Cavity-Stabilized Rotating Flames in a Circular Hele-Shaw Burner

Shengkai Wang; Xiangyu Nie

arxiv: 2604.08035 · v1 · submitted 2026-04-09 · ⚛️ physics.flu-dyn

Cavity-Stabilized Rotating Flames in a Circular Hele-Shaw Burner

Xiangyu Nie , Shengkai Wang This is my paper

Pith reviewed 2026-05-10 17:21 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn

keywords rotating flamesHele-Shaw burnercavity stabilizationpremixed combustionmicro-combustorsflame flashbacktraveling waves

0 comments

The pith

Rotating flames in a cavity-equipped circular Hele-Shaw burner transition to steady rings at a critical mass flow rate that stays constant across fuels, gaps, and mixtures.

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

The paper reports direct observations of premixed flames that spontaneously form rotating patterns in an open thin-gap burner fitted with an annular cavity. These patterns arise when flashback is limited by thermal quenching, so that flame heads glide along the cavity edge in a low-velocity zone created by rapid expansion. At higher flows the single rotating head splits into multiple equally spaced heads before the whole structure locks into a steady ring anchored at the cavity. The central result is that the mass flow rate at which rotation gives way to the steady ring is insensitive to equivalence ratio, gap height, and choice of fuel. This points to a stabilization mechanism that could be used to design micro-combustors that maintain stable operation without fine tuning for each fuel or geometry.

Core claim

Self-organized rotating flames form spontaneously at low flow rates through a dynamic balance between local flame speed and opposing flow velocity, with the cavity providing a low-speed zone that allows heads to glide stably along its leading edge; as total mass flow increases these flames split into multiple heads and then transition into steady ring-shaped flames, with the critical mass flow rate at the rotating-to-steady boundary remaining unchanged over wide ranges of equivalence ratio, gap distance, and fuel type.

What carries the argument

The annulus cavity flame holder that creates a localized low-speed zone, enabling a traveling-wave balance between flame propagation speed and bulk flow that is arrested by thermal quenching.

If this is right

Micro-combustor designs can use cavity holders to achieve stable operation over broad operating ranges without sensitivity to exact fuel composition.
Regime diagrams based on total mass flow can define safe boundaries between rotating and steady modes for thin-gap burners.
Traveling-wave flames that preserve near-constant shape at low flows provide a simplified test case for modeling flame-flow coupling in micro-channels.
The same cavity stabilization principle may extend to other premixed systems where flashback must be prevented at low throughput.

Where Pith is reading between the lines

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

If the mass-flow insensitivity holds generally, models could be simplified to treat the transition as a geometric and hydrodynamic threshold rather than a chemistry-dependent one.
Systematic variation of wall thermal conductivity in follow-up tests would clarify whether quenching remains the dominant arresting mechanism.
Scaling the burner radius while keeping gap fixed would test whether the observed head-spacing and frequency trends persist beyond the micro-scale regime.

Load-bearing premise

The rotating patterns arise purely from the local balance of flame speed against flow velocity plus thermal quenching, without major unmeasured contributions from varying heat losses or three-dimensional flow features.

What would settle it

Repeat the transition-boundary measurements while deliberately varying gap distance by a factor of two or testing a fuel with markedly different thermal diffusivity and checking whether the reported critical mass flow rate remains constant.

Figures

Figures reproduced from arXiv: 2604.08035 by Shengkai Wang, Xiangyu Nie.

**Figure 1.** Figure 1: Schematic of the current experimental setup. (a) Overall configuration of the burner and the optical diagnostic system. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: Schematic of the current computational setup and [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 4.** Figure 4: The measured rotation frequency (black) and the cal [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: Representative top-view OH* chemiluminescence [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗

**Figure 7.** Figure 7: Regime diagram of the experimentally observed [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗

**Figure 8.** Figure 8: Distributions of the heat release rate q˙ (left) and velocity magnitude with streamlines (right) for representative cases near the transition boundary between rotating and steady flames. From top to bottom, the cases correspond to ϕ = 0.70, 0.85, 1.00, 1.15 and 1.30, with total mass flow rates of 8.50, 8.50, 9.55. 10.75 and 10.75 SLPM, respectively. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗

**Figure 8.** Figure 8: In all cases, the flame remains attached to [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗

**Figure 10.** Figure 10: Critical total mass flow rate at the mode transition [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗

