Investigation of Thermal Radiation from Soot Particles and Gases in Oxy-Combustion Counter-Flow Flames

: Oxy-combustion with high ﬂame temperature, low heat loss, high combustion efﬁciency, and low NOx emissions is being extensively studied. The thermal radiation from soot particles and gases in oxy-combustion accounts for the vast majority of the total heat transfer. Based on a detailed chemical reaction mechanism coupled with the soot particle dynamics model and optically thin radiation model, the inﬂuence of the ﬂame structure and temperature distribution on the thermal radiation in oxygen-enriched counterﬂow diffusion ﬂames was studied in this paper. The results revealed that reasonable assignment of total recycled ﬂue gas and the degree of dilution of fuel and oxidant were critical, which can be used to adjust the overall radiation situation of the ﬂame. At the same adiabatic ﬂame temperature, as the fuel concentration decreased and the oxidant concentration increased (the stoichiometric mixture ratio is from 0.3 to 0.6), the soot formation decreased, which led to the particle radiation disappearing while the main radiation zone of gases moved 0.04 cm toward the fuel side. At the same stoichiometric mixture fraction (0.4), the radiation area was broadened and the radiation of soot particles was gradually enhanced with the adiabatic ﬂame increasing from 2300 K to 2700 K. enhances the gas to ‐ yield soot particles and concentra ‐ tion of CO 2 , the radiation from the particles can be ignored compared to gas radiation in the CO 2 /O 2 atmosphere. The sudden increase in CO 2 concentration leads gas radiation to become the most important radiation source.


Introduction
Traditional coal-fired boilers use air for combustion, in which N 2 in the air (approximately 79% by volume) dilutes CO 2 in the flue gas. The resulting low concentration of CO 2 in the flue gas makes it extremely difficult to capture and recover CO 2 . Oxy-combustion technology is considered an effective technology that can solve this problem, by enhancing the oxygen concentration and using recycled flue gas (RFG) [1][2][3][4]. Oxy-combustion technology can be used to obtain a high concentration of CO 2 in the products of the combustion system, which is beneficial to the storage and utilization of CO 2 . With the development of gas recirculation technology, many concepts of oxy-combustion based on RFG have been proposed. RFG (mainly CO 2 ) is used as a dilution gas to control the structure, temperature, and heat flux of the flame, and has been widely used in gas turbines and coal-fired power plants [5].
Through the transformation of the combustion system, RFG emissions can be significantly reduced, combustion efficiency can be improved, and pollutants emission costs can be reduced [6,7]. However, the increase of oxygen concentration and the decrease of fuel dilution in the diffusion flame will lead to the increase of flame temperature and soot concentration, and soot particles are emitted [8,9]. As soot particles are harmful to the environment and the human body, it is very important to understand the effects of RFG on soot formation and oxidation in the oxy-combustion system and also to further control the radiation from soot particles in flames [10]. Due to the necessity for soot research, many Processes 2021, 9,1756 2 of 13 studies have measured the soot volume fraction in flames through experiments [11,12], and studied the effects of oxygen concentration and CO 2 on soot formation characteristics in flames [13][14][15][16][17]. In addition, changing the structure of the flame (changing the concentration of the inert gas in the oxidant and fuel) can significantly change the soot formation and oxidant characteristics of the flame, and the bright yellow flame, which is full of soot particles, can be changed to a blue flame with radical chemiluminescence, even in the case of adiabatic flame temperature (T ad ) constant. This phenomenon has been observed in many types of non-premixed flames, such as counterflow flames [13][14][15] and laminar coflow diffusion flames [16,17]. The stoichiometric mixture fraction (Z st ) to describe the flame structure and the degree of dilution of the fuel and oxidant can be introduced as: where Y 0 is the mass fraction at the system boundary, W is the molecular mass, and ν is the stoichiometric coefficient. The subscripts F and O are fuel flow and oxidant flow, respectively. Changing Z st can influence the temperature, composition distribution, and soot yield, which ultimately affect the heat flow distribution. Atreya et al. studied thermal radiation and soot particulate emission in partially premixed counterflow flames [18]. Experimental results have found that the configuration of the soot zone spatially entrained between the premixed and non-premixed reaction zones may enhance radiative heat transfer while reducing soot emissions. Liu et al. studied the effects of gas and soot radiation in a counterflow ethylene diffusion flame by using the semiempirical two-equation soot model and the radiation heat transfer model calculated by the DOM/SNBCK method and found that gas radiation is more important than soot radiation in influencing the flame temperature and soot volume fraction (SVF) [19]. Based on the soot volume fraction per unit, soot radiation in a counterflow diffusion flame is less important than that in a coflow flame. Due to the gas radiation in the peak flame temperature region and the soot radiation at a much lower temperature, the distribution of the radiation source term presents a double valley structure. In O 2 /N 2 and O 2 /CO 2 atmospheres, Guo et al. studied the influence of the Z st flame structure on the combustion characteristics of different ethylene counterflow diffusion flames, through a variety of designed flames [14], which isolated the temperature and dilution degree effects. They found that with the increase in Z st , using N 2 or CO 2 as a diluent can inhibit the formation of soot, and that compared to N 2 , the effect of CO 2 on the inhibition of soot formation is more obvious.
In summary, the flame temperature distribution and flame structure changes could affect the formation of soot and the spatial distribution of the radiation medium, and then ultimately affect the overall thermal radiation of the flame. We will use pure CO 2 here instead of a more complex RFG for diluting fuel and oxidant to obtain different T ad and flame structures. The spatial distribution of radiation medium, including gases and soot particles, and the overall radiation of the flame in oxygen-enriched counterflow diffusion flame is studied by numerical calculations coupled with a detailed chemical reaction mechanism, soot particle dynamics model, and radiation model. These fundamental oxycombustion studies shed light on how best to utilize RFG to control the flame temperature, SVF, and heat flux, to achieve savings in fuel and oxygen resources and obtain the best working conditions.

