The re-initiation mechanism of detonation diffraction in a weakly unstable gaseous mixture. (English) Zbl 1460.76624
Summary: Numerical simulations were performed to investigate the re-initiation mechanism of a diffracted detonation wave near the critical channel width for a weakly unstable gas. Two scenarios were examined: diffraction of a planar detonation wave and of a cellular detonation wave inside the inlet channel. The results revealed that the critical channel width predicted using a cellular detonation wave is smaller than that predicted using a planar detonation wave. The re-initiation mechanisms are described in detail by tracing massless particles along both the plane of symmetry and the re-initiation path. For planar detonation diffractions, a compression wave is formed in the far field behind the diffracted shock. Re-initiation is closely related to the amplification of this compression wave and its coalescence with the diffracted shock. Depending on the inlet channel width, the strength of the reflected rarefaction wave is responsible for weakening the strength of the compression wave and its coalescence with the diffracted shock, consequently hindering the reaction of particles behind the diffracted shock wave. In cellular cases, the continuous collisions of transverse waves, which generate local explosion sites, sustain detonation wave propagation.
Keywords:
detonation wavesReferences:
| [1] | Arienti, M. & Shepherd, J.2005A numerical study of detonation diffraction. J. Fluid Mech.529, 117-146. · Zbl 1066.76069 |
| [2] | Austin, J., Pintgen, F. & Shepherd, J.2005Reaction zones in highly unstable detonations. Proc. Combust. Inst.30, 1849-1857. |
| [3] | Benedick, W., Knystautas, R. & Lee, J.1984Large-scale experiments on the transmission of fuel-air detonations from two-dimensional channels. Prog. Astronaut. Aeronaut.94, 546-555. |
| [4] | Benmahammed, M. A., Veyssiere, B., Khasainov, B. A. & Mar, M.2016Effect of gaseous oxidizer composition on the detonability of isooctane-air sprays. Combust. Flame165, 198-207. |
| [5] | Bourlioux, A., Majda, A. J. & Roytburd, V.1991Theoretical and numerical structure for unstable one-dimensional detonations. SIAM J. Appl. Maths51, 303-343. · Zbl 0731.76076 |
| [6] | Chang, S. C.1995The method of space-time conservation element and solution element—a new approach for solving the Navier-Stokes and Euler equations. J. Comput. Phys.119, 295-324. · Zbl 0847.76062 |
| [7] | Daimon, Y. & Matsuo, A.2003Detailed features of one-dimensional detonations. Phys. Fluids15, 112-122. · Zbl 1185.76102 |
| [8] | Desbordes, D., Guerraud, C., Hamada, L. & Presles, H.1993Failure of the classical dynamic parameters relationships in highly regular cellular detonation systems. Prog. Astronaut. Aeronaut.153, 347-359. |
| [9] | Edwards, D., Thomas, G. & Nettleton, M.1979The diffraction of a planar detonation wave at an abrupt area change. J. Fluid Mech.95, 79-96. |
| [10] | Gallier, S., Le Palud, F., Pintgen, F., Mével, R. & Shepherd, J.2017Detonation wave diffraction in H2-O2-Ar mixtures. Proc. Combust. Inst.36, 2781-2789. |
| [11] | Gamezo, V. N., Desbordes, D. & Oran, E. S.1999Formation and evolution of two-dimensional cellular detonations. Combust. Flame116, 154-165. |
| [12] | Han, W., Kong, W., Gao, Y. & Law, C. K.2017The role of global curvature on the structure and propagation of weakly unstable cylindrical detonations. J. Fluid Mech.813, 458-481. · Zbl 1383.76322 |
| [13] | He, L. & Lee, J. H.1995The dynamical limit of one-dimensional detonations. Phys. Fluids7, 1151-1158. · Zbl 1023.76599 |
| [14] | Jiang, Z. & Teng, H.2012Research on some fundamental problems of the universal framework for regular gaseous detonation initiation and propagation. Sci. Sin.-Phys. Mech. Astron.42, 421-435. |
| [15] | Jones, D., Kemister, G., Oran, E. & Sichel, M.1996The influence of cellular structure on detonation transmission. Shock Waves6, 119-129. |
| [16] | Kapila, A. K., Schwendeman, D. W., Quirk, J. J. & Hawa, T.2002Mechanisms of detonation formation due to a temperature gradient. Combust. Theor. Model.6, 553-594. · Zbl 1068.80517 |
| [17] | Kawasaki, A. & Kasahara, J.2019A novel characteristic length of detonation relevant to supercritical diffraction. Shock Waves30, 1-12. |
| [18] | Khasainov, B., Virot, F. & Veyssière, B.2013Three-dimensional cellular structure of detonations in suspensions of aluminium particles. Shock Waves23, 271-282. |
| [19] | Laffitte, P.1925Recherches expérimentales sur l’onde explosive et l’onde de choc. Ann. Phys. Ser.10, 587-694. |
