Thermodynamic Cycle Analysis for Propagating Detonations

Propagating detonations have recently been the focus of extensive work based on their use in pulse detonation engines [1]. The entropy minimum associated with Chapman–Jouguet (CJ) detonations [2] and its potential implications on the thermal efficiency of these systems [3] has been one of the main motivations for these efforts. The notion of applying thermodynamic cycles to detonation was considered first by Zel’dovich [4], who concluded that the efficiency of the detonation cycle is slightly larger than that of a cycle using constant-volume combustion. More recently, Heiser and Pratt [3] conducted a thermodynamic analysis of the detonation cycle for a perfect gas using a one-γ model of detonations. Other studies have used constant-volume combustion as a surrogate for the detonation process [5]. This work presents two main contributions. First, we present an alternative physical model for the detonation cycle handling propagating detonations in a purely thermodynamic fashion. The Fickett–Jacobs (FJ) cycle is a conceptual thermodynamic cycle that can be used to compute an upper bound to the amount of mechanical work that can be obtained from detonating a given mass of explosive. Second, we present computations of the cycle thermal efficiency for a number of fuel-oxygen and fuel-air mixtures using equilibrium chemistry, and we discuss the strong influence of dissociation reactions on the results.