**Figure 9.** Figure 9: Characteristic flame cross-section Af at the rotatingsteady mode transition boundary, calculated as a function of the equivalence ratio (top) and the gap distance (bottom). The relative insensitivity of the mode transition boundary to equivalence ratio was consistently observed across various gap distances ranging from 0.2 to 2.5 mm. The critical total mass flow rate at the mode transition boundary is sh… view at source ↗

**Figure 12.** Figure 12: Regime diagrams of the experimentally observed [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗

read the original abstract

We report direct experimental observations of self-organized rotating flames of premixed CH4 and air in an open circular Hele-Shaw burner equipped with an annulus cavity flame holder. These flames formed spontaneously at sufficiently low flow rates, where flame flashback was counteracted by thermal quenching, resulting in a dynamic balance between the local flame speed and flow velocity. Unlike flames propagating in closed micro-channels, these flames exhibited stable traveling-wave patterns with heads gliding along the leading edge of the cavity, where rapid expansion created a low-speed zone that facilitated flame stabilization. At low flow rates, the rotating flames were single-headed, with their rotation frequencies roughly proportional to the laminar flame speeds, suggesting that the flame fronts traveled in a nearly constant-shape fashion. As the flow rate increased, the rotating flames split into multiple heads at approximately equal spacing, and the number of heads and rotation frequency increased with the flow rate, until these rotating flames transitioned into steady ring-shaped flames anchored at the cavity leading edge. Blow-off or extinction occurred at sufficiently high flow rates, where the flame front was pushed out of the rear side of the cavity. Parametric measurements were conducted over a wide range of equivalence ratios and flow rates, from which a regime diagram of different flame modes and their transition boundaries was obtained. Additional experiments were conducted on C3H8 and DME. It was found that the critical total mass flow rate at the rotating-steady flame transition boundary is insensitive to equivalence ratio, gap distance, and fuel type. These results should be useful not only for the fundamental understanding of flame dynamics in micro-channels but also for the practical design of micro-combustors and the application of micro-combustion technologies.

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.

Desk Editor's Note private letter to a colleague

The paper shows new rotating and multi-headed flame patterns plus a regime diagram in a cavity-stabilized Hele-Shaw burner, but the headline claim of parameter-insensitive transition mass flow rates rests on limited controls and no reported uncertainties.

read the letter

This paper reports original observations of self-organized rotating flames in an open circular Hele-Shaw burner with an annulus cavity. At low flows the flames are single-headed and rotate with frequencies that scale roughly with laminar flame speed; they split into multiple heads at higher flows before settling into steady rings and eventually blowing off. The authors map the mode boundaries over a range of equivalence ratios and flow rates for methane-air, then repeat the key transition measurements with propane and DME. The regime diagram and the reported scaling are the concrete additions here. The work is useful for anyone cataloging stabilization mechanisms in confined micro-combustors. The central observation that the critical total mass flow rate at the rotating-to-steady boundary stays roughly constant across equivalence ratio, gap distance, and the three fuels is presented clearly. The proposed mechanism is a local balance between flame speed and flow velocity aided by thermal quenching at the cavity edge. The soft spot is exactly that insensitivity result. The abstract gives no error bars, repeatability counts, or local diagnostics, and the stress-test concern is fair: changing gap or equivalence ratio simultaneously alters quenching distance, plate heat loss, and possible three-dimensional recirculation, so an apparent invariance in total flow rate could arise from offsetting effects rather than the proposed balance alone. Without velocity or temperature data at the transition points it is hard to separate the contributions. The paper is coherent and reports what was seen without overclaiming theory. It is aimed at combustion researchers working on micro-scale flame patterns and stabilization. A reader who needs the specific regime boundaries or the multi-headed patterns for comparison would get value from it. I would bring it to a reading group on experimental confined combustion. I would cite the diagram if I were working in the same geometry. It deserves peer review because the observations are new and the setup is accessible, even though the quantitative claims will need tighter error analysis and controls.

Referee Report

2 major / 2 minor

Summary. The paper reports experimental observations of self-organized rotating premixed flames (CH4/air, with additional tests on C3H8 and DME) in an open circular Hele-Shaw burner with an annular cavity flame holder. At low flow rates, flames form single- or multi-headed rotating patterns stabilized by a dynamic balance between local flame speed and flow velocity, counteracted by thermal quenching at the cavity leading edge. As total mass flow rate increases, the number of heads and rotation frequency rise until a transition to steady ring-shaped flames occurs; further increase leads to blow-off. Parametric mapping yields a regime diagram, with the headline result that the critical total mass flow rate at the rotating-to-steady transition boundary is insensitive to equivalence ratio, gap distance, and fuel type.

