Abstract
The multidimensional structure of mildly unstable detonations are examined by numerical computations. These phenomenon have grown in interest since the development of propulsion devices such as pulsed and rotating detonation engines. Rectangular, diagonal and spinning modes are observed in a near-limit propagation detonation. High-order numerical integration of the reactive Euler equations have been performed to analyze the averaged structure, the shock dynamics of a single-cell detonation propagating in a square channel. Computations show a good agreement with the experimental cellular structure, showing the relevance of the slapping waves in the rectangular modes. The hydrodynamic thickness as well as the pdf shock dynamics are similar in the 2D and 3D cases, but the mean quantities vary on a quantitative basis. Moreover, the presence of strong forward jets is attested, which comes from simultaneous triple point line collisions with the walls.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. N. Williams, L. Bauwens, E. S. Oran, Detailed structure and propagation of three-dimensional detonations, in: Symposium (International) on Combustion, Vol. 26, Elsevier, 1996, pp. 2991–2998.
M. Hanana, M. Lefebvre, Pressure profiles in detonation cells with rectangular and diagonal structures, Shock Waves 11 (2) (2001) 77–88.
N. Tsuboi, S. Katoh, A. K. Hayashi, Threedimensional numerical simulation for hydrogen/air detonation: Rectangular and diagonal structures, Proceedings of the Combustion Institute 29 (2) (2002) 2783–2788.
R. Deiterding, Numerical structure analysis of regular hydrogen-oxygen detonations, in: WSSCI Fall 2003 Meeting, University of California, Los Angeles, 2003.
K. Eto, N. Tsuboi, A. K. Hayashi, Numerical study on three-dimensional cj detonation waves: detailed propagating mechanism and existence of OH radical, Proceedings of the Combustion Institute 30 (2) (2005) 1907–1913.
V. Deledicque, M. V. Papalexandris, Computational study of three-dimensional gaseous detonation structures, Combustion and flame 144 (4) (2006) 821–837.
H.-S. Dou, H. M. Tsai, B. C. Khoo, J. Qiu, Simulations of detonation wave propagation in rectangular ducts using a three-dimensional WENO scheme, Combustion and Flame 154 (4) (2008) 644–659.
H. S. Dou, B. C. Khoo, Effect of initial disturbance on the detonation front structure of a narrow duct, Shock Waves 20 (2) (2010) 163–173. doi:10.1007/s00193-009-0240-8.
N. Tsuboi, A. K. Hayashi, Numerical study on spinning detonations, Proceedings of the Combustion Institute 31 (2) (2007) 2389–2396.
C. Wang, C.-W. Shu, W. Han, J. Ning, High resolution WENO simulation of 3D detonation waves, Combustion and Flame 160 (2) (2013) 447–462.
Y. Huang, H. Ji, F. Lien, H. Tang, Numerical study of three-dimensional detonation structure transformations in a narrow square tube: from rectangular and diagonal modes into spinning modes, Shock Waves 24 (4) (2014) 375–392.
M. Reynaud, F. Virot, A. Chinnayya, A computational study of the interaction of gaseous detonations with a compressible layer, Physics of Fluids 29 (5) (2017) 056101.
A. Suresh, H. T. Huynh, Accurate monotonicitypreserving schemes with runge-kutta time stepping, Journal of Computational Physics 136 (1) (1997) 83–99.
E. F. Toro, M. Spruce, W. Speares, Restoration of the contact surface in the HLL-riemann solver, Shock Waves 4 (1) (1994) 25–34.
A. Sow, Modélisation numérique des détonations gazeuses en milieu confiné, Ph.D. thesis, University of Rouen, France (2014).
O. Heuzé, P. Bauer, H. Presles, C. Brochet, Equations of state for detonation products and their incorporation into the quatuor code, in: 8th Symp.(Int.) on Detonation, 1986, pp. 762–769.
J. H. Lee, The detonation phenomenon, Cambridge University Press Cambridge, 2008.
J. M. Austin, The role of instability in gaseous detonation, Ph.D. thesis, California Institute of Technology (2003).
M. I. Radulescu, G. J. Sharpe, C. K. Law, J. H. S. Lee, The hydrodynamic structure of unstable cellular detonations, Journal of Fluid Mechanics 580 (2007) 31–81.
M. Hanana, M. H. Lefebvre, P. J. V. Tiggelen, Pressure profiles in detonation cells with rectangular and diagonal structures, Shock Waves 11 (2001) 77–88.
A. Sow, A. Chinnayya, A. Hadjadj, Mean structure of one-dimensional unstable detonations with friction, Journal of Fluid Mechanics 743 (2014) 503–533.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Taileb, S., Reynaud, M., Chinnayya, A. et al. Numerical study of 3D gaseous detonations in a square channel. Aerotec. Missili Spaz. 97, 96–102 (2018). https://doi.org/10.1007/BF03405804
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03405804