Numerical Methods
Numerical simulations of counterflow flames were carried out using the OPPDIF program, transport properties were obtained from the CHEMKIN database [20,21] and T ad was calculated using NASA's Chemical Equilibrium with Applications program [22]. Cylindrical coordinates were selected. The tolerance of the solver was set to 1 × 10 −10 , and the relaxation factor in segregated scheme was 0.7. The following describes the soot model and the radiation model used in the calculation.

Soot Model
The formation of soot particles includes a series of complex physical and chemical processes, which are generally divided into two processes including gas-phase reaction kinetics and the evolution of particle dynamics after nucleation, corresponding to the formation of precursor, particle nucleation, and subsequent growth, and evolution, respectively. The gas-phase reaction process is studied by a detailed chemical reaction mechanism, while the evolutionary process of soot particles is described by soot aerosol dynamics models. In this paper, ethylene was chosen as the fuel; the C 2 H 4 combustion mechanism comes from Appel et al. [23,24], and consists of fuel pyrolysis, C0-C4 small molecule core reaction, initial benzene ring formation, polycyclic aromatic hydrocarbons (PAHs) formation, and growth reactions up to pyrene (A4), then soot particles are created by the dimerization of A4. Soot particles growth mainly involves the H-abstraction-C 2 H 2 -addition (HACA) process and PAH condensation [23,25]. The method of sectional was used to solve the particles equations. 25 sections were set, the spacing factor was 2.0, and the section minimum size was 32. The coagulation collision efficiency was set to 2.2, and the diffusion and thermophoresis of the particles were considered.

Radiation Model
Gases and soot particles radiations are the main ways of flame radiation heat transfer; therefore, it is important to couple them with an appropriate radiation model. Considering that the flame optical thickness is generally thin (in millimeter orders of magnitude) in counterflow diffusion flames, only the thermal radiation to the outside of the flame was calculated and the internal reabsorption of the flame can be ignored. The radiation heat-transfer model used an optically thin media radiative transmission; the radiation medium included gas (CO 2 , CO, H 2 O, and CH 4 ) and soot particles. The flame radiation was calculated by adding the radiation source to the energy equation, and the radiative heat transfer by soot, CO 2 , H 2 O, CO, and CH 4 were calculated using an optically thin radiation model with the Planck mean absorption coefficient. The Planck mean absorption coefficients for species i (i = CO 2 , H 2 O, CH 4, and CO) used when calculating the optically thin radiation heat loss were obtained by the RADCAL method [26,27], while the mean absorption coefficient for the particles was calculated by k par = 1862 * f v T [28]. Meanwhile, it was assumed that the local gas and the soot particles had the same temperature locally.

