Simulation of H2-Air Non-Premixed Flame Using Combustion Simulation Technique to Reduce Chemical Mechanisms

Combustion simulation that uses computational fluid dynamics (CFD) has been widely adopted as the design tool for combustion equipment. Because flow inside such equipment is generally turbulent, turbulence and combustion models are needed to simulate combustion; many combustion simulations have been performed to verify a system’s internal state, such as velocity, pressure, mole fractions of chemical species, and temperature. Combustion simulation of a confined impinging jet reactor has been performed by the large eddy simulation (LES) model serving as the turbulence model and the presumed probability density function (PDF) serving as the combustion model (Daniele, 2009). The analysis shows that a confined impinging jet reactor is indeed an interesting device because of its high mixing efficiency and absence of stagnant and recirculation zones. Under the condition of moderate or intense low-oxygen dilution (MILD), the effect of H2 on H2-CH4 turbulent non-premixed flames was investigated with the improved standard k   model as the turbulence model and with the eddy dissipation concept (EDC) model (Amir et al., 2010). Simulation results show that H2 addition to CH4 leads to improved mixing, increase in turbulent kinetic energy decay along the flame axis, increase in flame entrainment, higher reaction intensities, and increase in mixture ignitability and rate of heat release. Although combustion simulation was considered to be an efficient designing tool, considerable computational time was needed to calculate the chemical reaction. Combustion models that detail chemical mechanisms require reaction calculations involving ndimensional ordinary differential equations (ODEs) that are solved according to the number of chemical species involved. Therefore, reducing computation time for the combustion simulation is a significant problem. If computation time could be easily reduced according to the required prediction accuracy, we would be able to obtain the results more quickly. For example, O is a significant species whose mass fraction is necessary to compute the amount of NO present; therefore, the accuracy of the mass fraction of O cannot be neglected. To determine this mass fraction with sufficient accuracy, it is necessary to build a reduced mechanism including O. Generally, a quasi-steady state or partial equilibrium is assumed when the reduced mechanism is built (Warrants et al., 2006). The chemical equilibrium method (Nagai et al., 2002) does not use reaction equations; instead, the equilibrium composition of a chemical system is determined by minimizing the


