# Entropy Generation and Exergy Assessment of Methane–Nitrous Oxide Diffusion Flames in a Triple-Port Burner

Authors: Dean Chou; Wen-Yuan Tsai; Mohsen Davazdah Emami; Yueh-Heng Li
Journal: International Journal of Energy Research
 (2023)

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## Abstract

A triple-port burner was used in this study, and a numerical simulation was employed to investigate the entropy generation rate of CH4–N2O diffusion flames at the Rratio=1. Here, R ratio refers to the ratio of the oxidizer flow velocity to the fuel flow velocity. In order to scrutinize the decomposition effect of N2O on entropy generation, an oxygen-enriched gas with the same nitrogen to oxygen ratio as N2O (N-to-O=2) was used in CH4–N2–O2 diffusion flames. Besides, because the N2O could decompose into the oxygen-enriched gas, the oxygen-enriched effect was also studied by the CH4–air diffusion flames that were conducted in this research. The entropy generation rate comprises of three items in this study, including heat conduction, mass diffusion, and chemical reaction. As a result, the different reaction pathways would take part in the major reaction pathway in CH4–N2O diffusion flames, causing more entropy generation rate being produced through the more intense reactions in CH4–N2O diffusion flames. The irreversibility in CH4–air diffusion flames are dominated through heat conduction and chemical reaction, which is an identical result in CH4–N2–O2 diffusion flames. However, in CH4–N2O diffusion flames, chemical reactions dominated the irreversibility because of the more intense reaction caused by the thermal effect of N2O decomposition. As a result, the decomposition effect of N2O influences the availability of CH4–N2O diffusion flames.


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## Body

## 1. Introduction

The use of propellant is an essential part of rockets, and hydrazine (N2H4) is one of the common propellants. It is widely used because of its high efficiency [1]. However, a negative feature of hydrazine is its high toxicity [2]. Therefore, the current research focuses on finding green propellants with high efficiencies that can replace N2H4 [3–5]. In recent years, NOFBX (nitrous oxide fuel blend) is found to be the most promising propellant due to its low toxicity and low cost [2, 6]. Moreover, NOFBX has a specific impulse higher than that of N2H4 [7].NOFBX is the mixture of nitrous oxide (N2O) and fuel. Obviously, N2O is used as an oxidant in this propellant, and there have been several kinds of research on N2O as an oxidizer in rocket propellants [8–10]. Compared with oxygen, it is more convenient to liquefy and store in rockets. In addition, N2O will naturally decompose into oxygen-enriched mixed gas (67% nitrogen and 33% oxygen) under a high-temperature condition (850 K) [11] and will be accompanied by a large amount of heat release. Many studies worked on hydrocarbon fuel/N2O flames but primarily focused on the flame structure, laminar flame speed, and flame extinction. Vandooren et al. [12] compared the flame structure differences between CH4–O2 and CH4–N2O flames and elaborated the contribution of some species, HCO, HCN, and HNCO, on the reaction mechanism. Powell et al. [13] used a Mckenna flat flame burner to investigate the laminar flame speed of various hydrocarbon fuels (methane, acetylene, propane, and hydrogen) and N2O mixtures. In addition, they also found that the rate constant of N2O+H should be modified to have a better prediction of the laminar flame speed. Razus et al. [14] discussed the effect of N2 dilution on the change of laminar flame speed of CH4–N2O flames and found that the laminar flame speed decreased with the increase of N2 concentration. Besides, they also provided a database for developing the chemical kinetic models of fuel-nitrous oxide systems. Newman-Lehman et al. [15] studied the flame structures of CH4–N2O and C2H6–N2O flames and explored the flame extinction. Their results showed that the burning velocity decreases as the fraction of N2O increases, so they concluded that replacing the O2 with N2O would inhibit the flame. Pfahl et al. [16] observed the flammability of several fuels blended with N2O, and the results indicated no obvious dependence on small amounts of oxygen (<5%) in flammability limits of CH4–N2O–N2 flames. Shebeko et al. [17] investigated the flammability limits of the H2–N2O and CH4–N2O flames with the inertisation of fluorinated hydrocarbons and compared them with flames that had a different oxidizer, which was the mixture of 75% N2 and 25% O2. They concluded that the flammability limits were wider in the flame with the N2O as an oxidizer. Wang and Zhang [18] modified the chemical reaction mechanism of the C2H4–N2O flame based on the sensitivity analysis and estimated the laminar flame speed of the C2H4–N2O flame through the modified mechanism. Chen and Li [19] elucidated the increasing NOx emission in CH4–N2O diffusion flames through three primary reaction pathways of the prompt route, and they concluded the prompt-NO formation is dominated by the N2O.Entropy analysis is one of the practical and effective fashions to analyse energy efficiency. The entropy generation rate can be manifested to analyse how much energy is consumed by the irreversible process, which caused the reduction of exergy during the combustion process, making the second law efficiency decrease. Arpaci and Selamet [20] investigated the equation of entropy generation in one-dimensional flames and found that the research on the entropy of real flames should be related to existing models of the prediction of flame structure. Emadi and Emami [21] and Briones et al. [22] both examined the changes in the entropy generation rate when hydrogen was added into the nonpremixed methane–air flame and realised that the entropy generation rate would decrease with an increase in the percentage of hydrogen addition. Wu et al. [23] and Mohammadi et al. [24] inspected the difference in entropy generation rate of hydrogen–air and methane–air premixed flames in porous microburners. Their results show that the heat conduction term dominates the entropy generation, and porosity variation can affect the entropy generation. Moreover, they found that SiC and Al2O3 are the better appropriate materials for the porous medium and the combustor wall to achieve lower entropy generation. Datta [25] investigated the relationship between the entropy generation rate and gravity and concluded that the entropy generation rate would decrease with the reduction of the gravity from normal gravity to zero gravity. Yang et al. [26] studied the effect of the block inert on the temperature distribution and entropy generation in a microcombustor. Their results showed an increase in the mean wall temperature and a more uniform wall temperature distribution when the block inert was used.Most of the studies that concern the application of the entropy generation method in flames have focused on the effects of fuel types and fuel additives on the rate of entropy generation. This is justified on the ground that all of these studies have been performed on flames where air is used as the oxidizer. However, for oxygen enriched flames, such as fuel–N2O flames, the composition of the oxidizer would contribute to the entropy generation and would affect the second-law efficiency and combustion characteristics. The present work aims to address these points by studying entropy generation due to conduction, species mass transfer, and chemical reactions in CH4–N2O, CH4–67% N2–33% O2, and CH4–air nonpremixed flames. In addition, the reaction pathway analysis of CO2 and H2O is conducted to investigate the difference in entropy generation rate of these flames.


## 2. Experimental Apparatus and Simulation Setup

### 2.1. Measurement System

This study used a three-port coaxial burner for the experiments, where the experimental setup is shown in Figure1. The circular inner port of the burner supplies an oxidizer (N2O or 67% N2–33% O2), the annular inner port supplies methane gas, and the annular outer port provided coflow air that shields the flames. The inner and outer diameters of the three nozzles at the burner tip are 50/52mm, 4/5mm, and 1.5/2mm from the outside to the inside, respectively. To ensure a convenient observation from the side view, the circular inner port (oxidizer port) and the annular inner port (fuel port) protruded 12 mm from the burner exit of the third port (coflow port). The heights of the fuel port and oxidizer port are the same. The velocity of fuel (VF) and coflow are fixed at 0.1 m/s in this experiment. The velocity of the oxidizer (VO) varies with the value of the R ratio. The R ratio (VO/VF) refers to the ratio of the oxidizer flow velocity to the fuel flow velocity. The gas velocity was adjusted by the flowmeter (Model 5850E, Brooks Instrument, Hatfield, PA, USA) which was calibrated by a flow calibrator (Bios Defender 220, Mesa Labs Inc., Bensenville, IL, USA). The camera was used to photograph the flame structure under different oxidizer inlet velocities. The R-type thermocouple, which has a junction diameter of 3 μm, was used to gauge the temperature distribution at three different heights above the burner tip. The location of the measurement point was adjusted by the positioning system. In order to present a more statistically independent temperature profile, the average of ten measurements at each point is used. To avoid thermocouple damage, when measuring in-flame temperature, the pump was used to control the residence time of the thermocouple inside the flame. The response time of the thermocouple was short enough due to the small junction. The residence time of the thermocouple was set as 5 seconds.Figure 1
Schematic of the measurement system.Because of the thermal radiation effect, the thermocouple reading would be lower than the actual temperature; therefore, a radiation correction must be applied. The actual temperature may be derived as [27]:
(1)Tactual=Tt+εtσTt4ht,where the Tactual, Tt, and σ are the temperatures of actual gas (K) and the temperature measured by the thermocouple (K) and the Stefan-Boltzmann constant (5.67×10−8W/m2−K4), respectively. Parameters ht and εt are, respectively, the convection heat transfer coefficient (W/m2-K) and the emissivity of the thermocouple which is assigned a constant value of 0.22 [28]. The correlation for the convection heat transfer coefficient was given as [27]:
(2)htDtkg=Nu=0.42Pr1/5+0.57Pr1/3Re1/2,where the Nu, Pr, and Re are the Nusselt number, Prandtl number, and Reynold number, respectively. The Nusselt number has been defined based on the junction diameter Dt (m) and the thermal conductivity of the gas kg (W/m-K). The thermal conductivity, Prandtl number, and Reynold number could be calculated as:
(3)kg=3.75×10−5Tt+0.04,Pr=να,Re=uDtν.Here,u, α, and ν are the velocities of the gas relative to the junction (m/s), thermal diffusivity (m2/s), and the dynamic viscosity of the gas (m2/s). Therefore, the corrected temperature, Eq. (1), could be rewritten as:
(4)Tactual=Tt+εtDtσTt4Nukg,


### 2.2. Numerical Model

The commercial software STAR-CCM+ was used in this study. In order to shorten the calculation time, the flame case was simplified into a two-dimensional system for discussion. The governing equations consist of steady-state, the two-dimensional Navier-Stokes equations, mass and energy conservation equations, and species transfer equations for each chemical species. The thermal conductivity, dynamic viscosity, and specific heat of the multicomponent gas were determined by the mass-weighted of each component. The diffusivity was based on the kinetic theory:(5)Dm=1−Xi∑i=1,i≠mXi/Di,m,where the Dm, Di,m, and Xi are the diffusivity of species m (m2/s), the binary diffusivity of species i and m (m2/s) and the mole fraction of species i, respectively. From the gas kinetic theory, the expression of Di,m was based on the Chapman-Enskog theory [29]:
(6)Di,m=2.66×10−7T3/2PMi,m1/2σi,m2ΩT∗,where:
(7)Mi,m=2MiMmMi+MmIn addition,T and P are the temperature (K) and the static pressure (Pa), respectively. The Mi and the Mm are the molecular weight of species i and species m, respectively. σi,m and ΩT∗ are the collision diameter (m) for the pair of species i and species m and the collision integral which is the function of reduced temperature T∗ that is defined as:
(8)T∗=kTεi,m,where the k is the Boltzmann constant (1.38×10−23m2−kg/s2−K), and the εi,m is the characteristic Lennard-Jones energy for the pair of species i and species m.Figure2 shows a schematic of the modeled burner and the open environment in the simulation domain. Since the flame is symmetric, the model is reduced to half, saving more computational time. It is known from the experiment that the length of the main flame in this study does not exceed 2 cm, so the height of the open environment is set to 6 cm. The initial temperature of fuel, oxidizer, and coflow is 293 K, and the velocity field at the inlet is set to be uniformly distributed. The flow field is laminar, with the corresponding Reynolds number ranging from 17.9 to 302.9. The conditions at the outlet are ambient conditions, namely, a pressure of 101325 Pa. The stainless steel wall and the fluid boundary are coupled together to calculate the heat exchange between the fluid and the wall. The bottom of the tube wall is at a constant temperature of 293 K, which is measured by a K-type thermocouple.Figure 2
Schematic and boundary setup of the simulation model.In this numerical simulation, a nonuniform grid was used, whereas a more refined grid was employed in the reaction zone close to the centerline. Accordingly, the reaction zone has sufficient grid resolution. The grid independence analysis had been performed, and the grid density used in this numerical simulation was determined under the condition that there is no significant difference, which is lower than 1.5%, between the maximum temperature and species distribution when the number of nodes doubled. When the residual of the governing equations reaches below 10−5, it can be regarded as the converged simulation.The USM reaction mechanism [18], which comprises of 582 reactions and 96 species, was used in this numerical simulation. The USM reaction mechanism combines two detailed reaction mechanisms, namely the USC Mech II-2 [30] (529 reactions) carbon hydroxide reaction mechanism and San Diego [31] (53 reactions) N2O reaction mechanism, and some rate constants have been modified. This reaction mechanism has been extensively used and verified [18], and the results are pretty satisfactory. Besides, Li et al. [32] determined the laminar burning velocity of CH4/N2O premixed flames with a slot burner and compared the experimental results with the numerical results employed with USM and UGM mechanisms. It concluded that the USM mechanism is more accurate for the prediction of the laminar burning velocity of CH4/N2O flames.


