# Rotating Detonation Wave in an Annular Gap

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## Abstract

We consider a three-dimensional unsteady flow with a rotating detonation wave arising in an annular gap of an axially symmetric engine between two parallel planes perpendicular to its symmetry axis. The corresponding problem is formulated and studied. It is assumed that there is a reservoir with quiescent homogeneous propane–air combustible mixture with given stagnation parameters; the mixture flows from the reservoir into the annular gap through its external cylindrical surface toward the symmetry axis, and the parameters of the mixture are determined by the pressure in the reservoir and the static pressure in the gap. The detonation products flow out from the gap into a space bounded on one side by an impermeable wall that is an extension of a side of the gap. Through a hole on the other side of the gap and through a conical output section with a half-opening angle of 45°, the gas flows out from the engine into the external space. We formulate a model of detonation initiation by energy supply in which the direction of rotation of the detonation wave is defined by the position of the energy-release zone of the initiator with respect to the solid wall situated in a plane passing through the symmetry axis. After a while, this solid wall disappears (burns out). We obtain and analyze unsteady shock-wave structures that arise during the formation of a steady rotating detonation. The analysis is carried out within single-stage combustion kinetics by the numerical method based on the Godunov scheme with the use of an original software system developed for multiparameter calculations and visualization of flows. The calculations were carried out on the Lomonosov supercomputer at Moscow State University.

