卢臻; 杨越

doi:10.1007/s10409-021-09027-3

Modeling of the turbulent burning velocity for planar and Bunsen flames over a wide range of conditions

doi: 10.1007/s10409-021-09027-3

Lu Zhen^{1, 2},
Yang Yue^{1, 2, 3,*
, ,}

1.
State Key Laboratory for Turbulent and Complex Systems, College of Engineering, Peking University, Beijing, 100871, China;
2.
BIC-ESAT, Peking University, Beijing, 100871, China;
3.
HEDPS-CAPT, Peking University, Beijing, 100871, China;

Funds:

National Natural Science Foundation of China 91841302

National Key Research and Development Program of China 2020YFE0204200

Xplore Prize

More Information

Corresponding author: Yang Yue, E-mail address: yyg@pku.edu.cn (Yue Yang)

摘要

摘要: 本文提出并验证了一种适用于宽工况范围的湍流燃烧速度模型. 该模型具有显式表达式, 可用于湍流燃烧理论分析和模型构建. 模型主要由拉伸因子与湍流火焰面积两部分构成. 拉伸因子描述了湍流拉伸导致的局部火焰速度变化. 基于层流火焰的建表方法使拉伸因子模型能够考虑实际化学和输运特性的影响. 火焰面积模型根据自传播面的拉格朗日统计信息刻画了湍流火焰面的增长规律, 并考虑了湍流长度尺度和燃料特性的影响. 模型参数主要由流动及火焰参数、通用常数和层流火焰结果查表得到, 最后应用统一公式预测宽工况条件下的湍流燃烧速度变化. 本文应用宽工况范围下的自由传播平面火焰与本生灯火焰直接数值模拟和实验数据对模型开展评估与验证. 数据涵盖氢气至正十二烷等不同燃料、1–30个大气压、贫燃至富燃等不同当量比、湍流脉动速度与层流火焰速度比0.1–177.6, 湍流积分长度尺度与层流火焰厚度比0.5–66.7等条件下的共490个湍流燃烧工况. 对比不同工况的实验和模拟数据,模型预测的平均误差为28.1%. 相较其他现有模型, 该模型能正确描述不同燃料在宽工况范围下湍流燃烧速度变化趋势的差异.
Abstract: We develop and assess a model of the turbulent burning velocity $s_{T}$ over a wide range of conditions. The aim is to obtain an explicit $s_{T}$ model for turbulent combustion modeling and flame analysis. The model consists of sub models of the stretch factor and the turbulent flame area. The stretch factor characterizes the flame response of turbulence stretch and incorporates detailed chemistry and transport effects with a lookup table of laminar counterflow flames. The flame area model captures the area growth based on Lagrangian statistics of propagating surfaces and considers the effects of turbulence length scales and fuel characteristics. The present model predicts $s_{T}$ via an algebraic expression without free parameters. We assess the model using 490 cases of the direct numerical simulation or experiment reported from various research groups on planar and Bunsen flames over a wide range of conditions, covering fuels from hydrogen to n-dodecane, pressures from 1 to 30 atm, lean and rich mixtures, turbulence intensity ratios from 0.1 to 177.6, and turbulence length ratios from 0.5 to 66.7. Despite the scattering $s_{T}$ data in the literature, the comprehensive comparison shows that the proposed $s_{T}$ model has an overall good agreement over the wide range of conditions, with the averaged modeling error of 28.1%.
- Turbulent burning velocity /
- Turbulent premixed flame /
- Flame speed

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1. Parameters of DNS/experimental cases for model assessment in the regime diagram of turbulent premixed combustion. Each data point corresponds to one case, with different symbols for fuel species and colors for pressures.

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2. Comparison of $A_{T} / A_{L}$ calculated by model Eq. (12) for different fuels, with $L e$ from 0.4 to 2.6. All cases have $p = 1 atm$ and $l_{t} / δ_{L}^{0} = 1$ , and $u^{'} / s_{L}^{0}$ from 0 to 25.