### 2.3. Entropy Generation Rate Equations

The entropy generation rate is divided into four items in this study due to the effects of fluid viscosity, heat conduction, mass diffusion, and chemical reaction. These may be written as [21]:
(9)σvis′′=τ:∇uT,(10)σcond′′=λ∇T∙∇TT2,(11)σdiff′′=R∑iρDi−mixXi∇Yi∙∇Xi,(12)σchem′′=−∑iμiω̇iT,(13)σtot′′=σvis′′+σcond′′+σdiff′′+σchem′′.Here,σ′′ is the volumetric entropy generation rate (W/m3-K), τ and λ are the viscous stress (N/m2) and thermal conductivity (W/m-K), respectively. ω̇i and Di−mix are the production rate of species i (W/m-K) and the mass diffusivity of species i in the mixture (m2/s), respectively. u, T, R, and ρ are the velocity vector (m/s), temperature (K), gas constant (J/kg-K), and density (kg/m3), respectively. Yi and Xi are the mass and mole fraction of species i, respectively. μi is the chemical potential of species i, which is calculated as:
(14)μi=hiT−TsiT+RTlnXiPPref,where hi and si is the enthalpy (J/kg) and entropy (J/kg-K) of the species I; P and Pref are the total pressure (Pa) and reference total pressure (Pref=101325 Pa), respectively.The total local volumetric entropy generation rate can be obtained from the Eq. (13), which combines viscous dissipation, heat conduction, mass diffusion, and the chemical reaction terms. However, the fluid viscosity term is relatively small in all conditions, so it can be neglected. The total entropy generation rate, σ′ (W/K), could be calculated from the following equation:
(15)σtot′=∬2πrσtot′′drdz.From the Gouy-Stodola theorem [33], the irreversibility, İ (W), could be obtained by following equation:
(16)İ=T0σtot′,where the T0 is the reference temperature of 298 K. The second law efficiency could be calculated by the following equation [25]:
(17)ηII=1−İȦin,where the Ȧin is the incoming exergy (W) from the inlet gas to the combustion system. It should be noticed that the incoming exergy is usually dominated by the fuel, but here N2O was used as an oxidizer, which has more extensive chemical availability and contributes to the incoming exergy. The incoming exergy was calculated by [21]:
(18)Ȧin=ṁMmix∑iXiai,where the ṁ is the mass flow rate (kg/s) and the Mmix is the molecular weight of the mixture, respectively. The ai is the specific availability of the species i (J/kg), which could be obtained from:
(19)ai=hi−hi,0−T0si−si,0+V22+gz+aich,where the h0 and s0 are the enthalpy and entropy of species i under the reference temperature condition (298 K), respectively. The V, g, and z are the velocity (m/s), gravity (m2/s), and the axial distance (m), respectively. The aich is the specific chemical availability of the species i (J/kg) [34]. In this study, the specific chemical availability of each gas stream is obtained from Szargut [35].


## 2.1. Measurement System

This study used a three-port coaxial burner for the experiments, where the experimental setup is shown in Figure1. The circular inner port of the burner supplies an oxidizer (N2O or 67% N2–33% O2), the annular inner port supplies methane gas, and the annular outer port provided coflow air that shields the flames. The inner and outer diameters of the three nozzles at the burner tip are 50/52mm, 4/5mm, and 1.5/2mm from the outside to the inside, respectively. To ensure a convenient observation from the side view, the circular inner port (oxidizer port) and the annular inner port (fuel port) protruded 12 mm from the burner exit of the third port (coflow port). The heights of the fuel port and oxidizer port are the same. The velocity of fuel (VF) and coflow are fixed at 0.1 m/s in this experiment. The velocity of the oxidizer (VO) varies with the value of the R ratio. The R ratio (VO/VF) refers to the ratio of the oxidizer flow velocity to the fuel flow velocity. The gas velocity was adjusted by the flowmeter (Model 5850E, Brooks Instrument, Hatfield, PA, USA) which was calibrated by a flow calibrator (Bios Defender 220, Mesa Labs Inc., Bensenville, IL, USA). The camera was used to photograph the flame structure under different oxidizer inlet velocities. The R-type thermocouple, which has a junction diameter of 3 μm, was used to gauge the temperature distribution at three different heights above the burner tip. The location of the measurement point was adjusted by the positioning system. In order to present a more statistically independent temperature profile, the average of ten measurements at each point is used. To avoid thermocouple damage, when measuring in-flame temperature, the pump was used to control the residence time of the thermocouple inside the flame. The response time of the thermocouple was short enough due to the small junction. The residence time of the thermocouple was set as 5 seconds.Figure 1
Schematic of the measurement system.Because of the thermal radiation effect, the thermocouple reading would be lower than the actual temperature; therefore, a radiation correction must be applied. The actual temperature may be derived as [27]:
(1)Tactual=Tt+εtσTt4ht,where the Tactual, Tt, and σ are the temperatures of actual gas (K) and the temperature measured by the thermocouple (K) and the Stefan-Boltzmann constant (5.67×10−8W/m2−K4), respectively. Parameters ht and εt are, respectively, the convection heat transfer coefficient (W/m2-K) and the emissivity of the thermocouple which is assigned a constant value of 0.22 [28]. The correlation for the convection heat transfer coefficient was given as [27]:
(2)htDtkg=Nu=0.42Pr1/5+0.57Pr1/3Re1/2,where the Nu, Pr, and Re are the Nusselt number, Prandtl number, and Reynold number, respectively. The Nusselt number has been defined based on the junction diameter Dt (m) and the thermal conductivity of the gas kg (W/m-K). The thermal conductivity, Prandtl number, and Reynold number could be calculated as:
(3)kg=3.75×10−5Tt+0.04,Pr=να,Re=uDtν.Here,u, α, and ν are the velocities of the gas relative to the junction (m/s), thermal diffusivity (m2/s), and the dynamic viscosity of the gas (m2/s). Therefore, the corrected temperature, Eq. (1), could be rewritten as:
(4)Tactual=Tt+εtDtσTt4Nukg,


## 2.2. Numerical Model

The commercial software STAR-CCM+ was used in this study. In order to shorten the calculation time, the flame case was simplified into a two-dimensional system for discussion. The governing equations consist of steady-state, the two-dimensional Navier-Stokes equations, mass and energy conservation equations, and species transfer equations for each chemical species. The thermal conductivity, dynamic viscosity, and specific heat of the multicomponent gas were determined by the mass-weighted of each component. The diffusivity was based on the kinetic theory:(5)Dm=1−Xi∑i=1,i≠mXi/Di,m,where the Dm, Di,m, and Xi are the diffusivity of species m (m2/s), the binary diffusivity of species i and m (m2/s) and the mole fraction of species i, respectively. From the gas kinetic theory, the expression of Di,m was based on the Chapman-Enskog theory [29]:
(6)Di,m=2.66×10−7T3/2PMi,m1/2σi,m2ΩT∗,where:
(7)Mi,m=2MiMmMi+MmIn addition,T and P are the temperature (K) and the static pressure (Pa), respectively. The Mi and the Mm are the molecular weight of species i and species m, respectively. σi,m and ΩT∗ are the collision diameter (m) for the pair of species i and species m and the collision integral which is the function of reduced temperature T∗ that is defined as:
(8)T∗=kTεi,m,where the k is the Boltzmann constant (1.38×10−23m2−kg/s2−K), and the εi,m is the characteristic Lennard-Jones energy for the pair of species i and species m.Figure2 shows a schematic of the modeled burner and the open environment in the simulation domain. Since the flame is symmetric, the model is reduced to half, saving more computational time. It is known from the experiment that the length of the main flame in this study does not exceed 2 cm, so the height of the open environment is set to 6 cm. The initial temperature of fuel, oxidizer, and coflow is 293 K, and the velocity field at the inlet is set to be uniformly distributed. The flow field is laminar, with the corresponding Reynolds number ranging from 17.9 to 302.9. The conditions at the outlet are ambient conditions, namely, a pressure of 101325 Pa. The stainless steel wall and the fluid boundary are coupled together to calculate the heat exchange between the fluid and the wall. The bottom of the tube wall is at a constant temperature of 293 K, which is measured by a K-type thermocouple.Figure 2
Schematic and boundary setup of the simulation model.In this numerical simulation, a nonuniform grid was used, whereas a more refined grid was employed in the reaction zone close to the centerline. Accordingly, the reaction zone has sufficient grid resolution. The grid independence analysis had been performed, and the grid density used in this numerical simulation was determined under the condition that there is no significant difference, which is lower than 1.5%, between the maximum temperature and species distribution when the number of nodes doubled. When the residual of the governing equations reaches below 10−5, it can be regarded as the converged simulation.The USM reaction mechanism [18], which comprises of 582 reactions and 96 species, was used in this numerical simulation. The USM reaction mechanism combines two detailed reaction mechanisms, namely the USC Mech II-2 [30] (529 reactions) carbon hydroxide reaction mechanism and San Diego [31] (53 reactions) N2O reaction mechanism, and some rate constants have been modified. This reaction mechanism has been extensively used and verified [18], and the results are pretty satisfactory. Besides, Li et al. [32] determined the laminar burning velocity of CH4/N2O premixed flames with a slot burner and compared the experimental results with the numerical results employed with USM and UGM mechanisms. It concluded that the USM mechanism is more accurate for the prediction of the laminar burning velocity of CH4/N2O flames.


