Level set techniques applied to unsteady detonation propagation
Abstract
Here we are concerned with describing the dynamics of multidimensional detonation as a selfpropagating surface. The detonation shock surface has been shown under certain circumstance to be governed by an intrinsic relation between the normal shock velocity and the local curvature, obtaining a D(sub n)  (kappa) relation. Once the initial shock position is given, then subsequently the motion of the shock can be determined by solving a scalar partial differential equation for the shock position. One can think that in principle, the D(sub n)  (kappa) relation is determined by some means, theory or experiment, and then once prescribed, predictions of the physical system further depend wholly on the initial configuration. Thus we are also concerned about an efficient numerical solution of this equation in threedimensions, with possibly multiply connected and disjoint shock surfaces. This has led us to consider the levelset techniques of Osher and Sethian, which are naturally suited to these problems. In what follows, we discuss examples of propagating surfaces, from formulations in combustion and heat transfer to which levelset methods apply. We discuss the specific example from detonation theory. We briefly explain the derivation of the D(sub n)  (kappa) relation, in the context of detonation and mention some recent extensions of the theory, that includes shock acceleration terms and the possibility of extinction for reaction rates that have large activation energies. These new results can all be summarized as an extension of the D(sub n)  (kappa) relation. Importantly, the resulting equation is hyperbolic in character as opposed to parabolic, for a simple D(sub n)  (kappa). relation. Finally we indicate the interesting new features of the dynamics that can be observed in the detonation shock surface evolution, and speculate on their relevance to formation of sustained detonation cells.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1994
 Bibcode:
 1994STIN...9522901S
 Keywords:

 Curvature;
 Detonation;
 Heat Of Combustion;
 Heat Transfer;
 Partial Differential Equations;
 Scalars;
 Self Propagation;
 Activation Energy;
 Extinction;
 Reaction Kinetics;
 Fluid Mechanics and Heat Transfer