Model Verification and Flame Design
Before conducting the oxy-fuel flame calculations, the correctness of the numerical model was first verified. Based on the location of the stagnation plane, the counterflow flames can be divided into soot-formation (SF) flames and soot-formation-oxidation (SFO) flames [29]. SF flames usually mean that the flame sheet is located on the oxidant side of the stagnation plane, and it is usually a counterflow flame with pure fuel and low oxygen concentration. The flame sheet of SFO is on the fuel side of the stagnation plane, which is achieved by setting high fuel dilution and high oxygen concentration. As a result, we conducted model verifications on the two types of counterflow flames. For SF, we set the same conditions as in [30] for the C 2 H 4 counterflow diffusion flames. The separation distance between the nozzles was 1.42 cm, the fuel stream was pure C 2 H 4 for the nondiluted flame and the oxidant stream consisted of 24% O 2 and 76% N 2 by volume. To keep the overall strain rate constant, the nozzle exit velocities of the fuel and oxidant streams were maintained at 19.5 cm/s. At the same time, N 2 in oxidant streams was replaced with CO 2 under the same conditions to initially explore the difference between N 2 and CO 2 on the impact of temperature field, soot particle distribution, heat release or transmission, and so on. Figure 1 shows the computed and experimental SVFs and temperature profiles. Experimental and calculated peak values of SVF are 1.67 ppm and 1.48 ppm, respectively. The locations of peak SVF of the two differ by about 0.3 cm, and the calculated sooting zone is narrower than the experimental one, which may be because the numerical model of this manuscript does not have a good prediction of the thermophoresis and diffusion of soot particles, which are exactly responsible for the wide range of soot volume fraction in the experimental flame. The peak temperatures and distributions are consistent. and so on. Figure 1 shows the computed and experimental SVFs and temperature profile Experimental and calculated peak values of SVF are 1.67 ppm and 1.48 ppm, respectivel The locations of peak SVF of the two differ by about 0.3 cm, and the calculated sootin zone is narrower than the experimental one, which may be because the numerical mod of this manuscript does not have a good prediction of the thermophoresis and diffusio of soot particles, which are exactly responsible for the wide range of soot volume fractio in the experimental flame. The peak temperatures and distributions are consistent. CO2 replaces N2 as dilution progresses, showing significant impacts on the temper ture field, soot particle formation or distribution, heat release, and heat radiation. In Fi ure 1a, the peak value of SVF in the CO2/O2 atmosphere is about 0.43 ppm, only a quart of the value in the N2/O2 atmosphere. Figure 2a shows the net heat generated by the rea tion and the temperature distribution in N2/O2 and CO2/O2 atmospheres; the C2H4/O2 CO2 counterflow diffusion flame has more net heat production from gas-phase reaction than the C2H4/O2 + N2 flame, because CO2 is not an absolutely inert gas, it participated some chemical reactions, especially in some exothermic reactions [3]. Figure 2b is the r diation source from soot particles and gases (CO2, H2O, CO, and CH4). The radiatio source of the N2/O2 atmosphere generates two valleys. The valley at a distance of 0.6 c from the fuel nozzle is caused by the radiation of soot, which corresponds to the peak so position in Figure 1a. The valley at 0.8 cm is due to the peak temperature, which great enhances the gas radiation. However, due to low-yield soot particles and high concentr tion of CO2, the radiation from the particles can be ignored compared to gas radiation the CO2/O2 atmosphere. The sudden increase in CO2 concentration leads gas radiation become the most important radiation source. CO 2 replaces N 2 as dilution progresses, showing significant impacts on the temperature field, soot particle formation or distribution, heat release, and heat radiation. In Figure 1a, the peak value of SVF in the CO 2 /O 2 atmosphere is about 0.43 ppm, only a quarter of the value in the N 2 /O 2 atmosphere. Figure 2a shows the net heat generated by the reaction and the temperature distribution in N 2 /O 2 and CO 2 /O 2 atmospheres; the C 2 H 4 /O 2 + CO 2 counterflow diffusion flame has more net heat production from gas-phase reactions than the C 2 H 4 /O 2 + N 2 flame, because CO 2 is not an absolutely inert gas, it participated in some chemical reactions, especially in some exothermic reactions [3]. Figure 2b is the radiation source from soot particles and gases (CO 2 , H 2 O, CO, and CH 4 ). The radiation source of the N 2 /O 2 atmosphere generates two valleys. The valley at a distance of 0.6 cm from the fuel nozzle is caused by the radiation of soot, which corresponds to the peak soot position in Figure 1a. The valley at 0.8 cm is due to the peak temperature, which greatly enhances the gas radiation. However, due to low-yield soot particles and high concentration of CO 2 , the radiation from the particles can be ignored compared to gas radiation in the CO 2 /O 2 atmosphere. The sudden increase in CO 2 concentration leads gas radiation to become the most important radiation source.
Processes 2021, 9, x FOR PEER REVIEW 4 of and so on. Figure 1 shows the computed and experimental SVFs and temperature profile Experimental and calculated peak values of SVF are 1.67 ppm and 1.48 ppm, respectivel The locations of peak SVF of the two differ by about 0.3 cm, and the calculated sootin zone is narrower than the experimental one, which may be because the numerical mod of this manuscript does not have a good prediction of the thermophoresis and diffusio of soot particles, which are exactly responsible for the wide range of soot volume fractio in the experimental flame. The peak temperatures and distributions are consistent.