## 2.3. Entropy Generation Rate Equations

The entropy generation rate is divided into four items in this study due to the effects of fluid viscosity, heat conduction, mass diffusion, and chemical reaction. These may be written as [21]:
(9)σvis′′=τ:∇uT,(10)σcond′′=λ∇T∙∇TT2,(11)σdiff′′=R∑iρDi−mixXi∇Yi∙∇Xi,(12)σchem′′=−∑iμiω̇iT,(13)σtot′′=σvis′′+σcond′′+σdiff′′+σchem′′.Here,σ′′ is the volumetric entropy generation rate (W/m3-K), τ and λ are the viscous stress (N/m2) and thermal conductivity (W/m-K), respectively. ω̇i and Di−mix are the production rate of species i (W/m-K) and the mass diffusivity of species i in the mixture (m2/s), respectively. u, T, R, and ρ are the velocity vector (m/s), temperature (K), gas constant (J/kg-K), and density (kg/m3), respectively. Yi and Xi are the mass and mole fraction of species i, respectively. μi is the chemical potential of species i, which is calculated as:
(14)μi=hiT−TsiT+RTlnXiPPref,where hi and si is the enthalpy (J/kg) and entropy (J/kg-K) of the species I; P and Pref are the total pressure (Pa) and reference total pressure (Pref=101325 Pa), respectively.The total local volumetric entropy generation rate can be obtained from the Eq. (13), which combines viscous dissipation, heat conduction, mass diffusion, and the chemical reaction terms. However, the fluid viscosity term is relatively small in all conditions, so it can be neglected. The total entropy generation rate, σ′ (W/K), could be calculated from the following equation:
(15)σtot′=∬2πrσtot′′drdz.From the Gouy-Stodola theorem [33], the irreversibility, İ (W), could be obtained by following equation:
(16)İ=T0σtot′,where the T0 is the reference temperature of 298 K. The second law efficiency could be calculated by the following equation [25]:
(17)ηII=1−İȦin,where the Ȧin is the incoming exergy (W) from the inlet gas to the combustion system. It should be noticed that the incoming exergy is usually dominated by the fuel, but here N2O was used as an oxidizer, which has more extensive chemical availability and contributes to the incoming exergy. The incoming exergy was calculated by [21]:
(18)Ȧin=ṁMmix∑iXiai,where the ṁ is the mass flow rate (kg/s) and the Mmix is the molecular weight of the mixture, respectively. The ai is the specific availability of the species i (J/kg), which could be obtained from:
(19)ai=hi−hi,0−T0si−si,0+V22+gz+aich,where the h0 and s0 are the enthalpy and entropy of species i under the reference temperature condition (298 K), respectively. The V, g, and z are the velocity (m/s), gravity (m2/s), and the axial distance (m), respectively. The aich is the specific chemical availability of the species i (J/kg) [34]. In this study, the specific chemical availability of each gas stream is obtained from Szargut [35].


## 3. Result and Discussions

### 3.1. Experimental Result

To validate the accuracy of the numerical simulation, the flame structure and flame temperature distribution were determined experimentally under variousR ratios and compared with the numerical results. Figure 3 illustrates the structural evolution of CH4–N2O diffusion flames with the R ratio varying from 0 to 10. The results indicate that at R ratios lower than 3, these flames maintained a single-flame structure and exhibited a central CH4–N2O diffusion flame with a bright yellow flame tip surrounded by a blue CH4–air diffusion flame anchored on the periphery of the fuel port. When the R ratio was greater than or equal to 3, the entrainment effect between CH4 and N2O streams became substantial [36]. Thus, fuel was entrained in the central oxidizer stream, and an inner flame was formed and anchored on the rim of the oxidizer port. Thus, the flame structure changed to a dual-flame structure under the aforementioned condition. The height of the outer diffusion flame increased from 8.8 to 9.16 mm above the burner as the R ratio increased from 0 to 2. However, when the R ratio was 3, the dual-flame structure appeared, but the height of the outer diffusion flame suddenly decreased to 8.9 mm. The flame height and the luminosity of the yellow flame tip increased with an increase in the R ratio. The maximum flame height of 9.76 mm was achieved at an R ratio of 6. As the R ratio increased from 6 to 10, the flame height decreased again, and the luminous flame zone shrank and moved upstream. The minimum flame height of 6.36 mm was achieved when R was 10. Moreover, the height of the inner flame anchored on the rim of the fuel port increased from 0.36 to 1.84 mm when the R ratio increased from 3 to 10. This result is attributed to the corresponding increase in the velocity of the oxidizer flow at the inlet. The inner flames exhibited a dual-flame structure comprising an internal fuel-lean branch and an external fuel-rich branch. Li et al. [37, 38] demonstrated the onset of a duel-flame structure in hydrocarbon fuel–N2O diffusion flames through theoretical analysis. The temperature and reaction rate of C2H4–N2O diffusion flames are higher than those of C2H4/N2/½O2 diffusion flames because of the higher heat release from N2O decomposition in C2H4–N2O diffusion flames.Figure 3
Photograph of variations in the flame structure with theR ratio.To validate the numerical results, the experimental flame structure and temperature distribution of CH4–N2O diffusion flames at an R ratio of 1 were compared with the corresponding numerical predictions. Figure 4(a) illustrates the experimental flame image and the numerical flame temperature distribution overlaid with heat release rate contours (dark grey color lines) and three red lines indicating axial positions. This figure was used to compare the experimental and numerical temperature distributions at heights above the burner (HAB) values of 4, 8, and 12 mm. The numerical flame temperature distribution revealed that the high-temperature region was distributed along the diffusion flame sheet and that the temperature of the yellow flame tip was relatively low. In addition, the numerical heat release rate and temperature at the exit of the inner oxidizer tube were considerably high. This result implied the existence of an exothermal N2O decomposition reaction in the vicinity of the exit of the oxidizer tube; however, no flame was sustained. In summary, the high-temperature region was scattered in the vicinity of the primary heat release, and the yellow flame tip region is attributed to soot formation due to insufficient oxidation at low temperatures. Moreover, the heat was generated through the N2O decomposition reaction around the exit of the oxidizer tube.Figure 4
(a) Experimental flame image and numerical temperature distribution overlaid with heat release rate contours (dark gray color lines) and experimental and numerical temperature distributions along the radial direction at HAB values of (b) 4, (c) 8, and (d) 12 mm.
(a)(b)(c)(d)Figures4(b)–4(d) display a comparison of the experimental and numerical flame temperature distributions. The experimental flame temperatures were determined using an R-type thermocouple. Because of the high-temperature limit of the R-type thermocouple, the radial temperature distribution could not be measured completely, especially in a high-temperature zone. The measured temperature was subjected to radiation correction so that the corrected high-temperature value would exceed the high-temperature limit of the R-type thermocouple. The measured temperatures were lower than the predicted values, and the measurement position approached the high-temperature zone (temperature higher than 2000 K). This high-temperature discrepancy in the experimental and numerical results is clearly illustrated in Figures 4(b)–4(d). The maximum temperature discrepancy of 5.29% occurred at the innermost radial position (~2.8 mm in the radial position) depicted in Figure 4(c). The measured temperatures were greater than the numerical predictions for all the outermost radial positions. For example, the maximum temperature discrepancy was 8.16% and 13.33% at HAB values of 4 and 12 mm, respectively. The temperature values and temperature distribution were consistent between the experimental and numerical results. Thus, accurate numerical results were obtained in this study.To verify the accuracy of the obtained numerical flame structure, flame chemiluminescence imaging was performed. CH∗ is a short-lived flame radical that describes the reaction zone rather than the reactive interface only. Images of CH∗ were captured using a 16-bit intensified charge-coupled device with a 470 nm narrow bandpass filter (iStar–SCMOS–18F–E3, Andor Technology Limited, UK). To reduce the contamination when integrating the radical chemiluminescence intensity along the line of sight, Abel’s deconvolution was conducted, and the CH∗ image was then reconstructed accordingly. Figure 5(a) illustrates the CH∗ chemiluminescence image of CH4–N2O diffusion flames with an R ratio of 1, and Figure 5(b) depicts the distribution of the numerical CH mole fraction overlaid with OH and C2H2 mole fraction contours (white and yellow lines, respectively).Figure 5
(a) CH chemiluminescence image and (b) numerical CH mole fraction overlaid with OH and C2H2 mole fraction contours (white and yellow lines, respectively) under an R ratio of 1.Figure5(a) indicates that CH∗ was present in the flame sheet and flame tip. The CH radical is a dominant species in the predissociation and pyrolysis reactions of methane-containing diffusion flames. As displayed in Figure 5(b), in the simulations, the CH radicals concentrated in the major chemical reaction zone. C2H2 radicals, which are a precursor to soot formation, collected at flame tips. However, the OH radicals were scattered in the major reaction zone and high-temperature zone. The flame heights determined from the CH∗ chemiluminescence images and computed CH radical distribution were 8 and 9 mm, respectively. The distributions of these two CH radicals were marginally different; however, the main flame structure was similar in the experiments and simulations. Thus, the numerical results obtained according to the USM reaction mechanism had high accuracy.


