Abstract
The structure of an oblique detonation wave (ODW) induced by a wedge is investigated via numerical simulations and Rankine–Hugoniot analysis. The two-dimensional Euler equations coupled with a two-step chemical reaction model are solved. In the numerical results, four configurations of the Chapman–Jouguet (CJ) ODW reflection (overall Mach reflection, Mach reflection, regular reflection, and non-reflection) are observed to take place sequentially as the inflow Mach number increases. According to the numerical and analytical results, the change of the CJ ODW reflection configuration results from the interaction among the ODW, the CJ ODW, and the centered expansion wave.
Similar content being viewed by others
Abbreviations
- ODW:
-
Oblique detonation wave
- OSW:
-
Oblique shock wave
- CJ ODW:
-
Chapman–Jouguet oblique detonation wave (which locates at the end of the induction region)
- CEW:
-
Centered expansion wave (which locates behind the CJ ODW)
- RCEW:
-
Reflected expansion wave of the CEW
- ROSW:
-
Reflected shock wave of the OSW
- RCJ ODW:
-
Reflected shock wave of the CJ ODW
References
Kailasanath, K.: Review of propulsion applications of detonation waves. AIAA J. 38(9), 1698–1708 (2000)
Ma, F., Choi, J.-Y., Yang, V.: Propulsive performance of air breathing pulse detonation engines. J. Propuls. Power 22(6), 1188–1203 (2006)
Dunlap, R., Brehm, R.L., Nicholls, J.A.: A preliminary study of the application of steady-state detonative combustion to a reaction engine. J. Jet Propuls. 28(7), 451–456 (1958)
Pratt, D.T., Humphrey, J.W., Glenn, D.E.: Morphology of standing oblique detonation waves. J. Propuls. Power 7(5), 837–845 (1991)
Ghorbanian, K., Sterling, J.D.: Influence of formation processes on oblique detonation wave stabilization. J. Propuls. Power 12(3), 509–517 (1996)
Li, C., Kailasanath, K., Oran, E.S.: Detonation structures behind oblique shocks. Phys. Fluids 6(4), 1600–1611 (1994)
Choi, J.-Y., Kim, D.-W., Jeung, I.-S., Ma, F., Yang, V.: Cell-like structure of unstable oblique detonation wave from high-resolution numerical simulation. Proc. Combust. Inst. 31(2), 2473–2480 (2007)
Wang, A.-F., Zhao, W., Jiang, Z.-L.: Cellular structure of oblique detonation and propagation of transverse wave. Explos. Shock Waves 30(4), 349–354 (2010)
Gui, M.-Y., Fan, B.-C., Dong, G.: Periodic oscillation and fine structure of wedge-induced oblique detonation waves. Acta Mech. Sin. 27(6), 922–928 (2011)
Verreault, J., Higgins, A.J., Stowe, R.A.: Formation of transverse waves in oblique detonations. Proc. Combust. Inst. 34(2), 1913–1920 (2013)
Verreault, J., Higgins, A.J.: Initiation of detonation by conical projectiles. Proc. Combust. Inst. 33, 2311–2318 (2011)
Lefebvre, M.H., Fujiwara, T.: Numerical modeling of combustion processes induced by a supersonic conical blunt body. Combust. Flame 100, 85–93 (1995)
Liu, Y., Wu, D., Yao, S.-B., Wang, J.-P.: Analytical and numerical investigations of wedge-induced oblique detonation waves at low inflow Mach number. Combust. Sci. Technol. 187(6), 843–856 (2015)
Dabora, E. K., Broda, J.-C.: Standing normal detonations and oblique detonations for propulsion. AIAA paper 93–2325 (1993)
Viguier, C., Gourara, A., Desbordes, D.: Three-dimensional structure of stabilization of oblique detonation wave in hypersonic flow. Proc. Combust. Inst. 27(2), 2207–2214 (1998)
Maeda, S., Kasahara, J., Matsuo, A.: Oblique detonation wave stability around a spherical projectile by a high time resolution optical observation. Combust. Flame 159, 887–896 (2012)
Ashford, S.A., Emanuel, G.: Wave angle for oblique detonation waves. Shock Waves 3, 327–329 (1994)
Verreault, J., Higgins, A.J., Stowe, R.A.: Formation and structure of steady oblique and conical detonation waves. AIAA J. 50(8), 1766–1772 (2012)
Teng, H.-H., Zhao, W., Jiang, Z.-L.: A novel oblique detonation structure and its stability. Chin. Phys. Lett. 24(7), 1985–1988 (2007)
Li, C., Kailasanath, K., Oran, E. S.: Effects of boundary layers on oblique-detonation structures. In: 31st Aerospace Sciences Meeting & Exhibit, Reno, Nevada, AIAA-93-0450 (1993)
Kamel, M. R., Morris, C. I., Stouklov, I. G., Hanson, R. K.: PLIF imaging of hypersonic reactive flow around blunt bodies. In: 26th International Symposium on Combustion, Combustion Institute, Pittsburg, pp. 2909–2915 (1996)
Korobeinikov, V.P., Levin, V.A., Markov, V.V., Chernyi, G.G.: Propagation of blast waves in a combustible gas. Astronaut. Acta 17(4–5), 529–537 (1972)
Liu, Y.-F.: Numerical Studies on Detonation and Pulse Detonation Engines. Peking University, Beijing (2004)
Steger, J.L., Warming, R.F.: Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. J. Comput. Phys. 40(2), 263–293 (1981)
Balsara, D.S., Shu, C.-W.: Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comput. Phys. 160(2), 405–452 (2000)
Ben-Dor, G.: Shock Wave Reflection Phenomena, 2nd edn. Springer, New York (2007)
da Silva, L.F.F., Deshaies, B.: Stabilization of an oblique detonation wave by a wedge: a parametric numerical study. Combust. Flame 121, 152–166 (2000)
Acknowledgments
This work was sponsored by the National Natural Science Foundation of China (No. 91441110).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by A. Sasoh and A. Higgins.
Rights and permissions
About this article
Cite this article
Liu, Y., Liu, YS., Wu, D. et al. Structure of an oblique detonation wave induced by a wedge. Shock Waves 26, 161–168 (2016). https://doi.org/10.1007/s00193-015-0600-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00193-015-0600-5