Effects of disturbance on detonation initiation in ${\mathrm{H}}_2/{\mathrm{O}}_2/{\mathrm{N}}_2$ mixture

Detonation initiation has been extensively investigated in the past several decades. In the literature, there are many studies on detonation initiation using a large amount of blast energy and obstacles to respectively achieve direct detonation initiation or deflagration to detonation transition (DDT). However, there are few studies on detonation initiation with a nonuniform initiation zone. In this work, two-dimensional numerical simulations considering detailed chemistry and transport are conducted to investigate the effects of disturbance on detonation initiation in a stoichiometric ${\mathrm{H}}_2/{\mathrm{O}}_2/{\mathrm{N}}_2$ mixture. The high-pressure and high-temperature detonation initiation regime is imposed by a sinusoidal disturbance. Introduction of such disturbance is found to promote the onset of detonation and to reduce time and distance for detonation formation. This is mainly because such disturbance can induce shock-wave interaction, which generates transverse waves. The reflected transverse waves result in local autoignition and explosion. The coherent coupling between local autoignition and pressure wave resulting from a large amount of heat release eventually leads to the detonation development. It is found that the distance and duration for detonation initiation become shorter when a disturbance with smaller wavelength or larger amplitude is enforced. When the ratio between the wavelength and amplitude of disturbance is fixed, the change in wavelength and amplitude has little influence on detonation initiation. Therefore, disturbance with either small wavelength or large amplitude can be used to promote detonation initiation.

Figure 1

Schematic of the initial and boundary conditions used in the simulation of detonation initiation in ${\mathrm{H}}_2/{\mathrm{O}}_2/{\mathrm{N}}_2$ mixture. A sinusoidal perturbation with the amplitude of $A$ and wavelength of λ is introduced to the surface of the detonation initiation region at $x=1$ cm.

Figure 2

Distribution of the initial adaptive mesh for the case of $A=2$ mm and λ = 2 mm. The number shows the mesh level $L$ and the corresponding mesh size is equal to $500/2^L\mu \mathrm{m}$.

Figure 3

Shock-wave trajectories during detonation initiation and propagation processes predicted by simulations using different mesh level for λ = 15 mm and A = 2 mm. The coarsest mesh size is fixed at $\mathrm{\Delta }x=500\mu \mathrm{m}$. The maximum mesh level for mesh I, II, and III are, respectively, $L=4$, 5, and 6. The finest mesh size is equal to $\mathrm{\Delta }x/2^{\mathrm{L}}$., which is 31.2, 15.6, and 7.8 μm for mesh I, II, and III, respectively.

Figure 4

Numerical soot foils for detonation propagation in $2{\mathrm{H}}_2+{\mathrm{O}}_2+7\mathrm{Ar}$ mixture at 298 K and 6.67 KPa.

Figure 5

Temporal evolution of pressure distributions along the fixed line at $y=1.5$ cm for (a) $\lambda =\infty$ (i.e., without disturbance) and (b) λ = 30 mm and $A=2$ mm.

Figure 6

Evolution of temperature contour for λ = 30 mm and $A=2$ mm. For each frame, the vertical height is 30 mm (i.e., $0\le y\le 30\mathrm{mm})$.

Figure 7

Evolution of the trajectories of shock wave and reaction front along the fixed line at $y=1.5$ cm for λ = 30 mm and $A=2$ mm. The solid lines are obtained from a simulation including diffusion, while the symbols correspond to the inviscid case.

Figure 8

Evolution of density gradient contour for λ = 30 mm and $A=2$ mm.

Figure 9

Numerical soot foils for λ = 30 mm and $A=2$ mm. The vertical height is 30 mm.

Figure 10

Density gradient, pressure, and temperature contour. Top: λ = 15 mm; bottom: λ = 30 mm. The amplitude is fixed to be $A=2$ mm.

Figure 11

Evolution of shock-wave trajectories for disturbances with different wavelengths, but fixed amplitude of $A=2$ mm. The dashed lines indicate the time and position of detonation formation.

Figure 12

Evolution of shock-wave trajectories for disturbances with different amplitudes, but fixed wavelength of λ = 30 mm. The dashed lines indicate the time and position of detonation formation.

Figure 13

Change of the leading shock pressure $P_{\mathrm{shock}}$ with the shock position $X_{\mathrm{shock}}$ along the line at $y=1.5$ cm for disturbances with fixed wavelength of λ = 30 mm, but different amplitudes of $A=2$, 4, and 6 mm.

Figure 14

Change of the distance for detonation formation with wavelength or amplitude of the disturbance.