Introduction
Combustion simulation that uses computational fluid dynamics (CFD) has been widely adopted as the design tool for combustion equipment.Because flow inside such equipment is generally turbulent, turbulence and combustion models are needed to simulate combustion; many combustion simulations have been performed to verify a system's internal state, such as velocity, pressure, mole fractions of chemical species, and temperature.Combustion simulation of a confined impinging jet reactor has been performed by the large eddy simulation (LES) model serving as the turbulence model and the presumed probability density function (PDF) serving as the combustion model (Daniele, 2009).The analysis shows that a confined impinging jet reactor is indeed an interesting device because of its high mixing efficiency and absence of stagnant and recirculation zones.Under the condition of moderate or intense low-oxygen dilution (MILD), the effect of H 2 on H 2 -CH 4 turbulent non-premixed flames was investigated with the improved standard k   model as the turbulence model and with the eddy dissipation concept (EDC) model (Amir et al., 2010).Simulation results show that H 2 addition to CH 4 leads to improved mixing, increase in turbulent kinetic energy decay along the flame axis, increase in flame entrainment, higher reaction intensities, and increase in mixture ignitability and rate of heat release.Although combustion simulation was considered to be an efficient designing tool, considerable computational time was needed to calculate the chemical reaction.Combustion models that detail chemical mechanisms require reaction calculations involving ndimensional ordinary differential equations (ODEs) that are solved according to the number of chemical species involved.Therefore, reducing computation time for the combustion simulation is a significant problem.If computation time could be easily reduced according to the required prediction accuracy, we would be able to obtain the results more quickly.For example, O is a significant species whose mass fraction is necessary to compute the amount of NO present; therefore, the accuracy of the mass fraction of O cannot be neglected.To determine this mass fraction with sufficient accuracy, it is necessary to build a reduced mechanism including O. Generally, a quasi-steady state or partial equilibrium is assumed when the reduced mechanism is built (Warrants et al., 2006).The chemical equilibrium method (Nagai et al., 2002) does not use reaction equations; instead, the equilibrium composition of a chemical system is determined by minimizing the Gibbs free energy, which is subject to the conservation of the chemical elements involved in the combustion.The composition is obtained by solving a system of simultaneous nonlinear equations with five unknowns (one for each of the elemental species involved in that study, namely, C, H, O, and N, plus one).In another study, a partial non-premixed flame of CH 4 was modeled using the vortex method in combination with the chemical equilibrium method (Ogami et al., 2010).Although this method did not use any chemical equations, the calculated temperature and main products were in good agreement with experimental results.In some cases, the data obtained from the simulation concerning the minor products did not agree with the experimental results.A combustion simulation technique based on a combination of the chemical equilibrium method and the EDC model was developed in a previous study and validated by simulation of a H 2 -air turbulent non-premixed flame (Fukumoto et al., 2010) and a CO-H 2 -air turbulent non-premixed flame (Fukumoto et al., 2009).An advantage of the technique is the ease with which a reduced chemical mechanism can be built according to the accuracy requirement for the chemical species.Thus, the technique can predict intermediate species with high accuracy when a reduced mechanism for the minor species is built.The key to this proposed technique is the incorporation of the concept of equilibrium into the chemical kinetics, which decreases the dimensionality of the chemical reaction calculation and reduces the computational time for a combustion simulation.This chapter presents a technique for combustion simulation based on a chemical equilibrium method and an EDC model (Magnussen, 1989(Magnussen, , 2005)).The advantage of the proposed technique is that it makes it easy for us to construct a reduced mechanism according to the accuracy requirements of the chemical species.The proposed technique is validated through a simulation of a H 2 -air non-premixed flame (Barrow et al., 2003a).The results computed using the proposed technique are then compared with experimental data and computational data obtained by the EDC model.

Method
Ansys FLUENT version 13.0 (Ansys, Inc., 2011) was used in this study.The temperature, enthalpy, and reaction rate of the chemical species were calculated by a user-defined function (UDF) in FLUENT.The UDF is a function that can be programmed to load dynamically with the FLUENT solver in order to enhance the standard features of FLUENT.Moreover, the momentum equation, turbulence model, and mass fraction equation were computed using Ansys FLUENT.To solve the momentum equation, velocity and pressure were coupled by the SIMPLE method; the basic Reynolds stress model with a function of the enhanced wall treatment in Ansys FLUENT (Ansys, Inc., 2010) was chosen as the turbulence model.The temperature was obtained by computation of the following energy equation:

359
, where  represents the density, i u  represents the gas velocity of i components,  h is the enthalpy, rad q is the source term of the radiation, i x is the coordinate in the i direction, t  is the turbulent viscosity, h  is the effective Prandtl number,  is the heat conductivity, and T is the temperature.The symbols "~" and "-" placed over the variables indicate density weighted and time average, respectively.rad q was modeled as described on the TNF web site (Barrow, 2003b), and T was computed as where 0 298.15T  .0 J h represents the standard enthalpy of the formation of chemical species J , J Y  is the mass fraction of chemical species J , and J Cp is the mean specific heat at constant pressure of chemical species J .