### 3.2. Numerical Results

Figure6 illustrates the numerical results of temperature distributions and CO2 mole fraction distribution overlaid with the numerical contours of the heat release rate and H2O mole fraction distribution for three oxidizer conditions. Figures 6(a) and 6(b) compare the numerical results in oxidizer conditions of air and oxygen-enriched mixed gas (67% nitrogen and 33% oxygen) at the Rratio=1. The temperature distributions of these two cases were similar but slightly higher in the air condition. Figure 7 illustrates the numerical results of temperature distribution overlaid with the numerical contours of the O2 mole fraction. The results imply that the oxygen concentration was higher near the vicinity of the center nozzle rim in the oxygen-enriched case. It is beneficial to the combustion process to cause the reaction earlier and shorten the flame length than in the air case. The high-temperature area was located between 9 and 11.5 mm HABs for the air case and was located between 8 and 10 mm HABs for the oxygen-enriched case along the center line. The maximum temperature in the case of oxygen-enriched was slightly lower than the maximum temperature in the case of air. The value of the maximum temperature in air and oxygen-enriched cases are similar; both of them are about 2050 K. In this R ratio condition, the heat release rate has no significant difference between these two cases. The maximum value of the heat release rate is both 5 W, which is located near the vicinity of the fuel nozzle rim. But just like the temperature distribution, the heat release rate distribution, which corresponds to the high-temperature region, was higher in the case of air. The location in the axial direction was between 9 mm and 11 mm HABs for the air case and between 7.3 and 9 mm HABs for the oxygen-enriched case along the center line. The right panels of Figures 6(a) and 6(b) indicate that the distributions of the numerical CO2 and H2O mole fractions were consistent with the temperature distribution of the diffusion flame. The maximum value of CO2 concentration was similar in these two cases (about 0.94), but the CO2 distribution in the air case was larger than in the oxygen-enriched case. In addition, the maximum value of H2O concentration was higher in the oxygen-enriched case (0.2, and 0.165 for the air case), but the distribution of H2O was still narrower in the oxygen-enriched case.Figure 6
Temperature and CO2 mole fraction distributions overlaid with contours of the heat release rate and H2O mole fraction: results obtained when using (a) N2O under an R ratio of 1, (b) N2O under an R ratio of 3, and (c) an oxygen-enriched mixture.
(a)(b)(c)Figure 7
Temperature and mole fraction of O2 distributions in the case of (a) air (b) oxygen-enriched mixture at Rratio=1.
(a)(b)Figures6(b) and 6(c) compare the numerical results in the oxidizer condition of oxygen-enriched mixed gas (67% nitrogen and 33% oxygen) and N2O at the Rratio=1. The numerical result of temperature distribution in the condition of N2O as the oxidizer is higher than in the condition of oxygen-enriched mixed gas. The maximum temperatures of oxygen-enriched mixed gas and N2O were 2044 and 2457 K, respectively. The high-temperature region of the diffusion flame depicted in Figure 6(c) is located more downstream than that of the diffusion flame depicted in Figure 6(b). The high-temperature area was located between HAB values of 8 and 10 mm in the oxygen-enriched case and between HAB values of 9 and 12 mm when using N2O as an oxidizer. Moreover, when using N2O as an oxidizer, a high-temperature zone distributed in the vicinity of the central nozzle exit contributed to the thermal effect of N2O self-decomposition. It was also found in the heat release rate at the exit of the oxidizer port. The numerical heat release rate in the outer diffusion flame had a wider distribution when using N2O than when using oxygen-enriched mixed gas; however, the heat release did not differ considerably between these two cases. The maximum heat release rate near the vicinity of the fuel nozzle rim (around 0–0.5 mm in the axial direction and 3–4 mm in the radial direction) was approximately 5 W. However, when using N2O, higher heat release values (maximum value of approximately 15 W) were observed near the exit of the oxidizer nozzle, corresponding to the high-temperature area. The right panels of Figures 6(b) and 6(c) indicate that the distributions of the numerical CO2 and H2O mole fractions were consistent with the temperature distribution of the diffusion flame. The numerical distributions of CO2 and H2O were wider and situated more downstream of the outer region when using N2O than when using oxygen-enriched mixed gas. When using N2O under an R value of 1, the presence of CO2 and H2O extended to the inner oxidizer nozzle (Figure 6(c)). This result might indicate that methane diffuses toward the inner oxidizer tube and partially reacts with oxygen generated through N2O decomposition to produce H2O and CO2.Figures8 and 9 illustrate the distribution of temperature, flow velocity, and essential species concentration in the region near the center nozzle rim. Firstly, Figure 8 displays the temperature distribution overlaid with the vector vectors on the left-hand-side panel and HNCO mole fraction distribution overlaid with the HO2 mole fraction on the right-hand-side panel. Hydroperoxyl (HO2) could be seen as the indication of the preignition region. It would form the hydroperoxides (H2O2) in the low-temperature area (about 400 K to 1000 K) through R. 23 (HO2+HO2⟶H2O2+O2) and govern the low-temperature oxidation [39]. The presence of isocyanic acid (HNCO) is associated with N2O. HNCO is prone to react with H and O radical and yield NH or NH2. The NH and NH2 can react with O and product NOx emission, leading to the increase of NOx emission in CH4/N2O flames [19]. In Figures 8(a) and 8(b), there was no significant difference between air and oxygen-enriched cases. In the left-hand-side panel Figure 8(b), the velocity was slightly higher in the condition of oxygen-enriched, but the flow direction was similar in both cases, which was pointed to downstream. On the right-hand-side panel of Figures 8(a) and 8(b), the HNCO and HO2 were distributed in a wider area in the condition of oxygen-enriched than in the air case, but the maximum values of HNCO and HO2 mole fractions were similar in both cases (1.4×10−4 and 1.3×10−4 for air and oxygen-enriched cases, respectively). Because of the same components of the oxidizer and no different structure between the air and oxygen-enriched cases, these two cases were very similar in these parameters. In the comparison of Figures 8(b) and 8(c), the magnitude of the flow velocity in the center tube was accelerated due to the high-temperature region induced by N2O decomposition. These phenomena led to the fuel flow dragged toward the center line and enhanced the entrainment effect. In addition, HNCO has a high mole concentration (maximum was 8×10−4) congregated near the inner side of the central oxidizer tube and is consistent with the high-temperature region. Yet, HNCO is not found in the inner region of the central oxidizer tube in Figure 8(b). The difference came from the reverse R. 540 (HNCO⟶NH+CO) and the reverse R. 541 (HNCO+H⟶NH2+CO), which would produce HNCO, due to the relative equation to the N2O, including the reverse R. 554 (NH+NO⟶N2O+H), the reverse R. 556 (NH2+H⟶NH+H2), and the reverse R. 558 (NH2+OH⟶NH+H2O).Figure 8
Temperature and mole fraction distributions for HNCO as well as vector field and mole fraction distributions for HO2 when using different oxidizers: (a) air, (b) oxygen-enriched gas, and (c) N2O under an R ratio of 1.Figure 9
Mole fractions of CH4 and OH distributions as well as the mole fractions of H and O when using different oxidizers: (a) air, (b) oxygen-enriched gas, and (c) N2O under an R ratio of 1.For the HO2 distribution in Figure 8(c), there was a high concentration (maximum reached 3.2×10−4, which was almost three times greater than the outer region) distributed inside the center tube and located further upstream than the high-temperature region. However, in Figure 8(b), it has a slightly higher concentration (maximum value was 1.6×10−4) and wider distribution (starting from 2.1 mm in a radial direction) of HO2 in the outer region, but it is still similar to the case of N2O. It could be seen as the intermediate product of the reaction of the N2O and methane; the reactions R. 51 (HCO+O2⟶HO2+CO), R. 83 (CH2O+O2⟶HCO+HO2), and R. 578 (N2O+OH⟶N2+HO2), which could contribute to the HO2 formation, would be enhanced in the high-temperature zone near the vicinity of the center nozzle rim. The reactions, which had a significant difference between the two cases, were related to the radical OH, H, and O.Figure9 displays the CH4 mole fraction distribution overlaid with the H mole fraction on the left-hand-side panel and OH mole fraction distribution overlaid with the O mole fraction on the right-hand-side panel. In Figures 9(a) and 9(b), it could be found that there was a similar distribution of each species between air and oxygen-enriched cases. But, the distribution of each species in the conditions of air was slightly wider than the condition of oxygen-enriched. For the O radical, the maximum value was higher in oxygen-enriched case (2.4×10−3, and 1.8×10−3 for air case), which may cause more oxygen to be inputted in the oxygen-enriched condition. But, for the H radical, the maximum value was lower in the oxygen-enriched case (2.3×10−3, and 2.9×10−3 for air case), which means the reaction in the air case was more intense than in the oxygen-enriched case and caused the temperature to slightly lower in the condition of oxygen-enriched at the Rratio=1. Although there are some differences between air and oxygen-enriched case, these two conditions are still very close due to the similar structure (shown in Figure 6) between these two cases).The comparison of the oxygen-enriched and N2O case is shown in Figures 9(b) and 9(c). On the left-hand-side panel of Figure 9(b), it was clear to find that the methane would diffuse into the center tube in the oxygen-enriched case. But in Figure 9(c), the methane would start to decompose around the high-temperature region near the vicinity of the center nozzle rim, which could not be found in Figures 9(a) and 9(b). In Figure 9(c), it could be further explained why there was HO2, CO2, and H2O located near the vicinity of the center nozzle rim or inside the center tube in Figure 6(c) and Figure 8(c), although there was no flame formed in that region. Moreover, due to the decomposition of the methane in Figure 9(c), there was another high concentration of H radical (maximum value was 4.3×10−3) located near the vicinity of the center nozzle rim, which corresponds to the high-temperature region in Figure 8(c). In the outer region, the distribution was similar in both cases, but the intensity was slightly higher in the case of N2O. The peak value of the H radical was 2.3×10−3 and 2.8×10−3 for the cases of oxygen-enriched mixture and N2O, respectively. On the right-hand-side panel of Figure 9(c), it could be found that the distribution of the OH and O radicals were similar in both cases, but the intensity was higher in the case of N2O, which means there was a more intense reaction in that case. However, the most significant difference located inside the center tube was a high concentration of OH and O radicals in that region, which was further upstream than the H radical. These phenomena reveal that N2O started to decompose inside the center tube, which could not be found in Figures 9(a) and 9(b). In Figure 9, the OH, H, and O radicals have an intense distribution near the vicinity of the center nozzle rim in the case of N2O. With the inner distribution of these species, the reaction R. 3 (H2+OH⟶H+H2O), R. 30 (CO+O⟶CO2), and R. 31 (CO+OH⟶H+CO2) would be enhanced, causing more H2O and CO2 being produced near the vicinity of the center nozzle rim in the case of N2O.The distributions and concentrations of the final products (CO2 and H2O) were different in the oxygen-enriched, R1, and R3 cases, in which the fuel flow rate was the same. To determine these differences, the major reaction pathways for the production of the final products (CO2 and H2O) from fuel (CH4) were considered. Figure 10 illustrates the major reaction pathways for the formation of the product gases. The reaction constant (k) of each reaction can be determined using the Arrhenius expression as follows:
(20)k=ATbexp−EaRTwhere A, b, and Ea are the preexponential factor, temperature exponent, and activation energy, respectively. The reaction rate (Δυ) can then be calculated by multiplying the reaction constant with the molar concentration of the reactive species. Subsequently, the overall reaction rate is calculated using the following equation:
(21)∆υtot=∭Δυr,θ,zdV=∫0L∫0R2πrΔυr,zdrdzFigure 10
Major reaction pathways for the formation of CO2 and H2O when using different oxidizers: (a) air, (b) oxygen-enriched mixture, and (c) N2O at Rratio=1.
(a)(b)(c)Figure10 depicts the main reaction paths in the oxygen-enriched and R1 cases. Similar reaction pathways existed in these cases; however, the reaction rates were different. CH4 initially decomposed into CH3, H2, and H2O through R. 122 (CH4+H⟶CH3+H2) and R. 124 (CH4+OH⟶CH3+H2O), as displayed in Figure 10. Subsequently, H2O was produced through R. 3 (H2+OH⟶H2O+H). With regard to the CO2 formation pathway, CH3 transformed into CH2O through R. 87 (CH3+O⟶CH2O+H). CH2O was then converted to HCO through the R. 80 (CH2O+H⟶H2+HCO), R. 82 (CH2O+OH⟶H2O+HCO), and reverse R. 45 (H+HCO⟶CH2O) reactions. Subsequently, CO was produced from HCO through R. 46 (HCO+H⟶H2+CO), R. 49 (HCO+OH⟶H2O+CO), and R. 51. CH2CO was formed through R. 85 (CH2O+CH⟶CH2CO+H), which contributed to the formation of CO through the R. 181 (CH2CO+H⟶CO+CH3) and reverse R. 61 (CO+CH2⟶CH2CO) reactions. Ultimately, CO transformed into CO2 mainly through R. 30, R. 31, R. 33 (CO+O2⟶CO2+O), and R. 34 (especially R. 30 and R. 31) reactions. In Figures 10(a) and 10(b), it can be found that there was no significant difference between these two cases in the major reaction pathway, but the magnitude of the reaction rate has a difference with different conditions. There are more CH2O, which came from the CH3 through the reaction R. 87 (CH3+O⟶CH2O+H), transferred to HCO through the reaction R. 45 REV (CH2O⟶HCO+H). But, the CO, which came from the reaction R. 46 (HCO+H⟶H2+CO), became lower in the condition of the oxygen-enriched compared with the air case. Besides these two obvious differences, most of the major reactions in the condition of air were more intense than in the condition of oxygen-enriched. However, there are some differences between these two cases, but the reaction and magnitude of major reaction pathways are still similar in these two cases.As displayed in Figure10(c), when the oxygen-enriched mixture was replaced by N2O under an R value of 1, the intensities of R. 122 and R. 124 increased, which resulted in the increased formation of CH3, H2O, and H2. This phenomenon enhanced R. 87, which resulted in the formation of additional CH2O. Moreover, additional HCO was formed through the enhancement of the R. 80, R. 82, and reverse R. 45 reactions (Figure 10(c)). R. 46, R. 49, and R. 51 were enhanced marginally in the R1 case compared with the oxygen-enriched case; however, in the R1 case, CO formation was dominated by R. 541, which mainly came from the N2O reaction (Figure 10(c)). CO2 production was then enhanced mainly through R. 30 and R. 31. Moreover, because the decomposition reaction involving N2O at the exit of the oxidizer port had been completed, in addition to R. 541, many other chemical reactions, including R. 543, R. 544, and R. 578, occurred near the oxidizer nozzle. Because of the increased CO and HO2 production, additional CO2 and H2 were produced through the enhancement of R. 19, R. 30, R. 31, and R. 34. Furthermore, additional H2 was produced through the enhancement of R. 19, R. 80, R. 122, and R. 124, which led to the increased production of H2O further downstream through R. 3. From Figures 6–10, it could be found that there was a significant difference near the vicinity of the center nozzle rim between the cases of oxygen-enriched mixture and N2O, which was caused by the different reactions from the process of N2O combustion.


