8 Some Aspects on Pulsating Detonation Wave Numerical Simulation …
113
8.6 Concluding Remarks
The work demonstrates the possibility of numerical modeling of initiation and propagation of gaseous detonation waves using complex reaction kinetics. The mathematical model is based on the system of Euler equations for a multicomponent media.
The computational algorithm of the second approximation order based on the physical processes splitting technique, finite volume method, ENO-reconstruction, and
AUSM flux are described. To verify the implemented computational algorithm, the
0D ignition simulation was performed.
The numerical investigation of pulsating detonation wave propagation with the
use of Petersen and Hanson detailed kinetics corresponding to the stoichiometric
hydrogen–air mixture was carried out. The direct detonation initiation near the closed
end of the channel was considered. The cell size of the computational grid was
sufficient to obtain the pulsations of various modes. During the computation, the
high-frequency and high-amplitude pulsation modes were obtained. The characteristics and frequencies are both very different. The border separating the modes is
clearly defined. The features of both modes, as well as, the processes accompanying
pulsations are considered. The induction zone in the high-frequency mode fluctuates without significant change in contrast to the high-amplitude. The signal of the
pulsations in the high-amplitude mode is close to periodic.
Acknowledgements This work is carried out under the state task of the ICAD RAS.
References
1. Kailasanath, K.: Review of propulsion applications of detonation waves. AIAA J. 38(9), 1698–
1708 (2000)
2. Sharpe, G.J., Falle, S.A.: Numerical simulations of pulsating detonations: I. Nonlinear stability
of steady detonations. Combust. Theory Model. 4, 557–574 (2000)
3. Lopato, A.I., Utkin, P.S.: Toward second-order algorithm for the pulsating detonation wave
modeling in the shock-attached frame. Combust. Sci. Technol. 188, 1844–1856 (2016)
4. Lee, H.I., Stewart, D.S.: Calculation of linear detonation instability: one-dimensional instability
of plane detonation. J. Fluid Mech. 216, 103–132 (1990)
5. Lopato, A.I., Utkin, P.S.: Mathematical modeling of pulsating detonation wave propagation
using monotone numerical methods of different approximation orders. In: Transient Combustion and Detonation Phenomena: Fundamentals and Applications, pp. 261–268. Torus Press,
Moscow (2014)
6. Xiao, H., Oran, E.S.: Shock focusing and detonation initiation at a flame front. Combust. Flame
203, 397–406 (2009)
7. Gamezo, V., Ogawa, T., Oran, E.: Flame acceleration and DDT in channels with obstacles:
effect of obstacle spacing. Combust. Flame 155, 302–315 (2008)
8. Liberman, M., Wang, C., Qian, C., Liu, J.: Influence of chemical kinetics on spontaneous waves
and detonation initiation in highly reactive and low reactive mixtures. Combust. Theory Model.
23(3), 467–495 (2019)
9. Cole, L.K., Karagozian, A.R., Cambier, J.-L.: Stability of flame-shock coupling in detonation
waves: 1D dynamics. Combust. Sci. Technol. 184, 150–1525 (2012)
113
8.6 Concluding Remarks
The work demonstrates the possibility of numerical modeling of initiation and propagation of gaseous detonation waves using complex reaction kinetics. The mathematical model is based on the system of Euler equations for a multicomponent media.
The computational algorithm of the second approximation order based on the physical processes splitting technique, finite volume method, ENO-reconstruction, and
AUSM flux are described. To verify the implemented computational algorithm, the
0D ignition simulation was performed.
The numerical investigation of pulsating detonation wave propagation with the
use of Petersen and Hanson detailed kinetics corresponding to the stoichiometric
hydrogen–air mixture was carried out. The direct detonation initiation near the closed
end of the channel was considered. The cell size of the computational grid was
sufficient to obtain the pulsations of various modes. During the computation, the
high-frequency and high-amplitude pulsation modes were obtained. The characteristics and frequencies are both very different. The border separating the modes is
clearly defined. The features of both modes, as well as, the processes accompanying
pulsations are considered. The induction zone in the high-frequency mode fluctuates without significant change in contrast to the high-amplitude. The signal of the
pulsations in the high-amplitude mode is close to periodic.
Acknowledgements This work is carried out under the state task of the ICAD RAS.
References
1. Kailasanath, K.: Review of propulsion applications of detonation waves. AIAA J. 38(9), 1698–
1708 (2000)
2. Sharpe, G.J., Falle, S.A.: Numerical simulations of pulsating detonations: I. Nonlinear stability
of steady detonations. Combust. Theory Model. 4, 557–574 (2000)
3. Lopato, A.I., Utkin, P.S.: Toward second-order algorithm for the pulsating detonation wave
modeling in the shock-attached frame. Combust. Sci. Technol. 188, 1844–1856 (2016)
4. Lee, H.I., Stewart, D.S.: Calculation of linear detonation instability: one-dimensional instability
of plane detonation. J. Fluid Mech. 216, 103–132 (1990)
5. Lopato, A.I., Utkin, P.S.: Mathematical modeling of pulsating detonation wave propagation
using monotone numerical methods of different approximation orders. In: Transient Combustion and Detonation Phenomena: Fundamentals and Applications, pp. 261–268. Torus Press,
Moscow (2014)
6. Xiao, H., Oran, E.S.: Shock focusing and detonation initiation at a flame front. Combust. Flame
203, 397–406 (2009)
7. Gamezo, V., Ogawa, T., Oran, E.: Flame acceleration and DDT in channels with obstacles:
effect of obstacle spacing. Combust. Flame 155, 302–315 (2008)
8. Liberman, M., Wang, C., Qian, C., Liu, J.: Influence of chemical kinetics on spontaneous waves
and detonation initiation in highly reactive and low reactive mixtures. Combust. Theory Model.
23(3), 467–495 (2019)
9. Cole, L.K., Karagozian, A.R., Cambier, J.-L.: Stability of flame-shock coupling in detonation
waves: 1D dynamics. Combust. Sci. Technol. 184, 150–1525 (2012)