pith. sign in

arxiv: 2604.08061 · v1 · submitted 2026-04-09 · ⚛️ physics.flu-dyn

Effects of Soret diffusion on the intrinsic instability of premixed hydrogen/air flames

Qizhe Wen , Yan Wang , Linlin Yang , Youhi Morii , Thorsten Zirwes , Shengkai Wang , Zheng Chen This is my paper

Pith reviewed 2026-05-10 17:15 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords Soret diffusionhydrogen flamespremixed combustionflame instabilityequivalence ratiopreferential diffusiondirect numerical simulation
0
0 comments X

The pith

Soret diffusion increases linear instability growth rates in lean hydrogen flames while reducing them in richer mixtures and shrinking nonlinear finger structures by one-third.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper quantifies how Soret diffusion of light species near the flame front alters the evolution of intrinsic instabilities in premixed hydrogen/air flames across a wide range of equivalence ratios. One-dimensional counterflow analysis shows a reversal in perturbation growth rate around phi equals 1.7, with acceleration under lean conditions and damping above that value, accompanied by a similar reversal in Markstein length. Two-dimensional direct numerical simulations reveal that in the nonlinear regime Soret diffusion speeds formation of small-scale wrinkles in lean flames and reduces the size of large-scale finger structures, while also broadening distributions of Karlovitz number and density-weighted displacement speed. These changes occur even though local flame displacement speed rises, because overall flame surface area drops and global fuel consumption decreases. The work matters for predicting combustion behavior in hydrogen-fueled systems where instabilities influence efficiency, emissions, and safety.

Core claim

Soret diffusion increases the perturbation growth rate at phi less than 1.7, especially under lean conditions, but reduces the growth rate at phi greater than 1.7. In the nonlinear regime Soret diffusion accelerates small-scale wrinkle formation in lean hydrogen flames and reduces the characteristic size of large-scale finger structures by one-third. Although Soret diffusion promotes preferential diffusion and raises local flame displacement speed, the global fuel consumption rate decreases due to reduced overall flame surface area. Curvature-based analysis shows a synergistic interaction with Fickian diffusion that raises local equivalence ratio in positively curved regions and lowers it in

What carries the argument

Soret diffusion of light hydrogen species near the flame front, acting together with curvature and Fickian diffusion to modify local equivalence ratios and perturbation growth rates.

If this is right

  • Global fuel consumption falls in lean hydrogen flames despite higher local displacement speeds because flame surface area shrinks.
  • Markstein length exhibits a sensitivity reversal near the equivalence ratio of peak unstretched laminar flame speed.
  • Distributions of Karlovitz number and density-weighted displacement speed broaden, especially on the positive side, for lean flames.
  • Synergistic curvature effects with Fickian diffusion enhance local equivalence ratio in convex flame segments and reduce it in concave ones.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Combustion models for hydrogen engines may need explicit Soret terms to predict instability-driven wrinkling and heat release rates correctly.
  • The observed reversal at phi approximately 1.7 could be tested in other light-fuel mixtures to check whether the sign change tracks the Lewis number or the peak flame speed location.
  • Smaller finger structures under Soret influence might reduce the propensity for flame acceleration or transition to detonation in confined geometries.

Load-bearing premise

The numerical schemes and multicomponent transport models in the 1D and 2D simulations capture Soret diffusion effects accurately without introducing discretization artifacts in steep flame gradients.

What would settle it

An experimental measurement of linear perturbation growth rates in a lean hydrogen/air flame that shows no increase when Soret diffusion is selectively suppressed would contradict the central linear-regime claim.

Figures

Figures reproduced from arXiv: 2604.08061 by Linlin Yang, Qizhe Wen, Shengkai Wang, Thorsten Zirwes, Yan Wang, Youhi Morii, Zheng Chen.