### 3.3. Analysis of Entropy Generation Rate and Exergy

To investigate the thermal effect of N2O decomposition and the effect of oxidizer velocity on the entropy generation rate, an oxygen-enriched mixture and N2O (R=1) were used as oxidizers. Figures 11 and 12 show the distributions of the entropy generation rates contributed by heat conduction, mass diffusion, and the chemical reaction as well as the total entropy generation rate at the Rratio=1. The flame structures in both conditions are a single diffusion flame at this R ratio condition. The heat conduction term had a strong distribution near the nozzle and around the high-temperature region due to the high-temperature gradient, which came from the substantial temperature change. In addition, the mass diffusion term was distributed near the reaction region, which had the most intense reaction causing the significant species to change. Besides, the chemical reaction term had strong distribution in the major reaction region obviously. The comparison of the air and oxygen-enriched cases was shown in Figure 11. In Figure 11(d), the peak values were located at the similar location in air and oxygen-enriched cases (about 0.06 mm HABs in axial direction and about 3.0 mm in radial direction). Because of both flames were not attached to the nozzle, there was a small space for the mixing between methane and the air (coflow). Therefore, the chemical reaction term (Figure 11(c)) and the mass diffusion term (Figure 11(b)) both have the peak value at that place where the reactions and the species gradient could be enhanced due to the premixing process in both cases. The contribution to the total entropy generation was dominated by the chemical reaction term in air and oxygen-enriched cases. The chemical reaction term was about 1.11 times and 3.73 times greater than the heat conduction term and the mass diffusion term in the air case, respectively. And it was about 1.14 times and 3.44 times greater than the heat conduction term and mass diffusion term in the oxygen-enriched case, respectively. Furthermore, the temperature and heat release would be narrower in the oxygen-enriched case so that the entropy generation rate of three terms would distribute into a narrower area in the oxygen-enriched case (shown in Figures 11(a), 11(b), and 11(c)). Besides, the air case has slightly stronger chemical reactions than the oxygen-enriched case, causing higher temperature and species gradient. So, the entropy generation of three terms was slightly higher in the air case. The total entropy generation in the air case was about 1.13 times greater than in the oxygen-enriched case.Figure 11
Entropy generation rates contributed by (a) heat conduction, (b) mass diffusion, and (c) the chemical reaction in the air and oxygen-enriched cases as well as the (d) distribution of the overall entropy in these cases.Figure 12
Entropy generation rates contributed by (a) heat conduction, (b) mass diffusion, and (c) the chemical reaction in the oxygen-enriched and R1 cases as well as the (d) distribution of the overall entropy in these cases.Due to the chemical reaction term dominating the contribution of entropy generation, the major reaction pathway would be conducted and presented in Figures10(a) and 10(b) with a slight difference.Figure12 presents the entropy generation rates in the oxygen-enriched and R1 cases. In Figure 12(d), the peak entropy generation rate in the oxygen-enriched case occurred near the vicinity of the fuel nozzle rim (HABs of 0.06 mm in the axial direction and 3.0 mm in the radial direction). However, in the R1 case, the peak entropy generation rate occurred inside the oxidizer tube. Compared with the oxygen-enriched case, higher heat release occurred in the R1 case because of N2O decomposition, which resulted in the reactions becoming more intense in the R1 case; this caused increases in the temperature and species gradients near the vicinity of the central nozzle in this case. Therefore, high entropy generation rates contributed by heat conduction, mass diffusion, and the chemical reaction (especially the chemical reaction) were observed near the vicinity of the central nozzle rim (Figures 12(a)–12(c)). Thus, the total entropy generated in the R1 case was approximately 2.26 times higher than that generated in the oxygen-enriched case. Although the peak entropy values occurred at different locations in these two cases, the chemical reaction dominated the contribution to the total entropy generation rate in both cases. The entropy contributed by the chemical reaction was approximately 1.14 and 3.44 times higher than that contributed by heat conduction and mass diffusion, respectively, in the oxygen-enriched case. The entropy contributed by the chemical reaction was approximately 2.01 and 6.93 times higher than that contributed by heat conduction and mass diffusion, respectively, in the R1 case. Moreover, as depicted in Figures 12(a)–12(c), the distributions of the temperature and heat release rate in the outer region were considerably wider in the R1 case than in the oxygen-enriched case; that is, the volumetric entropy generation rates contributed by heat conduction, mass diffusion, and the chemical reaction were higher in the R1 case than in the oxygen-enriched case. However, the magnitudes were similar in these two cases because of the similar temperatures and reaction intensities in the cases. In addition, a single-flame structure was observed in the oxygen-enriched and R1 cases. Therefore, the distribution of the entropy generation rate in the outer region was similar in these cases. Because the chemical reaction was the main contributor to the overall entropy generation rate in both cases, the entropy generation rates contributed by the chemical reactions of major chemical species were determined. According to the results, the CO2 and H2O production varied considerably in the two cases. On the basis of the major reaction pathways for the formation of CO2 and H2O that are displayed in Figure 10, several differences in chemical reactions were identified between the oxygen-enriched and R1 cases.With the results, the significant difference between three different oxidizers at the condition of R1 almost came from the chemical reaction, so the volumetric entropy generation rate along the stoichiometric line, which could have the strongest reaction, would be conducted in Figure13(a). Two stoichiometric lines are observed in Figure 14 because two oxidizers existed, that is, one is situated inside, and the other is situated outside of the fuel port. The local equivalence ratio (ϕ) was calculated by the following equation [40]:
(22)ϕ=f1−fsfs1−f,where f and fs are the mixture fraction and the stoichiometric mixture fraction, respectively. The mixture fraction would be determined through the equation below [21]:
(23)f=2YC−YC,oxidizer/WC+YH−YH,oxidizer/2WH−YO−YO,oxidizer/WO2YC,fuel−YC,oxidizer/WC+YH,fuel−YH,oxidizer/2WH−YO,fuel−YO,oxidizer/WOwhere Y and W are the mass fraction and atomic weights (of the C, H, and O atoms), respectively. The stoichiometric mixture fractions were 0.055, 0.0826, and 0.0833 for the CH4/air, CH4/67%N2+33%O2, and CH4/N2O flames, respectively.Figure 13
(a) Total volumetric entropy generation rate and normalized entropy generation rates along the stoichiometric line in the (b) air, (c) oxygen-enriched, and (d) N2O cases at Rratio=1.Figure 14
(a) Total exergy and (b) normalized exergy observed in different oxidizer conditions.
(a)(b)The top panel of Figure13(a) depicts the outer stoichiometric line (coflow), and the bottom panel of Figure 13(a) depicts the inner stoichiometric line (oxidizer). Because the flame heights were different in the R1, air, and oxygen-enriched cases, the x-axis is the normalized axial direction (local axial distance divided by the maximum axial distance) for comparing these cases. As depicted in the top panel of Figure 13(a), the peak entropy generation rate in the R1 case (almost 1.2×106W/m3 K) occurred at a location where Z/Zmax=0.02. This rate then decreased suddenly and reached a stable value between approximately 5×104 and 7.5×104W/m3 K at locations where Z/Zmax>0.2. The aforementioned behavior was similar to that observed in the air case, in which the peak entropy generation rate (~9×105W/m3 K) occurred at a location where Z/Zmax=0.017, and this rate then decreased to the same stable value as in the R1 case at locations where Z/Zmax>0.041. In the oxygen-enriched case, the peak entropy generation rate (~5.3×105W/m3 K, which is smaller than the maximum entropy generation rate in the other two conditions) occurred at a location where Z/Zmax=0.072. This rate then decreased gradually until the minimum value of approximately 5.0×104W/m3 K was achieved (at the top of the stoichiometric line). This value differed from the minimum entropy generation rate achieved in the other two cases. As shown in the bottom panel of Figure 13(a), in the R1 case, the entropy generation rate (maximum value of ~2.6×106W/m3 K) was higher at locations further upstream of the nozzle rim. However, in the other two cases, this rate decreased with an increase in the flame height, with the decrease being higher in the oxygen-enriched case than in the air case.Subsequently, the dominant term should be found along the stoichiometric line. The relative entropy generation rates for the three oxidizers in the R1 case are displayed in Figures13(b)–13(d). As in the case of Figure 13(a), the top and bottom panels of the aforementioned three figures depict the outer and inner stoichiometric lines in each case. Moreover, the x-axis is still the normalized axial direction for comparison. As shown in the top panels of Figures 13(b)–13(d), heat conduction was the dominant contributor to the entropy generation when Z/Zmax<0, where it was close to the wall and did not have the reaction in these three cases. However, when Z/Zmax>0, the chemical reaction was the dominant contributor to the entropy generation in the R1, oxygen-enriched, and air cases. In the oxygen-enriched and R1 cases, mass diffusion had a higher contribution to entropy generation than did heat conduction when Z/Zmax>0. However, in the air case, mass diffusion and heat conduction had similar contributions to total entropy generation when Z/Zmax>0. The bottom panels of Figures 13(b)–13(d) indicate that mass diffusion dominated the contributions to entropy generation for the inner stoichiometric line. In the air and oxygen-enriched cases, the contribution of heat conduction to entropy generation gradually increased with flame height. However, in the R1 case, the chemical reaction dominated the contributions to entropy generation for the inner stoichiometric line because several reactions were induced through N2O decomposition near the central nozzle rim. Heat conduction exhibited the second-highest contribution to the entropy generation in this case because of the high temperature in the aforementioned region (Figure 6(c)).After analyzing the volumetric entropy distribution, the exergy, which represents the energy that can be used in the combustion process in the air, the oxygen-rich and R1 cases were examined in Figure14. Figure 14(a) displays the total exergy input and the exergy consumed by irreversibility in these cases. The total exergy values in the air, oxygen-rich, and R1 cases were 9068.6, 9073.6, and 9225.4 W, respectively. Because N2O has higher chemical availability than does the adopted oxygen-enriched mixture, the exergy input was higher in the R1 case than in the oxygen-enriched case.In Figure14(a), the air and oxygen-enriched cases have similar exergy remained, and the oxygen-enriched case was even slightly higher than the air case. The difference was about 135.9 W between these two cases. The values of the heat conduction, mass diffusion, and chemical reaction terms in the air case were 1.2, 1.02, and 1.1 times higher than those in the oxygen-enriched case. The second law efficiencies are 87.03% for the air case and 88.48% for the oxygen-enriched case. They have similar flame structures and reaction pathways in both cases. Besides, higher exergy was consumed in the R1 case than in the oxygen-enriched case, with the difference in exergy being approximately 1322 W. The values of the heat conduction, mass diffusion, and chemical reaction terms were 1.7, 1.45, and 3 times higher in the R1 case than in the oxygen-enriched case. Because the value of the mass diffusion term was lower than those of the heat conduction and chemical reaction terms (the chemical reaction term was more than three times higher than the mass diffusion term), the difference was dominated by the heat conduction and chemical reaction terms, especially the chemical reaction term. This result might be attributed to the heat release caused by the self-decomposition of N2O. Therefore, different reaction pathways exist when using N2O and oxygen-enriched gas as oxidizers. Consequently, the value of the chemical reaction term differs considerably in the R1 and oxygen-enriched cases. Moreover, the temperature was higher in the R1 case than in the oxygen-enriched case. Therefore, the values of the heat conduction term differed between these cases.Figure14(b) depicts the percentage contributions of the heat conduction, mass diffusion, and chemical reaction terms to the incoming exergy. The heat conduction and chemical reaction terms, whose contributions to the incoming exergy were 5.4% and 6.0% for air case and 4.6% and 5.3% for oxygen-enriched case, were both dominated by the consumption of the exergy. There was a slight difference between the air and oxygen-enriched case. But when the oxidizer was changed from the oxygen-enriched mixture to the N2O, the chemical reaction term was dominated by the exergy consumed, which occupied 15.7% of incoming exergy in the same R ratio condition. Besides, the heat conduction term had a significant difference between the condition of the oxygen-enriched and N2O, which increased from 4.6% to 7.8%, due to the increase in the temperature. In addition, 87.0%, 88.5%, and 74.3% of incoming exergy remained in the air, oxygen-enriched, and R1 cases.