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3. Comparison of $s_{T}$ calculated from the DNS [68] (symbols), the model Eq. (17) with length scale effects (solid lines), and the model Eq. (12) without length scale effects (dash-dotted lines).

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4. Fit of $C_{0}$ in Eq. (18) using the DNS/experimental cases listed in Table 1. Each marker represents one set of cases, and the marker size is proportional to the number of cases in the dataset.

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5. Comparisons of $s_{T}$ obtained from the DNS [42] (symbols with error bars for one standard deviation) and the proposed model Eq. (19) (solid lines) for lean hydrogen flames at $p = 1$ atm, $ϕ = 0.31$ and 0.4, and $l_{t} / δ_{L}^{0} = 0.5$ , along with $I_{0}$ (dashed lines). Only the shades for one standard deviation are presented for clarity.

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6. Comparisons of $s_{T}$ obtained from the DNS (symbols with error bars for one standard deviation) and the proposed model Eq. (19) (solid lines) for methane flames at $p = 1$ atm, $ϕ = 0.7$ , and $l_{t} / δ_{L}^{0} = 4$ and 1, along with $I_{0}$ (dashed lines). Note that the uncertainty of $s_{T}$ was not reported for the $l_{t} / δ_{L}^{0} = 4$ case. Dark and light shades denote one and two standard deviations for the model uncertainty range, respectively.

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7. Comparisons of $s_{T}$ obtained from the experiment [49] and the proposed model Eq. (19) for methane flames at various conditions.

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8. Comparisons of $s_{T}$ obtained from the DNS [32] (symbols) and the proposed model Eq. (19) (solid lines) for iso-octane flames with $ϕ = 0.9$ , $p = 0.1$ and 2.0 MPa, along with $I_{0}$ (dashed lines). Dark and light shades denote one and two standard deviations for the model uncertainty range, respectively.

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9. Comparison between DNS/experiment results and model predictions of $s_{T} / s_{L}^{0}$ for all the 490 data cases in Table 1. a The proposed model Eq. (19); b the model with ad hoc $C_{0}$ . The symbol shape represents the fuel species, and the color denotes the pressure, which is the same as those in Fig. 1.

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10. Comparison between DNS/experiment results and model predictions with Eq. (19) of $s_{T} / s_{L}^{0}$ for flames with different configurations in Table 1. a The planar flames; b the Bunsen flames. The symbol shape represents the fuel species, and the color denotes the pressure, which is the same as those in Fig. 1.

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. Table 1 Parameters of DNS/experimental datasets, along with the mean and root-mean-square (rms) modeling errors for each dataset

