Analytical Model for the Impulse of Single-Cycle Pulse Detonation Tube

Abstract

An analytical model for the impulse of a single-cycle pulse detonation tube has been developed and validated against experimental data. The model is based on the pressure history at the thrust surface of the detonation tube. The pressure history is modeled by a constant pressure portion, followed by a decay due to gas expansionout of the tube. The duration and amplitude of the constant pressure portion is determined by analyzing the gasdynamics of the self-similar ow behind a steadily moving detonation wave within the tube. The gas expansion process is modeledusing dimensionalanalysisand empirical observations.Themodel predictions are validatedagainstdirect experimental measurements in terms of impulse per unit volume, speci c impulse, and thrust. Comparisons are given with estimates of the speci c impulse based on numerical simulations. Impulse per unit volume and speci c impulse calculations are carried out for a wide range of fuel–oxygen–nitrogen mixtures (including aviation fuels) of varying initial pressure, equivalence ratio, and nitrogen dilution. The effect of the initial temperature is also investigated. The trends observed are explained using a simple scaling analysis showing the dependency of the impulse on initial conditions and energy release in the mixture. Nomenclature A = cross-sectionalarea of detonation tube C § = characteristics,left- and right-facing families