Detonation Stability for Disturbances of Small Transverse Wavelength

Abstract

The stability of one-dimensional, steady detonations to periodic disturbances transverse to the flow is examined in the limit of small wavelength, 2π/ε → 0. The asymptotic criterion for stability is found to depend largely on the steady-state profile of c02η (where c0 is the frozen sound speed, η is the sonic parameter 1 − u2/c02, and u is the mass velocity relative to the von Neumann shock) as a function of distance from the shock. Detonations for which c02η decreases monotonically are found to be stable in the ε → ∞ limit but stability in cases in which this quantity increases either monotonically or up to a maximum is determined through simple integral functions of the steady-flow variables. In contrast to the labor involved with application of the general theory of detonation stability, the asymptotic result can be applied straightforwardly to any detonation, irrespective of the equation of state and the complexity of the chemical kinetics. The results for an idealized, one-reaction, A → B, system with an Arrhenius rate constant are detailed.