Oscillations Characteristics of One-dimensional Detonation Waves in Non-Uniform Hydrogen-Air Mixture

doi:10.12382/bgxb.2021.0804

Abstract

Abstract:

The inhomogeneity of the medium in front of the waves has a significant effect on the propagation of gaseous detonation waves, but the interaction mechanism remains unclear. The two-step induction-exothermic reaction model is used to study the propagation characteristics of one-dimensional hydrogen/air detonation waves in a non-uniform medium, and the influence of perturbation wavelength on detonation waves under different oscillation modes is analyzed. The results show that as the perturbation frequency get closer to the inherent oscillation frequency of detonation waves, the inherent instability is more easily triggered, resulting in more irregular oscillations. There are two dominant mechanisms of detonation waves propagating in a non-uniform medium. Pressure oscillation of weakly unstable detonation waves are dominated by density perturbation, and the main frequency of detonation pressure oscillation is consistent with the perturbation frequency; the pressure oscillation of strong detonation waves are dominated by inherent instability, and the oscillation frequency is distributed in the low frequency region without obvious dominant frequency, where perturbation only enhances the oscillation amplitude. When the perturbation is applied, the detonation waves under atmospheric pressure and at high altitudes has the above oscillation characteristics, which further confirms the feasibility of regulating detonation waves by artificial perturbation.

Key words: one-dimensional detonation waves, instability, perturbation, propagation characteristics

XI Xuechen, YANG Pengfei, WANG Kuanliang. Oscillations Characteristics of One-dimensional Detonation Waves in Non-Uniform Hydrogen-Air Mixture[J]. Acta Armamentarii, 2023, 44(4): 982-993.

Figures/Tables 15

Fig.1 Schematic of 1D detonation propagation in non-uniform mixture

Fig.2 Schematic of moving computational domain

Table 1 Detonation parameters of two-step model and detailed mechanism at p=1atm, T=400K

参数	两步反应模型	详细反应模型
v_C-J/(m·s^-1)	1963.1	1963.1
M_C-J	4.17	4.17
p_C-J/atm	10.31	11.65
T_C-J/K	2445.08	2973.5
p_vn/atm	19.62	20.48
T_vn/K	1459.24	1605

Fig.3 Post-shock pressure history for different number of grids

Table 2 Kinetics parameters of two-step reaction model with different temperatures

参数	工况
参数	1	2	3
p/atm	1	1	1
T/K	600	500	400
Q	8.67	10.76	13.90
γ	1.31	1.31	1.32
E_I	6.03 T_s	6.20 T_s	6.63 T_s
k_I	5.97	6.25	6.67
E_R	0.5 T_s	0.5 T_s	0.5 T_s
k_R	1.54	1.94	2.50
T_s	2.69	3.08	3.65

Fig.4 Variation of post-shock pressure with perturbation wavelength for Case 1

Fig.5 Bifurcation diagram of maximum pressure for 1D detonation with different temperatures

Fig.6 Post-shock pressure evolution (left) with different λ and the corresponding power spectra (right) for Case 3

Fig.7 Power spectral density of the post-shock pressure with different λ for Case 2

Fig.8 Power spectral density of the post-shock pressure with different λ for Case 3

Fig.9 Effect of λ on the product of dominant frequency f and perturbation wavelength λ for Case 2 and Case 3

Table 3 Parameters of two-step model used at high altitudes for different flight Mach numbers

参数	工况
参数	4	5	6
Ma	5	4	3
p/atm	0.14	0.10	0.08
T/K	366.8	334.7	305.5
Q	14.39	15.81	17.33
γ	1.32	1.32	1.32
E_I	6.27 T_s	6.40 T_s	6.33 T_s
k_I	6.79	6.98	7.19
E_R	0.5 T_s	0.5 T_s	0.5 T_s
k_R	1.51	1.53	1.54
T_s	3.78	4.05	4.35

Fig.10 Variation of post-shock pressure with perturbation wavelength for Case 4

Fig.11 Post-shock pressure evolution with different λ and the corresponding power spectra for Case 4

Fig.12 Bifurcation diagram of maximum pressure for 1D detonation with different temperatures