Figure 1
Figure 1. Figure 1: Computational setup and boundary conditions. The [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the dispersion relations computed in [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Dispersion relations at various equivalence ratios [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The effect of Soret diffusion on the Markstein length. [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Temporal evolution of the finger size with (black) [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Joint probability density function (dot clouds) of the [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Probability density functions of the Karlovitz num [PITH_FULL_IMAGE:figures/full_fig_p006_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Partition of the flame front into three regions based [PITH_FULL_IMAGE:figures/full_fig_p007_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Distributions of the local equivalence ratio [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗
read the original abstract

Hydrogen flames exhibit multiple intrinsic instabilities. The low molar masses of H and H2 lead to significant Soret diffusion near the flame front; however, its influence on hydrogen flame instabilities remains to be quantified. This study investigates the effect of Soret diffusion on instability evolution dynamics via one-dimensional counterflow analysis and two-dimensional, high-fidelity direct numerical simulations covering both the linear growth regime and the fully developed nonlinear regime over a wide range of equivalence ratios (phi). In the linear regime, Soret diffusion increases the perturbation growth rate at phi < 1.7, especially under lean conditions, but reduces the growth rate at phi > 1.7. A similar sensitivity reversal is observed in the Markstein length near the peak equivalence ratio of unstretched laminar flame speed. In the nonlinear regime, Soret diffusion accelerates the formation of small-scale wrinkles in lean hydrogen flames and reduces the characteristic size of large-scale finger structure by one-third. An interesting observation is that, although Soret diffusion promotes preferential diffusion and increases the local flame displacement speed, the global fuel consumption rate decreases due to a reduction in the overall flame surface area. In addition, curvature-based flame segment analysis reveals a synergistic effect between Soret diffusion and Fickian diffusion that enhances/reduces the local equivalence ratio in positively/negatively curved regions of the flame front. The probability distributions of the Karlovitz number and the density-weighted displacement speed are also analyzed; results suggest that, for lean hydrogen flames, Soret diffusion broadens the distributions for both parameters, particularly on the positive side. These findings promise to advance the fundamental understanding of hydrogen flame dynamics under complex differential transport.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper investigates the effects of Soret diffusion on the intrinsic instabilities of premixed hydrogen/air flames using one-dimensional counterflow analysis for the linear regime and two-dimensional direct numerical simulations for both linear and nonlinear regimes across a range of equivalence ratios. Key findings include a reversal in the effect of Soret diffusion on perturbation growth rates at phi = 1.7, acceleration of small-scale wrinkles in lean flames, reduction in large-scale finger structure size by one-third, and impacts on local flame properties and consumption rates.

Significance. If the results are confirmed to be numerically robust, this work significantly advances the understanding of differential diffusion effects, particularly Soret diffusion, on hydrogen flame dynamics. The identification of the growth rate reversal and the nonlinear structural changes provides new insights that could improve predictive models for hydrogen combustion instabilities, which are critical for safe and efficient use of hydrogen as a fuel. The combination of linear stability analysis and high-fidelity DNS is a strength.

major comments (2)
  1. [Numerical Methods] The description of the transport model (mixture-averaged with thermal diffusion) lacks specific details on the implementation of Soret coefficients and the multicomponent diffusion matrix. This is load-bearing because the central claims rely on accurately isolating Soret effects from Fickian diffusion in high-gradient flame fronts; without this, discretization artifacts cannot be ruled out.
  2. [Results, linear regime] The reported reversal at phi=1.7 is presented without error bars or sensitivity to grid resolution in the 1D analysis. Given that the growth rate is a key quantitative output, demonstrating convergence and uncertainty would strengthen the claim that the sign change is physical rather than numerical.
minor comments (3)
  1. [Abstract] The statement that the finger structure size is reduced 'by one-third' should specify the definition of 'characteristic size' (e.g., average finger width or dominant wavelength) and how it was measured from the DNS data.
  2. [Nonlinear regime analysis] The curvature-based flame segment analysis could benefit from a clearer explanation of how segments are defined and the statistical sampling used for the probability distributions of Karlovitz number and displacement speed.
  3. [Overall] Consider adding a table summarizing the equivalence ratios studied and the corresponding growth rates with and without Soret to facilitate comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. We address each major comment below and will incorporate the suggested improvements in the revised manuscript.

read point-by-point responses

  1. Referee: [Numerical Methods] The description of the transport model (mixture-averaged with thermal diffusion) lacks specific details on the implementation of Soret coefficients and the multicomponent diffusion matrix. This is load-bearing because the central claims rely on accurately isolating Soret effects from Fickian diffusion in high-gradient flame fronts; without this, discretization artifacts cannot be ruled out.

