Applied and Interdisciplinary Mathematics Seminar

University of Michigan

Fall 2004
Friday, September 10, 3:10-4:00pm, 1084 East Hall

Low-frequency stability of multidimensional detonations in three models of combustion: A spectral equivalence theorem

Greg Lyng

University of Michigan


Abstract

We use the classical normal mode approach of hydrodynamic stability theory to define stability determinants (Evans functions) for multi-d strong detonations in three commonly studied combustion models: Reactive Navier-Stokes, Zeldovich-von Neumann-Doering, and Chapman-Jouguet. We compute first-order low-frequency expansions of the RNS and ZND determinants and show that the leading coefficient in each of the expansions is a constant multiple of the explicitly computable CJ determinant. By computing the CJ determinant, we are then able to compute low-frequency stability criteria in terms of physical quantities (Mach number, compression ratio, Gruneisen coefficient, heat release) that are valid for all three models of combustion. This is joint work with H.K. Jenssen (NC State) and M. Williams (UNC-Chapel Hill).