Combustion simulation technique
The proposed technique is explained using the example of a H 2 -air turbulent non-premixed flame.Figure 1 illustrates the scheme of the proposed technique.In this technique, chemical species are divided, roughly, into two groups: group a-the species categorized by the chemical equilibrium, and group b-the species categorized by the chemical kinetics (including the overall reaction).() www.intechopen.com, where J w represents the reaction rate of chemical species J ; J D , the effective diffusion coefficient of chemical species J ; and m  , the effective Schmidt number.The eddy dissipation concept (Magnussen, 1989;Gran et al., 1996;Magnussen, 2005) was used to model J w , and J D was estimated using Smooke's model.To obtain J w in Equation ( 5), calculations of the chemical reaction and chemical equilibrium were performed; the mass fraction equation can be computed by assignment of a value to J w .To perform the chemical equilibrium calculation, we needed the mass fraction of elemental species I and enthalpy in group b.We therefore added the mass fraction equation of elemental species J in group a: () , () where I Z  represents the mass fraction of elemental species I .I w is the source term that exchanges the mass in group b for that in group a: where a h  represents the enthalpy in group a.The source term in Equation ( 5) for the equilibrium species a J was modeled as aa e q a 2 0 () () , The proposed technique was needed to compute J w in Equation ( 5), and different expressions were used to compute , J w depending on the group that the species belonged to.The reaction rate of chemical species in group b can be obtained with the EDC model.The source term in Equation ( 5) for these modified chemical species was computed as  J obtained from the lookup table.Since the lookup table included the mass fraction of the chemical species in group b, the production resulting from using the values take from the table must be taken into account.When  16) is a stiff ODE, and therefore, the robust computational code CVODE (Hindmarsh et al., 2009) was used to acquire the steady solution.
Although the reaction rates of fuels can be computed by Equation ( 15), the flame sometimes blows out.That is why we used the following equations to estimate the reaction rates of the fuels in this study.If we assumed that the reaction rates of fuels were determined with an overall reaction such as 1(kg)fuel (kg)oxidant (1 Y can be modeled based on the expression of the overall reaction rate as The subscripts fu and ox represent the fuels and oxidants, respectively.st represents the theoretical weight of the oxidants, and A fu is the mixing parameter of fuels set to 1.0 (equal to the value in the original EDC model).

Chemical equilibrium method and reading lookup table
When preparing the lookup table, we developed a different program from the UDF based on the chemical equilibrium method, by minimization of the Gibbs free energy.This method assumes that the equilibrium composition of a chemical system can be determined by minimizing the Gibbs free energy.Under the minimum conditions of Gibbs free energy, the following simultaneous nonlinear equations are obtained:  19) and ( 20).In this study, the computational code KINSOL (Collier et al., 2009) was used to solve these equations, and the concentration of each species at given T was obtainable by 0 exp ln , where J X represents the molar concentration of chemical species J , and thermodynamic properties such as J G and J h were computed as functions of the temperature (Mcbride et al., 2002).According to this procedure, the concentration of the chemical species J at given T was acquired.However, the additional constraint that the enthalpy was constant before and after combustion was required so that the chemical equilibrium composition in combustion could be found.Thus, T must be found under the constraint , where J h represents the enthalpy of chemical species J , and r h represents the enthalpy of reactants (before combustion).When we found T using Equation ( 22), the obtained results were the concentrations after combustion.The equilibrium value Jeq Y was obtained from reading the lookup table and a h  .Then, a simple multi-linear interpolation was used to extract information from the lookup table.

NO prediction using the extended Zeldovich mechanism
FLUENT version 13.0 has a function for computing the amount of the thermal NO X using the extended Zeldovich mechanism as Because we used the basic function in FLUENT, we describe only the outline of the method to estimate the amount of NO here (Warnatz et al., 2006;Ansys, Inc, 2010).The reaction rate constants used in FLUENT were selected based on the evaluation of Hanson and Salimian (Hanson et al., 1984).To calculate the NO concentration in turbulence combustion, the timeaveraged formation rate of NO must be computed at each computational cell.Methods of modeling the mean turbulent reaction rate of NO can be based on the presumed PDF model (Peng et al., 2009).FLUENT adopted the PDF model to predict the mass fraction of NO, and the reaction rate of the NO was expressed as  23)-( 25), the extended Zeldovich mechanism includes intermediate species such as O, N, H, and OH.The mass fractions of these species can be obtained by using the proposed technique.Thus, only the reaction rate of NO was computed by the presumed PDF model, while those of the intermediate species were taken into account using the proposed technique.