Significance. If the reported insensitivity of the transition mass-flow-rate boundary holds under quantitative scrutiny, the work would demonstrate a robust, parameter-insensitive stabilization mechanism in an open micro-scale geometry. This could inform practical micro-combustor design and contribute to understanding of traveling-wave flame dynamics. The study provides direct visualization of pattern formation and transitions across a wide parameter space and multiple fuels, which is a strength for an observational fluid-dynamics paper.

major comments (2)

[Abstract] Abstract: The central claim that 'the critical total mass flow rate at the rotating-steady flame transition boundary is insensitive to equivalence ratio, gap distance, and fuel type' is presented without error bars, standard deviations, repeatability counts, or statistical measures of variability across runs. This is load-bearing for the headline result, as the skeptic concern about compensatory heat-loss or 3D-flow effects cannot be evaluated without these data.
[Results] Results/Parametric measurements: No local diagnostics (temperature, velocity, or heat-flux measurements) or estimates of conductive heat loss to the plates are reported at the transition points as functions of gap distance or equivalence ratio. Without these, the interpretation that the transition is set purely by local flame-speed/flow-velocity balance (rather than unmeasured variations in quenching distance or recirculation) remains untested.

minor comments (2)

[Abstract] The abstract refers to 'rapid expansion created a low-speed zone' without indicating whether this is inferred from flow visualization, PIV, or simple continuity arguments.
[Figures] Figure captions and regime diagrams should explicitly state the number of independent runs and the criterion used to identify each transition boundary.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address the two major comments below, indicating where revisions will be made to strengthen the presentation of our results.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that 'the critical total mass flow rate at the rotating-steady flame transition boundary is insensitive to equivalence ratio, gap distance, and fuel type' is presented without error bars, standard deviations, repeatability counts, or statistical measures of variability across runs. This is load-bearing for the headline result, as the skeptic concern about compensatory heat-loss or 3D-flow effects cannot be evaluated without these data.

Authors: We agree that the absence of statistical measures weakens the presentation of this central claim. In the revised version, we will include error bars on the critical transition mass flow rates in the regime diagram, derived from repeated experiments (at least three runs per condition). Our re-examination of the data shows that the variability is small (typically within 3-7% of the mean value), which reinforces the reported insensitivity. This addition will allow readers to assess the robustness against potential confounding effects. revision: yes
Referee: [Results] Results/Parametric measurements: No local diagnostics (temperature, velocity, or heat-flux measurements) or estimates of conductive heat loss to the plates are reported at the transition points as functions of gap distance or equivalence ratio. Without these, the interpretation that the transition is set purely by local flame-speed/flow-velocity balance (rather than unmeasured variations in quenching distance or recirculation) remains untested.

Authors: We recognize that local measurements would provide stronger direct evidence for the proposed mechanism. However, the thin gap and open configuration of the Hele-Shaw burner make it difficult to introduce probes without significantly disturbing the flow field or flame. Our interpretation is supported indirectly by the scaling of rotation frequency with laminar flame speed and, crucially, by the insensitivity of the transition boundary to gap distance and fuel type—parameters that would be expected to influence heat loss and quenching if those were dominant. We will revise the discussion section to include order-of-magnitude estimates of conductive heat loss based on literature correlations for parallel-plate burners, demonstrating that these losses do not vary in a manner consistent with the observed transitions. We also note this as a limitation for future work. revision: partial

Circularity Check

0 steps flagged

No circularity: purely observational experimental study

full rationale

The manuscript reports direct experimental observations of flame modes, transition boundaries, and parametric insensitivity in a Hele-Shaw burner. No equations, derivations, fitted parameters, or model predictions appear in the abstract or described content. The central claim of insensitivity of critical mass flow rate is obtained from measured regime diagrams across equivalence ratios, gap distances, and fuels, without any reduction to self-defined quantities or self-citation chains. The study is self-contained against external benchmarks as an empirical report.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No theoretical derivations, free parameters, or new postulated entities; the work relies on standard combustion and fluid-dynamics principles not detailed in the abstract.

