Numerical Simulation of Refraction of Gaseous Detonation Waves at Temperature Interfaces

doi:10.12382/bgxb.2025.0377

Abstract

Abstract:

The refractive behaviors of shock waves and detonation waves during their propagation and damage processes in gaseous media are studied. A computation program with finite volume method and adaptive mesh refinement method is developed based on the reactive Euler equations coupled with a two-step chemical reaction model. The transmission and refraction processes of shock waves and detonation waves at temperature interfaces are determined through theoretical analysis and numerical simulations. The variations of the transmitted shock wave speed and post-wave state with the amplitude of interface temperature are presented, and the typical shock wave structure is obtained. The refraction phenomenon of detonation waves at the temperature interface is further studied, and then the evolution process of cellular detonation wave is analyzed using numerical schlieren and smoked foil method. The results indicate that a shock wave forms a Mach stem and oblique shock wave at the interface when it refracts into low-temperature gas, and it generates a double triple-point structure and a convex wave front when entering high-temperature gas. The cellular detonation wave forms an inclined wave front at the interface when it refracts into low-temperature gas. In contrast, when entering high-temperature gas, it generates a convex wave front and a degenerated double triple point structure. The propagation of cellular detonation waves exhibits distinct spatio-temporal evolution properties.

Key words: gaseous detonation wave, reflection, cellular structure, Mach reflection, numerical simulation

CLC Number:

O382

LIU Xi, MA Tianbao, LI Jian. Numerical Simulation of Refraction of Gaseous Detonation Waves at Temperature Interfaces[J]. Acta Armamentarii, 2025, 46(10): 250377-.

Figures/Tables 27

Table 1 Parameters of gas

参数	数值	参数	数值
R/(J·kg^-1·K^-1)	218.79	γ	1.44
p₀/kPa	50	M_C-J	5.6
θ₀/K	295	E_I/RT_S	4.8
c₀/(m·s^-1)	304.86	E_R/RT_S	1.0
ρ₀/(kg·m^-3)	0.775	k₁$\sqrt{\gamma }$/c₀	1.387 5
Q/(RT₀)	19.7	k_R$\sqrt{\gamma }$/c₀	2.0

Fig.1 Block adaptive mesh refinement

Fig.2 Schematic diagram of computational domain

Fig.3 Grid convergence test

Fig.4 x-t plots of post states of the transmitted shock wave

Fig.5 Temperature curves at different temperature interfaces

Fig.6 Post-wave state of transmitted wave

Fig.7 Regular and irregular refraction structures and their corresponding polar plots

Fig.8 Refraction of shock waves (calculated by GSD theory)

Fig.9 Temperature contour of refraction at 295~50K interface

Fig.10 Step signal model

Fig.11 Temperature contour of refraction at 295~100K interface

Fig.12 Post-shock temperature

Fig.13 Comparison of χ in refraction and reflection

Fig.14 Temperature contour of refraction at 295~800K interface

Fig.15 Temperature contour of refraction at 295~600K interface

Fig.16 Post-shock temperature

Fig.17 Comparison of χ in refraction and reflection

Fig.18 Wavefront structure for T1=200K and θ=20°

Fig.19 Numerical smoked foil of detonation wave for T1=200K and θ=20°

Fig.20 Numerical smoked foil of shock wave for T1=200K and θ=20°

Fig.21 Wavefront and smoked foil for T1=200K and θ=30°

Fig.22 Numerical smoked foil for T1=220K

Fig.23 Wavefront structure for T1=600K

Fig.24 Numerical smoked foils of detonation and shock waves for T1=600K and θ=20°

Fig.25 Three development phases of Mach stem development

Fig.26 Height evolution of Mach stem at temperature interface

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