No CrossRef data available.
Article contents
Morphological evolutions and transverse dynamics of strong transverse wave structure in detonations near critical propagation state
Published online by Cambridge University Press: 14 March 2025
Abstract
Two-dimensional gaseous detonations near critical propagation state were studied numerically in a channel with stoichiometric H
$_2$/air and H
$_2$/O
$_2$ mixtures. Detonation waves exhibit a mode-locking effect (MLE) in a single-headed mode regime. Increasing the channel width alters the strength and propagation period of the single transverse wave. This leads to MLE failure and the occurrence of the single-dual-headed critical mode, featuring the emergence of a new transverse wave. For a stoichiometric H
$_2$/air mixture, generation of the new transverse wave is due to interactions between the detonation front and the local explosion wave originating from interactions between the transverse wave and unreacted gas pocket downstream. Whereas, for a stoichiometric H
$_2$/O
$_2$ mixture, a transverse wave interacting with the wall produces Mach reflection bifurcation, causing MLE failure and generation of the new transverse wave. Our results show that all transverse waves manifest as strong transverse wave (STW) structures, with most belonging to the second kind, and an acoustic coupling exists between the typical second kind of STW structure and the acoustic wave in the induction zone behind the Chapman–Jouguet detonation front. A high-pressure region close to the STW structure plays a crucial role in exploring the transverse dynamics of this structure. Shock polars with rational assumptions are adopted to predict flow states in this region. The roles of pivotal factors in influencing the flow states and wave structure are clarified, and characteristic pressure values derived adequately represent the STW structure’s transverse dynamic behaviours. Lastly, the relationship between the kinematics and kinds of STW structures is unveiled.
JFM classification
- Type
- JFM Papers
- Information
- Copyright
- © The Author(s), 2025. Published by Cambridge University Press
References
Austin, J.M. 2003 The role of instability in gaseous detonation. PhD thesis, California Institute of Technology.Google Scholar
Austin, J.M., Pintgen, F. & Shepherd, J.E. 2005 Reaction zones in highly unstable detonations. Proc. Combust. Inst. 30 (2), 1849–1857.CrossRefGoogle Scholar
Boulal, S., Vidal, P., Zitoun, R., Matsumoto, T. & Matsuo, A. 2018 Experimental investigation on detonation dynamics through a reactivity sink. Combust. Flame 196, 11–25.CrossRefGoogle Scholar
Browne, S.T., Ziegler, J.L., Bitter, N.P., Schmidt, B.E., Lawson, J. & Shepherd, J.E. 2023 Sdtoolbox: numerical solution methods for shock and detonation jump conditions. Tech. Rep. FM2018.001. Explosion Dynamics Laboratory, Graduate Aerospace Labortories, California Institute of Technology.Google Scholar
Burke, M.P., Chaos, M., Ju, Y., Dryer, F.L. & Klippenstein, S.J. 2012 Comprehensive H
$_2$/O$_2$ kinetic model for high-pressure combustion. Intl J. Chem. Kinet. 44, 444–474.CrossRefGoogle Scholar
$_2$/O
$_2$ kinetic model for high-pressure combustion. Intl J. Chem. Kinet. 44, 444–474.CrossRefGoogle ScholarCai, X., Xu, F., Deiterding, R., Chen, W. & Liang, J. 2023 Effects of activation energy on irregular detonation structures in supersonic flow. Phys. Fluids 35 (12), 125110.CrossRefGoogle Scholar
Chase, M.W., Curnutt, J.L., Prophet, H., McDonald, R.A. & Syverud, A.N. 1975 JANAF thermochemical tables, 1975 supplement. J. Phys. Chem. Ref. Data 4 (1), 1–176.CrossRefGoogle Scholar