Numerical conditions
A H 2 -air non-premixed flame was simulated to verify the accuracy of the proposed technique.The numerical conditions were based on Barrow's experimental data (Barrow et al., 2003a).Figure 2 shows the sketch of the computational domain used in this study.were assigned in air.The fuel was injected from a nozzle with a radius of 3.75 mm.The velocity of the fuel and ambient air were 296 and 1.0 m/s, respectively.The temperature of the fuel and ambient air was set to 300 K.In all cases, a second-order upwind difference was applied to the governing equations of the momentum, mass fraction of chemical species J and elemental species I , and the energy equation.The two-dimensional axisymmetric solver in FLUENT was chosen using the axis indicated by the centerline in Fig. 2. The Reynolds stress model was chosen as the turbulence model; 2 1.80 , and 0.7 m   of the model parameters were used to adjust the axial profile of the mixture fraction of the experimental data.In this study, the detailed chemical mechanism of H 2 suggested by Barrow (Barrow et al., 1999) was used to compute the reaction rates of the modified species in the proposed technique, and those of the chemical species taken into account by the EDC model.   of the Reynolds stress model were chosen to match the axial mixture fraction obtained by the experiment, the computational results were close to the experimental data at 0.2 / xL  .However, as shown in Fig. 3, those at /0 . 2 xL  were slightly smaller than the experimental data.The mixture fraction was related to mass diffusion, which in turn depended on turbulence models.It can be seen from this result that mass diffusion was not similar to the experimental data at / 0.2 xL  (near the nozzle), and the turbulence model would have to be modified to obtain the closer result.However, the objective in this section is to confirm the validity of the proposed technique.To that end, we performed the simulation using the EDC model for reference.The EDC model has been widely applied to the simulation of combustion equipment (Stefanidis et al., 2006;Minotti et al., 2010), and the results obtained using the EDC model have been considered to be reliable for the engineered approach.The prediction of the proposed technique must approach that of the EDC model, because the expression of the reaction rate in the proposed technique was based on the EDC model.were slightly larger than the experimental data.Fig. 5 shows the axial mole fraction of H 2 and O 2 .Both the computational results of H 2 and O 2 were lower than those of the experimental data.It was found that the simulations slightly overestimated the consumption of H 2 and O 2 as compared with those of the experiment.The mole fraction of OH is plotted in Fig. 6.Generally, reaction equations including OH are needed to obtain the mole fraction of OH, but it was not required in the proposed technique.(However, the reaction equation of OH can be taken into account in the proposed technique using Equations ( 15)-( 16) to improve the prediction accuracy.)As shown in Fig. 6, the result of OH was comparatively small as compared with major species such as H 2 , O 2 , and H 2 O; the amount of the radical species, such as H, O, and OH, were generally very subtle.For this reason, it was important to estimate the tendency of yield and consumption of the mole fraction of OH.In Fig. 6, the coordinates of the peaks of the mole fraction of OH obtained by the simulations were similar to the experimental data, and we found that the mole fraction of OH obtained using the proposed technique was qualitatively similar to that obtained by the EDC model and experimental data. .Although the results obtained by the EDC model and the proposed technique were in good agreement, they were not close to the experimental data.As mentioned above, the difference of the mixture fraction between the simulations and experiment was related to the turbulence model, and not to either the EDC model or the proposed technique.As we can observe from Fig. 8, the peaks of the temperature and the mole fraction of H 2 O predicted with the use of the EDC and proposed models were at approximately / 4 rD  , while that of the experimental data was at approximately / 2.9 rD  . The deference of coordinates of the peaks between the simulation data and the experimental data derived mainly from turbulence model accuracy.Fig. 9 shows the radial mole fraction of H 2 and O 2 .The mole fraction of O 2 obtained by the proposed technique was lower than that predicted by the EDC model.In the proposed technique, the mole fraction of O 2 was obtained from the lookup table, which was prepared using the chemical equilibrium method.For this reason, consumption of O 2 was sometimes overestimated at points where the reaction was in the state of strong nonequilibrium.to estimate the reaction rate of H 2 , while the reaction rate was computed using the detailed chemical mechanism in the EDC model.However, the difference of the results between the proposed technique and EDC model were small as compared to the maximum mole fraction of H 2 .Basically, the maximum mole fraction of H 2 was equal to 1.0 taken at / 0 xL  ; the difference at /0 .0 rD  between both computational results was about 0.03.As shown in Fig. 14, the peaks of the mole fractions of OH obtained by the simulations and that of the experiment were located at approximately / 7.6 rD  and / 6.4 rD  , respectively.The coordinates of the peaks obtained by the simulations were similar to each other, but they were slightly different from that of the experiment.As shown in Figs. 15,16,and 17,computational results for EDC and proposed models were in good agreement, but were either slightly greater or less than the experimental data, which showed a similar tendency to that of the other area, such as the radical direction at /1 / 8 xL  and / 1 / 2.   The radial mole fractions of OH at / 3 / 4 xL  are depicted in Fig. 18.The computational results were overestimated as compared with the experimental data, and the mole fraction of OH at 9 / rD  obtained using the proposed technique was similar to that obtained using the EDC model.In this portion of the experiment, we found that the results of the mixture fraction, major species, and temperature obtained by the proposed technique were roughly similar to those predicted by the EDC model.The mole fraction of OH was not quantitatively similar to that of the EDC model; however, the coordinate values of the peaks of mole fraction of OH predicted by the proposed technique and EDC model were in good agreement with one another.Thus, the tendency of yield and consumption of OH was predicted with the proposed technique, which did not use the chemical equation of OH.The computations show slight differences in the experimental data, even when the EDC model was applied to the combustion simulation.Moreover, we found that it is important to accurately predict the non-premixed flame using not only the combustion model but also the turbulence model.For this reason, further improvement of the combustion and turbulence models is a significant task for combustion simulation.