    Authors: We agree that additional implementation details are needed for full reproducibility and to confirm isolation of Soret effects. In the revised manuscript, we will expand the Numerical Methods section with the explicit formulation of the mixture-averaged transport model, including the computation of Soret coefficients from thermal diffusion ratios and the multicomponent diffusion matrix (following the standard approach in Cantera and our DNS solver). We will also include the governing equations for the species diffusion velocities to allow verification that Soret contributions are correctly separated from Fickian diffusion. revision: yes

  2. Referee: [Results, linear regime] The reported reversal at phi=1.7 is presented without error bars or sensitivity to grid resolution in the 1D analysis. Given that the growth rate is a key quantitative output, demonstrating convergence and uncertainty would strengthen the claim that the sign change is physical rather than numerical.

    Authors: We appreciate this suggestion to strengthen the quantitative claim. We have performed additional grid-resolution studies for the one-dimensional counterflow stability analysis across the full range of equivalence ratios, including at phi = 1.7. The growth rates converge under refinement, and the sign reversal of the Soret effect remains unchanged. In the revised manuscript, we will add a brief convergence study (with estimated uncertainties) to the linear-regime section and include error bars on the reported growth-rate curves. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from direct numerical simulation

full rationale

The paper derives its claims exclusively from numerical integration of the governing equations via 1D counterflow linear stability analysis and 2D DNS, with explicit separation of Soret from Fickian diffusion terms in the transport model. No algebraic reduction, parameter fitting followed by prediction, self-definitional loops, or load-bearing self-citations appear in the derivation chain. The reported growth-rate reversal at phi=1.7, wrinkle acceleration, and finger-size reduction are direct simulation outputs, not forced by normalization or prior author results. The work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard multicomponent transport models and numerical solution of reacting flow equations; no new entities are postulated.

axioms (2)
  • standard math Navier-Stokes equations with detailed multicomponent diffusion including Soret term
    Invoked for both 1D counterflow and 2D DNS throughout the study.
  • domain assumption Chemical kinetics and transport properties from standard hydrogen-air mechanisms
    Assumed accurate for capturing preferential and Soret diffusion near the flame front.

pith-pipeline@v0.9.0 · 5622 in / 1345 out tokens · 42982 ms · 2026-05-10T17:15:53.686988+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages

  1. [1]

    Mallapaty, et al., How China could be carbon neutral by mid-century, Nature 586 (7830) (2020) 482–483

    S. Mallapaty, et al., How China could be carbon neutral by mid-century, Nature 586 (7830) (2020) 482–483

    work page 2020

  2. [2]

    Landau, On the theory of slow combustion, in: Dy- namics of Curved Fronts, Elsevier, 1988, pp

    L. Landau, On the theory of slow combustion, in: Dy- namics of Curved Fronts, Elsevier, 1988, pp. 403–411

    work page 1988

  3. [3]

    Darrieus, Propagation d’un front de flamme, La Technique Moderne 30 (18) (1938)

    G. Darrieus, Propagation d’un front de flamme, La Technique Moderne 30 (18) (1938)

    work page 1938

  4. [4]

    Manton, G

    J. Manton, G. V on Elbe, B. Lewis, Nonisotropic prop- agation of combustion waves in explosive gas mixtures and the development of cellular flames, J. Chem. Phys. 20 (1) (1952) 153–157

    work page 1952

  5. [5]

    G. H. Markstein, Nonsteady flame propagation: AGARDograph, V ol. 75, Elsevier, 2014

    work page 2014

  6. [6]

    Palm-Leis, R

    A. Palm-Leis, R. A. Strehlow, On the propagation of turbulent flames, Combust. Flame 13 (2) (1969) 111– 129

    work page 1969

  7. [7]

    Sivashinsky, Diffusional-thermal theory of cellular flames, Combust

    G. Sivashinsky, Diffusional-thermal theory of cellular flames, Combust. Sci. Technol. 15 (3-4) (1977) 137– 145

    work page 1977

  8. [8]

    Matalon, B

    M. Matalon, B. J. Matkowsky, Flames as gasdynamic discontinuities, J. Fluid Mech. 124 (1982) 239–259

    work page 1982

  9. [9]

    Matalon, C

    M. Matalon, C. Cui, J. Bechtold, Hydrodynamic the- ory of premixed flames: effects of stoichiometry, vari- able transport coefficients and arbitrary reaction or- ders, J. Fluid Mech. 487 (2003) 179–210

    work page 2003

  10. [10]