Chinnayya, A., Hadjadj, A. & Ngomo, D. 2013 Computational study of detonation wave propagation in narrow channels. Phys. Fluids 25 (3), 036101.CrossRefGoogle Scholar
Crane, J., Lipkowicz, J.T., Shi, X., Wlokas, I., Kempf, A.M. & Wang, H. 2023 Three-dimensional detonation structure and its response to confinement. Proc. Combust. Inst. 39 (3), 2915–2923.CrossRefGoogle Scholar
Daimon, Y. & Matsuo, A. 2007 Unsteady features on one-dimensional hydrogen-air detonations. Phys. Fluids 19, 112–122.CrossRefGoogle Scholar
Edwards, D., Parry, D. & Jones, A.T. 1966 The structure of the wave front in spinning detonation. J. Fluid Mech. 26, 321–336.CrossRefGoogle Scholar
Fay, J.A. 1952 A mechanical theory of spinning detonation. J. Chem. Phys. 20, 942–950.CrossRefGoogle Scholar
Frederick, M.D., Gejji, R.M., Shepherd, J.E. & Slabaugh, C.D. 2023 Statistical analysis of detonation wave structure. Proc. Combust. Inst. 39 (3), 2847–2854.CrossRefGoogle Scholar
Gamezo, V.N., Vasil’ev, A.A., Khokhlov, A.M. & Oran, E.S. 2000 Fine cellular structures produced by marginal detonations. Proc. Combust. Inst. 28 (1), 611–617.CrossRefGoogle Scholar
Guo, H., Xu, Y., Zheng, H. & Zhang, H. 2023 Ignition limit and shock-to-detonation transition mode of n-heptane/air mixture in high-speed wedge flows. Proc. Combust. Inst. 39 (4), 4771–4780.CrossRefGoogle Scholar
Gutiérrez Marcantoni, L.F., Tamagno, J. & Elaskar, S. 2017 Two-dimensional numerical simulations of detonation cellular structures in H$_2$-O$_2$-Ar mixtures with OpenFOAM$^{\circledR }$. Intl J. Hydrogen Energ. 42, 26102–26113.CrossRefGoogle Scholar
$_2$-O
$_2$-Ar mixtures with OpenFOAM
$^{\circledR }$. Intl J. Hydrogen Energ. 42, 26102–26113.CrossRefGoogle ScholarHan, W., Ma, W., Qian, C., Wen, J. & Wang, C. 2019 Bifurcation of pulsation instability in one-dimensional H$_{2}$-O$_{2}$ detonation with detailed reaction mechanism. Phys. Rev. Fluids 4, 103202.CrossRefGoogle Scholar
$_{2}$-O
$_{2}$ detonation with detailed reaction mechanism. Phys. Rev. Fluids 4, 103202.CrossRefGoogle ScholarHuang, C., Wang, Y., Deiterding, R., Yu, D. & Chen, Z. 2022 Numerical studies on weak and strong ignition induced by reflected shock and boundary layer interaction. Acta Mechanica Sin. 38 (2), 121466.CrossRefGoogle Scholar
Huang, Z., Lefebvre, M.H. & Van Tiggelen, P.J. 2000 Experiments on spinning detonations with detailed analysis of the shock structure. Shock Waves 10 (2), 119–125.CrossRefGoogle Scholar
Ishii, K. & Grönig, H. 1998 Behavior of detonation waves at low pressures. Shock Waves 8 (1), 55–61.CrossRefGoogle Scholar
Jasak, H. 1996 Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London, UK.Google Scholar
Jia, X., Xu, Y., Zheng, H. & Zhang, H. 2023 Direct detonation initiation in hydrogen/air mixture: effects of compositional gradient and hotspot condition. J. Fluid Mech. 970, A22.CrossRefGoogle Scholar
Kellenberger, M. & Ciccarelli, G. 2020 Single-head detonation propagation in a partially obstructed channel. Combust. Flame 215, 283–294.CrossRefGoogle Scholar
Kurganov, A., Noelle, S. & Petrova, G. 2001 Semi-discrete central-upwind scheme for hyperbolic conservation laws and Hamilton–Jacobi equations. SIAM J. Sci. Comput. 23 (3), 707–740.CrossRefGoogle Scholar
Lau-Chapdelaine, S.S.M., Xiao, Q. & Radulescu, M.I. 2021 Viscous jetting and mach stem bifurcation in shock reflections: experiments and simulations. J. Fluid Mech. 908, A18.CrossRefGoogle Scholar