Dataset	Configuration	Fuel	$p$ (atm)	$ϕ$	$T_{u}$ (K)	Mean error (%)	rms error (%)
1. Aspden et al., 2011 [42]	planar	H $_{2}$	1	0.31,0.4	298	28.7	26.1
2. Aspden et al., 2015 [43]	planar	H $_{2}$	1	0.4	298	9.0	6.6
3. Lu and Yang, 2020 [41]	planar	H $_{2}$	1-10	0.6	300	9.0	5.0
4. Zhang et al., 2021 [44]	planar	H $_{2}$	1,5,10	0.6	300	9.4	8.6
5. Aspden et al., 2016 [35]	planar	CH $_{4}$	1	0.7	298	31.8	10.4
6. Aspden et al., 2017 [36]	planar	CH $_{4}$	1	0.7	298	15.0	3.9
7. Wang et al., 2017 [45]	planar	CH $_{4}$	20	0.5	810	26.7	7.0
8. Lapointe et al., 2015 [46]	planar	C $_{7}$ H $_{16}$	1	0.9	298, 500, 800	17.1	9.8
9. Savard et al., 2017 [32]	planar	C $_{8}$ H $_{18}$	1, 20	0.9	298	9.9	4.2
10. Aspden et al., 2017 [36]	planar	C $_{12}$ H $_{26}$	1	0.7	298	7.4	4.8
11. Kobayashi, 2002 [47]	Bunsen	CH $_{4}$	1-30	0.9	300	32.4	18.2
12. Kobayashi et al., 2005 [8]	Bunsen	CH $_{4}$	1-10	0.9	300, 573	41.7	15.0
13. Fragner et al., 2015 [48]	Bunsen	CH $_{4}$	1-4	0.7-1.0	300	8.3	10.7
14. Muppala et al., 2005 [13]	Bunsen	CH $_{4}$	1,5,10	0.9	298	22.8	16.7
15. Yuen and Gülder, 2013 [49]	Bunsen	CH $_{4}$	1	0.6-1.0	300	22.1	13.1
16. Tamadonfar and Gülder, 2014 [50]	Bunsen	CH $_{4}$	1	0.7-1.0	298	43.6	8.3
17. Tamadonfar and Gülder, 2015 [51]	Bunsen	CH $_{4}$	1	0.7-1.35	298	17.6	12.2
18. Wabel et al., 2017 [26]	Bunsen	CH $_{4}$	1	0.75	298	45.0	20.1
19. Wang et al., 2015 [52]	Bunsen	CH $_{4}$	5, 10	1.0	298	41.8	9.8
20. Zhang et al., 2018 [53]	Bunsen	CH $_{4}$	1	0.89	298	6.5	4.3
21. Cohé et al., 2009 [54]	Bunsen	CH $_{4}$	1,9	0.6	298	47.0	13.7
22. Venkateswaran et al,. 2015 [29]	Bunsen	CO/H $_{2}$	1,5,10	0.5-0.7	298	24.4	20.8
23. Zhang et al., 2018 [53]	Bunsen	CO/H $_{2}$	1	0.5-0.7	298	29.9	13.0
24. Cohé et al., 2007 [55]	Bunsen	CH $_{4}$ /H $_{2}$	1-9	0.6-0.8	298	47.7	13.5
25. Zhang et al., 2020 [56]	Bunsen	CH $_{4}$ /H $_{2}$	1	0.69-0.91	298	18.7	14.8
26. Ichikawa et al., 2019 [57]	Bunsen	CH $_{4}$ /NH $_{3}$	5	0.9	298	15.5	7.2
27. Muppala et al., 2005 [13]	Bunsen	C $_{2}$ H $_{4}$	5, 10	0.7	298	24.2	10.8
28. Tamadonfar and Gülder, 2015 [51]	Bunsen	C $_{2}$ H $_{6}$	1	0.7-1.45	298	23.7	12.4
29. Gülder et al., 2000 [58]	Bunsen	C $_{3}$ H $_{8}$	1	0.8,1.0	300	46.2	9.9
30. Zhang et al., 2018 [53]	Bunsen	C $_{3}$ H $_{8}$	1	0.76	298	3.5	3.1
31. Yuen and Gülder, 2013 [49]	Bunsen	C $_{3}$ H $_{8}$	1	0.7-1.0	300	20.0	12.9
32. Tamadonfar and Gülder, 2015 [51]	Bunsen	C $_{3}$ H $_{8}$	1	0.8-1.35	298	18.8	7.8
33. Muppala et al., 2005 [13]	Bunsen	C $_{3}$ H $_{8}$	5	0.9	298	32.9	17.3

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. Table 2 DNS parameters in Ref. [68]

Group	$l_{t}$ (cm)	$δ_{L}^{0}$ (cm)	$s_{L}^{0}$ (cm/s)	$l_{t} / δ_{L}^{0}$
R	0.65	0.22	0.300	2.955
T	0.65	0.40	0.163	1.625
L	0.34	0.22	0.300	1.545

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参考文献(76)