(a) (b) CO2 replaces N2 as dilution progresses, showing significant impacts on the temper ture field, soot particle formation or distribution, heat release, and heat radiation. In Fi ure 1a, the peak value of SVF in the CO2/O2 atmosphere is about 0.43 ppm, only a quart of the value in the N2/O2 atmosphere. Figure 2a shows the net heat generated by the rea tion and the temperature distribution in N2/O2 and CO2/O2 atmospheres; the C2H4/O2 CO2 counterflow diffusion flame has more net heat production from gas-phase reactio than the C2H4/O2 + N2 flame, because CO2 is not an absolutely inert gas, it participated some chemical reactions, especially in some exothermic reactions [3]. Figure 2b is the r diation source from soot particles and gases (CO2, H2O, CO, and CH4). The radiatio source of the N2/O2 atmosphere generates two valleys. The valley at a distance of 0.6 c from the fuel nozzle is caused by the radiation of soot, which corresponds to the peak so position in Figure 1a. The valley at 0.8 cm is due to the peak temperature, which great enhances the gas radiation. However, due to low-yield soot particles and high concentr tion of CO2, the radiation from the particles can be ignored compared to gas radiation the CO2/O2 atmosphere. The sudden increase in CO2 concentration leads gas radiation become the most important radiation source. For the SFO flames, the separation distance between the nozzles was 8 mm, the oxidant stream was composed of 90% O 2 and 10% N 2 by volume, and the fuel stream was composed of 28% C 2 H 4 and 72% N 2 . The nozzle exit velocities of the fuel and oxidant streams were maintained at 20 cm/s [31]. The comparison between the experimental and calculated SVF of the SFO flame is shown in Figure 3. The experimental and calculated peak values by Xu et al. were 0.21 ppm and 0.19 ppm, respectively, while the calculated peak SVF of this study was 0.189 ppm, and the peak position was relatively close. The results show that for the SFO flame with a high oxygen concentration and a high fuel dilution, this numerical model can accurately predict experimental results. For the SFO flames, the separation distance between the nozzles was 8 mm, the oxidant stream was composed of 90% O2 and 10% N2 by volume, and the fuel stream was composed of 28% C2H4 and 72% N2. The nozzle exit velocities of the fuel and oxidant streams were maintained at 20 cm/s [31]. The comparison between the experimental and calculated SVF of the SFO flame is shown in Figure 3. The experimental and calculated peak values by Xu et al. were 0.21 ppm and 0.19 ppm, respectively, while the calculated peak SVF of this study was 0.189 ppm, and the peak position was relatively close. The results show that for the SFO flame with a high oxygen concentration and a high fuel dilution, this numerical model can accurately predict experimental results. Overall, even if there is a difference in the sooting zone for SF flames, the peak values and positions are worthy of attention in the discussion of the results. In addition, SFO can be accurately simulated, so the model verification shows that this numerical model can be better used to predict and characterize the counterflow diffusion flame, especially in the conditions of fuel dilution and oxygen enhancement.
Here, three groups of flame were designed after comprehensive consideration, in which CO2 was used as a diluent, to research the effects of flame structure and Tad on soot formation and on radiation from gases and soot. Each group maintained a constant Tad with Zst increasing, but the Tad of each group was different. The flame cases were designed to simultaneously dilute both sides of the fuel stream and oxidant stream with a diluent gas, while ensuring that the total stoichiometric amount of CO2 per group was unchanged, so Tad was unaffected. The two nozzles of the burner were coaxial and flowed in opposite directions, with a diameter of 10 mm and a separation distance of 8 mm. The initial velocity of the reactant from the nozzle was maintained at 20 cm/s to ensure that the global strain rate remained nearly constant (50 s −1 ). The initial temperatures of the fuel stream, the oxidant stream, and the ambient temperature all were maintained at 300 K, and the pressure was 1 atm. Table 1 displays the details of the designed flames. Overall, even if there is a difference in the sooting zone for SF flames, the peak values and positions are worthy of attention in the discussion of the results. In addition, SFO can be accurately simulated, so the model verification shows that this numerical model can be better used to predict and characterize the counterflow diffusion flame, especially in the conditions of fuel dilution and oxygen enhancement.
Here, three groups of flame were designed after comprehensive consideration, in which CO 2 was used as a diluent, to research the effects of flame structure and T ad on soot formation and on radiation from gases and soot. Each group maintained a constant T ad with Z st increasing, but the T ad of each group was different. The flame cases were designed to simultaneously dilute both sides of the fuel stream and oxidant stream with a diluent gas, while ensuring that the total stoichiometric amount of CO 2 per group was unchanged, so T ad was unaffected. The two nozzles of the burner were coaxial and flowed in opposite directions, with a diameter of 10 mm and a separation distance of 8 mm. The initial velocity of the reactant from the nozzle was maintained at 20 cm/s to ensure that the global strain rate remained nearly constant (50 s −1 ). The initial temperatures of the fuel stream, the oxidant stream, and the ambient temperature all were maintained at 300 K, and the pressure was 1 atm. Table 1 displays the details of the designed flames.

