∗2 (2.39%), H∗2 O (1.1%), and CH3 H∗ (1%). An analysis of the results of the numerical simulation shows that the initial oxygen is mostly (93%) consumed in the formation of water H2 O and 0.5(HH∗ O) from the initial hydrogen H2 . The remaining oxygen (6.84%) is consumed in the formation of water 0.5(HH∗ O) from the initial methane, CO, and CO2 . This oxygen distribution in the reaction products corresponds to the additive case where oxygen is distributed between CH4 and H2 in accordance with their concentration in the mixture and with the stoichiometric ratio in the complete oxidation to H2 O and CO2 . The tracer method in the numerical simulation showed that methane added in a relatively small amount and hydrogen were oxidized equally at the flame front, and it also showed in what combustion products and in what amount labeled H∗ atoms are present. Thus, the role of small methane additives is not reduced to a reduction in the concentration of active centers, as is claimed in [12], but it also leads to heat release during formation of the products H2 O, CO, and CO2 .

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In the present work, the selectivity of oxidation was analyzed using as an example a mixture of 21% H∗ H∗ + 10.5% CH4 + air, which contains two competing fuels. The initial hydrogen molecule consists of labeled H∗ atoms. The calculations supported data [15–17] on the superadiabaticity of hydrocarbon flames doped with hydrogen additives. In the 21% H∗ H∗ + 10.5% CH4 + air flame, the maximum temperature is 1749 K, which is 91.8 K higher than the equilibrium value of 1657.2 K. Near the point of maximum temperature, the concentration of water, both labeled and unlabeled, exceeds the equilibrium value (Fig. 2). At the same time, the concentration of carbon oxides is much lower than the equilibrium value. The concentration of HH∗ and H2 hydrogen molecules is also below the equilibrium value. This suggests that, in the combustion products, most of the oxygen is in water molecules and the smaller part is in carbon oxides. After the temperature reached the maximum value, it tends to the equilibrium value from above. The same is true for the species concentration in the products. The water concentration decreases, and the concentrations of hydrogen (H2 + HH∗ + H∗ H∗ ) and carbon oxides increase. In the equilibrium products, the hydrogen mole fraction (H2 + HH∗ + H∗ H∗ ) (0.238974) is higher than the initial value (0.21). The preferential formation of water at the front produces the superadiabatic temperature effect in the flame considered. Estimates show that, at the point of maximum flame temperature, the standard enthalpy of formation of the products is below the standard enthalpy of formation of the equilibrium products. This is due to the fact that the standard enthalpy of formation of two moles of water from one mole of oxygen is (−483.68) kJ/mole, for two moles of CO it is (−221) kJ/mole, for one mole of CO2 , (−393.5) kJ/mole, i.e., the formation of superequilibrium water gives the largest difference between the total enthalpy and the standard enthalpy of formation of the products. Accordingly, more heat is released and the temperature is higher. Let us consider a near-limit 21% H∗ H∗ + 10.5% CH4 +air flame. The reaction equation is written as 0.21H∗ H∗ + 0.105CH4 + 0.14385O2 + 0.54115N2 → 0.059742H2 + 0.059742H∗ H∗ + 0.11949HH∗ + 0.038734H2 O + 0.0774669HH∗ O + 0.038734H∗ H∗ O + 0.082061CO + 0.01642CO2 + 0.50756N2 . On the right side of the equation are equilibrium products in mole fractions. The initial oxygen was consumed in the formation of CO, CO2 , and H2 O. In the case

Fig. 3. Curves of α(x) and β(x) in a 21% H∗ H∗ + 10.5% CH4 + air flame.