[[1]]	N. Peters. Turbulent Combustion. (Cambridge University Press, Cambridge, 2000).
[[2]]	A. N. Lipatnikov, and J. Chomiak, Turbulent flame speed and thickness: Phenomenology, evaluation, and application in multi-dimensional simulations, Prog. Energy Combust. Sci. 28, 1 (2002).
[[3]]	J. F. Driscoll, Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities, Prog. Energy Combust. Sci. 34, 91 (2008).
[[4]]	J. F. Driscoll, J. H. Chen, A. W. Skiba, C. D. Carter, E. R. Hawkes, and H. Wang, Premixed flames subjected to extreme turbulence: Some questions and recent answers, Prog. Energy Combust. Sci. 76, 100802 (2020).
[[5]]	D. You, Y. Huang, and V. Yang, A generalized model of acoustic response of turbulent premixed flame and its application to gas-turbine combustion instability analysis, Combust. Sci. Technol. 177, 1109 (2005).
[[6]]	P. Palies, T. Schuller, D. Durox, and S. Candel, Modeling of premixed swirling flames transfer functions, Proc. Combust. Institut. 33, 2967 (2011).
[[7]]	Ö. L. Gülder, Turbulent premixed flame propagation models for different combustion regimes, Sympos. (Int.) Combust. 23, 743 (1991).
[[8]]	H. Kobayashi, K. Seyama, H. Hagiwara, and Y. Ogami, Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature, Proc. Combust. Instit. 30, 827 (2005).
[[9]]	R. K. Cheng, and D. Littlejohn, Laboratory study of premixed H222, J. Eng. Gas Turbines Power 130, (2008).
[[10]]	D. Lee, and K. Y. Huh, Validation of analytical expressions for turbulent burning velocity in stagnating and freely propagating turbulent premixed flames, Combust. Flame 159, 1576 (2012).
[[11]]	S. Chaudhuri, V. Akkerman, and C. K. Law, Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability, Phys. Rev. E 84, 026322 (2011).
[[12]]	D. Bradley, A. K. C. Lau, M. Lawes, and F. T. Smith, Flame stretch rate as a determinant of turbulent burning velocity, Phil. Trans. R. Soc. Lond. A 338, 359 (1992).
[[13]]	S. P. R. Muppala, N. K. Aluri, F. Dinkelacker, and A. Leipertz, Development of an algebraic reaction rate closure for the numerical calculation of turbulent premixed methane, ethylene, and propane/air flames for pressures up to 1.0 MPa, Combust. Flame 140, 257 (2005).
[[14]]	D. Bradley, M. Lawes, K. Liu, and M. S. Mansour, Measurements and correlations of turbulent burning velocities over wide ranges of fuels and elevated pressures, Proc. Combust. Institut. 34, 1519 (2013).
[[15]]	M. T. Nguyen, D. W. Yu, and S. S. Shy, General correlations of high pressure turbulent burning velocities with the consideration of Lewis number effect, Proc. Combust. Institut. 37, 2391 (2019).
[[16]]	S. Verma, and A. N. Lipatnikov, Does sensitivity of measured scaling exponents for turbulent burning velocity to flame configuration prove lack of generality of notion of turbulent burning velocity?, Combust. Flame 173, 77 (2016).
[[17]]	G. Damköhler, Der einfluss der turbulenz auf die flammengeschwindigkeit in gasgemischen, Z. Elektrochem. Angew. Phys. Chem. 46, 601 626(1940).
[[18]]	F. C. Gouldin, An application of fractals to modeling premixed turbulent flames, Combust. Flame 68, 249 (1987).
[[19]]	Ö. L. Gülder, Turbulent premixed combustion modelling using fractal geometry, Sympos. (Int.) Combust. 23, 835 (1991).