Results and Analysis
As a general rule, a permanent blue flame can be obtained when there is no soot present (which leads to visible radiation) in the flames. With the increase of soot, the flames gradually change from pure blue to yellow (soot radiation), or even bright white. Therefore, the incipient soot formation was studied by varying the mole fraction of oxygen in the oxidant stream for a given mole fraction of fuel in the fuel stream, similar to the definition of Z st . Incipient soot formation is generally referred to as the sooting limit, which has been studied by many scholars, especially in diffusion flames [32][33][34]. Figure 4 shows the three calculated iso-T ad (solid lines) and six calculated iso-Z st (dotted lines) curves in the O 2 /CO 2 atmosphere, highlighting that flames with a lower T ad have larger ranges of Z st , corresponding to more varied flame structures. For instance, Z st ranges from 0.0662 to 0.7732 in the first group (T ad = 2300 K), whereas the range of variation of Z st is reduced from 0.0846 to 0.7098 in the second group (T ad = 2500 K), and further narrowed from 0.1113 to 0.6184 in the last group (T ad = 2700 K). In other words, the iso-Z st is getting denser as T ad gradually decreases.

Results and Analysis
As a general rule, a permanent blue flame can be obtained when there is no soot present (which leads to visible radiation) in the flames. With the increase of soot, the flames gradually change from pure blue to yellow (soot radiation), or even bright white. Therefore, the incipient soot formation was studied by varying the mole fraction of oxygen in the oxidant stream for a given mole fraction of fuel in the fuel stream, similar to the definition of Zst. Incipient soot formation is generally referred to as the sooting limit, which has been studied by many scholars, especially in diffusion flames [32][33][34]. Figure 4 shows the three calculated iso-Tad (solid lines) and six calculated iso-Zst (dotted lines) curves in the O2/CO2 atmosphere, highlighting that flames with a lower Tad have larger ranges of Zst, corresponding to more varied flame structures. For instance, Zst ranges from 0.0662 to 0.7732 in the first group (Tad = 2300 K), whereas the range of variation of Zst is reduced from 0.0846 to 0.7098 in the second group (Tad = 2500 K), and further narrowed from 0.1113 to 0.6184 in the last group (Tad = 2700 K). In other words, the iso-Zst is getting denser as Tad gradually decreases.

Position Changes of Flame Sheet and Stagnation Plane
It is generally believed that the change in Zst is mainly due to the change of position of the flame sheet and stagnation plane [29,31], which in turn affects the formation process of soot particles. Figure 5 shows the variation of the flame sheet position relative to the

Position Changes of Flame Sheet and Stagnation Plane
It is generally believed that the change in Z st is mainly due to the change of position of the flame sheet and stagnation plane [29,31], which in turn affects the formation process of soot particles. Figure 5 shows the variation of the flame sheet position relative to the stagnation plane location in the conditions from Table 1. The abscissa is the difference between the flame sheet position and the stagnation plane location (from the fuel side), the ordinate is the stoichiometric mixed fraction Z st .
Processes 2021, 9, x FOR PEER REVIEW 7 of 14 stagnation plane location in the conditions from Table 1. The abscissa is the difference between the flame sheet position and the stagnation plane location (from the fuel side), the ordinate is the stoichiometric mixed fraction Zst. When Zst is small (Zst = 0.1-0.4), the flame sheet is located on the oxidant side of the stagnation plane. At that time, the fuel flowing out of the fuel side nozzle is continuously pyrolyzed in the process of approaching the stagnation plane. After reaching the stagnation plane, a portion of the species appearing across the stagnation plane through a diffusion mechanism then participate in the reaction with the oxidant. At the same time, the When Z st is small (Z st = 0.1-0.4), the flame sheet is located on the oxidant side of the stagnation plane. At that time, the fuel flowing out of the fuel side nozzle is continuously pyrolyzed in the process of approaching the stagnation plane. After reaching the stagnation plane, a portion of the species appearing across the stagnation plane through a diffusion mechanism then participate in the reaction with the oxidant. At the same time, the small molecular substances produced by the pyrolysis of the fuel react with each other while moving toward the stagnation plane to produce C 2 H 2 , C 3 H 3 , n-C 4 H i , etc. A1 appears and grows up to A4, and then the soot particles are born and grown; eventually, the soot particles are pushed toward the stagnation plane by the gas flow. In this situation, the entire evolution of the soot particles is carried out on the fuel side of the flame sheet and does not pass through the highly oxidizing flame sheet, so the soot particle only grows and is not being consumed by oxidation.
As the Z st increases, the oxygen concentration in the oxidant gradually increases; the stagnation plane and flame sheet, which are relatively distant from each other at first, become close to each other and then gradually separate. In other words, the stagnation plane moves toward the oxidant side and the flame sheet moves continuously toward the fuel side. When the flame sheet moves to the fuel side of the stagnation plane (e.g., Z st = 0.6), the fuel flowing out of the fuel side nozzle has to pass through the flame sheet first in the process of approaching the stagnation plane, and so a large number of OH radicals with strong oxidation are found near the flame sheet, due to the increase in oxygen concentration. All of these inhibit the production of C 2 H 2 , PAHs, and other substances, as well as the inception and growth of soot particles, and other processes, resulting in a significant reduction in the number of soot particles reaching the stagnation plane.