pith-pipeline@v0.9.0 · 5606 in / 1051 out tokens · 63105 ms · 2026-05-10T17:21:12.673937+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages

[1]

Maruta, Micro and mesoscale combustion, Pro- ceedings of the Combustion Institute 33 (1) (2011) 125–150

K. Maruta, Micro and mesoscale combustion, Pro- ceedings of the Combustion Institute 33 (1) (2011) 125–150

work page 2011
[2]

A. C. Fernandez-Pello, Micropower generation using combustion: Issues and approaches, Proceedings of the Combustion Institute 29 (1) (2002) 883–899, pro- ceedings of the Combustion Institute

work page 2002
[3]

Mart ´ınez-Ruiz, F

D. Mart ´ınez-Ruiz, F. Veiga-L ´opez, D. Fern ´andez- Galisteo, V . N. Kurdyumov, M. S ´anchez-Sanz, The role of conductive heat losses on the formation of iso- lated flame cells in hele-shaw chambers, Combustion and Flame 209 (2019) 187–199

work page 2019
[4]

Al Sarraf, C

E. Al Sarraf, C. Almarcha, J. Quinard, B. Radisson, B. Denet, P. Garcia-Ybarra, Darrieus–landau instabil- ity and markstein numbers of premixed flames in a hele-shaw cell, Proceedings of the Combustion Insti- tute 37 (2) (2019) 1783–1789

work page 2019
[5]

S. Shen, J. Wongwiwat, P. Ronney, Flame propagation in quasi-2d channels: stability, rates and scaling, in: AIAA Scitech 2019 Forum, 2019, p. 2365

work page 2019
[6]

E. A. Sarraf, C. Almarcha, J. Quinard, B. Radisson, B. Denet, Quantitative analysis of flame instabilities in a hele-shaw burner, Flow, Turbulence and Combustion 101 (3) (2018) 851–868

work page 2018
[7]

Daou, Effect of taylor dispersion on the thermo- diffusive instabilities of flames in a hele–shaw burner, Combustion Theory and Modelling 25 (4) (2021) 765– 783

J. Daou, Effect of taylor dispersion on the thermo- diffusive instabilities of flames in a hele–shaw burner, Combustion Theory and Modelling 25 (4) (2021) 765– 783

work page 2021
[8]

Veiga-L ´opez, D

F. Veiga-L ´opez, D. Mart ´ınez-Ruiz, E. Fern ´andez- Tarrazo, M. S ´anchez-Sanz, Experimental analysis of oscillatory premixed flames in a hele-shaw cell prop- agating towards a closed end, Combustion and Flame 201 (2019) 1–11

work page 2019
[9]

Kumar, K

S. Kumar, K. Maruta, S. Minaev, On the formation of multiple rotating pelton-like flame structures in radial microchannels with lean methane–air mixtures, Pro- ceedings of the Combustion Institute 31 (2) (2007) 3261–3268

work page 2007
[10]

Kumar, K

S. Kumar, K. Maruta, S. Minaev, Pattern formation of flames in radial microchannels with lean methane-air mixtures, Physical Review E 75 (1) (2007) 016208

work page 2007
[11]

A. Fan, S. Minaev, E. Sereshchenko, R. Fursenko, S. Kumar, W. Liu, K. Maruta, Experimental and nu- merical investigations of flame pattern formations in a radial microchannel, Proceedings of the Combustion Institute 32 (2) (2009) 3059–3066

work page 2009
[12]

A. Fan, J. Wan, K. Maruta, H. Nakamura, H. Yao, W. Liu, Flame dynamics in a heated meso-scale ra- dial channel, Proceedings of the Combustion Institute 34 (2) (2013) 3351–3359

work page 2013
[13]

R. Zhou, D. Wu, J. Wang, Progress of continuously rotating detonation engines, Chinese Journal of Aero- nautics 29 (1) (2016) 15–29

work page 2016
[14]

X. Nie, S. Wang, Edge-stabilized rotating flames in a circular Hele-Shaw cell, Under Review (2026)

work page 2026
[15]

Ben-Yakar, R

A. Ben-Yakar, R. K. Hanson, Cavity flame-holders for ignition and flame stabilization in scramjets: an overview, Journal of Propulsion and Power 17 (4) (2001) 869–877

work page 2001
[16]

