Simulation of Shock Wave Focusing in Combustible Mixture

12 Simulation of Shock Wave Focusing in Combustible Mixture 

The gas-dynamics of the studied problem is described by a system of two-dimensional non-stationaiy Euler equations [87, 88]. The system is solved by the Lax-Wendroff scheme together with a flow correction algorithm for shock capturing. The detailed solution of the chemical reactions uses CHEMKIN-II and is included in the calculations. The solution domain consists of a half of a rectangular tube, divided into 400 X 200 cells. The spatial resolution in both x and y directions is uniform and equal to 0.3 mm. 

Two typical examples of the flow fields at detonation initiation in a 15% H2 + 85% air mixture, when shock waves are focusing on parabolic reflectors, are presented in Fig. 6.26. Double refinement of the cell size was used to increase the resolution near the boundaries of the reflector. The left-hand boundary conditions used an inflow with constant Mach number, corresponding to the incident shock wave. The reflector shape is specified by the canonical parabolic equation = Ikx with the focal characteristic k = 0.45 cm ( deep parabola) and k = 1.35 cm ( short parabola). The values of k correspond to the two types of reflectors in [85, 86]. 

In Fig. 6.26a, k = 0.45 cm, the shock wave reflected from the walls and intersect before the collision of the triple points. In Fig. 6.26b, k= 1.45 cm, the focusing occurs when the secondary pressure shocks are not observed. 

In the case of the deep parabolic reflector, self-ignition is recorded near its gas-dynamic focus, at the collision point of the triple Mach configurations. 

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