Front shock behavior of stable curved detonation waves in rectangular-cross-section curved channels

The propagation of curved detonation waves of gaseous explosives stabilized in rectangular-cross-section curved channels is investigated. Three types of stoichiometric test gases, C₂H₄ + 3O₂, 2H ₂ + O₂, and 2C₂H₂ + 5O₂ + 7Ar, are evaluated. The ratio of the inner radius of the curved channel (r _i) to the normal detonation cell width (λ) is an important factor in stabilizing curved detonation waves. The lower boundary of stabilization is around r_i/λ = 23, regardless of the test gas. The stabilized curved detonation waves eventually attain a specific curved shape as they propagate through the curved channels. The specific curved shapes of stabilized curved detonation waves are approximately formulated, and the normal detonation velocity (D_n)-curvature (κ) relations are evaluated. The D_n nondimensionalized by the Chapman-Jouguet (CJ) detonation velocity (D_CJ) is a function of the κ nondimensionalized by λ. The D_n/D_CJ-λκ relation does not depend on the type of test gas. The propagation behavior of the stabilized curved detonation waves is controlled by the D_n/D _CJ-λκ relation. Due to this propagation characteristic, the fully-developed, stabilized curved detonation waves propagate through the curved channels while maintaining a specific curved shape with a constant angular velocity. Self-similarity is seen in the front shock shapes of the stabilized curved detonation waves with the same r_i/λ, regardless of the curved channel and test gas.