H. Wang, Z. Wang, M. Sun, N. Qin, Combustion char- acteristics in a supersonic combustor with hydrogen in- jection upstream of cavity flameholder, Proceedings of the Combustion Institute 34 (2) (2013) 2073–2082

work page 2013
[17]

X. Yang, T. Tang, Q. Li, W. Han, R. Gu, H. Chen, Y . Huang, M. Sun, H. Wang, Y . Yang, J. Zhu, Cavity-enhanced combustion in a mach 6 axisym- metric scramjet, Combustion and Flame 286 (2026) 114807

work page 2026
[18]

H. Wang, Z. Yan, Y . Zhao, S. Wang, On the self- excited instabilities of premixed swirl flames near blow-off limits – An experimental study using simul- taneous measurements of thermal boundary conditions and core flow scalar fields, Combustion and Flame 277 (2025) 114171

work page 2025
[19]

I. H. Bockhorn, Implementation and validation of a solver for direct numerical simulations of turbulent re- acting flows in openfoam, Ph.D. thesis, Karlsruhe In- stitute of Technology (2012)

work page 2012
[20]

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, Turbulence and Combus- tion 111 (2) (2023) 567–602

work page 2023
[21]

H. G. Weller, G. Tabor, H. Jasak, C. Fureby, A ten- sorial approach to computational continuum mechan- ics using object-oriented techniques, Computers in Physics 12 (6) (1998) 620–631

work page 1998
[22]

Kazakov, M

A. Kazakov, M. Frenklach, Reduced reaction sets based on gri-mech 1.2, University of California at Berkeley, Berkeley, CA, http://www. me. berkeley. edu/drm (1994)

work page 1994
[23]

D. G. Goodwin, H. K. Moffat, I. Schoegl, R. L. Speth, B. W. Weber, Cantera: An object-oriented soft- ware toolkit for chemical kinetics, thermodynamics, and transport processes,https://www.cantera. org, version 3.1.0 (2024)

work page 2024
[24]

Zhang, W

Y . Zhang, W. Dong, L. Vandewalle, R. Xu, G. Smith, H. Wang, Foundational Fuel Chemistry Model Version 2.0 (FFCM-2) (2023)

work page 2023

[1] [1]

Maruta, Micro and mesoscale combustion, Pro- ceedings of the Combustion Institute 33 (1) (2011) 125–150

K. Maruta, Micro and mesoscale combustion, Pro- ceedings of the Combustion Institute 33 (1) (2011) 125–150

work page 2011

[2] [2]

A. C. Fernandez-Pello, Micropower generation using combustion: Issues and approaches, Proceedings of the Combustion Institute 29 (1) (2002) 883–899, pro- ceedings of the Combustion Institute

work page 2002

[3] [3]

Mart ´ınez-Ruiz, F

D. Mart ´ınez-Ruiz, F. Veiga-L ´opez, D. Fern ´andez- Galisteo, V . N. Kurdyumov, M. S ´anchez-Sanz, The role of conductive heat losses on the formation of iso- lated flame cells in hele-shaw chambers, Combustion and Flame 209 (2019) 187–199

work page 2019

[4] [4]

Al Sarraf, C

E. Al Sarraf, C. Almarcha, J. Quinard, B. Radisson, B. Denet, P. Garcia-Ybarra, Darrieus–landau instabil- ity and markstein numbers of premixed flames in a hele-shaw cell, Proceedings of the Combustion Insti- tute 37 (2) (2019) 1783–1789

work page 2019

[5] [5]

S. Shen, J. Wongwiwat, P. Ronney, Flame propagation in quasi-2d channels: stability, rates and scaling, in: AIAA Scitech 2019 Forum, 2019, p. 2365

work page 2019

[6] [6]

E. A. Sarraf, C. Almarcha, J. Quinard, B. Radisson, B. Denet, Quantitative analysis of flame instabilities in a hele-shaw burner, Flow, Turbulence and Combustion 101 (3) (2018) 851–868

work page 2018

[7] [7]

Daou, Effect of taylor dispersion on the thermo- diffusive instabilities of flames in a hele–shaw burner, Combustion Theory and Modelling 25 (4) (2021) 765– 783

J. Daou, Effect of taylor dispersion on the thermo- diffusive instabilities of flames in a hele–shaw burner, Combustion Theory and Modelling 25 (4) (2021) 765– 783

work page 2021

[8] [8]