[[20]]	A. R. Kerstein, W. T. Ashurst, and F. A. Williams, Field equation for interface propagation in an unsteady homogeneous flow field, Phys. Rev. A 37, 2728 (1988).
[[21]]	V. Yakhot, Propagation velocity of premixed turbulent flames, Combust. Sci. Technol. 60, 191 (1988).
[[22]]	P. D. Ronney, and V. Yakhot, Flame broadening effects on premixed turbulent flame speed, Combust. Sci. Technol. 86, 31 (1992).
[[23]]	V. L. Zimont, Theory of turbulent combustion of a homogeneous fuel mixture at high reynolds numbers, Combust. Explos. Shock Waves 15, 305 (1979).
[[24]]	Ö. L. Gülder, Contribution of small scale turbulence to burning velocity of flamelets in the thin reaction zone regime, Proc. Combust. Instit. 31, 1369 (2007).
[[25]]	G. V. Nivarti, R. S. Cant, and S. Hochgreb, Reconciling turbulent burning velocity with flame surface area in small-scale turbulence, J. Fluid Mech. 858, R1 (2019).
[[26]]	T. M. Wabel, A. W. Skiba, and J. F. Driscoll, Turbulent burning velocity measurements: Extended to extreme levels of turbulence, Proc. Combust. Instit. 36, 1801 (2017).
[[27]]	T. Poinsot, and D. Veynante, Theoretical and Numerical Combustion. 3rd ed (2012).
[[28]]	K. N. C. Bray, Studies of the turbulent burning velocity, Proc. R. Soc. Lond. A 431, 315 (1990).
[[29]]	P. Venkateswaran, A. Marshall, J. Seitzman, and T. Lieuwen, Scaling turbulent flame speeds of negative Markstein length fuel blends using leading points concepts, Combust. Flame 162, 375 (2015).
[[30]]	A. Amato, M. S. Day, R. K. Cheng, J. Bell, D. Dasgupta, and T. Lieuwen, Topology and burning rates of turbulent, lean, H2, Combust. Flame 162, 4553 (2015).
[[31]]	S. Lapointe, and G. Blanquart, Fuel and chemistry effects in high Karlovitz premixed turbulent flames, Combust. Flame 167, 294 (2016).
[[32]]	B. Savard, S. Lapointe, and A. Teodorczyk, Numerical investigation of the effect of pressure on heat release rate in iso, Proc. Combust. Instit. 36, 3543 (2017).
[[33]]	E. Abbasi-Atibeh, and J. M. Bergthorson, The effects of differential diffusion in counter-flow premixed flames with dilution and hydrogen enrichment, Combust. Flame 209, 337 (2019).
[[34]]	A. Trouvé, and T. Poinsot, The evolution equation for the flame surface density in turbulent premixed combustion, J. Fluid Mech. 278, 1 (1994).
[[35]]	A. J. Aspden, M. S. Day, and J. B. Bell, Three-dimensional direct numerical simulation of turbulent lean premixed methane combustion with detailed kinetics, Combust. Flame 166, 266 (2016).
[[36]]	A. J. Aspden, J. B. Bell, M. S. Day, and F. N. Egolfopoulos, Turbulence-flame interactions in lean premixed dodecane flames, Proc. Combust. Instit. 36, 2005 (2017).
[[37]]	R. S. Cant, B. Rogg, and K. N. C. Bray, On laminar flamelet modelling of the mean reaction rate in a premixed turbulent flame, Combust. Sci. Technol. 69, 53 (1990).
[[38]]	J. You, and Y. Yang, Modelling of the turbulent burning velocity based on Lagrangian statistics of propagating surfaces, J. Fluid Mech. 887, A11 (2020).
[[39]]	S. S. Girimaji, and S. B. Pope, Propagating surfaces in isotropic turbulence, J. Fluid Mech. 234, 247 (1992).
[[40]]	T. Zheng, J. You, and Y. Yang, Principal curvatures and area ratio of propagating surfaces in isotropic turbulence, Phys. Rev. Fluids 2, 103201 (2017).
