An analytical model for the impulse of a single-cycle pulse detonation engine

Abstract

An analytical model for the impulse of a single-cycle pulse detonation engine has been developed and validated against experimental data. The model analyzes the pressure differential at the thrust surface of the detonation tube. The pressure inside the tube is modeled with a constant pressure region and a blowdown process. A careful study of the gas dynamics inside the tube enables the derivation of a similarity solution for the constant pressure part. The blowdown process is modeled using dimensional analysis and empirical observations. The model predictions are validated against direct experimental measurements in terms of impulse per unit volume, specific impulse, and thrust. Impulse per unit volume and specific impulse calculations are carried out for a wide range of fueloxygen-nitrogen mixtures (including aviation fuels) varying initial pressure, equivalence ratio, and nitrogen dilution. The effect of the initial temperature is also investigated. Comparisons with numerical simulation estimates of the specific impulse are given. φ equivalence ratio ρ 1 initial density of reactants

Impulse Correlation for Partially Filled Detonation Tubes

“…To obtain a quantitative measure of comparison between the different facilities, we calculate the fill fraction of the combined tube and extension assembly given the published dimensions. This work is to extend previous modeling work on detonation tubes 6 to the case of partial filling and show how simple analytical estimates can be obtained for the impulse in both the fully and partially filled cases.…”

“…The single-cycle impulse I was normalized by the impulse I 0 for a fully filled tube. The predictions of our single-cycle impulse model 6 for a fully filled tube were used to normalize the experimental data of Zitoun and Desbordes 1 because experimental data of I 0 were not available. Because a diaphragm of finite mass is used to separate the initial explosive mixture from the inert mixture of the extension in the experimental tests, incremental impulse is imparted to the tube due to the additional tamping mass of the diaphragm.…”

Impulse Generation by an Open Shock Tube

“…The initial interaction of the detonation wave with the interface results in a transmitted shock and reflected expansion in almost all cases [16]. For example, in the case of a detonation propagating in a stoichiometric ethylene-oxygen section (initial state 1 0 ) bounded by air (initial state 1), a shock of Mach number 4.73 is transmitted into the air (postshock state 2).…”

“…Numerical computation [17] using realistic thermochemistry gives the result that the ratio of acoustic impedance across interface just following the wave interaction is a 2 =a 2 0 1:96. With flow out of the detonation tube, the products depressurize in a nearly isentropic manner [16], which results in the density and sound speed on both sides of the interface decreasing as the pressure drops. Numerical computation reveals that the ratio of acoustic impedance across the interface is practically independent of the pressure, and so we can take the ratio to be approximately constant (2) throughout the pulse detonation tube cycle of operation.…”

“…The wave interaction processes at the interface between the fueled and inert sections is determined for weak waves [15] by the ratio of acoustic impedances (the product of density and sound speed a) for the states on each side of the interface. In the case of detonation tubes, this ratio can be computed [16] by using one-dimensional wave interaction diagrams [15] to find the state of the gas on each side of the interface immediately after the detonation passes through the interface.…”