Effects of Flame Structure on Radiation
First, the maximal soot particle number density is showed in Figure 6. All groups show the same pattern of soot with increasing Z st , so the second group (T ad = 2500 K) was selected for a more detailed analysis.  Figure 7 shows the distributions of SVF and radiation source caused by soot and gases in cases 2.1-2.4. The peak of SVF in case 2.1 is about 0.23 ppm, while SVF is magnified by a factor of 100 in case 2.4 and almost no soot formation is predicted. With Zst increasing (ranging from 0.3 to 0.6), the peak value of the radiation source increases gradually, but not obviously, and the overall position progressively approaches the fuel side (from 0.43 to 0.39 cm). There is also a lower peak in the radiation source curve of case 2.1, which is the contribution of radiation from the soot particles. However, compared to gas radiation, soot particle radiation is very weak. With Zst increasing, soot formation is reduced and the contribution of radiation is almost negligible.  Figure 7 shows the distributions of SVF and radiation source caused by soot and gases in cases 2.1-2.4. The peak of SVF in case 2.1 is about 0.23 ppm, while SVF is magnified by a factor of 100 in case 2.4 and almost no soot formation is predicted. With Z st increasing (ranging from 0.3 to 0.6), the peak value of the radiation source increases gradually, but not obviously, and the overall position progressively approaches the fuel side (from 0.43 to 0.39 cm). There is also a lower peak in the radiation source curve of case 2.1, which is the contribution of radiation from the soot particles. However, compared to gas radiation, soot particle radiation is very weak. With Z st increasing, soot formation is reduced and the contribution of radiation is almost negligible. fied by a factor of 100 in case 2.4 and almost no soot formation is predicted. With Zst i creasing (ranging from 0.3 to 0.6), the peak value of the radiation source increases grad ally, but not obviously, and the overall position progressively approaches the fuel si (from 0.43 to 0.39 cm). There is also a lower peak in the radiation source curve of case 2 which is the contribution of radiation from the soot particles. However, compared to g radiation, soot particle radiation is very weak. With Zst increasing, soot formation is r duced and the contribution of radiation is almost negligible. As mentioned earlier in this article, the soot particle growth mechanism mainly i volves the HACA process and PAH condensation; soot particles are created by the dime ization of pyrene (A4) molecules, hydroxyl (OH) is mainly responsible for the oxidatio and consumption of soot particles. We show the concentration distribution of several com ponents, including C2H2, OH, A1 and A4 in Figure 8. An increase in the stoichiometr mixing fraction causes the concentration of fuel to be diluted and increases the oxyg concentration of oxidants. As mentioned earlier in this article, the soot particle growth mechanism mainly involves the HACA process and PAH condensation; soot particles are created by the dimerization of pyrene (A4) molecules, hydroxyl (OH) is mainly responsible for the oxidation and consumption of soot particles. We show the concentration distribution of several components, including C 2 H 2 , OH, A1 and A4 in Figure 8. An increase in the stoichiometric mixing fraction causes the concentration of fuel to be diluted and increases the oxygen concentration of oxidants.  Figure 9 shows the distributions of temperature (a), heat generation (b), CO2 m fraction (c), and H2O mole fraction (d) in cases 2.1-2.4. The peak temperature and the tribution of the temperature field do not differ much when Zst varies from 0.3 to 0.6, w the high-temperature zone moves about 0.01 cm toward the fuel side. Figure 9b shows heat generation profiles of the group flames (cases 2.1-2.4) in different Zst; the total ene release can be divided into three different regions: the endothermic fuel pyrolysis zo the primary reaction zone near the maximum peak, and the secondary oxidation z near the second peak. The peak in the secondary oxidation zone gradually fades with increase of Zst, because the pyrolysis zone becomes narrower and the peak of the en thermic fuel pyrolysis zone decreases. The radiation heat source of soot particles and is consistent with that of Figure 7.  Figure 9 shows the distributions of temperature (a), heat generation (b), CO 2 mole fraction (c), and H 2 O mole fraction (d) in cases 2.1-2.4. The peak temperature and the distribution of the temperature field do not differ much when Z st varies from 0.3 to 0.6, while the high-temperature zone moves about 0.01 cm toward the fuel side. Figure 9b shows the heat generation profiles of the group flames (cases 2.1-2.4) in different Z st ; the total energy release can be divided into three different regions: the endothermic fuel pyrolysis zone, the primary reaction zone near the maximum peak, and the secondary oxidation zone near the second peak. The peak in the secondary oxidation zone gradually fades with the increase of Z st , because the pyrolysis zone becomes narrower and the peak of the endothermic fuel pyrolysis zone decreases. The radiation heat source of soot particles and gas is consistent with that of Figure 7. Since CO2 is required to dilute fuel and oxygen at the same time, with the increase Zst, more and more CO2 is transferred from the oxidant side to the fuel side (the pea position has moved about 0.08 cm), making the four conditions in the boundary cond tions of CO2 concentration change significantly. The concentrations of CO2 in the distrib tions vary widely in the nonreaction zone, hardly affecting radiation, while in the hig temperature reaction zone, the concentration of CO2 changes very little with Zst changin At the same time, the H2O in all conditions is generated only in the reaction without e ternal introduction. The trend of the distribution of concentrations of H2O in the four cas remains essentially unchanged; the peak value gradually decreases (the peak H2O co centration at Zst = 0.6 is 12.4% lower than that at Zst = 0.3) and the position moves closer the fuel side (from 0.386 to 0.349 cm).