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## References

- 1.F. A. Bykovskii and S. A. Zhdan, “Current status of research of continuous detonation in fuel–air mixtures (review),” Fiz. Goreniya Vzryva
**51**(1), 31–46 (2015) [Combust. Explos. Shock Waves**51**, 21–35 (2015)].Google Scholar - 2.S. K. Godunov, A. V. Zabrodin, M. Ya. Ivanov, A. N. Kraiko, and G. P. Prokopov,
*Numerical Solution of Multidimensional Problems in Gas Dynamics*(Nauka, Moscow, 1976) [in Russian].Google Scholar - 3.V. P. Korobeinikov, V. A. Levin, V. V. Markov, and G. G. Chernyi, “Propagation of blast waves in a combustible gas,” Astronaut. Acta
**17**(5–6), 529–537 (1972).Google Scholar - 4.V. P. Korobeinikov and V. V. Markov, “On propagation of combustion and detonation,” Arch. Procesów Spalania
**8**(1), 101–118 (1977).Google Scholar - 5.V. A. Levin, I. S. Manuĭlovich, and V. V. Markov, “New effects of stratified gas detonation,” Dokl. Akad. Nauk
**430**(2), 185–188 (2010) [Dokl. Phys.**55**(1), 28–32 (2010)].Google Scholar - 6.V. A. Levin, I. S. Manuilovich, and V. V. Markov, “Distinctive features of galloping detonation in a supersonic combustible-mixture flow under an inert gas layer,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No.
**5**, 167–175 (2010) [Fluid Dyn.**45**, 827–834 (2010)].MathSciNetzbMATHGoogle Scholar - 7.V. A. Levin, I. S. Manuĭlovich, and V. V. Markov, “Formation of detonation in rotating channels,” Dokl. Akad. Nauk
**432**(6), 775–778 (2010) [Dokl. Phys.**55**(6), 308–311 (2010)].zbMATHGoogle Scholar - 8.V. A. Levin, I. S. Manuilovich, and V. V. Markov, “Detonation initiation by rotation of an elliptic cylinder inside a circular cylinder and deformation of the channel walls,” Prikl. Mekh. Tekh. Fiz.
**51**(4), 17–25 (2010) [J. Appl. Mech. Tech. Phys.**51**, 463–470 (2010)].zbMATHGoogle Scholar - 9.V. A. Levin, I. S. Manuylovich, and V. V. Markov, “Mathematical modeling of shock-wave processes under gas–solid boundary interaction,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk
**281**, 42–54 (2013) [Proc. Steklov Inst. Math.**281**, 37–48 (2013)].MathSciNetzbMATHGoogle Scholar - 10.V. A. Levin, I. S. Manuylovich, and V. V. Markov, “Numerical simulation of spinning detonation in circular section channels,” Zh. Vychisl. Mat. Mat. Fiz.
**56**(6), 1122–1137 (2016) [Comput. Math. Math. Phys.**56**, 1102–1117 (2016)].MathSciNetzbMATHGoogle Scholar - 11.V. A. Levin and V. V. Markov, “Initiation of detonation by concentrated release of energy,” Fiz. Goreniya Vzryva
**11**(4), 623–633 (1975) [Combust. Explos. Shock Waves**11**, 529–536 (1975)].Google Scholar - 12.V. A. Levin, V. V. Markov, and S. F. Osinkin, “Simulation of detonation initiation in a combustible mixture of gases by an electric discharge,” Khim. Fiz.
**3**(4), 611–614 (1984) [Sov. J. Chem. Phys.**3**, 917–920 (1985)].Google Scholar - 13.V. A. Levin, V. V. Markov, and S. F. Osinkin, “Direct initiation of detonation in a hydrogen–oxygen mixture diluted with nitrogen,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No.
**6**, 151–156 (1992) [Fluid Dyn.**27**, 873–876 (1992)].Google Scholar - 14.V. A. Levin, V. V. Markov, and S. F. Osinkin, “Initiation of detonation in hydrogen–air mixture by explosion of a spherical TNT charge,” Fiz. Goreniya Vzryva
**31**(2), 91–95 (1995) [Combust. Explos. Shock Waves**31**, 207–210 (1995)].Google Scholar - 15.V. A. Levin, V. V. Markov, and S. F. Osinkin, “Detonation wave reinitiation using a disintegrating shell,” Dokl. Akad. Nauk
**352**(1), 48–50 (1997) [Phys. Dokl.**42**(1), 25–27 (1997)].Google Scholar - 16.V. A. Levin, V. V. Markov, and S. F. Osinkin, “The effect of air interlayer on the shock initiation of detonation in a hydrogen–air mixture,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk
**223**, 136–143 (1998) [Proc. Steklov Inst. Math.**223**, 131–138 (1998)].zbMATHGoogle Scholar - 17.V. A. Levin, V. V. Markov, S. F. Osinkin, and T. A. Zhuravskaya, “Determination of critical conditions for detonation initiation in a finite volume by a converging shock wave,” Fiz. Goreniya Vzryva
**38**(6), 96–102 (2002) [Combust. Explos. Shock Waves**38**, 693–699 (2002)].Google Scholar - 18.V. A. Levin, V. V. Markov, and T. A. Zhuravskaya, “Direct detonation initiation in a hydrogen–air mixture by a converging shock wave,” Khim. Fiz.
**20**(5), 26–30 (2001).Google Scholar - 19.V. A. Levin, V. V. Markov, T. A. Zhuravskaya, and S. F. Osinkin, “Nonlinear wave processes that occur during the initiation and propagation of gaseous detonation,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk
**251**, 200–214 (2005) [Proc. Steklov Inst. Math.**251**, 192–205 (2005)].zbMATHGoogle Scholar - 20.V. A. Levin, V. V. Markov, T. A. Zhuravskaya, and S. F. Osinkin, “Determination of critical conditions for the propagation of detonation waves in channels of complex shape,” in
*Modern Problems in the Study of Fast Processes and Catastrophic Phenomena: On the Occasion of the 75th Birthday of V. P. Korobeinikov, Ed. by O. M. Belotserkovskii*(Nauka, Moscow, 2007), pp. 75–88 [in Russian].Google Scholar - 21.V. A. Levin, V. V. Markov, T. A. Zhuravskaya, and S. F. Osinkin, “Initiation, propagation and stabilization of detonation in the supersonic gas flow,” in
*Proc. Seventh Int. Symp. on Hazards, Prevention, and Migration of Industrial Explosions (ISHPMIE), St. Petersburg, July 7–11, 2008*(Torus Press, Moscow, 2008), Vol. 2, pp. 110–118.Google Scholar - 22.V. A. Levin, V. V. Markov, T. A. Zhuravskaya, and S. F. Osinkin, “Influence of obstacles on detonation wave propagation,” in
*Deflagrative and Detonative Combustion*, Ed. by G. Roy and S. Frolov (Torus Press, Moscow, 2010), pp. 221–228.Google Scholar - 23.V. V. Markov, “Numerical simulation of the formation of a multifrontal detonation-wave structure,” Dokl. Akad. Nauk SSSR
**258**(2), 314–317 (1981) [Sov. Phys., Dokl.**26**, 503–505 (1981)].zbMATHGoogle Scholar - 24.V. V. Mitrofanov and R. I. Soloukhin, “The diffraction of multifront detonation waves,” Dokl. Akad. Nauk SSSR
**159**(5), 1003–1006 (1964) [Sov. Phys., Dokl.**9**, 1055–1058 (1965)].Google Scholar - 25.L. I. Sedov, V. P. Korobeĭnikov, and V. V. Markov, “The theory of propagation of blast waves,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR
**175**, 178–216 (1986) [Proc. Steklov Inst. Math.**175**, 187–228 (1988)].zbMATHGoogle Scholar - 26.R. I. Soloukhin, “Structure of a multifront detonation wave in a gas,” Fiz. Goreniya Vzryva
**1**(2), 35–42 (1965) [Combust. Explos. Shock Waves**1**(2), 23–29 (1965)].Google Scholar - 27.
*Thermodynamic Properties of Individual Substances*, Ed. by L. V. Gurvich and I. V. Veyts (Nauka, Moscow, 1978; Hemisphere, New York, 1989), Vol. 1, Part 2.Google Scholar - 28.Vl. Voevodin, S. Zhumatii, S. Sobolev, A. Antonov, P. Bryzgalov, D. Nikitenko, K. Stefanov, and Vad. Voevodin, “Practice of the ‘Lomonosov’ Supercomputer,” Otkrytye Sistemy, SUBD, No.
**7**, 36–39 (2012).Google Scholar - 29.C. K. Westbrook and F. L. Dryer, “Chemical kinetic modeling of hydrocarbon combustion,” Prog. Energy Combust. Sci.
**10**(1), 1–57 (1984).CrossRefGoogle Scholar - 30.T. A. Zhuravskaya, V. A. Levin, V. V. Markov, and S. F. Osinkin, “Effect of the decomposing shell on the formation of detonation in a bounded volume by a converging shock wave,” Khim. Fiz.
**22**(8), 34–37 (2003).Google Scholar