of equilibrium, where there is no selective oxidation, 61.14% of the initial oxygen is consumed in water formation, and the remaining oxygen is consumed in the formation of CO and CO2 . The same ratio should be in the equilibrium products in the flame. Figure 3 shows the fraction profiles of oxygen atoms that formed labeled and unlabeled water β = OH /(OH + OC ), and the fraction profiles of oxygen atoms that formed labeled water α = (H∗ H∗ O + 0.5HH∗ O)/(H∗ H∗ O + HH∗ O + H2 O). Here OH is the number of oxygen atoms present in water and OC is the number of oxygen atoms in carbon oxides. The line βeq = 0.6114 corresponds to the oxygen distribution in the equilibrium products. It is evident that at the flame front, the total fraction of oxygen atoms in labeled and unlabeled water is higher than its fraction in the equilibrium products. This is also valid for the coordinate of the maximum flame temperature. The line αeq = 0.5 corresponds to the ratio of the oxygen concentrations in labeled and unlabeled water. In the equilibrium products, the amount of labeled water is equal to the amount of unlabeled water. On the other hand, over the entire flame front, the amount of labeled water is almost equal to the amount of unlabeled water (see Fig. 3). Since, at the flame front, the fraction of oxygen in water molecules is higher than the fraction of oxygen in the equilibrium products, it can be concluded that labeled water contains more oxygen than labeled water in the equilibrium products. Accordingly, the initial hydrogen has an advantage over methane in the competition for oxygen. Selective oxidation is the case. Selective oxidation of the initial hydrogen makes a contribution to the nature of superadiabatic flame temperatures. For the mixture studied, the entire water

Tracer Method in Numerical Simulation of Combustion Processes

Fig. 4. Curves of α(x) and β(x) in a 16% H∗ H∗ + 8% CH4 + air flame.

Fig. 5. Flammability limits in hydrogen–air mixtures versus methane additive: 1) spherical vessel (p0 = 0.12 MPa and T0 = 298 K); 2) flashback method; 3) according to Le Chatilier’s rule.

formed at the flame front consists of 50% unlabeled water and 50% labeled water (see Fig. 3). Therefore, the superadiabaticity of the flame, which is related to the formation of superequilibrium concentration of water in the products, is equally due to water formation from the initial molecular hydrogen and water formation from methane. For different ratios between methane and hydrogen in the initial mixture, the contributions to the superequilibrium water concentrations and, hence, to the superadiabatic flame temperature effect can be different. In flames closer to the stoichiometric compositions, the superadiabatic temperature effect disappears. Thus, in a 16% H∗2 + 8% CH4 + air mixture, whose composition is closer to the stoichiometry, the flame temperature constantly increases and reaches the equilibrium value at infinity, i.e., superadiabaticity of the flame is

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absent. The initial molecular hydrogen has no advantage over methane wit respect to oxygen. At the maximum flame temperature at a distance 30–40 cm from the main reaction zone, oxygen is distributed between water and carbon oxides according to the equilibrium values (Fig. 4). Figure 5 shows the rich flammability limits obtained for a H2 + CH4 + air mixture in spherical vessel of volume 3 liters with central firing (curve 1) and using the method of flashback into a tube of inner diameter 5 mm (curve 2). It is evident that character of these dependences is different. This is due to the fact that near curve 1 superadiabatic flame temperatures occur, which promote flame propagation over a wider range of mixture compositions. Near curve 2, the flame temperatures do not exceed the adiabatic equilibrium value and the boundary of the region has a linear segment, which is absent in curve 1. The tracer method in the numerical simulation provided data on the participation of the added “inert” water in the reactions. It is believed that water shows properties of an inert diluent, as well as CO2 . However, as was shown [2], carbon oxide CO2 actively participates in flame reactions. As a result, the total effect of the addition of CO2 is not equivalent to the inert dilution effect. By adding water with labeled hydrogen atoms to the mixture, it is possible to trace the behavior of this additive. Figure 6 shows profiles of some molecular species in a 16% H2 + 8% CH4 + air flame diluted by 10% H∗2 O. The figure clearly shows that almost 80% of the inert water additive disappears. Instead of water with two labeled hydrogen atoms, water with one labeled hydrogen atom HH∗ O (54.7% of the initial labels in the products), H∗2 hydrogen (6.7%), and HH∗ hydrogen (19.08%) appear. Water with two labeled hydrogen atoms remains in an amount of 19.4% of the initial labeled water. Thus, the labeled hydrogen atoms from the added labeled water move primarily to HH∗ O water molecules with one label and to HH∗ hydrogen molecules with one label. The fraction of labeled hydrogen atom in molecules with carbon atoms is less than 1%. The data presented in Fig. 6 clear show that the water molecules added to rich mixtures of hydrogen and methane actively participate in the reactions, and also show in what molecules and in what amount the labeled hydrogen atoms from the water molecules were redistributed. In [2], regarding the role of CO2 in the flame, it is only said that the added CO2 participates in the reactions because two versions were considered: CO2 does not participate in the reactions; CO2 participates in the reactions. Numerical results for laminar flame velocities for these two versions turned out to be different, i.e., the addition of CO2 leads not only to the thermal ef-

