Nonlinear Development of Low Frequency One-Dimensional Instabilities for ReactingShock Waves

摘要

It has been postulated that detonation waves are steady traveling waves with aquasi one-dimensional structure of an ordinary fluid dynamic shock followed by a reaction zone. In contrast, the detonations observed in many experimental circumstances demonstrate extremely complicated unstable wave patterns. The nature of these instabilities ranges from complex transverse Mach stems in gases to regular and chaotically irregular pulsating fronts in both gaseous and condensed phases. Understanding the mechanisms responsible for the correspondingly higher pressures in unstable detonations has obvious practical implications. In this paper the authors study the nonlinear development of instabilities in a single space dimension. Such (quasi) one-dimensional instabilities are produced in experiments by shooting a blunt body projectile into a dilute hydrogene-oxigene mixture. On schlieren photographs from these experiments one can clearly observe the large scale density fluctuations behind the leading detonation front. The phenomenon of one-dimensional detonation instability has attracted a substantial theoretical and experimental effort. The most complete treatment of the hydrodynamic stability of traveling wave solutions of reactive Euler's equations is due to Erpenbeck. The linearized analysis of Erpenbeck is based on a study of the temporal Laplace transform for the initial value problem. A formally equivalent approach is through the normal mode analysis of the linearized problem.