## 3.1. Experimental Result

To validate the accuracy of the numerical simulation, the flame structure and flame temperature distribution were determined experimentally under variousR ratios and compared with the numerical results. Figure 3 illustrates the structural evolution of CH4–N2O diffusion flames with the R ratio varying from 0 to 10. The results indicate that at R ratios lower than 3, these flames maintained a single-flame structure and exhibited a central CH4–N2O diffusion flame with a bright yellow flame tip surrounded by a blue CH4–air diffusion flame anchored on the periphery of the fuel port. When the R ratio was greater than or equal to 3, the entrainment effect between CH4 and N2O streams became substantial [36]. Thus, fuel was entrained in the central oxidizer stream, and an inner flame was formed and anchored on the rim of the oxidizer port. Thus, the flame structure changed to a dual-flame structure under the aforementioned condition. The height of the outer diffusion flame increased from 8.8 to 9.16 mm above the burner as the R ratio increased from 0 to 2. However, when the R ratio was 3, the dual-flame structure appeared, but the height of the outer diffusion flame suddenly decreased to 8.9 mm. The flame height and the luminosity of the yellow flame tip increased with an increase in the R ratio. The maximum flame height of 9.76 mm was achieved at an R ratio of 6. As the R ratio increased from 6 to 10, the flame height decreased again, and the luminous flame zone shrank and moved upstream. The minimum flame height of 6.36 mm was achieved when R was 10. Moreover, the height of the inner flame anchored on the rim of the fuel port increased from 0.36 to 1.84 mm when the R ratio increased from 3 to 10. This result is attributed to the corresponding increase in the velocity of the oxidizer flow at the inlet. The inner flames exhibited a dual-flame structure comprising an internal fuel-lean branch and an external fuel-rich branch. Li et al. [37, 38] demonstrated the onset of a duel-flame structure in hydrocarbon fuel–N2O diffusion flames through theoretical analysis. The temperature and reaction rate of C2H4–N2O diffusion flames are higher than those of C2H4/N2/½O2 diffusion flames because of the higher heat release from N2O decomposition in C2H4–N2O diffusion flames.Figure 3
Photograph of variations in the flame structure with theR ratio.To validate the numerical results, the experimental flame structure and temperature distribution of CH4–N2O diffusion flames at an R ratio of 1 were compared with the corresponding numerical predictions. Figure 4(a) illustrates the experimental flame image and the numerical flame temperature distribution overlaid with heat release rate contours (dark grey color lines) and three red lines indicating axial positions. This figure was used to compare the experimental and numerical temperature distributions at heights above the burner (HAB) values of 4, 8, and 12 mm. The numerical flame temperature distribution revealed that the high-temperature region was distributed along the diffusion flame sheet and that the temperature of the yellow flame tip was relatively low. In addition, the numerical heat release rate and temperature at the exit of the inner oxidizer tube were considerably high. This result implied the existence of an exothermal N2O decomposition reaction in the vicinity of the exit of the oxidizer tube; however, no flame was sustained. In summary, the high-temperature region was scattered in the vicinity of the primary heat release, and the yellow flame tip region is attributed to soot formation due to insufficient oxidation at low temperatures. Moreover, the heat was generated through the N2O decomposition reaction around the exit of the oxidizer tube.Figure 4
(a) Experimental flame image and numerical temperature distribution overlaid with heat release rate contours (dark gray color lines) and experimental and numerical temperature distributions along the radial direction at HAB values of (b) 4, (c) 8, and (d) 12 mm.
(a)(b)(c)(d)Figures4(b)–4(d) display a comparison of the experimental and numerical flame temperature distributions. The experimental flame temperatures were determined using an R-type thermocouple. Because of the high-temperature limit of the R-type thermocouple, the radial temperature distribution could not be measured completely, especially in a high-temperature zone. The measured temperature was subjected to radiation correction so that the corrected high-temperature value would exceed the high-temperature limit of the R-type thermocouple. The measured temperatures were lower than the predicted values, and the measurement position approached the high-temperature zone (temperature higher than 2000 K). This high-temperature discrepancy in the experimental and numerical results is clearly illustrated in Figures 4(b)–4(d). The maximum temperature discrepancy of 5.29% occurred at the innermost radial position (~2.8 mm in the radial position) depicted in Figure 4(c). The measured temperatures were greater than the numerical predictions for all the outermost radial positions. For example, the maximum temperature discrepancy was 8.16% and 13.33% at HAB values of 4 and 12 mm, respectively. The temperature values and temperature distribution were consistent between the experimental and numerical results. Thus, accurate numerical results were obtained in this study.To verify the accuracy of the obtained numerical flame structure, flame chemiluminescence imaging was performed. CH∗ is a short-lived flame radical that describes the reaction zone rather than the reactive interface only. Images of CH∗ were captured using a 16-bit intensified charge-coupled device with a 470 nm narrow bandpass filter (iStar–SCMOS–18F–E3, Andor Technology Limited, UK). To reduce the contamination when integrating the radical chemiluminescence intensity along the line of sight, Abel’s deconvolution was conducted, and the CH∗ image was then reconstructed accordingly. Figure 5(a) illustrates the CH∗ chemiluminescence image of CH4–N2O diffusion flames with an R ratio of 1, and Figure 5(b) depicts the distribution of the numerical CH mole fraction overlaid with OH and C2H2 mole fraction contours (white and yellow lines, respectively).Figure 5
(a) CH chemiluminescence image and (b) numerical CH mole fraction overlaid with OH and C2H2 mole fraction contours (white and yellow lines, respectively) under an R ratio of 1.Figure5(a) indicates that CH∗ was present in the flame sheet and flame tip. The CH radical is a dominant species in the predissociation and pyrolysis reactions of methane-containing diffusion flames. As displayed in Figure 5(b), in the simulations, the CH radicals concentrated in the major chemical reaction zone. C2H2 radicals, which are a precursor to soot formation, collected at flame tips. However, the OH radicals were scattered in the major reaction zone and high-temperature zone. The flame heights determined from the CH∗ chemiluminescence images and computed CH radical distribution were 8 and 9 mm, respectively. The distributions of these two CH radicals were marginally different; however, the main flame structure was similar in the experiments and simulations. Thus, the numerical results obtained according to the USM reaction mechanism had high accuracy.


