Perturbation Theory of Imploding Detonations

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  • 収束デトネーションの摂動理論

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Nonsteady one-dimensional imploding detonations of cylindrical and spherical symmetry are analyzed by using a perturbation method. Nonsteady onedimensional equations are perturbed with respect to time through the parameter ε=1/n[(t0/t)n-1], which vanishes initially (at t=t0) while tends to infinity at the moment of collapse (at t=0). Then there result a series of ordinary differential equations and perturbed shock relations corresponding to the each exponent of ε. Applying the regularity condition similar to GUDERLEY'S to each differential equation, the perturbed detonation velocity up to the third order of ε is obtained in an explicit algebraic form. Different from the usual perturbed solution, the obtained detonation velocity provides the time-dependency identical with that for the self-similar solution when ε→∞. Consequently, the detonation velocity profile holds in the fairly wide range of implosion and shows a reasonable coincidence with the existing experiments.

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