References 43

[1]	RADULESCU M I, SHARPE G J, LEE J H S, et al. The ignition mechanism in irregular structure gaseous detonations[J]. Proceedings of the Combustion Institute, 2005, 30(2):1859-1867. doi: 10.1016/j.proci.2004.08.047 URL
[2]	TENG H H, ZHANG Y H, YANG P F, et al. Oblique detonation wave triggered by a double wedge in hypersonic flow[J]. Chinese Journal of Aeronautics, 2022, 35(4):176-184.
[3]	张博, 白春华. 气相爆轰动力学特性研究进展[J]. 中国科学:物理学力学天文学, 2014, 44(7):665-681.
	ZHANG B, BAI C H. Research progress on the dynamic characteristics of gaseous detonation[J]. Scientia Sinica Physica, Mechanica & Astronomica, 2014, 44(7):665-681. (in Chinese)
[4]	CLAVIN P, DENET B. Diamond patterns in the cellular front of an over driven detonation[J]. Physical Review Letters, 2002, 88(4):044502. doi: 10.1103/PhysRevLett.88.044502 URL
[5]	CALVIN P, HE L T, WILLIAMS F A. Multidimensional stability analysis of overdriven gaseous detonations[J]. Physics of Fluids, 1997, 9(12):3764-3785. doi: 10.1063/1.869520 URL
[6]	LODATO G, VERVISCH L, CLAVIN P. Direct numerical simulation of shock wavy-wall interaction: analysis of cellular shock structures and flow patterns[J]. Journal of Fluid Mechanics, 2016, 789:221-258. doi: 10.1017/jfm.2015.731 URL
[7]	GAMEZO V N, DESBORDES D, ORAN E S. Formation and evolution of two-dimensional cellular detonations[J]. Combustion and Flame, 1999, 116:154-165. doi: 10.1016/S0010-2180(98)00031-5 URL
[8]	ROY G D, FROLOV S M, BORISOV A A, et al. Pulse detonation propulsion: challenges, current status, and future perspective[J]. Progress in Energy and Combustion Science, 2004, 30(6):545-672. doi: 10.1016/j.pecs.2004.05.001 URL
[9]	安复兴, 李磊, 苏伟, 等. 高超声速飞行器气动设计中的若干关键问题[J]. 中国科学: 物理学力学天文学, 2021, 51(10):104702.
	AN F X, LI L, SU W, et al. Key issues in hypersonic vehicle aerodynamic design[J]. Scientia Sinica Physica, Mechanica & Astronomica, 2021, 51(10):104702. (in Chinese)
[10]	RANKIN B A, FOTIA M L, NAPLES A G, et al. Overview of performance, application, and analysis of rotating detonation engine technologies[J]. Journal of Propulsion and Power, 2017, 30(1):131-143.
[11]	魏万里, 翁春生, 武郁文, 等. 氧化剂喷注面积对连续旋转爆轰波传播特性影响的实验研究[J]. 兵工学报, 2018, 39(12):2345-2353. doi: 10.3969/j.issn.1000-1093.2018.12.008
	WEI W L, WENG C S, WU Y W, et al. Experimental research on influence of oxidant injection area on the propagation characteristics of continuous rotating detonation wave[J]. Acta Armamentarii, 2018, 39(12):2345-2353. (in Chinese)
[12]	李宝星, 王中, 许桂阳, 等. 煤油燃料旋转爆轰波起爆与传播特性实验研究[J]. 兵工学报, 2020, 41(7):1339-1346. doi: 10.3969/j.issn.1000-1093.2020.07.011
	LI B X, WANG Z, XU G Y, et al. Experimental research on initiation and propagation characteristics of kerosene fuel rotating detonation wave[J]. Acta Armamentarii, 2020, 41(7): 1339-1346. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.07.011
[13]	王放, 翁春生, 武郁文, 等. 气体与液体两相连续旋转爆轰波二维数值模拟研究[J]. 兵工学报, 2020, 41(4):681-691. doi: 10.3969/j.issn.1000-1093.2020.04.007
	WANG F, WENG C S, WU Y W, et al. Two-dimensional numerical research on two-phase rotating detonation waves[J]. Acta Armamentarii, 2020, 41(4):681-691. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.04.007
[14]	滕宏辉, 杨鹏飞, 张义宁, 等. 斜爆震发动机的流动与燃烧机理[J]. 中国科学:物理学力学天文学, 2020, 50(9):090008.
