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https://hdl.handle.net/2142/19407
Description
Title
The dynamics of multi-dimensional detonation
Author(s)
Yao, Jin
Issue Date
1996
Doctoral Committee Chair(s)
Stewart, Donald S.
Department of Study
Mechanical Science and Engineering
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Aerospace
Engineering, Mechanical
Physics, Astronomy and Astrophysics
Language
eng
Abstract
"An asymptotic theory is presented for the dynamics of detonation when the radius of curvature of the detonation shock is large compared with the one-dimensional steady Chapman-Jouguet (CJ) detonation reaction-zone thickness. The analysis considers additional time-dependence in the slowly-varying reaction zone than that considered in previous works. The detonation is assumed to have a sonic point in the reaction-zone structure behind the shock, and is referred to as an eigenvalue detonation. A new iterative method is used to calculate the eigenvalue relation, which ultimately is expressed as an intrinsic partial differential equation (PDE) for the motion of the shock surface. Two cases are considered for an ideal equation of state. The first corresponds to a model of a condensed phase explosive, with modest reaction-rate sensitivity, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity $\.D\sb{n}$, the first normal time derivative of the normal shock velocity $D\sb{n}$, and the shock curvature $\kappa$. The second case corresponds to a gaseous explosive mixture, with the large reaction-rate sensitivity of Arrhenius kinetics, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity $D\sb{n}$, its first and second normal time derivatives $\.D\sb{n},\""D\sb{n}$, the shock curvature $\kappa$, and the first normal time derivative of the curvature $\.\kappa$. For the second case, one obtains a one-dimensional theory of pulsation of plane CJ detonation and a theory that predicts the evolution of self-sustained cellular detonation. Versions of the theory include the limit of near-CJ detonation, and the limit in which the normal detonation velocity is significantly below its CJ value. The curvature of the detonation can also be of either sign corresponding to either diverging or converging geometry."
The linear instability of a weakly curved, slowly varying detonation wave is also investigated under the assumption of frozen curvature. The governing equations and the boundary conditions required to formulate the instability problem are derived. The steady $D\sb{n}-\kappa$ relation and the quasi-steady state of the weakly curved detonation have been obtained numerically. The eigenvalues of the acoustic instability are calculated by a numerical shooting method.
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