[[41]]	Z. Lu, and Y. Yang, Modeling pressure effects on the turbulent burning velocity for lean hydrogen/air premixed combustion, Proc. Combust. Instit. 38, 2901 (2021).
[[42]]	A. J. Aspden, M. S. Day, and J. B. Bell, Turbulence-flame interactions in lean premixed hydrogen: Transition to the distributed burning regime, J. Fluid Mech. 680, 287 (2011).
[[43]]	A. J. Aspden, M. S. Day, and J. B. Bell, Turbulence-chemistry interaction in lean premixed hydrogen combustion, Proc. Combust. Instit. 35, 1321 (2015).
[[44]]	S. Zhang, Z. Lu, and Y. Yang, Modeling the displacement speed in the flame surface density method for turbulent premixed flames at high pressures, Phys. Fluids 33, 045118 (2021).
[[45]]	Z. Wang, V. Magi, and J. Abraham, turbulent flame speed dependencies in lean methane-air mixtures under engine relevant conditions, Combust. Flame 180, 53 (2017).
[[46]]	S. Lapointe, B. Savard, and G. Blanquart, Differential diffusion effects, distributed burning, and local extinctions in high Karlovitz premixed flames, Combust. Flame 162, 3341 (2015).
[[47]]	H. Kobayashi, Experimental study of high-pressure turbulent premixed flames, Exp. Therm. Fluid Sci. 26, 375 (2002).
[[48]]	R. Fragner, F. Halter, N. Mazellier, C. Chauveau, and I. Gökalp, Investigation of pressure effects on the small scale wrinkling of turbulent premixed Bunsen flames, Proc. Combust. Instit. 35, 1527 (2015).
[[49]]	F. T. C. Yuen, and Ö. L. Gülder, Turbulent premixed flame front dynamics and implications for limits of flamelet hypothesis, Proc. Combust. Instit. 34, 1393 (2013).
[[50]]	P. Tamadonfar, and Ö. L. Gülder, Flame brush characteristics and burning velocities of premixed turbulent methane/air Bunsen flames, Combust. Flame 161, 3154 (2014).
[[51]]	P. Tamadonfar, and Ö. L. Gülder, Effects of mixture composition and turbulence intensity on flame front structure and burning velocities of premixed turbulent hydrocarbon/air Bunsen flames, Combust. Flame 162, 4417 (2015).
[[52]]	J. Wang, S. Yu, M. Zhang, W. Jin, Z. Huang, S. Chen, and H. Kobayashi, Burning velocity and statistical flame front structure of turbulent premixed flames at high pressure up to 1.0 MPa, Exp. Therm. Fluid Sci. 68, 196 (2015).
[[53]]	W. Zhang, J. Wang, Q. Yu, W. Jin, M. Zhang, and Z. Huang, Investigation of the fuel effects on burning velocity and flame structure of turbulent premixed flames based on leading points concept, Combust. Sci. Technol. 190, 1354 (2018).
[[54]]	C. Cohé, C. Chauveau, I. Gökalp, and D. F. Kurtuluş, CO24, Proc. Combust. Instit. 32, 1803 (2009).
[[55]]	C. Cohé, F. Halter, C. Chauveau, I. Gökalp, and Ö. L. Gülder, Fractal characterisation of high-pressure and hydrogen-enriched CH4, Proc. Combust. Instit. 31, 1345 (2007).
[[56]]	W. Zhang, J. Wang, W. Lin, R. Mao, H. Xia, M. Zhang, and Z. Huang, Effect of differential diffusion on turbulent lean premixed hydrogen enriched flames through structure analysis, Int. J. Hydrogen Energy 45, 10920 (2020).
[[57]]	A. Ichikawa, Y. Naito, A. Hayakawa, T. Kudo, and H. Kobayashi, Burning velocity and flame structure of CH43, Int. J. Hydrogen Energy 44, 6991 (2019).