Veiga-L ´opez, D

F. Veiga-L ´opez, D. Mart ´ınez-Ruiz, E. Fern ´andez- Tarrazo, M. S ´anchez-Sanz, Experimental analysis of oscillatory premixed flames in a hele-shaw cell prop- agating towards a closed end, Combustion and Flame 201 (2019) 1–11

work page 2019

[9] [9]

Kumar, K

S. Kumar, K. Maruta, S. Minaev, On the formation of multiple rotating pelton-like flame structures in radial microchannels with lean methane–air mixtures, Pro- ceedings of the Combustion Institute 31 (2) (2007) 3261–3268

work page 2007

[10] [10]

Kumar, K

S. Kumar, K. Maruta, S. Minaev, Pattern formation of flames in radial microchannels with lean methane-air mixtures, Physical Review E 75 (1) (2007) 016208

work page 2007

[11] [11]

A. Fan, S. Minaev, E. Sereshchenko, R. Fursenko, S. Kumar, W. Liu, K. Maruta, Experimental and nu- merical investigations of flame pattern formations in a radial microchannel, Proceedings of the Combustion Institute 32 (2) (2009) 3059–3066

work page 2009

[12] [12]

A. Fan, J. Wan, K. Maruta, H. Nakamura, H. Yao, W. Liu, Flame dynamics in a heated meso-scale ra- dial channel, Proceedings of the Combustion Institute 34 (2) (2013) 3351–3359

work page 2013

[13] [13]

R. Zhou, D. Wu, J. Wang, Progress of continuously rotating detonation engines, Chinese Journal of Aero- nautics 29 (1) (2016) 15–29

work page 2016

[14] [14]

X. Nie, S. Wang, Edge-stabilized rotating flames in a circular Hele-Shaw cell, Under Review (2026)

work page 2026

[15] [15]

Ben-Yakar, R

A. Ben-Yakar, R. K. Hanson, Cavity flame-holders for ignition and flame stabilization in scramjets: an overview, Journal of Propulsion and Power 17 (4) (2001) 869–877

work page 2001

[16] [16]

H. Wang, Z. Wang, M. Sun, N. Qin, Combustion char- acteristics in a supersonic combustor with hydrogen in- jection upstream of cavity flameholder, Proceedings of the Combustion Institute 34 (2) (2013) 2073–2082

work page 2013

[17] [17]

X. Yang, T. Tang, Q. Li, W. Han, R. Gu, H. Chen, Y . Huang, M. Sun, H. Wang, Y . Yang, J. Zhu, Cavity-enhanced combustion in a mach 6 axisym- metric scramjet, Combustion and Flame 286 (2026) 114807

work page 2026

[18] [18]

H. Wang, Z. Yan, Y . Zhao, S. Wang, On the self- excited instabilities of premixed swirl flames near blow-off limits – An experimental study using simul- taneous measurements of thermal boundary conditions and core flow scalar fields, Combustion and Flame 277 (2025) 114171

work page 2025

[19] [19]

I. H. Bockhorn, Implementation and validation of a solver for direct numerical simulations of turbulent re- acting flows in openfoam, Ph.D. thesis, Karlsruhe In- stitute of Technology (2012)

work page 2012

[20] [20]

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, Turbulence and Combus- tion 111 (2) (2023) 567–602

work page 2023

[21] [21]

H. G. Weller, G. Tabor, H. Jasak, C. Fureby, A ten- sorial approach to computational continuum mechan- ics using object-oriented techniques, Computers in Physics 12 (6) (1998) 620–631

work page 1998

[22] [22]

Kazakov, M

A. Kazakov, M. Frenklach, Reduced reaction sets based on gri-mech 1.2, University of California at Berkeley, Berkeley, CA, http://www. me. berkeley. edu/drm (1994)

work page 1994

[23] [23]

D. G. Goodwin, H. K. Moffat, I. Schoegl, R. L. Speth, B. W. Weber, Cantera: An object-oriented soft- ware toolkit for chemical kinetics, thermodynamics, and transport processes,https://www.cantera. org, version 3.1.0 (2024)

work page 2024

[24] [24]

Zhang, W

Y . Zhang, W. Dong, L. Vandewalle, R. Xu, G. Smith, H. Wang, Foundational Fuel Chemistry Model Version 2.0 (FFCM-2) (2023)

work page 2023