Prediction of NO
We show the application of the proposed technique to the simulation of NO in this section.In Figs.[19][20][21][22][23][24][25][26][27][28][29][30]"Proposed" indicates computational 15)-( 16).As can be seen in Fig. 19, the peaks of the mole fraction of NO obtained by the simulation and that of the experiment were located at approximately / 0.82 xL  . Those of the EDC model and proposed technique with modified reaction rates of H, O, and OH were bigger than the experimental data, while the peak obtained using the proposed technique without modified reaction rates was similar to that of the experiment.On the other hand, as shown in Fig. 20, the mole fraction of NO obtained by the proposed technique without the modified reaction rates was not similar to the experimental data.Thus, we did not determine which cases were most accurate in these simulations.As can be observed from Figs. 19 and 20, the amount of NO was very small as compared to the major species such as H 2 , O 2 , and H 2 O. Therefore, the most important aim of the NO prediction was to simulate the tendency of yield and consumption of NO.On the other hand, as can be seen in Figs. 25 and 26, either the mole fraction of O or T obtained using the proposed technique with modified reaction rates of H, O, and OH were larger than those of the EDC model.Therefore, the radial mole fraction of NO at / 1 / 8 xL  was also larger than that computed by the EDC model.We found that the amount of NO was determined by the amount of O and T, and those of prediction accuracy were so important of obtaining the accurate mole fraction of NO.In the proposed technique, the reaction rates of the intermediate species such as H, O, and OH were computed, and the mole fractions can be obtained taking into account the chemical equations.Generally, when the reaction rates were modified using the chemical equations, the prediction accuracy of the chemical species was also increased (Fukumoto et al., 2010).However, even without the modified reaction rates, the proposed technique well simulated the mole fraction of O, and the improvement of the modified reaction rates was relatively small.Therefore, the computing the reaction rates of H, O, and OH can be omitted in this flame.