[[58]]	Ö. L. Gülder, G. J. Smallwood, R. Wong, D. R. Snelling, R. Smith, B. M. Deschamps, and J. C. Sautet, Flame front surface characteristics in turbulent premixed propane/air combustion, Combust. Flame 120, 407 (2000).
[[59]]	S. Kheirkhah, and Ö. L. Gülder, Consumption speed and burning velocity in counter-gradient and gradient diffusion regimes of turbulent premixed combustion, Combust. Flame 162, 1422 (2015).
[[60]]	S. Chaudhuri, F. Wu, D. Zhu, and C. K. Law, Flame speed and self-similar propagation of expanding turbulent premixed flames, Phys. Rev. Lett. 108, 044503 (2012).
[[61]]	S. S. Shy, C. C. Liu, J. Y. Lin, L. L. Chen, A. N. Lipatnikov, and S. I. Yang, Correlations of high-pressure lean methane and syngas turbulent burning velocities: Effects of turbulent Reynolds, Damköhler, and Karlovitz numbers, Proc. Combust. Institut. 35, 1509 (2015).
[[62]]	M. Klein, H. Nachtigal, M. Hansinger, M. Pfitzner, and N. Chakraborty, Flame curvature distribution in high pressure turbulent bunsen premixed flames, Flow Turbul. Combust. 101, 1173 (2018).
[[63]]	D. Bradley, P. H. Gaskell, X. J. Gu, and A. Sedaghat, Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity, Combust. Flame 143, 227 (2005).
[[64]]	H. Kobayashi, H. Hagiwara, H. Kaneko, and Y. Ogami, Effects of CO2, Proc. Combust. Instit. 31, 1451 (2007).
[[65]]	Y. Shim, S. Tanaka, M. Tanahashi, and T. Miyauchi, Local structure and fractal characteristics of H2, Proc. Combust. Instit. 33, 1455 (2011).
[[66]]	C. Meneveau, and T. Poinsot, Stretching and quenching of flamelets in premixed turbulent combustion, Combust. Flame 86, 311 (1991).
[[67]]	G. Nivarti, and S. Cant, Direct numerical simulation of the bending effect in turbulent premixed flames, Proc. Combust. Instit. 36, 1903 (2017).
[[68]]	D. Lee, and K. Y. Huh, Statistically steady incompressible DNS to validate a new correlation for turbulent burning velocity in turbulent premixed combustion, Flow Turbul. Combust. 84, 339 (2010).
[[69]]	F. Creta, P. E. Lapenna, R. Lamioni, N. Fogla, and M. Matalon, Propagation of premixed flames in the presence of Darrieus-Landau and thermal diffusive instabilities, Combust. Flame 216, 256 (2020).
[[70]]	Z. Lu, and Y. Yang, STModel. https://github.com/YYgroup/STmodel (2021).
[[71]]	G. P. Smith, Y. Tao, and H. Wang. Foundational fuel chemistry model version 1.0 (FFCM-1). http://nanoenergy.stanford.edu/ffcm1(2016).
[[72]]	S. G. Davis, A. V. Joshi, H. Wang, and F. N. Egolfopoulos, An optimized kinetic model of H2, Proc. Combust. Instit. 30, 1283 (2005).
[[73]]	Mechanical and Aerospace Engineering (Combustion Research), University of California at San Diego. Chemical-kinetic mechanisms for combustion applications. http://combustion.ucsd.edu (2016).
[[74]]	D. G. Goodwin, R. L. Speth, H. K. Moffat, and B. W. Weber, Cantera: An object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes. https://www.cantera.org (2021). Version 2.5.1.
[[75]]	C. T. Bowman, R. K. Hanson, D. F. Davidson, W. C. Gardiner, V. Lissianski Jr., G. P. Smith, D. M. Golden, M. Frenklach, and M. Goldenberg. GRI-Mech 2.11. http://combustion.berkeley.edu/gri_mech/ (1997).
[[76]]	C. S. Yoo, Z. Luo, T. Lu, H. Kim, and J. H. Chen, A DNS study of ignition characteristics of a lean iso, Proc. Combust. Instit. 34, 2985 (2013).