Lee, J.J., Garinis, D., Frost, D.L., Lee, J.H.S. & Knystautas, R. 1995 Two-dimensional autocorrelation function analysis of smoked foil patterns. Shock Waves 5 (3), 169–174.CrossRefGoogle Scholar
Liang, Z. & Bauwens, L. 2005 a Cell structure and stability of detonations with a pressure-dependent chain-branching reaction rate model. Combust. Theor. Model. 9 (1), 93–112.CrossRefGoogle Scholar
Liang, Z. & Bauwens, L. 2005 b Detonation structure with pressure-dependent chain-branching kinetics. Proc. Combust. Inst. 30 (2), 1879–1887.CrossRefGoogle Scholar
Liang, Z., Browne, S., Deiterding, R. & Shepherd, J.E. 2007 Detonation front structure and the competition for radicals. Proc. Combust. Inst. 31 (2), 2445–2453.CrossRefGoogle Scholar
Lu, X., Kaplan, C.R. & Oran, E.S. 2021 A chemical-diffusive model for simulating detonative combustion with constrained detonation cell sizes. Combust. Flame 230, 111417.CrossRefGoogle Scholar
Mach, P. & Radulescu, M.I. 2011 Mach reflection bifurcations as a mechanism of cell multiplication in gaseous detonations. Proc. Combust. Inst. 33 (2), 2279–2285.CrossRefGoogle Scholar
Mahmoudi, Y., Karimi, N., Deiterding, R. & Emami, S. 2014 Hydrodynamic instabilities in gaseous detonations: comparison of Euler, Navier–Stokes, and large-eddy simulation. J. Propul. Power 30 (2), 384–396.CrossRefGoogle Scholar
Mahmoudi, Y. & Mazaheri, K. 2015 High resolution numerical simulation of triple point collision and origin of unburned gas pockets in turbulent detonations. Acta Astronaut. 115, 40–51.CrossRefGoogle Scholar
Mazaheri, K., Mahmoudi, Y. & Radulescu, M.I. 2012 Diffusion and hydrodynamic instabilities in gaseous detonations. Combust. Flame 159, 2138–2154.CrossRefGoogle Scholar
Meagher, P.A., Shi, X., Santos, J.P., Muraleedharan, N.K., Crane, J., Poludnenko, A.Y., Wang, H. & Zhao, X. 2023 Isolating gasdynamic and chemical effects on the detonation cellular structure: a combined experimental and computational study. Proc. Combust. Inst. 39 (3), 2865–2873.CrossRefGoogle Scholar
Monnier, V., Rodriguez, V., Vidal, P. & Zitoun, R. 2022 An analysis of three-dimensional patterns of experimental detonation cells. Combust. Flame 245, 112310.CrossRefGoogle Scholar
Ng, H.D., Ju, Y. & Lee, J.H.S. 2007 Assessment of detonation hazards in high-pressure hydrogen storage from chemical sensitivity analysis. Intl J. Hydrogen Energy 32, 93–99.CrossRefGoogle Scholar
Peng, J., Zhang, Z., Hu, Z. & Jiang, Z. 2019 A theoretical and computational study of the vibration excitation on the transition criteria of shock wave reflections. Aerosp. Sci. Technol. 89, 299–306.CrossRefGoogle Scholar
Pintgen, F., Eckett, C.A., Austin, J.M. & Shepherd, J.E. 2003 Direct observations of reaction zone structure in propagating detonations. Combust. Flame 133 (3), 211–229.CrossRefGoogle Scholar
Radulescu, M.I. 2018 A detonation paradox: why inviscid detonation simulations predict the incorrect trend for the role of instability in gaseous cellular detonations? Combust. Flame 195, 151–162.CrossRefGoogle Scholar
Radulescu, M.I. & Lee, J.H.S. 2002 The failure mechanism of gaseous detonations: experiments in porous wall tubes. Combust. Flame 131 (1-2), 29–46.CrossRefGoogle Scholar
Radulescu, M.I., Sharpe, G.J., Law, C.K. & Lee, J.H.S. 2007 The hydrodynamic structure of unstable cellular detonations. J. Fluid Mech. 580, 31–81.CrossRefGoogle Scholar
Rojas Chavez, S.B., Chatelain, K.P. & Lacoste, D.A. 2023 Two-dimensional visualization of induction zone in hydrogen detonations. Combust. Flame 255, 112905.CrossRefGoogle Scholar
