Stability of Idealized One-Reaction Detonations

TLDR

The study investigates the hydrodynamic stability of steady, one‑dimensional detonations in an ideal‑gas medium undergoing the irreversible unimolecular reaction A→B, and examines how one‑dimensional instability depends on the heat of reaction Q. The authors numerically apply the general theory of det.

Abstract

The hydrodynamic stability of steady, one-dimensional detonations in an ideal-gas medium, undergoing the irreversible, unimolecular reaction A → B, having Arrhenius rate constant, is obtained in numerical form by application of the general theory of detonation stability. Stability results, as well as the pressure and progress variable profiles for the steady detonations, are presented for a (constant) heat capacity ratio γ of 1.2, a heat of reaction Q, relative to thermal energy in the cold reactants, of 50, activation energies Q‡ (in the same units) of 10 and 50, and at several detonation velocities, D. The neutral stability curves, consisting of the values of the disturbance wavelength transverse to the steady flow for which the steady detonation of given velocity changes stability (as functions of detonation velocity), are investigated. One-dimensional disturbances are found to be unstable at low detonation velocities (i.e., near the CJ point), for the larger activation energy (but not the smaller) but are stabilized by sufficient overdrive. At fixed detonation velocity, a range of wave lengths are unstable and for Q‡ = 50, this instability appears to persist for all detonation velocities. For decreasing heat of reaction (at fixed Q‡, γ, and D/DCJ) the detonation is found to become stable although for Q‡ = 50 the instability persists to very small values of the heat of reaction. Thus, the system Q = 0.3, Q‡ = 50, γ = 1.2 is found to be unstable when f = (D/DCJ)2 ≤ 1.1. The phenomenon of one-dimensional instability and its dependence on Q is also investigated.