	TENG H H, YANG P F, ZHANG Y N, et al. Flow and combustion mechanism of oblique detonation engines[J]. Scientia Sinica: Physica, Mechanica & Astronomica, 2020, 50(9):090008. (in Chinese)
[15]	SONG Q G, HAN Y, CAO W. Numerical investigation of self-sustaining modes of 2D planar detonations under concentration gradients in hydrogen-oxygen mixtures[J]. International Journal of Hydrogen Energy, 2020, 45(53):29606-29615. doi: 10.1016/j.ijhydene.2020.08.014 URL
[16]	陈达, 宁建国, 李健. 周期性非均匀介质中气相爆轰波演变模式研究[J]. 力学学报, 2021, 53(10):2865-2879.
	CHEN D, NING J G, LI J. Study on evolution model of gaseous detonation wave in periodic inhomogeneous medium[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10):2865-2879. (in Chinese)
[17]	ISHII K, KOJIMA M. Behavior of detonation propagation in mixtures with concentration gradients[J]. Shock Waves, 2007, 17:95-102. doi: 10.1007/s00193-007-0093-y URL
[18]	BOECK L R, BERGER F M, HASSLBERGER J, et al. Detonation propagation in hydrogen-air mixtures with transverse concentration gradients[J]. Shock Waves, 2016, 26:181-192. doi: 10.1007/s00193-015-0598-8 URL
[19]	THOMAS G O, SUTTON P, EDWARDS D H. The behavior of detonation waves at concentration gradients[J]. Combustion and Flame, 1991, 84:312-322. doi: 10.1016/0010-2180(91)90008-Y URL
[20]	BJERKETVEDT D, SONJU O K, MOEN I O. The influence of experimental condition on the reinitiation of detonation across an inert region[J]. AIAA Journal, 1986, 106:109-130.
[21]	WANG Y, HUANG C Y, DEITERDING R, et al. Propagation of gaseous detonation across inert layers[J]. Proceedings of the Combustion Institute, 2021, 38:3555-3563. doi: 10.1016/j.proci.2020.07.022 URL
[22]	NING J G, CHEN D, LI J. Numerical studies on propagation mechanisms of gaseous detonations in the inhomogeneous medium[J]. Applied Sciences, 2020, 10(13):4585. doi: 10.3390/app10134585 URL
[23]	TANG-YUK K C, LEE J H, NG H D, et al. Transmission of cellular detonation waves across a density/temperature interface[C]// Proceedings of the 27th International Colloquium on the Dynamics of Explosions and Reactive Systems. Beijing, China: ICDERS, 2019.
[24]	TANG-YUK K C, LEE J H, NG H D, et al. Detonation transmission across an inert gap[C]// Proceedings of the 27th International Colloquium on the Dynamics of Explosions and Reactive Systems. Beijing, China: ICDERS, 2019.
[25]	NG H D, BOTROS B B, CHAO J, et al. Head-on collision of a detonation with a planar shock wave[J]. Shock Waves, 2006, 15(5):341-352. doi: 10.1007/s00193-006-0022-5 URL
[26]	BOTROS B B, NG H D, ZHU Y J, et al. The evolution and cellular structure of a detonation subsequent to a head-on interaction with a shock wave[J]. Combustion and Flame, 2007, 151:573-580. doi: 10.1016/j.combustflame.2007.07.018 URL
[27]	MI X C, HIGGINS A J, KIYANDA C B. Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium[J]. Physical Review Fluids, 2017, 2(5):053201. doi: 10.1103/PhysRevFluids.2.053201 URL
[28]	MI X C, TIMOFEEV E V, HIGGINS A J. Effect of spatial discretization of energy on detonation wave propagation[J]. Journal of Fluid Mechanics, 2017, 817:306-338. doi: 10.1017/jfm.2017.81 URL
[29]	LEE J H S. The detonation phenomenon[M]. New York, NY, US: Cambridge University Press, 2008:108-118.
