STUDY ON EVOLUTION MODEL OF GASEOUS DETONATION WAVE IN PERIODIC INHOMOGENEOUS MEDIUM
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摘要: 气相爆轰波在周期性非均匀介质中的起爆, 稳态传播和失效机制都极为复杂, 很多物理机制尚不明确, 是当前爆轰物理领域研究的热点和难点. 本文使用反应欧拉方程和两步化学反应模型对爆轰波在非均匀介质中的传播机理进行了数值模拟研究, 非均匀性由横向周期性分布的温度扰动体现, 重点分析不同波长、不同幅度的温度扰动对波阵面波系结构的影响. 计算结果表明, ZND爆轰波在温度扰动下向胞格爆轰波的转变主要受制于两种竞争性因素: 一是爆轰波内在的不稳定性; 二是温度扰动的波长和幅度, 前者是内因, 后者是外因. 温度扰动的存在抑制横波的发展, 延迟了ZND爆轰波向胞格爆轰波的演化, 并且内在不稳定性的增加可以减慢这种延迟现象. 这说明, 温度扰动可以在一定的范围内抑制胞格不稳定性的发展, 但是不能够终止这一过程. 温度的不连续性使得爆轰波阵面更为扭曲, 并在横波附近存在较弱的三波点结构, 即温度扰动可增加爆轰波固有的不稳定性, 改变爆轰波阵面的传播机理. 幅值较大的人工温度扰动可抑制爆轰波的传播和爆轰波自身的不稳定性. 爆轰波阵面胞格结构的形成取决于温度扰动与其自身的不稳定性.Abstract: The initiation, steady propagation and failure mechanism of gaseous detonation wave in periodic inhomogeneous media are very complex, and many physical mechanisms are still unclear, which is an active topic in detonation physics. Numerical simulation of propagation of gaseous detonations in the inhomogeneous medium is studied by using the reactive Euler equations coupled with a two-step chemical reaction model. The inhomogeneity is generated by placing artificial temperature perturbations with different wavelengths and amplitudes. The influence of temperature disturbance with different wavelength and amplitude on the structure of wave front is analyzed. The results show that, the transition of ZND detonation to cellular detonation under artificial temperature disturbance is mainly controlled by two competitive factors: one is the intrinsic instability of detonation wave, the other is the wavelength and amplitude of artificial disturbance, the former is the internal factor, the latter is the external factor. The existence of artificial temperature disturbance delays the evolution of ZND detonation to cellular detonation by suppressing the development of shear wave, and the increase of internal instability can slow down this delay phenomenon. This shows that the artificial temperature disturbance can restrain the development of cell instability in a certain range, but it cannot stop the process. The discontinuity of temperature makes the detonation wave front more distorted, which leads to the existence of a weak triple-wave structure near the shear wave, which is, the artificial disturbance increases the inherent instability of detonation wave and changes the propagation mechanism of detonation wave front. The propagation of detonation and the instability of detonation are restrained by the artificial temperature disturbance with large amplitude. The formation of detonation front cellular structure depends on the artificial temperature disturbance and its own instability.
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Key words:
- inhomogeneity /
- temperature perturbations /
- gaseous detonation /
- instability /
- cellular structure
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图 3 二维胞格爆轰波网格分辨率测试(无扰动, kR = 2.0)
Figure 3. Numerical resolution test for transition of ZND to cellular detonations (without disturbance, kR = 2.0)
图 5 二维激波波阵面演化图, 温度扰动振幅A = 105 K
Figure 5. Evolution of shock front structures during the two-dimensional with A = 105 K
图 6 不同温度扰动幅值下激波波阵面纹影图和最大压力历史
Figure 6. Schlieren photography of the shock front at the same instant for cases with different temperature perturbations and pressure history
图 7 二维爆轰波波阵面演化图, 温度扰动振幅A = 105 K, kR = 2.0
Figure 7. Evolution of detonation front structures during the two-dimensional with A = 105 K and kR = 2.0
图 8 不同时刻下沿中心线和边界线压力与温度分布和流线图, 温度扰动振幅A = 105 K, kR = 2.0
Figure 8. Pressure, temperature distribution and streamlines along the centering and boundary lines at two instants with A = 105 K, kR = 2.0
图 9 不同稳定性下爆轰波波阵面纹影、温度扰动幅度以及胞格结构
Figure 9. Schlieren photography of the detonation front at the same instant for cases with different instability
图 10 均匀介质中无扰动时ZND爆轰波到胞格爆轰波的演化
Figure 10. Transition from ZND to cellular detonation without artificial perturbations
图 11 存在人工温度扰动时的数值胞格, A = 15 K, s = 10ΔI
Figure 11. Numerical smoked foils for cases with artificial perturbations of A = 15 K, s = 10ΔI
图 12 存在人工温度扰动时的数值胞格, A = 15 K, s = 20ΔI
Figure 12. Numerical smoked foils for cases with artificial perturbations of A = 15 K, s = 20ΔI
图 13 存在人工温度扰动时的数值胞格, A = 15 K, s = 40ΔI
Figure 13. Numerical smoked foils for cases with artificial perturbations of A = 15 K, s = 40ΔI
图 14 存在人工温度扰动时爆轰波的压力历史曲线
Figure 14. Pressure history for cases with artificial perturbations
图 16 存在不同振幅人工温度扰动时(kR = 4.0, s = 20ΔI)的压力历史曲线图
Figure 16. Pressure history for cases with artificial perturbations of kR = 4, s = 20ΔI
图 17 人工温度扰动s = 20ΔI, kR = 4.0时,波阵面的纹影结构
Figure 17. Schlieren photography of detonation front under artificial perturbations with different amplitude with s = 20ΔI and
$ {k_{\text{R}}} $ = 4.0
图 15 存在不同振幅人工温度扰动时(kR = 4.0, s = 20ΔI)的数值胞格
Figure 15. Numerical smoked foils for cases with artificial perturbations of kR = 4, s = 20ΔI
表 1 爆轰参数
Table 1. Detonation parameters
Parameter Value Unit R 218.79 J/kg· K p0 50 kPa T0 295 K c0 304.86 m/s ρ0 0.775 kg/m3 Q/(RT0) 19.7 − γ 1.44 − MCJ 5.6 − ${\varepsilon _{\rm{I}}}$ 4.8 − ${\varepsilon _{\rm{R}}}$ 1.0 − kI = ${\tilde k_{{\rm{I}}}}{x_{{\text{ref}}}}/{c_0}$ 1.3875 − kR = ${\tilde k_{\text{R}}}{x_{{\text{ref}}}}/{c_0}$ 2.0~5.0 − 
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