Effects of Temperature Distribution on Radiation
Cases 1.4, 2.2, and 3.1 have different Tad of 2300 K, 2500 K, and 2700 K, respectivel but all the flames have the same Zst (0.4). Figure 10 shows the SVF distributions and radiation source caused by soot and gas in cases 1.4, 2.2, and 3.1. With the increase of Tad, soot formation gradually increases (fro 0.019 to 0.205 ppm) and the distance between the peak SVF and the fuel nozzle drops fro 0.35 to 0.315 cm. In Figure 10, we note a lower peak in the radiation source curve of ca 3.1 contributed by soot particles. It was found that the gas radiation did not change si nificantly with the increase of temperature, because the Planck mean absorption coeff cient for CO2 gradually decreased [35], while the radiation distribution area gradual widened. Since CO 2 is required to dilute fuel and oxygen at the same time, with the increase of Z st , more and more CO 2 is transferred from the oxidant side to the fuel side (the peak position has moved about 0.08 cm), making the four conditions in the boundary conditions of CO 2 concentration change significantly. The concentrations of CO 2 in the distributions vary widely in the nonreaction zone, hardly affecting radiation, while in the high-temperature reaction zone, the concentration of CO 2 changes very little with Z st changing. At the same time, the H 2 O in all conditions is generated only in the reaction without external introduction. The trend of the distribution of concentrations of H 2 O in the four cases remains essentially unchanged; the peak value gradually decreases (the peak H 2 O concentration at Z st = 0.6 is 12.4% lower than that at Z st = 0.3) and the position moves closer to the fuel side (from 0.386 to 0.349 cm).

