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 expansion out 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 modeled using dimensional analysis and empirical observations. The model predictions are validated against direct 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. = time taken by the rst re ected characteristic to reach the thrust surface t 3 = time associated with pressure decay period t ¤ = time at which the rst re ected characteristic exits the Taylor wave U CJ = Chapman-Jouguet detonation velocity u = ow velocity u e = exhaust velocity u 2 = ow velocity just behind detonation wave V = volume of gas within detonation tube X F = fuel mass fraction ® = nondimensional parameter corresponding to time t 2 = nondimensional parameter corresponding to pressure decay period°= ratio of speci c heats 1P = pressure differential 1P 3 = pressure differential at the thrust surfacé = similarity variablȩ = cell size 5 = nondimensional pressure ½ e = exhaust density ½ 1 = initial density of reactants ¿ = nondimensional time ct=L Á = equivalence ratio

= pendulum mass P = pressure P env = environment pressure P lip = pressure on lip at exit of tube P TS = pressure on thrust surface in detonation tube interior P 1 = initial pressure of reactants P 2 = Chapman-Jouguet pressure P 3 = pressure of burned gases behind Taylor wave p = pitch of spiral obstacles S = wetted surface area of tube's inner diameter T 1 = initial temperature of reactants t = time U CJ = Chapman-Jouguet detonation velocity V = internal volume of detonation tubē = ratio of N 2 -to-O 2 concentration in initial mixture°= ratio of speci c heats in combustion products 1x = horizontal pendulum displacemenţ = cell size ½ 1 = density of combustible mixture at the initial temperature and pressure ¿ = wall shear stress

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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

= pendulum mass P = pressure P env = environment pressure P lip = pressure on lip at exit of tube P TS = pressure on thrust surface in detonation tube interior P 1 = initial pressure of reactants P 2 = Chapman-Jouguet pressure P 3 = pressure of burned gases behind Taylor wave p = pitch of spiral obstacles S = wetted surface area of tube's inner diameter T 1 = initial temperature of reactants t = time U CJ = Chapman-Jouguet detonation velocity V = internal volume of detonation tubē = ratio of N 2 -to-O 2 concentration in initial mixture°= ratio of speci c heats in combustion products 1x = horizontal pendulum displacemenţ = cell size ½ 1 = density of combustible mixture at the initial temperature and pressure ¿ = wall shear stress

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The effect of nozzles on the impulse obtained from a detonation tube has been the focus of many experimental and numerical studies. We develop a partial-fill model to predict the impulse obtained from a detonation tube containing an extension (considered a partially-filled detonation tube). The experimental impulse values are found to be linearly dependent on the fraction of the tube volume filled with the explosive mixture. Data from numerical simulations were used to predict the impulse for small fill fractions not experimentally tested. The analytical Gurney model provides a method for correcting the experimental data for the tamping provided by diaphragms of a finite mass. A thermodynamic cycle analysis of a detonation is conducted to evaluate the fraction of stored chemical energy in an explosive mixture that can be converted into mechanical work. It is found that approximately 46%-64% of the ideal work from a detonation can be converted into impulse. This fraction increases with increasing nitrogn dilution. The partial-fill model is validated with multi-cycle experimental data and numerical simulations. We compare the partial-fill model with experimental data of diverging nozzles. Ideal ideal detonation efficiency calculated from Jacobs cycle Isp detonation efficiency based on predicted specific impulse ρ 1 density of reactants ρ air density of air mixture in extension

Burning aluminized propellants eject reacting molten aluminum drops with a broad size distribution. Prior to this work, in situ measurement of the drop size statistics and other quantitative flow properties was complicated by the narrow depth-of-focus of microscopic videography. Here, digital in-line holography (DIH) is demonstrated for quantitative volumetric imaging of the propellant plume. For the first time, to the best of our knowledge, in-focus features, including burning surfaces, drop morphologies, and reaction zones, are automatically measured through a depth spanning many millimeters. By quantifying all drops within the line of sight, DIH provides an order of magnitude increase in the effective data rate compared to traditional imaging. This enables rapid quantification of the drop size distribution with limited experimental repetition.