    C. K. Law, Combustion Physics, Cambridge Univer- sity Press, 2010

    work page 2010

  11. [11]

    Clavin, Dynamic behavior of premixed flame fronts in laminar and turbulent flows, Prog

    P. Clavin, Dynamic behavior of premixed flame fronts in laminar and turbulent flows, Prog. Energy Combust. Sci. 11 (1) (1985) 1–59

    work page 1985

  12. [12]

    Berger, K

    L. Berger, K. Kleinheinz, A. Attili, H. Pitsch, Char- acteristic patterns of thermodiffusively unstable pre- mixed lean hydrogen flames, Proc. Comb. Inst. 37 (2) (2019) 1879–1886

    work page 2019

  13. [13]

    Berger, A

    L. Berger, A. Attili, H. Pitsch, Intrinsic instabilities in premixed hydrogen flames: Parametric variation of pressure, equivalence ratio, and temperature. part 1-dispersion relations in the linear regime, Combust. Flame 240 (2022) 111935

    work page 2022

  14. [14]

    Gaucherand, D

    J. Gaucherand, D. Laera, C. Schulze-Netzer, T. Poinsot, Intrinsic instabilities of hydrogen and hydrogen/ammonia premixed flames: Influence of equivalence ratio, fuel composition and pressure, Combust. Flame 256 (2023) 112986

    work page 2023

  15. [15]

    C. E. Frouzakis, N. Fogla, A. G. Tomboulides, C. Al- tantzis, M. Matalon, Numerical study of unstable hy- drogen/air flames: shape and propagation speed, Proc. Comb. Inst. 35 (1) (2015) 1087–1095

    work page 2015

  16. [16]

    Altantzis, C

    C. Altantzis, C. Frouzakis, A. Tomboulides, M. Mat- alon, K. Boulouchos, Hydrodynamic and thermodiffu- sive instability effects on the evolution of laminar pla- nar lean premixed hydrogen flames, J. Fluid Mech. 700 (2012) 329–361

    work page 2012

  17. [17]

    L. Yang, Y . Wang, T. Zhang, X. Gou, W. Kong, Z. Chen, Propagation of ultra-lean hydrogen/air flames in a hele-shaw cell, Combust. Flame 281 (2025) 114444

    work page 2025

  18. [18]

    A. Ern, V . Giovangigli, Thermal diffusion effects in hydrogen-air and methane-air flames, Combust. The- ory Model. 2 (4) (1998) 349

    work page 1998

  19. [19]

    A. Ern, V . Giovangigli, Impact of detailed multicom- ponent transport on planar and counterflow hydro- gen/air and methane/air flames, Combust. Sci. Tech- nol. 149 (1-6) (1999) 157–181

    work page 1999

  20. [20]

    F. Yang, C. K. Law, C. Sung, H. Zhang, A mechanistic study of soret diffusion in hydrogen–air flames, Com- bust. Flame 157 (1) (2010) 192–200

    work page 2010

  21. [21]

    Faghih, W

    M. Faghih, W. Han, Z. Chen, Effects of soret diffusion on premixed flame propagation under engine-relevant conditions, Combust. Flame 194 (2018) 175–179

    work page 2018

  22. [22]

    F. Yang, H. Zhang, X. Wang, Effects of soret diffusion on the laminar flame speed of n-butane-air mixtures, Proc. Combust. Inst. 33 (1) (2011) 947–953

    work page 2011

  23. [23]

    Xin, C.-J

    Y . Xin, C.-J. Sung, C. K. Law, A mechanistic evalua- tion of soret diffusion in heptane/air flames, Combust. Flame 159 (7) (2012) 2345–2351

    work page 2012

  24. [24]

    Liang, Z

    W. Liang, Z. Chen, F. Yang, H. Zhang, Effects of Soret diffusion on the laminar flame speed and Markstein length of syngas/air mixtures, Proc. Comb. Inst. 34 (1) (2013) 695–702

    work page 2013

  25. [25]

    Garc ´ıa-Ybarra, C

    P. Garc ´ıa-Ybarra, C. Trevi˜no, Analysis of the thermal diffusion effects on the ignition of hydrogen-air mix- tures in the boundary layer of a hot flat plate, Combust. Flame 96 (3) (1994) 293–303

    work page 1994

  26. [26]