Effects of Temperature Distribution on Radiation
Cases 1.4, 2.2, and 3.1 have different T ad of 2300 K, 2500 K, and 2700 K, respectively, but all the flames have the same Z st (0.4). Figure 10 shows the SVF distributions and radiation source caused by soot and gases in cases 1.4, 2.2, and 3.1. With the increase of T ad , soot formation gradually increases (from 0.019 to 0.205 ppm) and the distance between the peak SVF and the fuel nozzle drops from 0.35 to 0.315 cm. In Figure 10, we note a lower peak in the radiation source curve of case 3.1 contributed by soot particles. It was found that the gas radiation did not change significantly with the increase of temperature, because the Planck mean absorption coefficient for CO 2 gradually decreased [35], while the radiation distribution area gradually widened.  Figure 11 shows the mole fraction distributions of C2H2, OH, A1, and A4 in cases 1. 2.2, and 3.1. On the whole, whether it is conducive to the growth of soot (C2H2, A1, an A4 species), or not (OH species), the molar concentration of species increases with th increase of temperature. This shows that the formation and oxidation of soot particles ar accelerated simultaneously; however, compared to the oxidation rate of soot, its formatio rate is faster.   Figure 11 shows the mole fraction distributions of C 2 H 2 , OH, A1, and A4 in cases 1.4, 2.2, and 3.1. On the whole, whether it is conducive to the growth of soot (C 2 H 2 , A1, and A4 species), or not (OH species), the molar concentration of species increases with the increase of temperature. This shows that the formation and oxidation of soot particles are accelerated simultaneously; however, compared to the oxidation rate of soot, its formation rate is faster.  Figure 11 shows the mole fraction distributions of C2H2, OH, A1, and A4 in cases 1 2.2, and 3.1. On the whole, whether it is conducive to the growth of soot (C2H2, A1, a A4 species), or not (OH species), the molar concentration of species increases with t increase of temperature. This shows that the formation and oxidation of soot particles a accelerated simultaneously; however, compared to the oxidation rate of soot, its formati rate is faster.   Figure 12 shows the distributions of temperature (a), heat generation (b), CO 2 mole fraction (c), and H 2 O mole fraction (d) in cases 1.4, 2.2, and 3.1. The temperature area does not move significantly (about 0.4 cm), while the temperature increases significantly with a decrease in the total amount of CO 2 (for every 200 K increase in T ad , the peak temperature increases by about 300 K). With a decrease in the total amount of CO 2 as a diluent, more fuel and oxidant are involved in reaction per unit volume, including pyrolysis of the fuel; in other words, more fuel is pyrolyzed and more heat is released, and eventually, the temperature of the flame becomes higher by unit volume as demonstrated in Figure 12b. Figure 12 shows the distributions of temperature (a), heat generation (b), CO2 mo fraction (c), and H2O mole fraction (d) in cases 1.4, 2.2, and 3.1. The temperature area doe not move significantly (about 0.4 cm), while the temperature increases significantly wit a decrease in the total amount of CO2 (for every 200 K increase in Tad, the peak temperatu increases by about 300 K). With a decrease in the total amount of CO2 as a diluent, mo fuel and oxidant are involved in reaction per unit volume, including pyrolysis of the fue in other words, more fuel is pyrolyzed and more heat is released, and eventually, the tem perature of the flame becomes higher by unit volume as demonstrated in Figure 12b. Due to the highly strained nature of the counterflow flame, soot formation is low compared to the coflow and other flames, such as flames in the actual coal-fired boiler, s the radiation from particles would change violently with the amount of RFG. Therefor it must be emphasized that the practice of reducing the amount of RFG requires mo experimental and theoretical research.

Conclusions
In this paper, the effects of flame structure and temperature distribution on the rad ation emission of soot particulate matter and gases in oxygen-enriched counterflow diffu sion flame were studied by coupling a detailed chemical reaction mechanism with so and radiation models. The first calculation indicated that under the same conditions, al hough CO2 can inhibit the formation of soot due to its strong radiation properties, th overall radiation heat does not fall but instead rises. At the same Tad, the fuel concentratio decreases and the oxygen concentration increases causing the soot particle radiation disappear and the main radiating zone moves integrally toward the fuel side. At the sam Zst, the radiation area is broadened and the soot particle radiation is gradually enhanced Due to the highly strained nature of the counterflow flame, soot formation is low, compared to the coflow and other flames, such as flames in the actual coal-fired boiler, so the radiation from particles would change violently with the amount of RFG. Therefore, it must be emphasized that the practice of reducing the amount of RFG requires more experimental and theoretical research.

Conclusions
In this paper, the effects of flame structure and temperature distribution on the radiation emission of soot particulate matter and gases in oxygen-enriched counterflow diffusion flame were studied by coupling a detailed chemical reaction mechanism with soot and radiation models. The first calculation indicated that under the same conditions, although CO 2 can inhibit the formation of soot due to its strong radiation properties, the overall radiation heat does not fall but instead rises. At the same T ad , the fuel concentration decreases and the oxygen concentration increases causing the soot particle radiation to disappear and the main radiating zone moves integrally toward the fuel side. At the same Z st , the radiation area is broadened and the soot particle radiation is gradually enhanced.
Author Contributions: C.W. performed the data analysis and wrote the manuscript; G.T. and H.Y. contributed to the numerical calculation; L.L. and X.Y. reviewed the manuscript; Z.L. made the charts and performed analysis; C.L. contributed to the conception of the study and funded the data acquisition. All authors have read and agreed to the published version of the manuscript.
Funding: National Natural Science Foundation of China (51827808).
Institutional Review Board Statement: Not applicable.