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Fig. 7. Concentration profiles of species in a (16% H2 + 8% CH4 + air)–10% CO∗2 flame. Fig. 6. Concentration profiles of species in a (16% H2 + 8% CH4 + air)–10% H∗2 O flame.

fect related to changes in the heat capacity and thermal conductivity of the system. CO2 actively participates in the flame reactions. In our work, the presence of a label on CO∗2 molecules made it possible to show where and in what amount this label moved as a result of participation of the molecules in the flame reactions considered. In the products of this flame, the labeled oxygen atoms were distributed as follows (Fig. 7): 14.5% of the labels remained on the initial CO∗2 molecules, 17.56% of the labels moved to CO∗ molecules, 20.78% to COO∗ molecules, and 47.14% to H2 O∗ molecules. It is of interest to examine the degree of interaction of the hydrogen and methane oxidation schemes. This interest is directly related to the question of the flame inhibition mechanism. The tracer method in numerical simulation allows one to partially or completely eliminate interaction between the two schemes, except for thermal interaction. Figure 8 gives temperature profiles for three versions of interaction of the two oxidation schemes of the initial mixture of 21% H2 + 10.5% CH4 + air. For the complete interaction, the laminar flame velocity is equal to 10 cm/sec. The temperature profile is extended. The maximum temperature at the flame front is 1749 K. If reactions between labeled and unlabeled species are excluded and atomic oxygen and molecular oxygen are assumed to be common to the two oxidation schemes, the flame velocity increases to 54.4 cm/sec. The temperature profile becomes steeper, and the temperature maximum is 15 K higher — 1764 K. If interaction between the two oxidation schemes (except for thermal one) is com-

Fig. 8. Temperature profiles in 21% H2 + 10.5% CH4 + air flame for three versions of interaction of the hydrogen and methane oxidation schemes.

pletely excluded, the maximum temperature gradient at the flame front increases further and the laminar flame velocity reaches 62.7 cm/sec. Although this or that exclusion leads to a reduction in the concentration of some species in isolated systems and to a decrease in the corresponding reaction rates, the laminar flame velocity increases. To some extent, the above data show the extent to which methane affects flame propagation in hydrogen–air mixtures. It is clear that the added methane, which, unlike molecular hydrogen, reacts primarily with active species, strongly reduces the radical

Tracer Method in Numerical Simulation of Combustion Processes concentration. This is the role of the hydrocarbon as an inhibitor. It is sufficient to separate the oxidation schemes of methane and hydrogen, and the reactivity of hydrogen in the presence of methane increases sharply. This suggests that the reactivity of hydrocarbons in the presence of hydrogen in unseparated oxidation schemes is higher than the reactivity of hydrogen. Thus, the tracer method in numerical simulation offers great opportunities for studies of combustion processes. It provides answers to many questions related to flame propagation in complex multicomponent mixtures.

REFERENCES

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