| [20] | Lee, J., Knystautas, R. & Yoshikawa, N.1978Photochemical initiation of gaseous detonations. Acta Astron.5, 971-982. |
| [21] | Lee, J. H.1996On the critical diameter problem. In Dynamics of Exothermicity, pp. 321-336. Gordon and Breech. |
| [22] | Lee, J. H.2008The Detonation Phenomenon. Cambridge University Press. |
| [23] | Li, J., Ning, J., Kiyanda, C. B. & Ng, H. D.2016Numerical simulations of cellular detonation diffraction in a stable gaseous mixture. Propul. Power Res.5, 177-183. |
| [24] | Liu, Y., Lee, J. & Knystautas, R.1984Effect of geometry on the transmission of detonation through an orifice. Combust. Flame56, 215-225. |
| [25] | Maxwell, B. M., Bhattacharjee, R. R., Lau-Chapdelaine, S. S., Falle, S. A., Sharpe, G. J. & Radulescu, M. I.2017Influence of turbulent fluctuations on detonation propagation. J. Fluid Mech.818, 646-696. · Zbl 1383.76210 |
| [26] | Mehrjoo, N., Gao, Y., Kiyanda, C. B., Ng, H. D. & Lee, J. H.2015Effects of porous walled tubes on detonation transmission into unconfined space. Proc. Combust. Inst.35, 1981-1987. |
| [27] | Mitrofanov, V. V. & Soloukhin, R. I.1965The diffraction of multifront detonation waves. Sov. Phys. Dokl.9, 1055-1058. |
| [28] | Nagura, Y., Kasahara, J., Sugiyama, Y. & Matsuo, A.2013Comprehensive visualization of detonation-diffraction structures and sizes in unstable and stable mixtures. Proc. Combust. Inst.34, 1949-1956. |
| [29] | Pintgen, F. & Shepherd, J.2009Detonation diffraction in gases. Combust. Flame156, 665-677. |
| [30] | Radulescu, M. I.2018A detonation paradox: Why inviscid detonation simulations predict the incorrect trend for the role of instability in gaseous cellular detonations?Combust. Flame.195, 151-162. |
| [31] | Radulescu, M. I. & Borzou, B.2018Dynamics of detonations with a constant mean flow divergence. J. Fluid Mech.845, 346-377. · Zbl 1404.76156 |
| [32] | Sharpe, G.1997Linear stability of idealized detonations. Proc. R. Soc. Lond. A453, 2603-2625. · Zbl 0898.76041 |
| [33] | Sharpe, G. & Falle, S.2000Numerical simulations of pulsating detonations: I. Nonlinear stability of steady detonations. Combust. Theor. Model.4, 557-574. · Zbl 1010.76096 |
| [34] | Shen, H. & Parsani, M.2017The role of multidimensional instabilities in direct initiation of gaseous detonations in free space. J. Fluid Mech.813, R4. · Zbl 1383.76324 |
| [35] | Shen, H. & Wen, C.-Y.2016A characteristic space-time conservation element and solution element method for conservation laws II. Multidimensional extension. J. Comput. Phys.305, 775-792. · Zbl 1349.65483 |
| [36] | Shen, H., Wen, C.-Y., Liu, K. & Zhang, D.2015aRobust high-order space-time conservative schemes for solving conservation laws on hybrid meshes. J. Comput. Phys.281, 375-402. · Zbl 1354.65196 |
| [37] | Shen, H., Wen, C.-Y., Parsani, M. & Shu, C.-W.2017Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids. J. Comput. Phys.330, 668-692. · Zbl 1378.76086 |
| [38] | Shen, H., Wen, C.-Y. & Zhang, D.-L.2015bA characteristic space-time conservation element and solution element method for conservation laws. J. Comput. Phys.288, 101-118. · Zbl 1354.65197 |
| [39] | Shi, L., Shen, H., Zhang, P., Zhang, D. & Wen, C.2017Assessment of vibrational non-equilibrium effect on detonation cell size. Combust. Sci. Technol.189, 841-853. |
| [40] | Short, M. & Stewart, D.1998Cellular detonation stability. Part 1. A normal-mode linear analysis. J. Fluid Mech.368, 229-262. · Zbl 0926.76051 |
| [41] | Skews, B. W.1967The shape of a diffracting shock wave. J. Fluid Mech.29, 297-304. |
| [42] | Uy, K. C., Shi, L. & Wen, C.2018Chemical reaction mechanism related vibrational nonequilibrium effect on the Zel’dovich-von Neumann-Döring (ZND) detonation model. Combust. Flame196, 174-181. |
| [43] | Uy, K. C. K., Shi, L. S. & Wen, C. Y.2019Prediction of half reaction length for H_2O_2Ar detonation with an extended vibrational nonequilibrium Zel’dovich-von Neumann-Döring (ZND) model. Intl J. Hydrog. Energy44, 7667-7674. |
| [44] | Wen, C.-Y., Massimi, H. S. & Shen, H.2018Extension of CE/SE method to non-equilibrium dissociating flows. J. Comput. Phys.356, 240-260. · Zbl 1380.76030 |
| [45] | Yuan, X. Q., Mi, X. C., Ng, H. D. & Zhou, J.2019A model for the trajectory of the transverse detonation resulting from re-initiation of a diffracted detonation. Shock Waves30, 1-15. |
| [46] | Zel’Dovich, I. B.1956An experimental investigation of spherical detonation of gases. Sov. Phys. Tech. Phys.1, 1689-1713. |
| [47] | Zhang, F.2009Shock Wave Science and Technology Reference Library. Springer. |
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