## 3.2. Numerical Results

Figure6 illustrates the numerical results of temperature distributions and CO2 mole fraction distribution overlaid with the numerical contours of the heat release rate and H2O mole fraction distribution for three oxidizer conditions. Figures 6(a) and 6(b) compare the numerical results in oxidizer conditions of air and oxygen-enriched mixed gas (67% nitrogen and 33% oxygen) at the Rratio=1. The temperature distributions of these two cases were similar but slightly higher in the air condition. Figure 7 illustrates the numerical results of temperature distribution overlaid with the numerical contours of the O2 mole fraction. The results imply that the oxygen concentration was higher near the vicinity of the center nozzle rim in the oxygen-enriched case. It is beneficial to the combustion process to cause the reaction earlier and shorten the flame length than in the air case. The high-temperature area was located between 9 and 11.5 mm HABs for the air case and was located between 8 and 10 mm HABs for the oxygen-enriched case along the center line. The maximum temperature in the case of oxygen-enriched was slightly lower than the maximum temperature in the case of air. The value of the maximum temperature in air and oxygen-enriched cases are similar; both of them are about 2050 K. In this R ratio condition, the heat release rate has no significant difference between these two cases. The maximum value of the heat release rate is both 5 W, which is located near the vicinity of the fuel nozzle rim. But just like the temperature distribution, the heat release rate distribution, which corresponds to the high-temperature region, was higher in the case of air. The location in the axial direction was between 9 mm and 11 mm HABs for the air case and between 7.3 and 9 mm HABs for the oxygen-enriched case along the center line. The right panels of Figures 6(a) and 6(b) indicate that the distributions of the numerical CO2 and H2O mole fractions were consistent with the temperature distribution of the diffusion flame. The maximum value of CO2 concentration was similar in these two cases (about 0.94), but the CO2 distribution in the air case was larger than in the oxygen-enriched case. In addition, the maximum value of H2O concentration was higher in the oxygen-enriched case (0.2, and 0.165 for the air case), but the distribution of H2O was still narrower in the oxygen-enriched case.Figure 6
Temperature and CO2 mole fraction distributions overlaid with contours of the heat release rate and H2O mole fraction: results obtained when using (a) N2O under an R ratio of 1, (b) N2O under an R ratio of 3, and (c) an oxygen-enriched mixture.
(a)(b)(c)Figure 7
Temperature and mole fraction of O2 distributions in the case of (a) air (b) oxygen-enriched mixture at Rratio=1.
(a)(b)Figures6(b) and 6(c) compare the numerical results in the oxidizer condition of oxygen-enriched mixed gas (67% nitrogen and 33% oxygen) and N2O at the Rratio=1. The numerical result of temperature distribution in the condition of N2O as the oxidizer is higher than in the condition of oxygen-enriched mixed gas. The maximum temperatures of oxygen-enriched mixed gas and N2O were 2044 and 2457 K, respectively. The high-temperature region of the diffusion flame depicted in Figure 6(c) is located more downstream than that of the diffusion flame depicted in Figure 6(b). The high-temperature area was located between HAB values of 8 and 10 mm in the oxygen-enriched case and between HAB values of 9 and 12 mm when using N2O as an oxidizer. Moreover, when using N2O as an oxidizer, a high-temperature zone distributed in the vicinity of the central nozzle exit contributed to the thermal effect of N2O self-decomposition. It was also found in the heat release rate at the exit of the oxidizer port. The numerical heat release rate in the outer diffusion flame had a wider distribution when using N2O than when using oxygen-enriched mixed gas; however, the heat release did not differ considerably between these two cases. The maximum heat release rate near the vicinity of the fuel nozzle rim (around 0–0.5 mm in the axial direction and 3–4 mm in the radial direction) was approximately 5 W. However, when using N2O, higher heat release values (maximum value of approximately 15 W) were observed near the exit of the oxidizer nozzle, corresponding to the high-temperature area. The right panels of Figures 6(b) and 6(c) indicate that the distributions of the numerical CO2 and H2O mole fractions were consistent with the temperature distribution of the diffusion flame. The numerical distributions of CO2 and H2O were wider and situated more downstream of the outer region when using N2O than when using oxygen-enriched mixed gas. When using N2O under an R value of 1, the presence of CO2 and H2O extended to the inner oxidizer nozzle (Figure 6(c)). This result might indicate that methane diffuses toward the inner oxidizer tube and partially reacts with oxygen generated through N2O decomposition to produce H2O and CO2.Figures8 and 9 illustrate the distribution of temperature, flow velocity, and essential species concentration in the region near the center nozzle rim. Firstly, Figure 8 displays the temperature distribution overlaid with the vector vectors on the left-hand-side panel and HNCO mole fraction distribution overlaid with the HO2 mole fraction on the right-hand-side panel. Hydroperoxyl (HO2) could be seen as the indication of the preignition region. It would form the hydroperoxides (H2O2) in the low-temperature area (about 400 K to 1000 K) through R. 23 (HO2+HO2⟶H2O2+O2) and govern the low-temperature oxidation [39]. The presence of isocyanic acid (HNCO) is associated with N2O. HNCO is prone to react with H and O radical and yield NH or NH2. The NH and NH2 can react with O and product NOx emission, leading to the increase of NOx emission in CH4/N2O flames [19]. In Figures 8(a) and 8(b), there was no significant difference between air and oxygen-enriched cases. In the left-hand-side panel Figure 8(b), the velocity was slightly higher in the condition of oxygen-enriched, but the flow direction was similar in both cases, which was pointed to downstream. On the right-hand-side panel of Figures 8(a) and 8(b), the HNCO and HO2 were distributed in a wider area in the condition of oxygen-enriched than in the air case, but the maximum values of HNCO and HO2 mole fractions were similar in both cases (1.4×10−4 and 1.3×10−4 for air and oxygen-enriched cases, respectively). Because of the same components of the oxidizer and no different structure between the air and oxygen-enriched cases, these two cases were very similar in these parameters. In the comparison of Figures 8(b) and 8(c), the magnitude of the flow velocity in the center tube was accelerated due to the high-temperature region induced by N2O decomposition. These phenomena led to the fuel flow dragged toward the center line and enhanced the entrainment effect. In addition, HNCO has a high mole concentration (maximum was 8×10−4) congregated near the inner side of the central oxidizer tube and is consistent with the high-temperature region. Yet, HNCO is not found in the inner region of the central oxidizer tube in Figure 8(b). The difference came from the reverse R. 540 (HNCO⟶NH+CO) and the reverse R. 541 (HNCO+H⟶NH2+CO), which would produce HNCO, due to the relative equation to the N2O, including the reverse R. 554 (NH+NO⟶N2O+H), the reverse R. 556 (NH2+H⟶NH+H2), and the reverse R. 558 (NH2+OH⟶NH+H2O).Figure 8
Temperature and mole fraction distributions for HNCO as well as vector field and mole fraction distributions for HO2 when using different oxidizers: (a) air, (b) oxygen-enriched gas, and (c) N2O under an R ratio of 1.Figure 9
Mole fractions of CH4 and OH distributions as well as the mole fractions of H and O when using different oxidizers: (a) air, (b) oxygen-enriched gas, and (c) N2O under an R ratio of 1.For the HO2 distribution in Figure 8(c), there was a high concentration (maximum reached 3.2×10−4, which was almost three times greater than the outer region) distributed inside the center tube and located further upstream than the high-temperature region. However, in Figure 8(b), it has a slightly higher concentration (maximum value was 1.6×10−4) and wider distribution (starting from 2.1 mm in a radial direction) of HO2 in the outer region, but it is still similar to the case of N2O. It could be seen as the intermediate product of the reaction of the N2O and methane; the reactions R. 51 (HCO+O2⟶HO2+CO), R. 83 (CH2O+O2⟶HCO+HO2), and R. 578 (N2O+OH⟶N2+HO2), which could contribute to the HO2 formation, would be enhanced in the high-temperature zone near the vicinity of the center nozzle rim. The reactions, which had a significant difference between the two cases, were related to the radical OH, H, and O.Figure9 displays the CH4 mole fraction distribution overlaid with the H mole fraction on the left-hand-side panel and OH mole fraction distribution overlaid with the O mole fraction on the right-hand-side panel. In Figures 9(a) and 9(b), it could be found that there was a similar distribution of each species between air and oxygen-enriched cases. But, the distribution of each species in the conditions of air was slightly wider than the condition of oxygen-enriched. For the O radical, the maximum value was higher in oxygen-enriched case (2.4×10−3, and 1.8×10−3 for air case), which may cause more oxygen to be inputted in the oxygen-enriched condition. But, for the H radical, the maximum value was lower in the oxygen-enriched case (2.3×10−3, and 2.9×10−3 for air case), which means the reaction in the air case was more intense than in the oxygen-enriched case and caused the temperature to slightly lower in the condition of oxygen-enriched at the Rratio=1. Although there are some differences between air and oxygen-enriched case, these two conditions are still very close due to the similar structure (shown in Figure 6) between these two cases).The comparison of the oxygen-enriched and N2O case is shown in Figures 9(b) and 9(c). On the left-hand-side panel of Figure 9(b), it was clear to find that the methane would diffuse into the center tube in the oxygen-enriched case. But in Figure 9(c), the methane would start to decompose around the high-temperature region near the vicinity of the center nozzle rim, which could not be found in Figures 9(a) and 9(b). In Figure 9(c), it could be further explained why there was HO2, CO2, and H2O located near the vicinity of the center nozzle rim or inside the center tube in Figure 6(c) and Figure 8(c), although there was no flame formed in that region. Moreover, due to the decomposition of the methane in Figure 9(c), there was another high concentration of H radical (maximum value was 4.3×10−3) located near the vicinity of the center nozzle rim, which corresponds to the high-temperature region in Figure 8(c). In the outer region, the distribution was similar in both cases, but the intensity was slightly higher in the case of N2O. The peak value of the H radical was 2.3×10−3 and 2.8×10−3 for the cases of oxygen-enriched mixture and N2O, respectively. On the right-hand-side panel of Figure 9(c), it could be found that the distribution of the OH and O radicals were similar in both cases, but the intensity was higher in the case of N2O, which means there was a more intense reaction in that case. However, the most significant difference located inside the center tube was a high concentration of OH and O radicals in that region, which was further upstream than the H radical. These phenomena reveal that N2O started to decompose inside the center tube, which could not be found in Figures 9(a) and 9(b). In Figure 9, the OH, H, and O radicals have an intense distribution near the vicinity of the center nozzle rim in the case of N2O. With the inner distribution of these species, the reaction R. 3 (H2+OH⟶H+H2O), R. 30 (CO+O⟶CO2), and R. 31 (CO+OH⟶H+CO2) would be enhanced, causing more H2O and CO2 being produced near the vicinity of the center nozzle rim in the case of N2O.The distributions and concentrations of the final products (CO2 and H2O) were different in the oxygen-enriched, R1, and R3 cases, in which the fuel flow rate was the same. To determine these differences, the major reaction pathways for the production of the final products (CO2 and H2O) from fuel (CH4) were considered. Figure 10 illustrates the major reaction pathways for the formation of the product gases. The reaction constant (k) of each reaction can be determined using the Arrhenius expression as follows:
(20)k=ATbexp−EaRTwhere A, b, and Ea are the preexponential factor, temperature exponent, and activation energy, respectively. The reaction rate (Δυ) can then be calculated by multiplying the reaction constant with the molar concentration of the reactive species. Subsequently, the overall reaction rate is calculated using the following equation:
(21)∆υtot=∭Δυr,θ,zdV=∫0L∫0R2πrΔυr,zdrdzFigure 10
Major reaction pathways for the formation of CO2 and H2O when using different oxidizers: (a) air, (b) oxygen-enriched mixture, and (c) N2O at Rratio=1.
(a)(b)(c)Figure10 depicts the main reaction paths in the oxygen-enriched and R1 cases. Similar reaction pathways existed in these cases; however, the reaction rates were different. CH4 initially decomposed into CH3, H2, and H2O through R. 122 (CH4+H⟶CH3+H2) and R. 124 (CH4+OH⟶CH3+H2O), as displayed in Figure 10. Subsequently, H2O was produced through R. 3 (H2+OH⟶H2O+H). With regard to the CO2 formation pathway, CH3 transformed into CH2O through R. 87 (CH3+O⟶CH2O+H). CH2O was then converted to HCO through the R. 80 (CH2O+H⟶H2+HCO), R. 82 (CH2O+OH⟶H2O+HCO), and reverse R. 45 (H+HCO⟶CH2O) reactions. Subsequently, CO was produced from HCO through R. 46 (HCO+H⟶H2+CO), R. 49 (HCO+OH⟶H2O+CO), and R. 51. CH2CO was formed through R. 85 (CH2O+CH⟶CH2CO+H), which contributed to the formation of CO through the R. 181 (CH2CO+H⟶CO+CH3) and reverse R. 61 (CO+CH2⟶CH2CO) reactions. Ultimately, CO transformed into CO2 mainly through R. 30, R. 31, R. 33 (CO+O2⟶CO2+O), and R. 34 (especially R. 30 and R. 31) reactions. In Figures 10(a) and 10(b), it can be found that there was no significant difference between these two cases in the major reaction pathway, but the magnitude of the reaction rate has a difference with different conditions. There are more CH2O, which came from the CH3 through the reaction R. 87 (CH3+O⟶CH2O+H), transferred to HCO through the reaction R. 45 REV (CH2O⟶HCO+H). But, the CO, which came from the reaction R. 46 (HCO+H⟶H2+CO), became lower in the condition of the oxygen-enriched compared with the air case. Besides these two obvious differences, most of the major reactions in the condition of air were more intense than in the condition of oxygen-enriched. However, there are some differences between these two cases, but the reaction and magnitude of major reaction pathways are still similar in these two cases.As displayed in Figure10(c), when the oxygen-enriched mixture was replaced by N2O under an R value of 1, the intensities of R. 122 and R. 124 increased, which resulted in the increased formation of CH3, H2O, and H2. This phenomenon enhanced R. 87, which resulted in the formation of additional CH2O. Moreover, additional HCO was formed through the enhancement of the R. 80, R. 82, and reverse R. 45 reactions (Figure 10(c)). R. 46, R. 49, and R. 51 were enhanced marginally in the R1 case compared with the oxygen-enriched case; however, in the R1 case, CO formation was dominated by R. 541, which mainly came from the N2O reaction (Figure 10(c)). CO2 production was then enhanced mainly through R. 30 and R. 31. Moreover, because the decomposition reaction involving N2O at the exit of the oxidizer port had been completed, in addition to R. 541, many other chemical reactions, including R. 543, R. 544, and R. 578, occurred near the oxidizer nozzle. Because of the increased CO and HO2 production, additional CO2 and H2 were produced through the enhancement of R. 19, R. 30, R. 31, and R. 34. Furthermore, additional H2 was produced through the enhancement of R. 19, R. 80, R. 122, and R. 124, which led to the increased production of H2O further downstream through R. 3. From Figures 6–10, it could be found that there was a significant difference near the vicinity of the center nozzle rim between the cases of oxygen-enriched mixture and N2O, which was caused by the different reactions from the process of N2O combustion.


