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Title:  The dynamics of multidimensional detonation 
Author(s):  Yao, Jin 
Doctoral Committee Chair(s):  Stewart, Donald S. 
Department / Program:  Mechanical Science and Engineering 
Discipline:  Theoretical and Applied Mechanics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Engineering, Aerospace
Engineering, Mechanical Physics, Astronomy and Astrophysics 
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 onedimensional steady ChapmanJouguet (CJ) detonation reactionzone thickness. The analysis considers additional timedependence in the slowlyvarying reaction zone than that considered in previous works. The detonation is assumed to have a sonic point in the reactionzone 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 reactionrate 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 reactionrate 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 onedimensional theory of pulsation of plane CJ detonation and a theory that predicts the evolution of selfsustained cellular detonation. Versions of the theory include the limit of nearCJ 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 quasisteady state of the weakly curved detonation have been obtained numerically. The eigenvalues of the acoustic instability are calculated by a numerical shooting method. 
Issue Date:  1996 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/19407 
ISBN:  9780591089363 
Rights Information:  Copyright 1996 Yao, Jin 
Date Available in IDEALS:  20110507 
Identifier in Online Catalog:  AAI9702723 
OCLC Identifier:  (UMI)AAI9702723 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois 
Dissertations and Theses  Mechanical Science and Engineering