Influence of number of modified species and computational time
Due to the time required to compute reaction rates of these species, the computational time is dependent on the number of the chemical species in group a.Our proposed technique enables the shortening of these computational times.The purpose of this section is to discuss the prediction accuracy for the minor species and computational time required by the proposed technique.The numerical condition of the EDC model conformed to that presented in the previous sections, and the other two cases of the proposed technique were performed in this part of the experiment.In the first case of the proposed technique, the reaction rate of H 2 was computed by the estimated by Equations ( 17)-( 18).In the second case, those of H, O, and OH were modified, and the reaction rate of H 2 was estimated.Fig. 31 shows a comparison of the computational time in the case of the EDC model and two cases of the proposed technique.Each computational time per iteration was measured after the solution was converged and was measured during the 100 iterations of performing the reaction calculation and reading the lookup table.The CPU used in these simulations was the Intel Core i7-980X Processor Extreme Edition with 12M Cache, and 3.33 GHz.GFORTRAN 4.4.4 was chosen as a compiler, and CVODE 2.6 (Hindmarsh et al., 2009) was adopted to solve the ODEs of the reaction calculation.As can be seen in Fig. 31, the computational times for the EDC model-the two proposed techniques with modified H, O, and OH (second case) and with no modified species (first case)-were 8.99 s, 2.83 s, and 0.04 s, respectively.We found that the lower the number of included modified species, the fewer were the demands on lower computational time.On the other hand, the prediction accuracy also depended on the number of modified species included.Therefore, when the proposed technique is used, the number of modified species should be determined according to the required prediction accuracy.In the proposed technique, the computational time required increased with an increase in the number of modified species.However, the proposed technique has an advantage: We only chose the modified species and then the reduced mechanism was automatically built from the detailed mechanism.

Conclusion
In this chapter, we presented a combustion simulation technique based on a chemical equilibrium method combined with the EDC model.The proposed technique makes it easy to construct a reduced mechanism according to the accuracy requirements of the chemical species, so that the computational time can be minimized.We draw the following conclusions:  The prediction accuracy of the proposed technique for the mixture fraction, major mole fraction, and T was similar to that of the EDC model.


The coordinates of the peak OH mole fractions predicted by the proposed technique and EDC model were in good agreement.Thus, the tendency of yield and consumption of OH can be predicted using the proposed technique, which did not use the chemical equation of OH.


The tendency of yield and consumption of NO was simulated by the proposed technique with the extended Zeldovich mechanism.


A lower number modified species led to lower computational time.However, the prediction accuracy also relied on the number of modified species included.Modified species should be included according to the required prediction accuracy.

Fig. 1 .
Fig. 1.Overview of proposed techniqueIn the proposed technique, the mass fraction equation of chemical species J was used as atomic weight of species I , b J the chemical species J in group b, b IJ a the number of elemental species I included in chemical species b these equations were similar to what was seen in the EDC model.b J Y  was obtained by calculating the detailed chemical mechanism.The EDC model assumes that combustion occurs in a constant pressure reactor.The following equation was integrated under the initial conditions obtained from the current mass fractions, density, and temperature in each computational cell: the reaction rate of chemical species b J in the fine structures, and b J w  can be obtained by computing detailed chemical mechanisms based on the Arrhenius equation.Equation ( Fig. 2. Sketch of computational domain

Fig. 3
shows the axial profile of the mixture fraction.Because the parameters 2 1.80,