## 3.3. Analysis of Entropy Generation Rate and Exergy

To investigate the thermal effect of N2O decomposition and the effect of oxidizer velocity on the entropy generation rate, an oxygen-enriched mixture and N2O (R=1) were used as oxidizers. Figures 11 and 12 show the distributions of the entropy generation rates contributed by heat conduction, mass diffusion, and the chemical reaction as well as the total entropy generation rate at the Rratio=1. The flame structures in both conditions are a single diffusion flame at this R ratio condition. The heat conduction term had a strong distribution near the nozzle and around the high-temperature region due to the high-temperature gradient, which came from the substantial temperature change. In addition, the mass diffusion term was distributed near the reaction region, which had the most intense reaction causing the significant species to change. Besides, the chemical reaction term had strong distribution in the major reaction region obviously. The comparison of the air and oxygen-enriched cases was shown in Figure 11. In Figure 11(d), the peak values were located at the similar location in air and oxygen-enriched cases (about 0.06 mm HABs in axial direction and about 3.0 mm in radial direction). Because of both flames were not attached to the nozzle, there was a small space for the mixing between methane and the air (coflow). Therefore, the chemical reaction term (Figure 11(c)) and the mass diffusion term (Figure 11(b)) both have the peak value at that place where the reactions and the species gradient could be enhanced due to the premixing process in both cases. The contribution to the total entropy generation was dominated by the chemical reaction term in air and oxygen-enriched cases. The chemical reaction term was about 1.11 times and 3.73 times greater than the heat conduction term and the mass diffusion term in the air case, respectively. And it was about 1.14 times and 3.44 times greater than the heat conduction term and mass diffusion term in the oxygen-enriched case, respectively. Furthermore, the temperature and heat release would be narrower in the oxygen-enriched case so that the entropy generation rate of three terms would distribute into a narrower area in the oxygen-enriched case (shown in Figures 11(a), 11(b), and 11(c)). Besides, the air case has slightly stronger chemical reactions than the oxygen-enriched case, causing higher temperature and species gradient. So, the entropy generation of three terms was slightly higher in the air case. The total entropy generation in the air case was about 1.13 times greater than in the oxygen-enriched case.Figure 11
Entropy generation rates contributed by (a) heat conduction, (b) mass diffusion, and (c) the chemical reaction in the air and oxygen-enriched cases as well as the (d) distribution of the overall entropy in these cases.Figure 12
Entropy generation rates contributed by (a) heat conduction, (b) mass diffusion, and (c) the chemical reaction in the oxygen-enriched and R1 cases as well as the (d) distribution of the overall entropy in these cases.Due to the chemical reaction term dominating the contribution of entropy generation, the major reaction pathway would be conducted and presented in Figures10(a) and 10(b) with a slight difference.Figure12 presents the entropy generation rates in the oxygen-enriched and R1 cases. In Figure 12(d), the peak entropy generation rate in the oxygen-enriched case occurred near the vicinity of the fuel nozzle rim (HABs of 0.06 mm in the axial direction and 3.0 mm in the radial direction). However, in the R1 case, the peak entropy generation rate occurred inside the oxidizer tube. Compared with the oxygen-enriched case, higher heat release occurred in the R1 case because of N2O decomposition, which resulted in the reactions becoming more intense in the R1 case; this caused increases in the temperature and species gradients near the vicinity of the central nozzle in this case. Therefore, high entropy generation rates contributed by heat conduction, mass diffusion, and the chemical reaction (especially the chemical reaction) were observed near the vicinity of the central nozzle rim (Figures 12(a)–12(c)). Thus, the total entropy generated in the R1 case was approximately 2.26 times higher than that generated in the oxygen-enriched case. Although the peak entropy values occurred at different locations in these two cases, the chemical reaction dominated the contribution to the total entropy generation rate in both cases. The entropy contributed by the chemical reaction was approximately 1.14 and 3.44 times higher than that contributed by heat conduction and mass diffusion, respectively, in the oxygen-enriched case. The entropy contributed by the chemical reaction was approximately 2.01 and 6.93 times higher than that contributed by heat conduction and mass diffusion, respectively, in the R1 case. Moreover, as depicted in Figures 12(a)–12(c), the distributions of the temperature and heat release rate in the outer region were considerably wider in the R1 case than in the oxygen-enriched case; that is, the volumetric entropy generation rates contributed by heat conduction, mass diffusion, and the chemical reaction were higher in the R1 case than in the oxygen-enriched case. However, the magnitudes were similar in these two cases because of the similar temperatures and reaction intensities in the cases. In addition, a single-flame structure was observed in the oxygen-enriched and R1 cases. Therefore, the distribution of the entropy generation rate in the outer region was similar in these cases. Because the chemical reaction was the main contributor to the overall entropy generation rate in both cases, the entropy generation rates contributed by the chemical reactions of major chemical species were determined. According to the results, the CO2 and H2O production varied considerably in the two cases. On the basis of the major reaction pathways for the formation of CO2 and H2O that are displayed in Figure 10, several differences in chemical reactions were identified between the oxygen-enriched and R1 cases.With the results, the significant difference between three different oxidizers at the condition of R1 almost came from the chemical reaction, so the volumetric entropy generation rate along the stoichiometric line, which could have the strongest reaction, would be conducted in Figure13(a). Two stoichiometric lines are observed in Figure 14 because two oxidizers existed, that is, one is situated inside, and the other is situated outside of the fuel port. The local equivalence ratio (ϕ) was calculated by the following equation [40]:
(22)ϕ=f1−fsfs1−f,where f and fs are the mixture fraction and the stoichiometric mixture fraction, respectively. The mixture fraction would be determined through the equation below [21]:
(23)f=2YC−YC,oxidizer/WC+YH−YH,oxidizer/2WH−YO−YO,oxidizer/WO2YC,fuel−YC,oxidizer/WC+YH,fuel−YH,oxidizer/2WH−YO,fuel−YO,oxidizer/WOwhere Y and W are the mass fraction and atomic weights (of the C, H, and O atoms), respectively. The stoichiometric mixture fractions were 0.055, 0.0826, and 0.0833 for the CH4/air, CH4/67%N2+33%O2, and CH4/N2O flames, respectively.Figure 13
(a) Total volumetric entropy generation rate and normalized entropy generation rates along the stoichiometric line in the (b) air, (c) oxygen-enriched, and (d) N2O cases at Rratio=1.Figure 14
(a) Total exergy and (b) normalized exergy observed in different oxidizer conditions.
(a)(b)The top panel of Figure13(a) depicts the outer stoichiometric line (coflow), and the bottom panel of Figure 13(a) depicts the inner stoichiometric line (oxidizer). Because the flame heights were different in the R1, air, and oxygen-enriched cases, the x-axis is the normalized axial direction (local axial distance divided by the maximum axial distance) for comparing these cases. As depicted in the top panel of Figure 13(a), the peak entropy generation rate in the R1 case (almost 1.2×106W/m3 K) occurred at a location where Z/Zmax=0.02. This rate then decreased suddenly and reached a stable value between approximately 5×104 and 7.5×104W/m3 K at locations where Z/Zmax>0.2. The aforementioned behavior was similar to that observed in the air case, in which the peak entropy generation rate (~9×105W/m3 K) occurred at a location where Z/Zmax=0.017, and this rate then decreased to the same stable value as in the R1 case at locations where Z/Zmax>0.041. In the oxygen-enriched case, the peak entropy generation rate (~5.3×105W/m3 K, which is smaller than the maximum entropy generation rate in the other two conditions) occurred at a location where Z/Zmax=0.072. This rate then decreased gradually until the minimum value of approximately 5.0×104W/m3 K was achieved (at the top of the stoichiometric line). This value differed from the minimum entropy generation rate achieved in the other two cases. As shown in the bottom panel of Figure 13(a), in the R1 case, the entropy generation rate (maximum value of ~2.6×106W/m3 K) was higher at locations further upstream of the nozzle rim. However, in the other two cases, this rate decreased with an increase in the flame height, with the decrease being higher in the oxygen-enriched case than in the air case.Subsequently, the dominant term should be found along the stoichiometric line. The relative entropy generation rates for the three oxidizers in the R1 case are displayed in Figures13(b)–13(d). As in the case of Figure 13(a), the top and bottom panels of the aforementioned three figures depict the outer and inner stoichiometric lines in each case. Moreover, the x-axis is still the normalized axial direction for comparison. As shown in the top panels of Figures 13(b)–13(d), heat conduction was the dominant contributor to the entropy generation when Z/Zmax<0, where it was close to the wall and did not have the reaction in these three cases. However, when Z/Zmax>0, the chemical reaction was the dominant contributor to the entropy generation in the R1, oxygen-enriched, and air cases. In the oxygen-enriched and R1 cases, mass diffusion had a higher contribution to entropy generation than did heat conduction when Z/Zmax>0. However, in the air case, mass diffusion and heat conduction had similar contributions to total entropy generation when Z/Zmax>0. The bottom panels of Figures 13(b)–13(d) indicate that mass diffusion dominated the contributions to entropy generation for the inner stoichiometric line. In the air and oxygen-enriched cases, the contribution of heat conduction to entropy generation gradually increased with flame height. However, in the R1 case, the chemical reaction dominated the contributions to entropy generation for the inner stoichiometric line because several reactions were induced through N2O decomposition near the central nozzle rim. Heat conduction exhibited the second-highest contribution to the entropy generation in this case because of the high temperature in the aforementioned region (Figure 6(c)).After analyzing the volumetric entropy distribution, the exergy, which represents the energy that can be used in the combustion process in the air, the oxygen-rich and R1 cases were examined in Figure14. Figure 14(a) displays the total exergy input and the exergy consumed by irreversibility in these cases. The total exergy values in the air, oxygen-rich, and R1 cases were 9068.6, 9073.6, and 9225.4 W, respectively. Because N2O has higher chemical availability than does the adopted oxygen-enriched mixture, the exergy input was higher in the R1 case than in the oxygen-enriched case.In Figure14(a), the air and oxygen-enriched cases have similar exergy remained, and the oxygen-enriched case was even slightly higher than the air case. The difference was about 135.9 W between these two cases. The values of the heat conduction, mass diffusion, and chemical reaction terms in the air case were 1.2, 1.02, and 1.1 times higher than those in the oxygen-enriched case. The second law efficiencies are 87.03% for the air case and 88.48% for the oxygen-enriched case. They have similar flame structures and reaction pathways in both cases. Besides, higher exergy was consumed in the R1 case than in the oxygen-enriched case, with the difference in exergy being approximately 1322 W. The values of the heat conduction, mass diffusion, and chemical reaction terms were 1.7, 1.45, and 3 times higher in the R1 case than in the oxygen-enriched case. Because the value of the mass diffusion term was lower than those of the heat conduction and chemical reaction terms (the chemical reaction term was more than three times higher than the mass diffusion term), the difference was dominated by the heat conduction and chemical reaction terms, especially the chemical reaction term. This result might be attributed to the heat release caused by the self-decomposition of N2O. Therefore, different reaction pathways exist when using N2O and oxygen-enriched gas as oxidizers. Consequently, the value of the chemical reaction term differs considerably in the R1 and oxygen-enriched cases. Moreover, the temperature was higher in the R1 case than in the oxygen-enriched case. Therefore, the values of the heat conduction term differed between these cases.Figure14(b) depicts the percentage contributions of the heat conduction, mass diffusion, and chemical reaction terms to the incoming exergy. The heat conduction and chemical reaction terms, whose contributions to the incoming exergy were 5.4% and 6.0% for air case and 4.6% and 5.3% for oxygen-enriched case, were both dominated by the consumption of the exergy. There was a slight difference between the air and oxygen-enriched case. But when the oxidizer was changed from the oxygen-enriched mixture to the N2O, the chemical reaction term was dominated by the exergy consumed, which occupied 15.7% of incoming exergy in the same R ratio condition. Besides, the heat conduction term had a significant difference between the condition of the oxygen-enriched and N2O, which increased from 4.6% to 7.8%, due to the increase in the temperature. In addition, 87.0%, 88.5%, and 74.3% of incoming exergy remained in the air, oxygen-enriched, and R1 cases.


## 4. Conclusions

In this study, the effects of N2O as an oxidizer on entropy generation were studied through numerical simulation and experiments. The obtained simulation and experimental results were in good agreement with each other. The results indicated that under the same nitrogen–oxygen ratio (N-to-O=2), higher exergy input is achieved when using N2O as the oxidizer than when using oxygen-enriched gas as the oxidizer; however, the thermal effect caused by N2O decomposition enhances the intensities of the relevant reactions and causes the production of a high-temperature zone near the nozzle of the inner tube, resulting in the fluid near the inner tube being accelerated and CH4 being dragged toward the inner tube for a reaction. Moreover, the major reaction pathways, which are dominated by the N2O and HNCO species as well as the OH, H, and O radicals, contribute to the generation of chemical-induced irreversibility. The second law efficiency would be greater than 80% when the single flame structure appears in that condition, except in the N2O case. The irreversibility would be dominated by heat conduction and chemical reaction terms. With the results, the N2O could perform a higher temperature due to the combination of the oxygen-enriched effect and thermal effect from the decomposition. But the efficiency of N2O in the combustion process would be poorer than the other oxidizers. With the entropy analysis, the chemical reaction was the one that dominated the difference. Owing to the difficulty and high cost of the liquefied air or other oxygen and nitrogen mixed gas, N2O was the potential candidate to provide the liquefied oxidizer of the rocket propellant. With the catalyst to assist N2O decomposition, the chemical-induced and thermal-induced irreversibilities could be further reduced.



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*Source: 5364917-2023-02-20.xml*