Semenov, A.N., Berezkina, M. & Krassovskaya, I.V. 2012 Classification of pseudo-steady shock wave reflection types. Shock Waves 22, 307–316.CrossRefGoogle Scholar
Sharpe, G.J. 2001 Transverse waves in numerical simulations of cellular detonations. J. Fluid Mech. 447, 31–51.CrossRefGoogle Scholar
Sharpe, G.J. & Falle, S.A.E.G. 2000 Numerical simulations of pulsating detonations: I. Nonlinear stability of steady detonations. Combust. Theor. Model. 4, 557–574.CrossRefGoogle Scholar
Shi, X., Zhu, Y., Yang, J. & Luo, X. 2019 Mach stem deformation in pseudo-steady shock wave reflections. J. Fluid Mech. 861, 407–421.CrossRefGoogle Scholar
Sow, A., Lau-Chapdelaine, S.M. & Radulescu, M.I. 2021 The effect of the polytropic index $\gamma$ on the structure of gaseous detonations. Proc. Combust. Inst. 38, 3633–3640.CrossRefGoogle Scholar
$\gamma$ on the structure of gaseous detonations. Proc. Combust. Inst. 38, 3633–3640.CrossRefGoogle ScholarStrehlow, R.A., Maurer, R.E. & Rajan, S. 1969 Transverse waves in detonations. I - Spacing in the hydrogen-oxygensystem. AIAA J. 7 (2), 323–328.CrossRefGoogle Scholar
Sugiyama, Y. & Matsuo, A. 2012 Numerical investigation on the detonation regime with longitudinal pulsation in circular and square tubes. Combust. Flame 159 (12), 3646–3651.CrossRefGoogle Scholar
Sugiyama, Y. & Matsuo, A. 2013 Numerical study of acoustic coupling in spinning detonation propagating in a circular tube. Combust. Flame 160 (11), 2457–2470.CrossRefGoogle Scholar
Taylor, B.D., Kessler, D.A., Gamezo, V.N. & Oran, E.S. 2013 Numerical simulations of hydrogen detonations with detailed chemical kinetics. Proc. Combust. Inst. 34 (2), 2009–2016.CrossRefGoogle Scholar
Tsuboi, N. & Hayashi, A.K. 2007 Numerical study on spinning detonations. Proc. Combust. Inst. 31 (2), 2389–2396.CrossRefGoogle Scholar
Tsuboi, N., Morii, Y. & Hayashi, A.K. 2013 Two-dimensional numerical simulation on galloping detonation in a narrow channel. Proc. Combust. Inst. 34 (2), 1999–2007.CrossRefGoogle Scholar
Tsuboi, N., Hayashi, A.K. & Koshi, M. 2009 Energy release effect of mixture on single spinning detonation structure. Proc. Combust. Inst. 32 (2), 2405–2412.CrossRefGoogle Scholar
Watanabe, H., Matsuo, A., Chinnayya, A., Itouyama, N., Kawasaki, A., Matsuoka, K. & Kasahara, J. 2023 Lagrangian dispersion and averaging behind a two-dimensional gaseous detonation front. J. Fluid Mech. 968, A28.CrossRefGoogle Scholar
Xiao, Q., Sow, A., Maxwell, B.M. & Radulescu, M.I. 2021 Effect of boundary layer losses on 2D detonation cellular structures. Proc. Combust. Inst. 38 (3), 3641–3649.CrossRefGoogle Scholar
Yan, H., Han, X., Xiong, H., Shi, C. & You, Y. 2024 Curved detonation and its reflections. J. Fluid Mech. 984, A11.CrossRefGoogle Scholar
Yuan, X., Zhou, J., Lin, Z. & Cai, X. 2016 Adaptive simulations of detonation propagation in 90-degree bent tubes. Intl J. Hydrogen Energy 41 (40), 18259–18272.CrossRefGoogle Scholar
Zadok, N., Oruganti, S.K., Alves, M.M. & Kozak, Y. 2023 Dimensional analysis and simplified modeling for the cellular structure of premixed gas-phase detonation numerical simulations with single-step kinetics. Combust. Flame 256, 112954.CrossRefGoogle Scholar
Zhang, B., Liu, H. & Yan, B. 2019 a Effect of acoustically absorbing wall tubes on the near-limit detonation propagation behaviors in a methane-oxygen mixture. Fuel 236, 975–983.CrossRefGoogle Scholar
Zhang, Y., Fang, Y., Ng, H.D. & Teng, H. 2019 b Numerical investigation on the initiation of oblique detonation waves in stoichiometric acetylene–oxygen mixtures with high argon dilution. Combust. Flame 204, 391–396.CrossRefGoogle Scholar