    W. Han, Z. Chen, Effects of soret diffusion on spheri- cal flame initiation and propagation, Int. J. Heat Mass Transf. 82 (2015) 309–315

    work page 2015

  27. [27]

    Jayachandran, F

    J. Jayachandran, F. N. Egolfopoulos, Thermal and ludwig–soret diffusion effects on near-boundary ig- nition behavior of reacting mixtures, Proc. Combust. Inst. 36 (1) (2017) 1505–1511

    work page 2017

  28. [28]

    Gopalakrishnan, J

    V . Gopalakrishnan, J. Abraham, Effects of multi- component diffusion on predicted ignition characteris- tics of an n-heptane diffusion flame, Combust. Flame 136 (4) (2004) 557–566

    work page 2004

  29. [29]

    D. Yu, Z. Chen, Premixed flame ignition: Theoretical development, Prog. Energy Combust. Sci. 104 (2024) 101174

    work page 2024

  30. [30]

    D. Fong, J. Bechtold, C. K. Law, Asymptotic struc- ture of laminar diffusion flames at high pressure, Phys. Fluids 24 (9) (2012)

    work page 2012

  31. [31]

    W. Han, Z. Chen, Effects of soret diffusion on pre- mixed counterflow flames, Combust. Sci. Technol. 187 (8) (2015) 1195–1207

    work page 2015

  32. [32]

    Liang, C

    W. Liang, C. K. Law, Z. Chen, Ignition of hydrogen/air mixtures by a heated kernel: Role of Soret diffusion, Combust. Flame 197 (2018) 416–422

    work page 2018

  33. [33]

    Rosner, R

    D. Rosner, R. Israel, B. La Mantia, “heavy” species ludwig–soret transport effects in air-breathing com- bustion, Combust. Flame 123 (4) (2000) 547–560

    work page 2000

  34. [34]

    Dworkin, M

    S. Dworkin, M. Smooke, V . Giovangigli, The impact of detailed multicomponent transport and thermal dif- fusion effects on soot formation in ethylene/air flames, Proc. Comb. Inst. 32 (1) (2009) 1165–1172

    work page 2009

  35. [35]

    M. R. Acquaviva, A. Porcarelli, I. Langella, Influence of soret effect on flame structure and nox emissions in highly strained lean premixed counterflow hydrogen flames, Fuel 395 (2025) 134939

    work page 2025

  36. [36]

    Garcia-Ybarra, C

    P. Garcia-Ybarra, C. Nicoli, P. Clavin, Soret and dilu- tion effects on premixed flames, Combust. Sci. Tech- nol. 42 (1-2) (1984) 87–109

    work page 1984

  37. [37]

    J. F. Grcar, J. B. Bell, M. S. Day, The Soret effect in naturally propagating, premixed, lean, hydrogen–air flames, Proc. Comb. Inst. 32 (1) (2009) 1173–1180

    work page 2009

  38. [38]

    Z. Zhou, F. E. Hern ´andez-P´erez, Y . Shoshin, J. A. van Oijen, L. P. de Goey, Effect of Soret diffusion on lean hydrogen/air flames at normal and elevated pres- sure and temperature, Combust. Theory Model. 21 (5) (2017) 879–896

    work page 2017

  39. [39]

    D’Alessio, C

    F. D’Alessio, C. Matteucci, P. Lapenna, F. Creta, In- trinsic instability of lean hydrogen/ammonia premixed flames: Influence of Soret effect and pressure, Fuel Commun. 19 (2024) 100110

    work page 2024

  40. [40]

    Zirwes, F

    T. Zirwes, F. Zhang, T. L. Kaiser, K. Oberleithner, O. T. Stein, H. Bockhorn, A. Kronenburg, The role of thermodiffusion and dimensionality in the forma- tion of cellular instabilities in hydrogen flames, Proc. Comb. Inst. 40 (1-4) (2024) 105665

    work page 2024

  41. [41]

    Howarth, A

    T. Howarth, A. Aspden, An empirical characteristic scaling model for freely-propagating lean premixed hydrogen flames, Combust. Flame 237 (2022) 111805

    work page 2022

  42. [42]