Fig. 3 .
Fig. 3. Axial mixture fractionThe axial temperature T and mole fraction of H 2 O are shown in Fig.4.The mixture fractions of the computational results are in good agreement with each other, although those at 0.6 / xL  were slightly larger than the experimental data.Fig.5shows the axial mole fraction of H 2 and O 2 .Both the computational results of H 2 and O 2 were lower than those of the experimental data.It was found that the simulations slightly overestimated the consumption of H 2 and O 2 as compared with those of the experiment.The mole fraction of H 2 at 0.3 / 0.6 xL   obtained by the proposed technique was slightly larger than that of the EDC model.The reaction rate of H 2 was determined by the overall reaction, choosing

Fig. 4 .
Fig. 4. Axial temperature T and mole fraction of H 2 O

Fig. 5 .
Fig. 5. Radial temperature and mole fraction of H 2 and O 2

Fig. 6 .
Fig. 6.Radial temperature and mole fraction of OH Fig. 7 shows the radial mixture fraction at / 1 / 8 xL .Although the results obtained by the EDC model and the proposed technique were in good agreement, they were not close to the experimental data.As mentioned above, the difference of the mixture fraction between the simulations and experiment was related to the turbulence model, and not to either the EDC model or the proposed technique.As we can observe from Fig.8, the peaks of the temperature and the mole fraction of H 2 O predicted with the use of the EDC and proposed models were at approximately / 4 rD  , while that of the experimental data was at approximately / 2.9 rD .The deference of coordinates of the peaks between the simulation data and the experimental data derived mainly from turbulence model accuracy.

Fig. 9 .
Fig. 9. Radial mole fraction of H 2 and O 2 at x/L = 1/8 As shown in Fig. 10, the coordinate values of the peak of the mole fraction of OH obtained by the simulations and experimental data are located at approximately / 4.1 rD  and /2 .7 rD , respectively.These values were slightly different from what was seen in the experiment.The coordinate of the peak mole fraction of OH was close to that of the mole fraction of H 2 O and T. It can be seen from this tendency that OH was the indicative species of extinction and ignition phenomena.

Fig. 21 .Fig. 22 .
Fig. 21.Radial mole fraction of NO at x/L = 1/2However, in Fig.19, the axial mole fraction of NO obtained by the proposed technique with modified reaction rates of H, O, and OH was smaller than that of the EDC model.This was because axial T by the EDC model was overestimated as compared to that Fig. 23.Axial mole fraction of O

a Species obtained by Look-up table of chemical equilibrium b Species modified by chemical equations
table was prepared before the combustion simulation, and it included the following species: H 2 , O 2 , H 2 O, O, H, OH, HO 2 , H 2 O 2 , NO, HNO, N 2 O, N, NO 2 , and N 2 .In Figs.3-18, x represents the axial distance from the exit of the nozzle; r, the radial distance from the centerline of the nozzle; L , the approximate visible flame length, which is equal to 675 mm in this flame; D , the diameter of the nozzle, which is equal to 3.75 mm in this flame; T, the temperature; EXP, the experimental data; EDC, the computational data predicted by the EDC model with Other symbols in Figs.19-30 are as they were in the previous section.Two lookup tables were prepared before the combustion simulation.One table includes the species H 2 , O 2 , H 2 O, O, H, OH, HO 2 , H 2 O 2 , NO, HNO, N 2 O, N, NO 2 , and N 2 ; it was used for the case of the proposed technique with Fig. 20.Radial mole fraction of NO at x/L=1/8 predicted with the extended Zeldovich mechanismIt can be seen from Figs. 19-22 that the amounts of the NO prediction were not quantitatively correct; however, the peaks of the mole fractions obtained by the simulations were similar.Thus, we found that the tendency of yield and consumption of NO was simulated by all the cases in this part of the experiment.The prediction accuracy of O is significant in the computation of the mass fraction of NO because the first reaction of the extended Zeldovich mechanism, expressed as O + N 2 N + NO, is the rate-limiting step(Warnatz et al., 2006).Thus, the amount of NO increases with an increase in O.As shown in Fig.23, the axial mole fraction of O obtained using the proposed technique with modified reaction rates of H, O, and OH was larger than that of the EDC model.