A Caltech Library Service

Detonation Stability with Reversible Kinetics


Kao, Shannon Theresa (2008) Detonation Stability with Reversible Kinetics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/H8JN-VS03.


Detonation propagation is unsteady due to the innate instability of the reaction zone structure. Up until the present, investigations of detonation stability have been exclusively concerned with model systems using the perfect gas equation of state and primarily single-step irreversible reaction mechanisms.

This study investigates detonation stability characteristics with reversible chemical kinetics models. To allow for more general kinetics models, we generalize the perfect gas, one-step irreversible kinetics, linear stability equations to a set of equations using the ideal gas equation of state and a general reaction scheme. We linearly perturb the reactive Euler equations following the method of Lee and Stewart (1990) and Short and Stewart (1998). Our implementation uses Cantera (Goodwin, 2005) to evaluate all thermodynamic quantities and evaluate generalized analytic derivatives of quantities dependent on the kinetics model.

The computational domain is the reaction zone in the shock-fixed frame such that the left boundary conditions are the perturbed shock jump conditions which we have derived for a general equation of state and implemented for an ideal gas equation of state. At the right boundary, the system must satisfy a radiation condition requiring that all waves travel out of the domain. Unlike the case of a single reversible reaction, in a truly multistep kinetics model, the radiation boundary condition cannot be solved analytically. In this work, we provide a general methodology for satisfying the appropriate boundary condition.

We then investigate the effects of reversibility on the characteristics of the instability in one and two dimensions. These characteristics are quantified by the unstable eigenvalues as well as the shape of the base flow and eigenfunctions. We show that there is an exchange of stability as a function of reversibility. To confirm the results our work, we have performed unsteady calculations. We show that we can match the frequencies predicted by our linear stability calculations near the stability threshold.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:detonation; normal modes; stability
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Shepherd, Joseph E.
Group:Explosion Dynamics Laboratory
Thesis Committee:
  • Shepherd, Joseph E. (chair)
  • Pullin, Dale Ian
  • Meiron, Daniel I.
  • Colonius, Tim
Defense Date:27 May 2008
Record Number:CaltechETD:etd-06022008-170629
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2409
Deposited By: Imported from ETD-db
Deposited On:05 Jun 2008
Last Modified:25 Oct 2023 22:52

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page