[30]	HE L, LEE J H S. The dynamical limit of one-dimensional detonations[J]. Physics of Fluids, 1995, 7(5):1151-1158. doi: 10.1063/1.868556 URL
[31]	KASIMOV A R, GONCHAR A R. Reactive Burgers model for detonation propagation in a non-uniform medium[J]. Proceedings of the Combustion Institute, 2021, 38:3723-3732.
[32]	KIM M, MI X C, KIYANDA C B, et al. Nonlinear dynamics and chaos regularization of one-dimensional pulsating detonations with small sinusoidal density perturbations[J]. Proceedings of the Combustion Institute, 2021, 38:3701-3708. doi: 10.1016/j.proci.2020.07.138 URL
[33]	MA W J, WANG C, HAN W H. Effect of concentration inhomogeneity on the pulsating instability of hydrogen-oxygen detonations[J]. Shock Waves, 2020, 30:703-711. doi: 10.1007/s00193-020-00976-7
[34]	HAN W H, WANG C, LAW C K. Pulsation in one-dimensional H₂-O₂ detonation with detailed reaction mechanism[J]. Combustion and Flame, 2019, 200:242-261. doi: 10.1016/j.combustflame.2018.11.024 URL
[35]	NG H D, RADULESCU M I, HIGGINS A J, et al. Numerical investigation of the instability for one-dimensional Chapman-Jouguet detonations with chain-branching kinetics[J]. Combustion Theory and Modelling, 2005, 9(3):385-401. doi: 10.1080/13647830500307758 URL
[36]	张涵信. 无波动、无自由参数的耗散差分格式[J]. 空气动力学学报, 1988, 6(2):143-165.
	ZHANG H X. Non-oscillatory and non-free-parameter dissipation difference scheme[J]. Acta Aerodynamica Sinica, 1988, 6(2):143-165. (in Chinese)
[37]	郗雪辰, 杨鹏飞, 滕宏辉. 一维爆轰波在扰动来流中传播的数值研究[J]. 气体物理, 2022, 7(4):1-9.
	XI X C, YANG P F, TENG H H. Numerical study of one-dimensional detonation propagation in perturbed inflow[J]. Physics of Gases, 2022, 7(4):1-9. (in Chinese)
[38]	TENG H H, ZHOU L, YANG P F, et al. Numerical investigation of wavelet features in rotating detonations with a two-step induction-reaction model[J]. International Journal of Hydrogen Energy, 2020, 45:4991-5001. doi: 10.1016/j.ijhydene.2019.12.063 URL
[39]	MALIK K, ZBIKOWSKI M, BAK D, et al. Numerical and experimental investigation of H₂-air and H₂-O₂ detonation parameters in a 9 m long tube, introduction of a new detonation model[J]. International Journal of Hydrogen Energy, 2019, 44(17):8743-8750. doi: 10.1016/j.ijhydene.2018.04.161 URL
[40]	BURKE M P, CHAOS M, JU Y, et al. Comprehensive H₂/O₂ kinetic model for high-pressure combustion[J]. International Journal of Chemical Kinetics, 2012, 44(7):444-474. doi: 10.1002/kin.20603 URL
[41]	姜宗林, 滕宏辉. 气相规则胞格爆轰波起爆与传播统一框架的几个关键基础问题研究[J]. 中国科学:物理学力学天文学, 2012, 42(4):421-435.
	JIANG Z L, TENG H H. Research on some fundamental problems of the universal framework for regular gaseous detonation initiation and propagation[J]. Scientia Sinica: Physica, Mechanica & Astronomica, 2012, 42(4):421-435. (in Chinese)
[42]	SHARPE G J, FALLE S A E G. One-dimensional numerical simulations of idealized detonations[J]. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences, 1999, 455:1203-1214. doi: 10.1098/rspa.1999.0355 URL
[43]	BIAN J, ZHOU L, TENG H H. Structural and thermal analysis on oblique detonation influenced by different forebody compressions in hydrogen-air mixtures[J]. Fuel, 2021, 286:119458. doi: 10.1016/j.fuel.2020.119458 URL