    Howarth, M

    T. Howarth, M. S. Day, H. Pitsch, A. Aspden, Thermal diffusion, exhaust gas recirculation and blending ef- fects on lean premixed hydrogen flames, Proc. Comb. Inst. 40 (1-4) (2024) 105429

    work page 2024

  43. [43]

    Korsakova, V

    A. Korsakova, V . Gubernov, V . Bykov, U. Maas, The effect of soret diffusion on stability of rich premixed hydrogen–air flames, Int. J. Hydrogen Energy 41 (39) (2016) 17670–17675

    work page 2016

  44. [44]

    Zheng, H

    J. Zheng, H. Wang, K. Luo, J. Fan, The stability and morphology of laminar premixed hydrogen/air flames under various gravity conditions, Combust. Flame 267 (2024) 113602

    work page 2024

  45. [45]

    Al Kassar, L

    S. Al Kassar, L. Berger, P. E. Lapenna, F. Creta, H. Pitsch, A. Attili, Efficient and accurate calculation of dispersion relations for intrinsically unstable pre- mixed flames, Combust. Flame 269 (2024) 113640

    work page 2024

  46. [46]

    Zirwes, M

    T. Zirwes, M. Sontheimer, F. Zhang, A. Abdelsamie, F. E. H. P´erez, O. T. Stein, H. G. Im, A. Kronenburg, H. Bockhorn, Assessment of numerical accuracy and parallel performance of openfoam and its reacting flow extension ebidnsfoam, Flow, Turbul. Combust. 111 (2) (2023) 567–602

    work page 2023

  47. [47]

    J. Li, Z. Zhao, A. Kazakov, F. L. Dryer, An updated comprehensive kinetic model of hydrogen combustion, Int. J. Chem. Kinet. 36 (10) (2004) 566–575

    work page 2004

  48. [48]

    Schlup, G

    J. Schlup, G. Blanquart, Validation of a mixture- averaged thermal diffusion model for premixed lean hydrogen flames, Combust. Theory Model. 22 (2) (2018) 264–290

    work page 2018

  49. [49]

    Zirwes, A

    T. Zirwes, A. Kronenburg, Assessment of approxi- mate Soret diffusion models for hydrogen and ammo- nia combustion, Flow, Turbul. Combust. (2025) 1–20

    work page 2025

  50. [50]

    D. G. Goodwin, R. L. Speth, H. K. Moffat, B. W. We- ber, Cantera: An object-oriented software toolkit for chemical kinetics, thermodynamics, and transport pro- cesses, Zenodo (2018)

    work page 2018

  51. [51]

    Vervisch, E

    L. Vervisch, E. Bidaux, K. Bray, W. Kollmann, Sur- face density function in premixed turbulent combus- tion modeling, similarities between probability density function and flame surface approaches, Phys. Fluids 7 (10) (1995) 2496–2503

    work page 1995

  52. [52]

    Berger, A

    L. Berger, A. Attili, H. Pitsch, Intrinsic instabilities in premixed hydrogen flames: parametric variation of pressure, equivalence ratio, and temperature. Part 2–non-linear regime and flame speed enhancement, Combust. Flame 240 (2022) 111936

    work page 2022

  53. [53]

    A. L. S ´anchez, F. A. Williams, Recent advances in un- derstanding of flammability characteristics of hydro- gen, Prog. Energy Combust. Sci. 41 (2014) 1–55

    work page 2014

  54. [54]

    M. Day, J. Bell, P.-T. Bremer, V . Pascucci, V . Beck- ner, M. Lijewski, Turbulence effects on cellular burn- ing structures in lean premixed hydrogen flames, Com- bust. Flame 156 (5) (2009) 1035–1045

    work page 2009

  55. [55]

    X. Wen, L. Berger, F. V om Lehn, A. Parente, H. Pitsch, Numerical analysis and flamelet modeling of NOx formation in a thermodiffusively unstable hydrogen flame, Combust. Flame 253 (2023) 112817

    work page 2023

  56. [56]

    Lehmann, N

    T. Lehmann, N. Dimidziev, T. L. Howarth, M. Gaud- ing, H. Pitsch, Effects of intrinsic flame instabilities on nitrogen oxide formation in laminar premixed ammo- nia/hydrogen/air flames, Proc. Comb. Inst. 41 (2025) 105961. 10

    work page 2025